Patent Publication Number: US-2019168215-A1

Title: Three-stage thermal convection apparatus and uses thereof

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     The present application is a continuation-in-part application of PCT/IB2011/050103, filed on Jan. 11, 2011 which claims priority to U.S. Provisional Application No. 61/294,445 as filed on Jan. 12, 2010, the disclosure of which is incorporated herein by reference. 
    
    
     FIELD OF THE INVENTION 
     The present invention features a multi-stage thermal convection apparatus, particularly a three-stage thermal convection apparatus and uses thereof. The apparatus includes at least one temperature shaping element that assists a polymerase chain reaction (PCR). The invention has a wide variety of applications including amplifying a DNA template without the cumbersome and often expensive hardware associated with prior devices. In one embodiment, the apparatus can fit in the palm of a user&#39;s hand for use as a portable PCR amplification device. 
     BACKGROUND 
     The polymerase chain reaction (PCR) is a technique that amplifies a polynucleotide sequence each time a temperature changing cycle is completed. See for example,  PCR: A Practical Approach , by M. J. McPherson, et al., IRL Press (1991),  PCR Protocols: A Guide to Methods and Applications , by Innis, et al., Academic Press (1990), and  PCR Technology: Principals and Applications for DNA Amplification , H. A. Erlich, Stockton Press (1989). PCR is also described in many patents, including U.S. Pat. Nos. 4,683,195; 4,683,202; 4,800,159; 4,965,188; 4,889,818; 5,075,216; 5,079,352; 5,104,792; 5,023,171; 5,091,310; and 5,066,584. 
     In many applications, PCR involves denaturing a polynucleotide of interest (“template”), followed by annealing a desired primer oligonucleotide (“primer”) to the denatured template. After annealing, a polymerase catalyzes synthesis of a new polynucleotide strand that incorporates and extends the primer. This series of steps: denaturation, primer annealing, and primer extension, constitutes a single PCR cycle. These steps are repeated many times during PCR amplification. 
     As cycles are repeated, the amount of newly synthesized polynucleotide increases geometrically. In many embodiments, primers are selected in pairs that can anneal to opposite strands of a given double-stranded polynucleotide. In this case, the region between the two annealing sites can be amplified. 
     There is a need to vary the temperature of the reaction mixture during a multi-cycle PCR experiment. For example, denaturation of DNA typically takes place at about 90° C. to about 98° C. or a higher temperature, annealing a primer to the denatured DNA is typically performed at about 45° C. to about 65° C., and the step of extending the annealed primers with a polymerase is typically performed at about 65° C. to about 75° C. These temperature steps must be repeated, sequentially, for PCR to progress optimally. 
     To satisfy this need, a variety of commercially available devices has been developed for performing PCR. A significant component of many devices is a thermal “cycler” in which one or more temperature controlled elements (sometimes called “heat blocks”) hold the PCR sample. The temperature of the heat block is varied over a time period to support the thermal cycling. Unfortunately, these devices suffer from significant shortcomings. 
     For example, most of the devices are large, cumbersome, and typically expensive. Large amounts of electric power are usually required to heat and cool the heat block to support the thermal cycling. Users often need extensive training. Accordingly, these devices are generally not suitable for field use. 
     Attempts to overcome these problems have not been entirely successful. For instance, one attempt involved use of multiple temperature controlled heat blocks in which each block is kept at a desired temperature and sample is moved between heat blocks. However, these devices suffer from other drawbacks such as the need for complicated machinery to move the sample between different heat blocks and the need to heat or cool one or a few heat blocks at a time. 
     There have been some efforts to use thermal convection in some PCR processes. See Krishnan, M. et al. (2002)  Science  298: 793; Wheeler, E. K. (2004)  Anal. Chem.  76: 4011-4016; Braun, D. (2004)  Modern Physics Letters  18: 775-784; and WO02/072267. However, none of these attempts has produced a thermal convection PCR device that is compact, portable, more affordable and with a less significant need for electric power. Moreover, such thermal convection devices often suffer from low PCR amplification efficiency and limitation in the size of amplicon. 
     SUMMARY 
     The present invention provides a multi-stage thermal convection apparatus, particularly a three-stage thermal convection apparatus and uses thereof. The apparatus generally includes at least one temperature shaping element to assist a polymerase chain reaction (PCR). As described below, a typical temperature-shaping element is a structural and/or positional feature of the apparatus that supports thermal convection PCR. Presence of the temperature shaping element enhances the efficiency and speed of the PCR amplification, supports miniaturization, and reduces need for significant power. In one embodiment, the apparatus readily fits in the palm of a user&#39;s hand and has low power requirements sufficient for battery operation. In this embodiment, the apparatus is smaller, less expensive and more portable than many prior PCR devices. 
     Accordingly, and in one aspect, the present invention features a three-stage thermal convection apparatus adapted to perform thermal convection PCR amplification (“apparatus”). Preferably, the apparatus has at least one of and preferably all of the following elements as operably linked components:
         (a) a first heat source for heating or cooling a channel and comprising a top surface and a bottom surface, the channel being adapted to receive a reaction vessel for performing PCR,   (b) a second heat source for heating or cooling the channel and comprising a top surface and a bottom surface, the bottom surface facing the top surface of the first heat source,   (c) a third heat source for heating or cooling the channel and comprising a top surface and a bottom surface, the bottom surface facing the top surface of the second heat source, wherein the channel is defined by a bottom end contacting the first heat source and a through hole contiguous with the top surface of the third heat source, and further wherein center points between the bottom end and the through hole form a channel axis about which the channel is disposed,   (d) at least one temperature shaping element adapted to assist thermal convection PCR; and   (e) a receptor hole adapted to receive the channel within the first heat source.       

     Also provided is a method of making the forgoing apparatus which method includes assembling each of (a)-(e) in an operable combination sufficient to perform thermal convection PCR as described herein. 
     In another aspect of the present invention, there is provided a thermal convection PCR centrifuge (“PCR centrifuge”) adapted to perform PCR using at least one of the apparatus as described herein. 
     Further provided by the present invention is a method for performing a polymerase chain reaction (PCR) by thermal convection. In one embodiment, the method includes at least one of and preferably all of the following steps:
         (a) maintaining a first heat source comprising a receptor hole at a temperature range suitable for denaturing a double-stranded nucleic acid molecule and forming a single-stranded template,   (b) maintaining a third heat source at a temperature range suitable for annealing at least one oligonucleotide primer to the single-stranded template,   (c) maintaining a second heat source at a temperature suitable for supporting polymerization of the primer along the single-stranded template; and   (d) producing thermal convection between the receptor hole and third heat source under conditions sufficient to produce the primer extension product.       

     In another aspect, the invention provides reaction vessels adapted to be received by an apparatus of the invention. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a schematic drawing showing an overhead view of an embodiment of the apparatus. Sectional planes through the apparatus (A-A and B-B) are depicted. 
         FIGS. 2A-C  are schematic drawings showing sectional views of an apparatus embodiment having a first chamber  100 .  FIGS. 2A-C  are cross-sectional views taken along the A-A ( FIGS. 2A, 2B ) and B-B planes ( FIG. 2C ). 
         FIGS. 3A-B  are schematic drawings showing sectional views of apparatus embodiments taken along the A-A plane. Each apparatus has a first  100  and a second  110  chamber of unequal widths with respect to the channel axis  80 . 
         FIGS. 4A-B  are schematic drawings showing a sectional view (A-A) of an embodiment of the apparatus.  FIG. 4B  shows an expanded view of the region (identified by the dotted circle in  FIG. 4A ). The apparatus has a first  100 , a second  110  and a third  120  chamber. A region between the first and second chambers includes a first thermal brake  130 . A region between the second and third chambers includes a second thermal brake  140 . 
         FIGS. 5A-D  are schematic drawings showing channel embodiments of the apparatus (A-A plane). 
         FIGS. 6A-J  are schematic drawings showing channel embodiments of the apparatus. The plane of section is perpendicular to the channel axis  80 . 
         FIGS. 7A-I  are drawings showing various chamber embodiments of the apparatus. The plane of section is perpendicular to the channel axis  80 . Hatched parts represent the second or third heat source. 
         FIGS. 8A-P  are drawings showing various chamber and channel embodiments of the apparatus. The plane of section is perpendicular to the channel axis  80 . Hatched parts represent the second or third heat source. 
         FIGS. 9A-B  are schematic drawings showing sectional views (A-A plane) of apparatus embodiments. The first chamber  100  is tapered. 
         FIGS. 10A-F  are schematic drawings showing sectional views (A-A plane) of various apparatus embodiments having a first thermal brake  130 .  FIGS. 10B, 10D, and 10F  show expanded views of the region identified by the dotted circle shown in  FIGS. 10A, 10C and 10E , respectively, to illustrate structural details of the first thermal brake  130 . 
         FIGS. 11A-B  are schematic drawings showing a sectional view (A-A) of one embodiment of the apparatus.  FIG. 11B  illustrates an expanded view of the region identified by the dotted circle shown in  FIG. 11A  to highlight locations of the first  130  and second  140  thermal brakes. 
         FIG. 12A  is a schematic drawing showing a sectional view (A-A) of one embodiment of the apparatus. The first  20  and second  30  heat sources feature protrusions ( 23 ,  24 ,  33 ,  34 ) along the channel axis  80 . A first thermal brake  130  is shown below the first chamber  100 . 
         FIG. 12B  shows a positioning embodiment of the apparatus shown in  FIG. 12A . The apparatus is tilted (by an angle defined by θ g ) with respect to the direction of gravity. 
         FIG. 13  is a schematic drawing showing a sectional view (A-A) of one embodiment of the apparatus. The receptor hole  73  is asymmetrically disposed around the channel axis  80  and forms a receptor hole gap  74 . 
         FIG. 14A  is a schematic drawing showing a sectional view (A-A plane) of an embodiment of the apparatus. The first  100  and second  110  chambers are positioned in the second  30  and third  40  heat sources, respectively. 
         FIG. 14B  is a schematic drawing showing a sectional view (A-A plane) of an embodiment of the apparatus. The first  100  and second  110  chambers are positioned in the second heat source  30  and a third chamber  120  is positioned in the third heat source  40 . The first thermal brake  130  is positioned between the first  100  and second  110  chambers within the second heat source  30 . 
         FIG. 14C  is a schematic drawing showing a sectional view (A-A) of an embodiment of the apparatus with the first  100  and second  110  chambers positioned in the second  30  and third  40  heat sources, respectively. The first thermal brake  130  is shown below the first chamber  100 . 
         FIGS. 15A-B  are schematic drawings showing sectional views (A-A plane) of apparatus embodiments in which the first chamber  100  is positioned in the third heat source  40 . In  FIG. 15B , the first heat source  20  features protrusions ( 23 ,  24 ) disposed symmetrically about the receptor hole  73 . 
         FIGS. 16A-C  are schematic drawings showing sectional views of an apparatus embodiment.  FIGS. 16A-C  are cross-sectional views taken along the A-A ( FIGS. 16A-B ) and B-B planes ( FIG. 16C ). The second heat source  30  comprises protrusions ( 33 ,  34 ) disposed symmetrically about the channel axis  80  that extend the length of the first chamber  100 . 
         FIGS. 17A-C  are schematic drawings of an apparatus embodiment taken along the A-A ( FIGS. 17A-B ) and B-B planes ( FIG. 17C ). The first  20 , second  30  and third  40  heat sources include protrusions ( 23 ,  24 ,  33 ,  34 ,  43 ,  44 ) that are each positioned symmetrically about the channel axis  80 . 
         FIG. 18A  is a schematic drawings showing a sectional view (A-A) of an embodiment of the apparatus. The apparatus is tilted (by an angle defined by θ g ) with respect to the direction of gravity. 
         FIG. 18B  shows an apparatus embodiment in which the channel  70  and the first chamber  100  are tilted with respect to the direction of gravity within the second heat source  30 . The direction of gravity remains perpendicular with respect to the heat sources. 
         FIG. 19  is a schematic drawing showing a sectional view (A-A) of one embodiment of the apparatus. In this embodiment, the first heat source  20  features a receptor hole  73  with a receptor hole gap  74 . 
         FIGS. 20A-B  are schematic drawings showing sectional views of apparatus embodiments taken along the A-A plane. The first heat source  20  includes a receptor hole gap  74 . In the embodiment shown by  FIG. 20B , the receptor hole gap  74  includes a top surface that is inclined with respect to the channel axis  80 . 
         FIGS. 21A-B  are schematic drawings showing sectional views of apparatus embodiments taken along the A-A plane. The first heat source  20  features a protrusion  23  disposed asymmetrically around the receptor hole  73 . In  FIG. 21A , the protrusion  23  next to the receptor hole  73  has multiple top surfaces one of which has a greater height and is closer to the first chamber  100 . In  FIG. 21B , the protrusion  23  has one top surface that is inclined with respect to the channel axis  80  so that one side has a greater height and is closer to the first chamber  100  than another side opposite to the receptor hole  73 . 
         FIGS. 22A-D  are schematic drawings showing sectional views of apparatus embodiments taken along the A-A plane. In these embodiments, the first  20  and second  30  heat sources feature protrusions  23  and  33  disposed asymmetrically about the channel axis  80 . The protrusions  23  and  33  have a greater height on one side than another side opposite to the channel axis  80 . The top end of the protrusion  23  and the bottom end of the protrusion  33  have multiple surfaces ( FIGS. 22A and 22C ) or are inclined with respect to the channel axis  80  ( FIGS. 22B and 22D ). In  FIGS. 22A and 22B , the first chamber  100  features a bottom end  102  in which a portion is closer to one side of the protrusion  23  than another portion opposite to the channel axis  80 . In  FIGS. 22C and 22D , the bottom end  102  of the first chamber  100  is located essentially at a constant distance from the top surface of the protrusion  23 . 
         FIGS. 23A-B  are schematic drawings showing sectional views of apparatus embodiments taken along the A-A plane. In these embodiments, the first heat source  20  features a protrusion  23  disposed symmetrically around the receptor hole  73  and the second heat source  30  features a protrusion  33  disposed asymmetrically about the channel axis  80 . In  FIG. 23A , the bottom end  102  of the first chamber  100  features multiple surfaces so that a portion of the bottom end  102  that is closer to one side of the protrusion  23  than another portion opposite to the channel axis  80 . In  FIG. 23B , the bottom end  102  of the first chamber  100  is inclined with respect to the channel axis  80  so that a portion of the bottom end  102  is closer to the protrusion  23  than another portion opposite to the channel axis  80 . 
         FIGS. 24A-B  are schematic drawings showing sectional views of apparatus embodiments taken along the A-A plane. In these embodiments, the second heat source  30  features protrusions  33  and  34  that are disposed asymmetrically about the channel axis  80 . The bottom end of the protrusion  33  and the top end of the protrusion  34  are inclined with respect to the channel axis  80  ( FIG. 24A ) or have multiple surfaces ( FIG. 24B ). The first chamber  100  features a portion of the bottom end  102  that is closer to the top surface of the first heat source  20  than another portion opposite to the channel axis  80 . The top end  101  also features a portion that is closer to the bottom surface of the third heat source  40  than another portion opposite to the channel axis  80 . 
         FIG. 25  is a schematic drawing showing a sectional view of an apparatus embodiment taken along the A-A plane showing the first  100  and second  110  chambers disposed asymmetrically about the channel axis  80  within the second heat source  30 . 
         FIG. 26  is a schematic drawing showing a sectional view taken along the A-A plane of an apparatus embodiment in which the first chamber  100  includes a wall  103  disposed at an angle with respect to the channel axis  80 . 
         FIGS. 27A-B  are schematic drawings showing sectional views of apparatus embodiments taken along the A-A plane. In these embodiments, the second heat source  30  features protrusions ( 33 ,  34 ) that are disposed asymmetrically about the channel axis  80 . The bottom end of the protrusion  33  and the top end of the protrusion  34  are inclined with respect to the channel axis  80  ( FIG. 27A ) or have multiple surfaces ( FIG. 27B ). In  FIG. 27B , the first  20  and third  40  heat sources feature protrusions ( 23 ,  24 ,  43 ,  44 ) disposed symmetrically about the channel axis  80 . In both  FIGS. 27A  and B, a portion of the bottom end  102  of the first chamber  100  is positioned closer to the top surface of the first heat source  20  than another portion opposite to the channel axis  80 . Also, the top end  101  has a portion that is positioned closer to the bottom surface of the third heat source  40  than another portion opposite to the channel axis  80 . 
         FIGS. 28A-B  are schematic drawings showing a sectional view of an apparatus embodiment taken alone the A-A plane with the first chamber  100  and the second chamber  110  within the second heat source  30 . As shown in  FIG. 28B , the apparatus features a first thermal brake  130  asymmetrically disposed about the channel  70  and between the first  100  and second  110  chambers with the wall  133  contacting the channel  70  on one side. 
         FIG. 29A  is a schematic drawing showing a sectional view of an apparatus embodiment in which the first chamber  100  is within the second heat source  30  and is disposed asymmetrically (off-centered) about the channel  70 . 
         FIGS. 29B-C  are schematic drawings showing sectional views of an apparatus embodiment along the A-A plane. The first chamber  100  is disposed asymmetrically about the channel  70 . As shown in  FIG. 29C , the thermal brake  130  is shown disposed asymmetrically about the channel  70  with the wall  133  contacting the channel  70  on one side. 
         FIGS. 30A-B  are schematic drawings showing a sectional view of an apparatus embodiment along the A-A plane in which the first  100  and second  110  chambers are within the second heat source  30 . The first  100  and second  110  chambers are disposed asymmetrically about the channel axis  80 . In an expanded view shown in  FIG. 30B , the thermal brake  130  is shown disposed symmetrically about the channel  70  between the first  100  and second  110  chambers. The wall  133  of the thermal brake  130  contacts the channel  70 . 
         FIGS. 30C-D  are schematic drawings showing a sectional view of an apparatus embodiment along the A-A plane in which the first  100  and second  110  chambers are within the second heat source  30 . The first  100  and second  110  chambers are disposed asymmetrically about the channel axis  80 . The width of the first chamber  100  perpendicular to the channel axis  80  is smaller than the width of the second chamber  110  along the channel axis  80 . In an expanded view shown in  FIG. 30D , the first thermal brake  130  is shown disposed asymmetrically about the channel  70  with the wall  133  contacting the channel  70  on one side. 
         FIGS. 31A-B  are schematic drawings showing a sectional view of an apparatus embodiment along the A-A plane in which the first  100  and second  110  chambers are within the second heat source  30 . The first  100  and second  110  chambers are disposed asymmetrically about the channel axis  80  in opposite directions along the A-A plane. The thermal brake  130  is shown disposed symmetrically about the channel  70  with the wall  133  contacting the channel  70 . 
         FIGS. 32A-B  are schematic drawings showing a sectional view of an apparatus embodiment along the A-A plane in which the first  100  and second  110  chambers are within the second heat source  30 . The first  100  and second  110  chambers are disposed asymmetrically about the channel axis  80 . As shown in  FIG. 32B , the first thermal brake  130  is also disposed asymmetrically about the channel  70  with the wall  133  contacting the channel  70  on one side. 
         FIGS. 32C-D  are schematic drawings showing a sectional view of an apparatus embodiment along the A-A plane in which the first  100  and second  110  chambers are within the second heat source  30  and are disposed asymmetrically about the channel axis  80 . As shown in  FIG. 32D , the first thermal brake  130  is also asymmetrically disposed about the channel  70  with the wall  133  contacting the channel  70  on one side. 
         FIGS. 33A-B  are schematic drawings showing a sectional view of an apparatus embodiment along the A-A plane in which the first  100  and second  110  chambers are within the second heat source  30  and are disposed asymmetrically about the channel axis  80  in opposite directions along the A-A plane. In an expanded view shown in  FIG. 33B , the first thermal brake  130  is shown disposed asymmetrically with the wall  133  contacting the channel  70  on one side within the first chamber  100 . The second thermal brake  140  is also shown disposed asymmetrically with the wall  143  contacting the channel  70  on one side within the second chamber  110 . The top end  131  of the first thermal brake  130  is positioned essentially at the same height as the bottom end  142  of the second thermal brake  140 . 
         FIGS. 33C-D  are schematic drawings showing a sectional view of an apparatus embodiment along the A-A plane in which the first  100  and second  110  chambers are within the second heat source  30  and are disposed asymmetrically about the channel axis  80  in opposite directions along the A-A plane. In an expanded view shown in  FIG. 33D , the first  130  and second  140  thermal brakes are shown disposed asymmetrically with the walls ( 133 ,  143 ) each contacting the channel  70  on one side. The top end  131  of the first thermal brake  130  is positioned higher than the bottom end  142  of the second thermal brake  140 . 
         FIGS. 33E-F  are schematic drawings showing a sectional view of an apparatus embodiment along the A-A plane in which the first  100  and second  110  chambers are within the second heat source  30  and are disposed asymmetrically about the channel axis  80  in opposite directions along the A-A plane. In an expanded view shown in  FIG. 33F , the first  130  and second  140  thermal brakes are shown disposed asymmetrically with the walls ( 133 ,  143 ) each contacting the channel  70  on one side. The top end  131  of a first thermal brake  130  is shown positioned lower than the bottom end  142  of the second thermal brake  140 . 
         FIGS. 34A-B  are schematic drawings showing a sectional view of an apparatus embodiment along the A-A plane in which the first  100  and second  110  chambers are within the second heat source  30  and are disposed asymmetrically about the channel axis  80 . The top end  101  of the first chamber  100  and the bottom end  112  of the second chamber  110  are inclined (tilted) with respect to the channel axis  80 . The wall  103  of the first chamber  100 , the wall  113  of the second chamber  110  are each essentially parallel to the channel axis  80 . In an expanded view shown in  FIG. 34B , the first thermal brake  130  is shown inclined (tilted) with respect to the channel axis  80  and the wall  133  contacts the channel  70 . 
         FIGS. 35A-D  are schematic drawings showing sectional views of apparatus embodiments along the A-A plane in which the first  100  and second  110  chambers are within the second heat source  30  and are disposed asymmetrically about the channel axis  80 . In  FIGS. 35A-D , the wall  103  of the first chamber  100  and the wall  113  of the second chamber  110  are shown inclined (tilted) with respect to the channel axis  80 . In an expanded view shown in  FIG. 35B , the thermal brake  130  is shown symmetrically disposed about the channel  70  with the wall  133  contacting the channel  70 . In an expanded view shown in  FIG. 35D , the first thermal brake  130  is shown inclined (tilted) with respect to the channel axis  80  with the wall  133  contacting the channel  70 . 
         FIGS. 36A-C  are schematic drawings showing sectional views of various apparatus embodiments taken along the A-A plane in which the first chamber  100  is within the second heat source  30  and the second chamber  110  is within the third heat source  40  ( FIGS. 36A  and C), or the first chamber  100  and the second chamber  110  are within the second heat source  30  and the third chamber  120  is within the third heat source  40  ( FIG. 36B ). In all figures, the chambers are disposed symmetrically about the channel axis  80 . In  FIGS. 36A-C , the second heat source  30  features a protrusion  33  that defines the first chamber  100  and is disposed symmetrically about the channel axis  80  and the first heat source  20  features protrusions  23  and  24 . In  FIGS. 36A-B , the bottom end  102  of the first chamber  100  contacts the first insulator  50 . In  FIG. 36C , the bottom end  102  of the first chamber  100  contacts the second heat source  30 . 
         FIGS. 37A-C  are schematic drawings showing sectional views of various apparatus embodiments taken along the A-A plane in which the first chamber  100  is within the second heat source  30  and the second chamber  110  is within the third heat source  40  ( FIGS. 37A  and C) or the first chamber  100  and the second chamber  110  are within the second heat source  30  and the third chamber  120  is within the third heat source  40  ( FIG. 37B ). In all figures, the chambers are disposed symmetrically about the channel axis  80 . Protrusions  23 ,  24 ,  33 , and  34  are disposed symmetrically about the channel axis  80 . In  FIGS. 37A-B , the bottom end  102  of the first chamber  100  contacts the first insulator  50  while in  FIG. 37C  it contacts the second heat source  30 . 
         FIGS. 38A-C  are schematic drawings showing sectional views of various apparatus embodiments taken along the A-A plane. In  FIGS. 38A  and C, the first chamber  100  is within the second heat source  30  and the second chamber  110  is within the third heat source  40 , and in  FIG. 38B  the first chamber  100  and the second chamber  110  are within the second heat source  30  and the third chamber  120  is within the third heat source  40 . The chambers are disposed symmetrically about the channel axis  80 . Protrusions  23 ,  24 ,  33 ,  34 , and  43  are disposed symmetrically about the channel axis  80 . In  FIGS. 38A-B , the bottom end  102  of the first chamber  100  contacts the first insulator  50  while in  FIG. 37C  it contacts the second heat source  30 . 
         FIG. 39  is a schematic drawing showing an overhead view of an embodiment of the apparatus  10  showing first securing element  200 , second securing element  210 , heating/cooling elements ( 160   a - c ), and temperature sensors ( 170   a - c ). Various sectional planes are indicated (A-A, B-B, and C-C). 
         FIGS. 40A-B  are schematic drawings of cross-sectional views of the apparatus embodiment shown in  FIG. 39  taken along the A-A ( FIG. 40A ) and B-B ( FIG. 40B ) planes. 
         FIG. 41  is a schematic drawing of a cross-sectional view of the first securing element  200  taken along the C-C plane. 
         FIG. 42  is a schematic drawing of an overhead view of an apparatus embodiment showing various securing elements, heat source structures, heating/cooling elements, and temperature sensors. 
         FIGS. 43A-B  are schematic drawings of an overhead view ( FIG. 43A ) and a cross-sectional view ( FIG. 43B ) of an apparatus embodiment showing a first housing element  300  defining a third  310  and fourth  320  insulator. 
         FIGS. 44A-B  are schematic drawings of an overhead view ( FIG. 44A ) and a cross-sectional view ( FIG. 44B ) of an apparatus embodiment comprising a second housing element  400  and a fifth  410  and sixth  420  insulator. 
         FIGS. 45A-B  are schematic drawings of an embodiment of a PCR centrifuge.  FIG. 45A  shows an overhead view and  FIG. 45B  shows a cross-sectional view taken along the A-A plane. 
         FIG. 46  is a schematic drawing showing a cross-sectional view of an apparatus embodiment of the PCR centrifuge taken along the A-A plane. 
         FIGS. 47A-B  are schematic drawings showing an embodiment of a PCR centrifuge comprising a first chamber and a first thermal brake. In  FIG. 47A , the plane of section along A-A is through the channel  70 . In  FIG. 47B , the plane of section along B-B is through the first  200  and second  210  securing means. 
         FIGS. 48A-C  are schematic drawings showing embodiments of a first ( FIG. 48A ), second ( FIG. 48B ) and third ( FIG. 48C ) heat source for use in the PCR centrifuge shown in  FIGS. 47A-B . Sectional planes through the apparatus (A-A and B-B) are indicated. 
         FIGS. 49A-B  are schematic drawings showing an embodiment of a PCR centrifuge comprising no chamber structure. In  FIG. 49A , the plane of section along A-A is through the channel  70 . In  FIG. 49B , the plane of section along B-B is through the first  200  and second  210  securing means. 
         FIGS. 50A-C  are schematic drawings showing embodiments of a first ( FIG. 50A ), second ( FIG. 50B ) and third ( FIG. 50C ) heat source for use in the PCR centrifuge shown in  FIGS. 49A-B . Sectional planes through the apparatus (A-A and B-B) are indicated. 
         FIGS. 51A-D  are schematic drawings showing a cross-sectional view of various reaction vessel embodiments. 
         FIGS. 52A-J  are schematic drawings showing cross-sectional views of various reaction vessel embodiments taken perpendicular to the reaction vessel axis  95 . 
         FIGS. 53A-C  are results of thermal convection PCR using the apparatus of  FIG. 12A  showing amplification of a 373 bp sequence from a 1 ng plasmid sample with three different DNA polymerases from Takara Bio, Finnzymes, and Kapa Biosystems, respectively. 
         FIGS. 54A-C  are results of thermal convection PCR using the apparatus of  FIG. 12A  showing amplification of three target sequences (with size 177 bp, 960 bp and 1,608 bp, respectively) from 1 ng plasmid samples. 
         FIG. 55  shows results of thermal convection PCR using the apparatus of  FIG. 12A  showing amplification of various target sequences (with size between about 200 bp to about 2 kbp) from 1 ng plasmid samples. 
         FIGS. 56A-C  are results of thermal convection PCR using the apparatus of  FIG. 12A  showing acceleration of PCR amplification at elevated denaturation temperatures (100° C., 102° C., and 104° C., respectively). 
         FIGS. 57A-C  are results of thermal convection PCR using the apparatus of  FIG. 12A  showing amplification of three target sequences (with size 363 bp, 475 bp, and 513 bp, respectively) from 10 ng human genome samples. 
         FIG. 58  shows results of thermal convection PCR using the apparatus of  FIG. 12A  showing amplification of various sequences (with size between about 100 bp to about 800 bp) from 10 ng human genome and cDNA samples. 
         FIG. 59  shows results of thermal convection PCR using the apparatus of  FIG. 12A  showing amplification of a 363 bp β-globin sequence from very low copy human genome samples. 
         FIG. 60  shows temperature variations of the first, second and third heat sources of the apparatus of  FIG. 12A  as a function of time when target temperatures were set to 98° C., 70° C., and 54° C., respectively. 
         FIG. 61  shows power consumption of the apparatus of  FIG. 12A  having 12 channels as a function of time. 
         FIGS. 62A-E  are results of thermal convection PCR using the apparatus of  FIG. 12B  showing acceleration of PCR amplification as a function of the gravity tilting angle. The gravity tilting angle was 0°, 10°, 20°, 30°, and 45° for  FIGS. 62A-E , respectively. 
         FIGS. 63A-D  are results of thermal convection PCR using the apparatus of  FIG. 12B  showing acceleration of PCR amplification as a function of the gravity tilting angle. The gravity tilting angle was 0°, 10°, 20°, and 30° for  FIGS. 63A-D , respectively. 
         FIGS. 64A-B  are results of thermal convection PCR using the apparatus of  FIG. 12B  showing acceleration of PCR amplification as a function of the gravity tilting angle. The gravity tilting angle was 0° for  FIG. 64A  and 20° for  FIG. 64B . 
         FIG. 65  shows results of thermal convection PCR using the apparatus of  FIG. 12B  showing amplification of a 363 bp β-globin sequence from very low copy human genome samples when the gravity tilting angle was introduced. 
         FIG. 66  shows results of thermal convection PCR using the apparatus of  FIG. 14C  showing amplification of a 152 bp sequence from a 1 ng plasmid sample. 
         FIG. 67  shows results of thermal convection PCR using the apparatus of  FIG. 14C  showing amplification of various sequences (with size between about 100 bp to about 800 bp) from 1 ng plasmid samples. 
         FIGS. 68A-B  are results of thermal convection PCR using the apparatus of  FIG. 14C  showing amplification of 500 bp β-globin ( FIG. 68A ) and 500 bp β-actin ( FIG. 68B ) sequences from 10 ng human genome samples. 
         FIG. 69  shows results of thermal convection PCR using the apparatus of  FIG. 14C  showing amplification of a 152 bp sequence from very low copy plasmid samples. 
         FIGS. 70A-D  are results of thermal convection PCR using the apparatus of  FIG. 17A  showing dependence of PCR amplification as a function of the chamber diameter when the receptor hole depth was about 2 mm. The chamber diameter was about 4 mm for  FIG. 70A , about 3.5 mm for  FIG. 70B , about 3 mm for  FIG. 70C , and about 2.5 mm for  FIG. 70D . 
         FIGS. 71A-D  are results of thermal convection PCR using the apparatus of  FIG. 17A  showing dependence of PCR amplification as a function of the chamber diameter when the receptor hole depth was about 2.5 mm. The chamber diameter was about 4 mm for  FIG. 71A , about 3.5 mm for  FIG. 71B , about 3 mm for  FIG. 71C , and about 2.5 mm for  FIG. 71D . 
         FIGS. 72A-D  are results of thermal convection PCR using the apparatus of  FIG. 17A  showing dependence of PCR amplification as a function of the chamber diameter when the receptor hole depth was about 2 mm and the gravity tilting angle of 10° was introduced. The chamber diameter was about 4 mm for  FIG. 72A , about 3.5 mm for  FIG. 72B , about 3 mm for  FIG. 72C , and about 2.5 mm for  FIG. 72D . 
         FIGS. 73A-D  are results of thermal convection PCR using the apparatus of  FIG. 17A  showing dependence of PCR amplification as a function of the chamber diameter when the receptor hole depth was about 2.5 mm and the gravity tilting angle of 10° was introduced. The chamber diameter was about 4 mm for  FIG. 73A , about 3.5 mm for  FIG. 73B , about 3 mm for  FIG. 73C , and about 2.5 mm for  FIG. 73D . 
         FIGS. 74A-F  are results of thermal convection PCR using the apparatuses having the first thermal brake, showing dependence of PCR amplification as a function of the position of the first thermal brake along the channel axis. The bottom end of the first thermal brake was positioned at 0 mm ( FIG. 74A ), about 1 mm ( FIG. 74B ), about 2.5 mm ( FIG. 74C ), about 3.5 mm ( FIG. 74D ), about 4.5 mm ( FIG. 74E ), and about 5.5 mm ( FIG. 74F ) above the bottom of the second heat source. The thickness of the first thermal brake along the channel axis was about 1 mm. 
         FIGS. 75A-E  are results of thermal convection PCR using the apparatuses with and without the first thermal brake, showing dependence of PCR amplification as a function of the thickness of the first thermal brake along the channel axis when no gravity tilting angle was used. The thickness of the first thermal brake along the channel axis was 0 mm ( FIG. 75A , i.e., without the first thermal brake), about 1 mm ( FIG. 75B ), about 2 mm ( FIG. 75C ), about 4 mm ( FIG. 75D ), and about 5.5 mm ( FIG. 75E , i.e., channel only without the chamber structure). The bottom end of the first thermal brake was located on the bottom of the second heat source. 
         FIGS. 76A-E  are results of thermal convection PCR using the apparatuses with and without the first thermal brake, showing dependence of PCR amplification as a function of the thickness of the first thermal brake along the channel axis when the gravity tilting angle of 10° was introduced. The thickness of the first thermal brake along the channel axis was 0 mm ( FIG. 76A , i.e., without the first thermal brake), about 1 mm ( FIG. 76B ), about 2 mm ( FIG. 76C ), about 4 mm ( FIG. 76D ), and about 5.5 mm ( FIG. 76E , i.e., channel only without the chamber structure). The bottom end of the first thermal brake was located on the bottom of the second heat source. 
         FIG. 77  shows results of thermal convection PCR using the apparatus of  FIG. 12A  having a symmetric heating structure. 
         FIGS. 78A-B  show results of thermal convection PCR using the apparatus having an asymmetric receptor hole. The receptor hole was deeper on one side than the opposite side by about 0.2 mm for  FIG. 78A  and about 0.4 mm for  FIG. 78B . 
         FIG. 79  shows results of thermal convection PCR using the apparatus having an asymmetric thermal brake. 
         FIG. 80A-B  are schematic drawings showing sectional views of apparatus embodiments having one or more optical detection units  600 - 603  spaced from the first heat source  20  along the channel axis  80  and sufficient to detect a fluorescence signal from the samples in the reaction vessels  90 . The apparatus includes a single optical detection unit  600  to detect the fluorescence signal from multiple reaction vessels ( FIG. 80A ) or multiple optical detection units  601 - 603  ( FIG. 80B ) to detect the fluorescence signal from each reaction vessel. In the embodiments shown in  FIGS. 80A-B , the optical detection unit detects the fluorescence signal from the bottom end  92  of the reaction vessel  90 . The first heat source  20  comprises an optical port  610  positioned about the channel axis  80  between the bottom end  72  of the channel  70  and the first heat source protrusion  24  that provides a path for the excitation and emission of light parallel to the channel axis  80  (shown as upward and downward arrows, respectively). 
         FIGS. 81A-B  are schematic drawings showing sectional views of apparatus embodiments having one optical detection unit  600  ( FIG. 81A ) or more than one optical detection units  601 - 603  ( FIG. 81B ). Each of optical detection units  600 - 603  is spaced from the third heat source  40  along the channel axis  80  sufficient to detect a fluorescence signal from the samples located in the reaction vessels  90 . In these embodiments, a center part of a reaction vessel cap (not shown) that typically fits to the top opening of the reaction vessel  90  functions as an optical port for the excitation and emission light parallel to the channel axis  80  (shown in  FIGS. 81A-B  as downward and upward arrows, respectively). 
         FIG. 82  is a schematic drawing showing a sectional view of an apparatus embodiment having an optical detection unit  600  spaced from the second heat source  30 . In this embodiment, the optical port  610  is positioned in the second heat source  30  along a path perpendicular to the channel axis  80  toward the optical detection unit  600  sufficient to detect a fluorescence signal from the side of the samples in the reaction vessels  90 . The optical port  610  provides a path for the excitation and emission light between the reaction vessel  90  and the optical detection unit  600  (shown as left and right pointing arrows or vice versa). A side part of the reaction vessel  90  and a portion of the first chamber  100  along the light path also function as optical port in this embodiment. 
         FIG. 83  is a schematic drawing showing a sectional view of an optical detection unit  600  positioned to detect a fluorescence signal from the bottom end  92  of the reaction vessel  90 . In this embodiment, a light source  620 , an excitation lens  630 , and an excitation filter  640  that are configured to generate an excitation light are located along a direction at a right angle with respect to the channel axis  80 , and a detector  650 , an aperture or slit  655 , an emission lens  660 , and an emission filter  670  that are operable to detect an emission light are located along the channel axis  80 . A dichrocic beam-splitter  680  that transmits the fluorescence emission and reflects the excitation light is also shown. 
         FIG. 84  is a schematic drawing showing a sectional view of an optical detection unit  600  positioned to detect a fluorescence signal from the bottom end  92  of the reaction vessel  90 . In this embodiment, a light source  620 , an excitation lens  630 , and an excitation filter  640  are positioned to generate an excitation light along the channel axis  80 . A detector  650 , an aperture or slit  655 , an emission lens  660 , and an emission filter  670  are positioned to detect an emission light as located along a direction at a right angle with respect to the channel axis  80 . A dichrocic beam-splitter  680  that transmits the excitation light and reflects the fluorescence emission is shown. 
         FIGS. 85A-B  are schematic drawings showing sectional views of an optical detection unit  600  positioned to detect a fluorescence signal from the bottom end  92  of the reaction vessel  90 . In these embodiments, a single lens  635  is used to shape the excitation light and also to detect the fluorescence emission. In the embodiment shown in  FIG. 85A , the light source  620  and the excitation filter  640  are located along a direction at a right angle to the channel axis  80 . In the embodiment shown in  FIG. 85B , the optical elements for detecting the fluorescence emission ( 650 ,  655 , and  670 ) are located along a direction at a right angle to the channel axis  80 . 
         FIG. 86  is a schematic drawing showing a sectional view of an optical detection unit  600  positioned to detect a fluorescence signal from the top end  91  of the reaction vessel  90 . As in  FIG. 83 , the light source  620 , the excitation lens  630 , and the excitation filter  640  are located along a direction at a right angle to the channel axis  80 , and the detector  650 , the aperture or slit  655 , the emission lens  660 , and the emission filter  670  are located along the channel axis  80 . Also shown in this embodiment is a reaction vessel cap  690  sealably attached to the top end  91  of the reaction vessel  90  and including an optical port  695  disposed around a center point of the top end  91  of the reaction vessel  90  and for transmission of the excitation and emission light. The optical port  695  is further defined by the upper part of the reaction vessel cap  690  and the upper part of the reaction vessel  90  in this embodiment. 
         FIGS. 87A-B  are schematic drawings showing sectional views of reaction vessels  90  with reaction vessel caps  690  and optical ports  695 . The reaction vessel cap  690  is sealably attached to the upper part of the reaction vessel  90  and the optical port  695 . In these embodiments, the bottom end  696  of the optical port  695  is made to contact the sample when the reaction vessel  90  is sealed with the reaction vessel cap  690 . An open space  698  is provided on the side of the bottom end  696  of the optical port  695  and the reaction vessel cap  690  so that the sample can fill up the open space when the reaction vessel  90  is sealed with the reaction vessel cap  690 . The sample meniscus is located higher than the bottom end  696  of the optical port  695 . In  FIGS. 87A-B , the optical port  695  is disposed around a center point of the lower part of the reaction vessel cap  690  and is further defined by the lower part of the reaction vessel cap  690  and the upper part of the reaction vessel  90 . 
         FIG. 88  is a schematic drawing showing a sectional view of a reaction vessel  90  with an optical detection unit  600  disposed above the reaction vessel  90 . The reaction vessel  90  is sealed with the reaction vessel cap  690  having an optical port  695  disposed around a center point of the upper part of the reaction vessel  90  sufficient to make contact with sample. In this embodiment, the excitation light and the fluorescence emission pass through the optical port  695  and reach the sample or vice versa without passing air contained inside the reaction vessel  90 . 
     
    
    
     DETAILED DESCRIPTION 
     The following figure key may help the reader better appreciate the invention including the Drawings and claims:
       10 : Apparatus embodiment     20 : First heat source (bottom stage)     21 : Top surface of the first heat source     22 : Bottom surface of the first heat source     23 : First heat source protrusion (pointing toward the second heat source)     24 : First heat source protrusion (pointing toward table)     30 : Second heat source (intermediate stage)     31 : Top surface of the second heat source     32 : Bottom surface of the second heat source     33 : Second heat source protrusion (pointing toward the first heat source)     34 : Second heat source protrusion (pointing toward the third heat source)     40 : Third heat source (top stage)     41 : Top surface of the third heat source     42 : Bottom surface of the third heat source     43 : Third heat source protrusion (pointing toward the second heat source)     44 : Third heat source protrusion (pointing away from unit)     50 : First insulator (or first insulating gap)     51 : First insulator chamber     60 : Second insulator (or second insulating gap)     61 : Second insulator chamber     70 : Channel     71 : Top end of the channel/through hole     72 : Bottom end of the channel     73 : receptor hole     74 : receptor hole gap     80 : (Center) axis of the channel     90 : Reaction vessel     91 : Top end of the reaction vessel     92 : Bottom end of the reaction vessel     93 : Outer wall of the reaction vessel     94 : Inner wall of the reaction vessel     95 : (Center) axis of the reaction vessel     100 : First Chamber     101 : Top end of the first chamber, defining an upper limit of the chamber     102 : Bottom end of the first chamber, defining a lower limit of the chamber     103 : First wall of the first chamber, defining a horizontal limit of the chamber     105 : Gap of the first chamber     106 : (Center) axis of the first chamber     110 : Second Chamber     111 : Top end of the second chamber     112 : Bottom end of the second chamber     113 : First wall of the second chamber     115 : Gap of the second chamber     120 : Third Chamber     121 : Top end of the third chamber     122 : Bottom end of the third chamber     123 : First wall of the third chamber     125 : Gap of the third chamber     130 : First thermal brake     131 : Top end of the first thermal brake     132 : Bottom end of the first thermal brake     133 : First wall of the first thermal brake, essentially contacting at least part of the channel     140 : Second thermal brake     141 : Top end of the second thermal brake     142 : Bottom end of the second thermal brake     143 : First wall of the second thermal brake, essentially contacting at least part of the channel     160 : Heating/cooling elements     160   a : Heating (and/or cooling) element of the first heat source     160   b : Heating (and/or cooling) element of the second heat source     160   c : Heating (and/or cooling) element of the third heat source     170 : Temperature Sensors     170   a : Temperature sensor of the first heat source     170   b : Temperature sensor of the second heat source     170   c : Temperature sensor of the third heat source     200 : First securing element comprising at least one of following elements     201 : Screw or fastener (typically made of a thermal insulator)     202   a : Washer or positioning standoff (typically made of a thermal insulator)     202   b : Spacer or positioning standoff (typically made of a thermal insulator)     202   c : Spacer or positioning standoff (typically made of a thermal insulator)     203   a : Securing element of the first heat source     203   b : Securing element of the second heat source     203   c : Securing element of the third heat source     210 : Second securing element (typically made as a wing structure)
       Used to assemble the heat source assembly to the first housing element  300           300 : First housing element     310 : Third insulator (or third insulating gap)
       Located between the sides of the heat sources and the side walls of the first housing element; and   Filled with a thermal insulator such as air, a gas, or a solid insulator         320 : Fourth insulator (or fourth insulating gap)
       Located between the bottom of the first heat source and the bottom wall of the first housing element; and   Filled with a thermal insulator such as air, a gas, or a solid insulator         330 : Support     400 : Second housing element     410 : Fifth insulator (or fifth insulating gap)
       Located between the side walls of the first housing element and those of the second housing element; and   Filled with a thermal insulator such as air, a gas, or a solid insulator         420 : Sixth insulator (or sixth insulating gap)
       Located between the bottom wall of the first housing element and that of the second housing element; and   Filled with a thermal insulator such as air, a gas, or a solid insulator.         500 : Centrifuge unit     501 : Motor     510 : Axis of centrifugal rotation     520 : Rotation arm     530 : Tilt shaft     600 - 603 : Optical detection units     610 : Optical port     620 : Light source     630 : Excitation lens     635 : Lens     640 : Excitation filter     650 : Detector     655 : Aperture or slit     660 : Emission lens     670 : Emission filter     680 : Dichroic beam-splitter     690 : Reaction vessel cap     695 : Optical port     696 : Bottom end of optical port     697 : Top end of optical port     698 : Open space between inner wall of reaction vessel and side wall of optical port     699 : Side wall of optical port   

     As discussed, and in one embodiment, the present invention features a three-stage thermal convection apparatus adapted to perform thermal convection PCR amplification. 
     In one embodiment, the apparatus includes as operably linked components the following elements:
         (a) a first heat source for heating or cooling a channel and comprising a top surface and a bottom surface, the channel being adapted to receive a reaction vessel for performing PCR,   (b) a second heat source for heating or cooling the channel and comprising a top surface and a bottom surface, the bottom surface facing the top surface of the first heat source,   (c) a third heat source for heating or cooling the channel and comprising a top surface and a bottom surface, the bottom surface facing the top surface of the second heat source, wherein the channel is defined by a bottom end contacting the first heat source and a through hole contiguous with the top surface of the third heat source, and further wherein center points between the bottom end and the through hole form a channel axis about which the channel is disposed,   (d) at least one temperature shaping element such as at least one gap or space (e.g., a chamber) disposed around the channel and within at least part of the second or third heat source, the chamber gap being sufficient to reduce heat transfer between the second or third heat source and the channel; and   (e) a receptor hole adapted to receive the channel within the first heat source.       

     In operation, the apparatus uses multiple heat sources, typically three, four or five heat sources, preferably three heat sources positioned within the apparatus so that each is essentially parallel to the other heat sources in typical embodiments. In this embodiment, the apparatus will generate a temperature distribution suitable for a convection-based PCR process that is fast and efficient. A typical apparatus includes a plurality of channels disposed within the first, second and third heat sources so that a user can perform multiple PCR reactions at the same time. For instance, the apparatus can include at least one or two, three, four, five, six, seven, eight, nine channels up to about ten, eleven or twelve channels, twenty, thirty, forty, fifty or up to several hundred channels extending through the first, second, and third heat sources, with between about eight to about one hundred channels being generally preferred for many invention applications. A preferred channel function is to receive a reaction vessel holding the user&#39;s PCR reaction and to provide direct or indirect thermal communication between the reaction vessel and at least one of and preferably all of a) the heat sources, b) the temperature shaping element(s), and c) the receptor hole. 
     The relative position of each of the three heat sources to the other is an important feature of the invention. The first heat source of the apparatus is typically located on the bottom and maintained at a temperature suitable for nucleic acid denaturation, and the third heat source is typically located on the top and maintained at a temperature suitable for annealing of denatured nucleic acid template with one or more oligonucleotide primers. In some embodiments, the third heat source is maintained at a temperature suitable for both annealing and polymerization. The second heat source is typically located in between the first and third heat sources and maintained at a temperature suitable for polymerization of the primer along the denatured template. Thus in one embodiment, the bottom part of the channel in the first heat source and the top part of the channel in the third heat source are subject to a temperature distribution suitable for the denaturation and annealing steps of the PCR reaction, respectively. In between the top and bottom part of the channel in which the second heat source is located is the transition region in which most of temperature change from the denaturation temperature of the first heat source (the highest temperature) to the annealing temperature of the third heat source (the lowest temperature) takes place. Thus, in typical embodiments, at least part of the transition region is subject to a temperature distribution suitable for polymerization of the primer along the denaturated template. When the third heat source is maintained at a temperature suitable for both annealing and polymerization, the top part of the channel in the third heat source also provides a temperature distribution suitable for the polymerization step in addition to an upper part of the transition region. Therefore, temperature distribution in the transition region is important for achieving efficient PCR amplification, particularly regarding the primer extension. Thermal convection inside the reaction vessel typically depends on the magnitude and direction of the temperature gradient generated in the transition region, and thus temperature distribution in the transition region is also important for generating suitable thermal convection inside the reaction vessel that is conducive to PCR amplification. Various temperature shaping elements can be used with the apparatus to generate a suitable temperature distribution in the transition region to support fast and efficient PCR amplification. 
     Typically, each individual heat source is maintained at a temperature suitable for inducing each step of thermal convection PCR. Moreover, and in embodiments in which the apparatus features three heat sources, temperatures of the three heat sources are suitably arranged to induce thermal convection across a sample inside a reaction vessel. One general condition for inducing suitable thermal convection according to the invention is, a heat source maintained at a higher temperature is located at a lower position within the apparatus than a heat source maintained at a lower temperature. Thus in a preferred embodiment, the first heat source is positioned lower in the apparatus than the second or third heat source. In this embodiment, it will be generally preferred to place the second heat source lower in the apparatus than the third heat source. Other configurations are possible provided intended results are achieved. 
     As discussed, it is an object of the invention to provide an apparatus with at least one temperature shaping element. In most embodiments, each channel of the apparatus will include less than about ten of such elements, for example, one, two, three, four, five, six, seven, eight, nine or ten of the temperature shaping elements for each channel. One function of the temperature shaping element is to provide for efficient thermal convection mediated PCR by providing a structural or positional feature that supports PCR. As will be more apparent from the examples and discussion which follows, such features include, but are not limited to, at least one gap or space such as a chamber; at least one insulator or insulating gap located between the heat sources; at least one thermal brake; at least one protrusion structure in at least one of the first, second, and third heat sources; at least one asymmetrically disposed structure within the apparatus, particularly in at least one of the channels, first heat source, second heat source, third heat source, gap such as a chamber, thermal brake, protrusion, first and second insulators, or the receptor hole; or at least one structural or positional asymmetry. Structural asymmetry is typically defined in reference to the channel and/or channel axis. An example of positional asymmetry is tilting or otherwise displacing the apparatus with respect to the direction of gravity. 
     The words “gap” and “space” will often be used herein interchangeably. A gap is a small enclosed or semi-enclosed space within the apparatus that is intended to assist thermal convection PCR. A large gap or large space with a defined structure will be referred to herein as a “chamber”. In many embodiments, the chamber will include a gap and be referred to herein as a “chamber gap”. A gap may be empty, filled or partially filled with an insulating material as described herein. For many applications, a gap or chamber filled with air will be generally useful. 
     One or a combination of temperature shaping elements (the same or different) can be used with the invention apparatus. Illustrative temperature shaping elements will now be discussed in more detail. 
     Illustrative Temperature Shaping Elements 
     A. Gap or Chamber 
     In one embodiment of the present apparatus, each channel will include at least one gap or chamber as the temperature shaping element. In a typical embodiment, the apparatus will include one, two, three, four, five or even six chambers disposed around each channel and within at least one of the second and third heat sources, for example, one, two or three of such chambers for each channel. In this example of the invention, the chamber creates a space between the channel and the second or third heat source that allows the user to precisely control temperature distribution within the apparatus. That is, the chamber assists in shaping the temperature distribution of the channel in the transition region. By “transition region” is meant the region of the channel roughly in between an upper part of the channel that contacts the third heat source and a lower part of the channel that contacts the first heat source. The chamber can be positioned nearly anywhere around the channel provided intended results are achieved. For instance, positioning the chamber (or more than one chamber) within or near the second heat source, the third heat source or both the second and third heat sources will be useful for many invention applications. In embodiments in which a channel in the apparatus has multiple chambers, each chamber may be separated from the other and may in some instances contact one or more other chambers within the apparatus. 
     One or a combination of different gap or chamber structures is compatible with the invention. As general requirements, the chamber should generate a temperature distribution in the transition region that fulfills at least one and preferably all of the following conditions: (1) the temperature gradient generated (particularly across the vertical profile of the channel) must be large enough so as to generate a thermal convection across the sample inside the reaction vessel; and (2) the thermal convection thus generated by the temperature gradient must be sufficiently slow (or appropriately fast) so that sufficient time periods can be provided for each step of the PCR process. In particular, it is especially important to make the time period of the polymerization step sufficiently long since the polymerization step typically takes more time than the denaturation and annealing steps. Examples of particular gap or chamber configurations are disclosed below. 
     If desired, the channel within an invention apparatus may have at least one chamber disposed essentially symmetrically or asymmetrically about the channel axis. In many embodiments, an apparatus with one, two or three chambers will be preferred. The chambers may be disposed in one or a combination of the heat sources, for example, the first heat source, the second heat source, the third heat source, or both the second and third heat sources. For some apparatuses, having one, two, or three chambers within the second heat source or the second and third heat sources will be especially useful. Examples of such chamber embodiments are provided below. 
     In one embodiment, the chamber will be further defined by what is referred to herein as a “protrusion” from at least one of the first heat source, the second heat source, and the third heat source. In a particular embodiment, the protrusion will extend from the second heat source toward the first heat source in a direction generally parallel to the channel axis. Other embodiments are possible such as including a second protrusion extending from the second heat source to the third heat source generally parallel to the channel axis. Additional embodiments include an apparatus with a protrusion extending from the first heat source toward the second heat source generally parallel to the channel axis. Still further embodiments include an apparatus with a protrusion extending from the third heat source toward the second heat source also generally parallel to the channel axis. In some embodiments, the apparatus may comprise at least one protrusion that is tilted with respect to the channel axis. In these examples of the invention, it is possible to substantially reduce the volume of the first, second and/or third heat sources as well as the heat transfer between the heat sources while lengthening chamber dimensions along the channel axis. These features have been found to enhance thermal convection PCR efficiency while reducing power consumption. 
       FIGS. 2A, 3A, 4A, 9B, 12A, 14A, 15A, and 22A  provide a few examples of acceptable chambers for use with the invention. Other suitable chamber structures are disclosed below. 
     B. Thermal Brake 
     Each channel within an invention apparatus may include one, two, three, four, five, six or more thermal brakes, typically one or two thermal brakes to control the temperature distribution within the apparatus. In many embodiments, the thermal brake will be defined by a top and bottom end and a wall that will be in optional thermal contact with the channel. The thermal brake is typically disposed adjacent or near a wall of the gap or chamber (if present). An undesirable intrusion of a temperature profile from one heat source to another can be controlled and usually reduced by including the thermal brake as a temperature shaping element. As will be described in more detail below, it was found that thermal convection PCR amplification efficiency is sensitive to the position and thickness of the thermal brake. An acceptable thermal brake may be disposed with respect to the channel either symmetrically or asymmetrically. 
     One or more thermal brakes as described herein may be placed in nearly any position around each channel of the apparatus provided intended results are achieved. Thus in one embodiment, a thermal brake can be positioned adjacent or near a chamber to block or reduce undesired heat flow from an adjacent heat source and achieve suitable PCR amplification. 
       FIGS. 10B, 10D, 10F, 11B, 14B, and 14C  provide a few examples of suitable thermal brakes for use with the invention. Other suitable thermal brakes are disclosed below. 
     C. Positional or Structural Asymmetry 
     It was found that thermal convection PCR was faster and more efficient when an invention apparatus included at least one positional or structural asymmetric element, for example, one, two, three, four, five, six, or seven of such elements for each channel. Such elements can be placed around one or more channels up to the entire apparatus. Without wishing to be bound by theory, it is believed that presence of an asymmetric element within the apparatus increases the buoyancy force in ways that make the amplification process faster and more efficient. It has been found that by introducing at least one positional or structural asymmetry within the apparatus that can cause “horizontally asymmetric heating or cooling” with respect to the channel axis or the direction of gravity, it is possible to assist thermal convection PCR. Without wishing to be bound by theory, it is believed that an apparatus with at least one asymmetric element therein breaks apparatus symmetry with regard to heating or cooling the channel and helps or enhances generation of the buoyancy force so as to make the amplification process faster and more efficient. By a “positional asymmetric element” is meant that a structural element that makes the channel axis or the apparatus tilted with respect to the direction of gravity. By a “structural asymmetric element” is meant that a structural element that is not symmetrically disposed within the apparatus with respect to the channel and/or channel axis. 
     As discussed, it is necessary to generate a vertical temperature gradient inside a sample fluid in order to generate thermal convection (and also to fulfill the temperature requirements for the PCR process). However, even in the presence of a vertical temperature gradient, the buoyancy force that induces the thermal convection may not be generated if isothermal contours of the temperature distribution are flat (i.e., horizontal) with respect to the direction of gravity (i.e., the vertical direction). Within such a flat temperature distribution, the fluid does not experience any buoyancy force since each part of the fluid has the same temperature (and thus the same density) as other parts of the fluid at the same height. In symmetric embodiments, all the structural elements are symmetric with respect to the channel or channel axis and the direction of gravity is aligned essentially parallel to the channel or channel axis. In such symmetric embodiments, isothermal contours of the temperature distribution inside the channel or the reaction vessel often become nearly or perfectly flat with respect to the gravitational field, and thus it is often difficult to generate the thermal convection that is sufficiently fast. Without wishing to be bound by theory, it is believed that presence of certain perturbations that can induce a fluctuation or instability in the temperature distribution often helps or enhances generation of the buoyancy force and makes the PCR amplification faster and more efficient. For instance, a small vibration that typically exists in usual environment may disturb the near or perfectly flat temperature distribution, or a small structural defect in the apparatus may break the symmetry of the channel/chamber structure or the reaction vessel structure so as to disturb the near or perfectly flat temperature distribution. In such a perturbed temperature distribution, the fluid can have different temperature for at least part of the fluid as compared to other part of the fluid at the same height, and thus the buoyancy force can be readily generated due to such temperature fluctuation or instability. Such natural or incidental perturbations are usually important in generating the thermal convection in the symmetric embodiments. When a positional or structural asymmetry is present within the apparatus, the temperature distribution within the channel or the reaction vessel can be controllably made uneven at the same height (i.e., horizontally uneven or asymmetric). In the presence of such horizontally asymmetric temperature distribution, the buoyancy force can be readily and usually more strongly generated so as to make the thermal convection PCR faster and more efficient. Useful positional or structural asymmetric elements cause “horizontally asymmetric heating or cooling” of the channel with respect to the channel axis or the direction of gravity. 
     Asymmetry can be introduced into an invention apparatus by one or a combination of strategies. In one embodiment, it is possible to make an invention apparatus with a positional asymmetry imposed on the apparatus, for example, by tilting the apparatus or the channel with respect to the direction of gravity. Nearly any of the apparatus embodiments disclosed herein can be tilted by incorporating a structure capable of offsetting the channel axis with respect to the direction of gravity. An example of an acceptable structure is a wedge or related inclined shape, or an inclined or tilted channel. See  FIGS. 12B and 18A -B for examples of this invention embodiment. 
     In other embodiments, at least one of the following elements can be asymmetrically disposed within the apparatus with respect to the channel axis: a) the channel, b) a gap such as a chamber, c) the receptor hole d) the first heat source, e) the second heat source, f) the third heat source; g) the thermal brake; and h) the insulator. Thus in one invention embodiment, the apparatus features a chamber as the structural asymmetric element. In this invention example, the apparatus may include one or more other structural asymmetric elements such as the channel, receptor hole, thermal brake, insulator, or one or more of the heat sources. In another embodiment, the structural asymmetric element is the receptor hole. In yet another embodiment, the structural asymmetric element is the thermal brake or more than one thermal brake. The apparatus may include one or more other asymmetric or symmetric structural elements such as the first heat source, the second heat source, the third heat source, the chamber, the channel, the insulator etc. 
     In embodiments in which the first heat source, the second heat source and/or the third heat source features a structural asymmetric element, the asymmetry may reside particularly in a protrusion (or more than one protrusion) that extends generally parallel to the channel axis. 
     Further examples are provided below. In particular, see  FIGS. 21A-B ,  22 A-D,  23 A-B,  24 A-B,  25 ,  26 , and  27 A-B. 
     As discussed, one or both of the channel and chamber can be symmetrically or asymmetrically disposed in the apparatus with respect to the channel axis. See also  FIGS. 6A-J ,  7 A-I, and  8 A-P for examples in which the channel and/or chamber are the symmetric or asymmetric structural element. 
     It will often be desirable to have an apparatus in which the receptor hole is the structural asymmetric element. Without wishing to be bound to any theory, it is believed that the region between the receptor hole and the bottom end of the chamber or the second heat source is a location in the apparatus where a major driving force for thermal convection flow is generated. As will be readily apparent, this region is where initial heating to the highest temperature (i.e., the denaturation temperature) and transition toward a lower temperature (i.e., the polymerization temperature) take place, and thus the largest driving force should originate from this region. 
     See, for example,  FIGS. 13 and 21A -B showing asymmetric receptor hole structures. 
     D. Insulator and Insulating Gap 
     It will often be useful to insulate each of the heat sources from the other to achieve the objects of this invention. As will be apparent from the following discussion, the apparatus can be used with a wide variety of insulators placed in the insulating gaps between each of the heat sources. Thus in one embodiment, a first insulator is placed in the first insulating gap between the first and second heat sources and a second insulator is placed in the second insulating gap between the second and third heat sources. One or a combination of gas or solid insulators having low thermal conductivity can be used. A generally useful insulator for many purposes of the invention is air (having low thermal conductivity of about 0.024 W·m −1 ·K −1  at room temperature for static air, with a gradual increase with increasing temperature). Although materials that have a thermal conductivity larger than that of static air can be used without significantly reducing the performance of the apparatus other than the power consumption, it is generally preferred to use gas or solid insulators that have a thermal conductivity similar to or smaller than air. Examples of good thermal insulators include, but not limited to, wood, cork, fabrics, plastics, ceramics, rubber, silicon, silica, carbon, etc. Rigid foams made of such materials are particularly useful since they represent very low thermal conductivity. Examples of rigid foams includes, but not limited to, Styrofoam, polyurethane foam, silica aerosol, carbon aerosol, SEAgel, silicone or rubber foam, wood, cork, etc. In addition to air, polyurethane foam, silica aerosol and carbon aerosol are particularly useful thermal insulators to use at elevated temperatures. 
     In embodiments in which an invention apparatus has the insulating gaps, advantages will be apparent. For instance, a user of the apparatus will have the ability to 1) reduce the power consumption by substantially reducing heat transfer from one heat source to next heat source; 2) control the temperature gradient for generating the driving force (and therefore control the thermal convection) since large temperature change from one heat source to next heat source occurs in the insulating gap regions; and 3) balance heat transfer between the three heat sources so as to simplify the machinery of simultaneously maintaining the temperatures of the three adjacently disposed heat sources and thereby minimize the power consumption. It has been found that larger insulating gaps with low thermal conductivity insulators generally help reducing the power consumption. Use of the protrusion structures is particularly useful for substantially reducing the power consumption since larger average gaps can be provided while independently controlling different regions of each insulating gap (i.e., regions near and distant from the channel, separately). It has been also found that by changing the insulating gaps, particularly in the region near the channel, it is possible to control the speed of the thermal convection and thus the speed of the PCR amplification. Controlling the first insulating gap near the channel region has been found to be particularly useful in modulating the speed of the thermal convection. Moreover, the ratio of the average thickness of the first and second insulating gaps along the channel axis has been found to be very useful in balancing the heat transfer between the three heat sources. Amount of heat transfer between two adjacent heat sources is inversely proportional to the distance between the two heat sources. Therefore, by adjusting the ratio of the average thickness of the first and second insulating gaps, the second heat source located in between the first and third heat sources can be heated near the desired temperature without power consumption as a result of a balance in the heat transfer between the three heat sources. This makes not only the power consumption of the apparatus substantially reduced but also the temperature control machinery and mechanism required for the apparatus much simple. For many instances, by choosing the average thickness ratio as suitable for the desired temperatures of the three heat sources, the apparatus can be built with using heating elements only without necessity for a cooling element that is typically more power consuming and frequently bulkier. Other advantages of having the insulating gaps will be apparent from the discussion and Examples that follow. 
     It will be apparent from the following discussion and examples that an invention apparatus may include one or a combination of the foregoing temperature shaping elements. Thus in one embodiment, the apparatus features at least one chamber (e.g., one, two or three chambers) disposed symmetrically about the channel and typically parallel to the channel axis along with the first and second insulators separating the first, second and third heat sources from each other. In this embodiment, the apparatus may further include one or two thermal brakes to further assist thermal convection PCR. In an embodiment in which the apparatus includes two chambers, for instance within the second heat source, each chamber may have the same or different horizontal position with respect to the channel axis. In another embodiment, the second heat source features protrusions extending toward the first and/or third heat sources generally parallel to the channel axis in which the protrusions define the chamber. In this embodiment, the apparatus may further include a protrusion extending from the first heat source to the second heat source; and optionally a protrusion extending from the third heat source toward the second heat source generally parallel to the channel axis. In these embodiments, the second heat source may include no chamber, one chamber, or two chambers disposed symmetrically with respect to the channel axis and the third heat source may include no chamber, one chamber or two chambers disposed symmetrically with respect to the channel axis with the proviso that at least one of the heat sources includes a chamber. 
     As discussed, it will often be useful to include asymmetric structural element within the apparatus. Thus it is an object of the invention to include within the apparatus a receptor hole that is disposed asymmetrically with respect to the channel axis. In this embodiment, the apparatus may include one or more chambers disposed symmetrically or asymmetrically with respect to the channel axis. Alternatively, or in addition, the apparatus may feature at least one thermal brake that is disposed asymmetrically with respect to the channel axis. In this embodiment, the apparatus may include one or more chambers disposed symmetrically or asymmetrically with respect to the channel axis. Alternatively, or in addition, the apparatus may feature at least one of the protrusions disposed asymmetrically with respect to the channel axis. In one embodiment, the protrusion extending from the first heat source is disposed asymmetrically about the channel axis while one or both protrusions (and chamber) extending from the second heat source is disposed symmetrically about the channel axis. Alternatively, or in addition, the one or more protrusions (and chamber) of the second heat source can be disposed asymmetrically about the channel axis. In these embodiments, the apparatus may further include a protrusion extending from the third heat source to the second heat source that is disposed symmetrically or asymmetrically with respect to the channel axis. 
     However, in another embodiment, one or more of the channels up to all of the channels within the apparatus need not include any chamber or gap structure. In this example, the apparatus will preferably include one or more other temperature shaping elements such as tilting the angle of the channel with respect to gravity (an example of positional asymmetry). Alternatively, or in addition, the channel can include a structural asymmetry or be subjected to centrifugal acceleration as provided herein. For instance, see Example 6 and  FIG. 76E  (channel only with the gravity tilting angle of 10°) in comparison with  FIG. 75E  (channel only without the gravity tilting angle). 
     As will be appreciated, it is possible to have an invention apparatus in which other or further asymmetric elements are present. For example, the apparatus can include two or three chambers in which one or more of the chambers are disposed asymmetrically with respect to the channel axis. In embodiments in which the apparatus includes a single chamber, that chamber may be disposed asymmetrically with respect to the channel axis. Embodiments include an apparatus in which protrusions extending from the second heat source toward each of the first and third heat sources are disposed asymmetrically with respect to the channel axis. 
     If desired, any of the foregoing invention embodiments can include a positional asymmetry by tilting the device or the channel with respect to the direction of gravity or placing it on a wedge or other inclined shape. 
     As will be appreciated, nearly any temperature shaping element of an apparatus embodiment (whether symmetrically or asymmetrically disposed within the apparatus with respect to the channel axis) can be combined with one or more other temperature shaping elements including other structural or positional features of the apparatus so long as intended results are achieved. 
     As will also be appreciated, the invention is flexible and includes an apparatus in which each channel includes the same or different temperature shaping elements. For example, one channel of the apparatus can have no chamber or gap structures while another channel of the apparatus includes one, two, or three of such chamber or gap structures. The invention is not limited to any channel configuration (or group of channel configurations) so long as intended results are achieved. However, it will often be preferred to have all the channels of an invention apparatus have the same number and type of temperature shaping element to simplify use and manufacturing considerations. 
     Reference to the following figures and examples is intended to provide greater understanding of the thermal convection PCR apparatus. It is not intended and should not be read as limiting the scope of the present invention. 
     Turning now to  FIGS. 1 and 2A -C, the apparatus  10  features the following elements as operably linked components:
         (a) a first heat source  20  for heating or cooling a channel  70  and comprising a top surface  21  and a bottom surface  22  in which the channel  70  is adapted to receive a reaction vessel  90  for performing PCR;   (b) a second heat source  30  for heating or cooling the channel  70  and comprising a top surface  31  and a bottom surface  32  in which the bottom surface  32  faces the top surface of the first heat source  21 ,   (c) a third heat source  40  for heating or cooling the channel  70  and comprising a top surface  41  and a bottom surface  42  in which the bottom surface  42  faces the top surface of the second heat source  31 , wherein the channel  70  is defined by a bottom end  72  contacting the first heat source  20  and a through hole  71  contiguous with the top surface of the third heat source  41 . In this embodiment, center points between the bottom end  72  and the through hole  71  form a channel axis  80  about which the channel  70  is disposed;   (d) at least one chamber disposed around the channel  70  and within at least part of the second  30  or third  40  heat source. In this embodiment, the first chamber  100  includes a chamber gap  105  between the second  30  or third  40  heat source and the channel  70  sufficient to reduce heat transfer between the second  30  or third  40  heat source and the channel  70 ; and   (e) a receptor hole  73  adapted to receive the channel  70  within the first heat source  20 .       

     By the phrase “operably linked”, “operably associated” or like phrase is meant one or more elements of the apparatus that are operationally linked to one or more other elements. More specifically, such an association can be direct or indirect (e.g., thermal), physical and/or functional. An apparatus in which some elements are directly linked and others indirectly (e.g., thermally) linked is within the scope of the present invention. 
     In the embodiment shown in  FIG. 2A , the apparatus further includes a first insulator  50  positioned between the top surface  21  of the first heat source  20  and the bottom surface  32  of the second heat source  30 . The apparatus further includes a second insulator  60  positioned between the top surface  31  of the second heat source  30  and the bottom surface  42  of the third heat source  40 . As will be appreciated, practice of the invention is not limited to having only two insulators present provided the number of insulators is sufficient for intended results to be achieved. That is, the invention may include multiple insulators (e.g. 2, 3 or 4 insulators). In the embodiment shown in  FIG. 2A , the length of the first insulator  50  along the channel axis  80  is greater than the length of the second insulator  60  along the channel axis  80 . In other embodiments, the length of the first insulator  50  may be smaller than or essentially the same as that of the second insulator  60 . However, it is generally preferred to have the length of the first insulator  50  greater than that of the second insulator  60 . Such embodiment is advantageous in reducing power consumption and facilitating temperature control. In another embodiment, it is preferred to have the length of the second heat source  30  greater than the length of the first heat source  20  or the third heat source  30  along the channel axis  80 . Although in other embodiments the length of the second heat source  30  can be smaller or essentially the same as that of the first  20  or third  40  heat source, it is advantageous to have a greater length for the second heat source  30  to achieve a longer path length for the polymerization step. 
     In one embodiment shown in  FIG. 2A , the first insulator  50 , the second insulator  60  or both insulators  50 ,  60  are filled with a thermal insulator having a low thermal conductivity. Preferred thermal insulators have a thermal conductivity between about a few tenths of W·m −1 ·K −1  to about 0.01 W·m −1 ·K −1  or smaller. In this embodiment, the length of the first insulator  50  along the channel axis  80  and preferably also that of the second insulator  60  are made to be small, for instance, between about 0.1 mm to about 5 mm, preferably between about 0.2 mm to about 4 mm. In this example of the invention, heat loss from one heat source to an adjacent heat source can be substantially large, resulting in large power consumption in operating the apparatus. For many applications, it will often be preferred to have at least one of the three heat sources (e.g.,  20 ,  30  and  40 ) isolated from the others, preferably two heat sources thermally isolated from another (e.g.,  20  and  30  isolated from each other,  30  and  40  isolated from each other, etc.) with all of the three heat sources (e.g.,  20 ,  30  and  40 ) thermally isolated from each other being generally preferred for many invention applications. Use of one or more thermal insulators will often be helpful. For instance, use of a thermal insulator in the first  50  and second  60  insulating gaps can often lower power consumption. 
     Thus in the invention embodiment of the invention shown in  FIGS. 2A-C , the first insulator  50  comprises or consists of a solid or a gas. Alternatively, or in addition, the second insulator  60  includes or consists of a solid or a gas. 
     Turning again to the apparatus shown in  FIGS. 2A-C , the chamber gap  105  between the chamber wall  103  and the channel  70  inside the second heat source may be partially or totally filled with a thermal insulator such as a gas, solid, or gas-solid combination. Typically useful insulators include air, and gas or solid insulators that have a thermal conductivity similar to or smaller than air. Since one important function of the chamber gap  105  is to control (typically to reduce) heat transfer from the second heat source to the channel inside the second heat source, materials that have a thermal conductivity larger than that of air such as plastics or ceramics can also be used. However, when such higher thermal conductivity materials are used, the chamber gap  105  should be adjusted to be larger compared to the embodiment of using air as an insulator. Similarly, if a material having a lower thermal conductivity than air is used, the chamber gap  105  should be adjusted to be smaller than that of the air insulator embodiment. 
     In particular,  FIGS. 2A-C  show an apparatus embodiment in which air or a gas is used as an insulator in the first insulator  50  and second insulator  60 , and the chamber gap  105 . The channel structures inside these gaps are depicted with dashed lines to represent invisibility of these structures when air (or a gas) is used as an insulator. If desired to achieve a particular invention objective, the apparatus can be adapted so that a solid insulator is used in the chamber gap  105 . Alternatively, or in addition, the apparatus may include solid insulators in the first insulator  50  and second insulator  60 . 
       FIGS. 2B and 2C  show perspective views of section A-A and B-B of the apparatus as marked in  FIG. 1 . An embodiment in which air or a gas is used as an insulator is shown. 
     As shown in the embodiment of  FIGS. 1 and 2A -C, the apparatus features twelve channels (sometimes referred herein to as reaction vessel channels). However, more or less channels are possible depending on intended use, for instance, from about one or two to about twelve channels, or between about twelve to several hundred channels, preferably about eight to about one hundred channels. Preferably, each channel is independently adapted to receive a reaction vessel  90  that is typically defined by a bottom end  92  within the first heat source  20  and a top end  91  on the top of the third heat source  41 . The channel  70  in the first  20 , second  30  and third  40  heat sources typically passes through the first  50  and second  60  insulators. Center points between the top  71  and bottom  72  ends of the channel  70  form an axis of the channel  80  (sometimes referred herein to as channel axis) about which the heat sources and insulators are disposed. 
     Referring again to the embodiment shown in  FIGS. 1 and 2A -C, the channel  70  is adapted so that the reaction vessel  90  can fit snugly therein i.e., it has a dimensional profile that is essentially the same as that of a lower part of the reaction vessel as depicted in  FIG. 2A . In the operation, the channel functions as a receptor for receiving a reaction vessel. However as will be explained in more detail below, the structure of the channel  70  can be adjusted and/or moved in relation to the channel axis  80  to provide different thermal contact possibilities between the reaction vessel  90  and one or more of the heat sources  20 ,  30 , and  40 . 
     As an example, the through hole  71  formed in the third heat source can function as a top part of the channel  70 . In this embodiment, the channel  70  inside the third heat source  40  is in physical contact with the third heat source  40 . That is, a wall of the through hole  71  extending into the third heat source  40  is in physical contact with the reaction vessel  90 . In this embodiment, the apparatus can provide efficient heat transfer from the third heat source  40  to the channel  70  and reaction vessel  90 . 
     For many invention applications, it will be generally preferred to have the size of the through hole in the third heat source essentially the same as that of the channel or reaction vessel. However, other through hole embodiments are within the scope of the present invention and are disclosed herein. For example, and referring again to  FIGS. 2A-C , the through hole  71  in the third heat source  40  may be made larger than the size of the reaction vessel  90 . However, in such case, heat transfer from the third heat source  40  to the reaction vessel  90  may become less efficient. In this embodiment, it may be useful to lower the temperature of the third heat source  40  for optimal practice of the invention. For most invention applications, it will be generally useful to have the size of the through hole  71  in the third heat source  40  essentially the same size as that of the reaction vessel  90 . 
     In invention embodiments in which the receptor hole  73  has a closed bottom end  72  formed in the first heat source  20 , it will often function as a bottom portion of the channel  70 . See  FIG. 2A , for instance. In such an embodiment, the receptor hole  73  of the first heat source  20  has a size essentially the same as that of the bottom part of the reaction vessel  92  which in most embodiments will provide physical contact and efficient heat transfer to the reaction vessel  90 . In some invention embodiments, the receptor hole  73  in the first heat source  20  may have a partial chamber structure or a size slightly larger than that of the bottom part of the reaction vessel as will be discussed. 
     Chamber Structure and Function 
     Turning again to the apparatus shown in  FIGS. 2A-C , the first chamber  100  is symmetrically disposed about the channel  70  and within the second heat source  30 . Presence of such a physically non-contacting (but thermally contacting) space within the apparatus  10  provides many benefits and advantages. For example, and without wishing to be bound to any theory, presence of the first chamber  100  provides heat transfer from the second heat source  30  to the channel  70  or the reaction vessel  90  that is desirably less efficient. That is, the chamber  100  reduces heat transfer substantially between the second heat source  30  and the channel  70  or the reaction vessel  90 . As will become more apparent from the discussion that follows, this invention feature supports robust and faster thermal convection PCR within the apparatus  10 . 
     While it will often be useful to include a physically non-contacting space within the second heat source  30 , it is within the scope of the present invention to include such a space within one or more additional heat sources in the apparatus  10  such as one or both of the first  20  and third  40  heat sources. For example, the first heat source  20  or the third heat source  40  may include one or more chambers intended to reduce heat transfer between one or more of the heat sources and the channel  70  or the reaction vessel  90 . 
     The invention embodiment shown in  FIGS. 2A-C  includes a first chamber  100  in the second heat source  20  as a key structural element. In this example of the invention, the first chamber  100  is independently adapted to receive the channel  70  from the top of the second heat source  31  toward the bottom of the second heat source  32  and the top of the first heat source  21 . The first chamber  100  is defined by a top end  101  on the top of the second heat source  30 , a bottom end  102  on the bottom of the second heat source  30 , and the first chamber wall  103  that is disposed around the channel axis  80  and spaced from the channel  70  inside the second heat source  30 . The chamber wall  103  surrounds the channel  70  inside the second heat source  20  at a distance, forming a chamber gap  105 . The chamber gap  105  between the chamber wall  103  and the channel  70  is preferably in the range between from about 0.1 mm to about 6 mm, more preferably from about 0.2 mm to about 4 mm. The length of the first chamber  100  is between about 1 mm to about 25 mm, preferably between about 2 mm to about 15 mm. 
     The invention is compatible with a wide variety of heat source and insulator configurations. For instance, the first heat source  20  can have a length larger than about 1 mm along the channel axis  80 , preferably from about 2 mm to about 10 mm; the second heat source  30  can have a length between from about 2 mm to about 25 mm along the channel axis  80 , preferably from about 3 mm to about 15 mm; the third heat source  40  can have a length larger than about 1 mm along the channel axis  80 , preferably from about 2 mm to about 10 mm. As discussed, it will be generally useful to have an apparatus with a first insulator  50  and a second insulator  60 . For example, in embodiments without the protrusions, the first insulator  50  can have a length along the channel axis  80  between about 0.2 mm to about 5 mm along the channel axis  80 , preferably between about 0.5 mm to 4 mm. The second insulator  60  can have a length along the channel axis  80  between about 0.1 mm to about 3 mm along the channel axis  80 , preferably between about 0.2 mm to about 2.5 mm. In other embodiments in which the protrusion structure is present, the first  50  and second  60  insulators can have different lengths along the channel axis  80  depending on the position with respect to the channel  70 . For instance, in the region near or around the channel (i.e., within the protrusions), the first insulator  50  can have a length along the channel axis between about 0.2 mm to about 5 mm, preferably between about 0.5 mm to 4 mm, and the second insulator  60  can have a length along the channel axis  80  between about 0.1 mm to about 3 mm, preferably between about 0.2 mm to 2.5 mm. In the region distant from the channel (i.e., outside the protrusion structures), the first insulator  50  can have a length along the channel axis between about 0.5 mm to about 10 mm, preferably between about 1 mm to 8 mm, and the second insulator  60  can have a length along the channel axis  80  between about 0.2 mm to about 5 mm, preferably between about 0.5 mm to 4 mm. 
     As discussed, an invention apparatus may include multiple chambers (for example, two, three, four, five or more chambers) within at least one of the heat sources such as the second heat source. 
     In the embodiment shown in  FIGS. 3A-B , the apparatus includes a first chamber  100  positioned entirely within the second heat source  30 . In this embodiment, the first chamber  100  includes the chamber top end  101  facing a first chamber bottom end  102  along the channel axis  80 . The apparatus further includes a second chamber  110  positioned entirely within the second heat source  30  and in contact with the top end  101  of the first chamber  100 . The wall  103  of the first chamber  100  is aligned essentially parallel to the channel axis  80 . The second chamber  110  is further defined by the wall  113  positioned essentially parallel to the channel axis  80 . The second chamber  110  is further defined by a top end  111  in contact with the top end  31  of the second heat source  30  and a bottom end  112  in contact with the top end  101  of the first chamber  100 . As shown, the first chamber  100  and the second chamber  110  include gaps  105  and  115 , respectively. In the embodiment shown, each of the top end  111  and bottom end  112  of the second chamber  110  are perpendicular to the channel axis  80 . As shown in  FIG. 3A , the width or radius of the first chamber  100  from the channel axis  80  is smaller (about 0.9 to 0.3 times smaller) than the width or radius of the second chamber  110  from the channel axis  80 . However as shown in the embodiment of  FIG. 3B , the width or radius of the first chamber  100  from the channel axis  80  is greater (about 1.1 to about 3 times greater) than the width of the second chamber  110  from the channel axis  80 . 
     Turning again to  FIGS. 3A-B , the first chamber  100  and the second chamber  110  provide a highly useful temperature controlling or shaping effect. In these embodiments, the first chamber  100  ( FIG. 3A ) or the second chamber  110  ( FIG. 3B ) has a smaller diameter or width compared to the other chamber. The narrower portion of the second chamber  110  ( FIG. 3B ) or first chamber  100  ( FIG. 3A ) provides more efficient heat transfer from the second heat source  30  compared to the other chamber. In addition, the chamber configuration shown in these embodiments preferentially blocks heat transfer from a heat source located closer to the narrower portion (e.g., the first heat source  20  in  FIG. 3A ). 
     Unless otherwise mentioned, embodiments with multiple chambers will be described by numbering the chambers from the first heat source (typically located nearest the bottom of the apparatus). Thus the chamber closest to the first heat source will be designated “first chamber”, the next closest chamber to the first heat source will be designated “second chamber”, etc. 
     Thermal Brake Structure and Function 
       FIG. 4A  shows an invention embodiment with three chambers positioned in one of the heat sources. In particular, the apparatus  10  has the first chamber  100 , the second chamber  110  and a third chamber  120  positioned in the second heat source  30 . In this embodiment, the third chamber  120  includes a gap  125 . The third chamber  120  includes the wall  123  positioned essentially parallel to the channel axis  80 . The third chamber  120  is further defined by a top end  121  adjacent to the top  31  of the second heat source. The third chamber  120  is further defined by a bottom end  122  contacting a specific region within the second heat source  30  (see dotted circle in  FIG. 4A ). As shown, the top end  121  and bottom end  122  of the third chamber  120  are perpendicular to the channel axis  80 . 
       FIG. 4B  is an expanded view of the dotted circle shown in  FIG. 4A . In particular, the region between the first chamber  100  and the second chamber  110  defines a first thermal brake  130 . As mentioned above, the first thermal brake  130  is intended to control the temperature distribution within the apparatus  10 . In the embodiment shown, the first thermal brake  130  is defined by a top end  131  and a bottom end  132  and a wall  133  that essentially contacts the channel  70 . In this embodiment, a function of the first thermal brake  130  is to reduce or block an undesirable intrusion of a temperature profile from the first heat source  20  to the second heat source  30  and the third heat source  40 . Another function of the first thermal brake  130  is to provide an efficient heat transfer between the second heat source  30  and the channel  70  so as to make the channel in that region quickly approach the temperature of the second heat source  30 . The first thermal brake  130  is disposed symmetrically about the channel  70 . 
     As shown in  FIG. 4B , this invention embodiment includes a second thermal brake  140  defined by the region between the second chamber  110  and the third chamber  120 . In particular, the second thermal brake  140  is further defined by a top end  141  and a bottom end  142  that essentially contacts at least part of the channel  70  through a wall  143 . An important function of the second thermal brake  140  is further assist in the control of the temperature distribution within the apparatus  10 . In this embodiment, the second thermal brake  140  is particularly useful for reducing or blocking an undesirable intrusion of a temperature profile from the third heat source  40  to the second heat source  30  and also for providing an efficient heat transfer between the second heat source  30  and the channel  70  so as to maintain that region at a temperature close to the temperature of the second heat source  30 . The second thermal brake  140  is disposed symmetrically about the channel  70 . 
     If desired, at least one of the first chamber  100 , the second chamber  110 , and the third chamber  120  (or a portion thereof) may include a suitable solid or a gas insulator. Alternatively, or in addition, one or both of the first insulator  50  and/or the second insulator  60  shown may include or consist of a suitable solid or a gas. An example of suitable insulating gas is air. 
     Channel Structure 
     A. Vertical Profiles 
     The invention is fully compatible with several channel configurations. For example,  FIGS. 5A-D  show vertical sections of suitable channel configurations. As shown, the vertical profile of the channel may be shaped as a linear ( FIGS. 5C-D ) or tapered ( FIG. 5A-B ) channel. In a tapered embodiment, the channel may be tapered either from the top to the bottom or from the bottom to the top. Although various modifications are possible regarding the vertical profile of the channel (e.g., a channel having a side wall that is curved, or tapered with two or more different angles, etc.), it is generally preferred to use a channel that is (linearly) tapered from the top to the bottom because such structure facilitates not only the fabrication process but also introduction of the reaction vessel to the channel. A generally useful taper angle (θ) is in the range between from about 0° to about 15°, preferably from about 2° to about 10°. 
     In the embodiments shown in  FIGS. 5A-B , the channel  70  is further defined by an open top  71  and a closed bottom end  72  which ends may be perpendicular to the channel axis  80  ( FIG. 5A ) or curved ( FIG. 5B ). The bottom end  72  may be curved with a convex or concave shape having a radius of curvature equal to or larger than the radius or half width of the horizontal profile of the bottom end. Flat or near flat bottom end with its radius of curvature at least two times larger than the radius or half width of the horizontal profile of the bottom end is more preferred over other shapes since it can provide an enhanced heat transfer for the denaturation process. The channel  70  is further defined by a height (h) along the channel axis  80  and a width (w 1 ) perpendicular to the channel axis  80 . 
     For many invention applications, it will be useful to have a channel  70  that is essentially straight (i.e., not bent or tapered). In the embodiments shown in  FIGS. 5C-D , the channel  70  has the open top end  71  and the closed bottom end  72  which may be perpendicular to the channel axis  80  ( FIG. 5C ) or curved ( FIG. 5D ). As in the tapered channel embodiments, the bottom end  72  may be curved with a convex or concave shape and flat or near flat bottom end having a large curvature is typically more preferred. The channel  70  is further defined in these embodiments by a height (h) along the channel axis  80  and a width (w 1 ) perpendicular to the channel axis  80 . 
     In the channel embodiments shown in  FIGS. 5A-D , the height (h) is at least about 5 mm to about 25 mm, preferably 8 mm to about 16 mm for a sample volume of about 20 microliters. Each channel embodiment is further defined by the average of the width (w 1 ) along the channel axis  80  which is typically at least about 1 mm to about 5 mm. Each of the channel embodiments shown in  FIGS. 5A-D  can be further defined by a vertical aspect ratio which is the ratio of the height (h) to the width (w 1 ), and a horizontal aspect ratio which is the ratio of the first width (w 1 ) to the second width (w 2 ) along first and second directions, respectively, that are mutually perpendicular to each other and aligned perpendicular to the channel axis. A generally suitable vertical aspect ratio is between about 4 to about 15, preferably from about 5 to about 10. The horizontal aspect ratio is typically between about 1 to about 4. In embodiments in which the channel  70  is tapered ( FIGS. 5A-B ), the width or diameter of the channel changes across the vertical profile of the channel. By way of general guidance, for sample volumes larger or smaller than 20 microliters, the height and width (or diameter) may be scaled by a factor of cubic root or sometimes square root of the volume ratio. 
     As discussed, the bottom end  72  of the channel may be flat, rounded, or curved as depicted in  FIG. 5A-D . When the bottom end is rounded or curved, it typically has a convex or concave shape. As discussed, a flat or near flat bottom end is more preferred over other shapes for many invention embodiments. While not wishing to be bound to any theory, it is believed that such a bottom design can enhance heat transfer from the first heat source  20  to the bottom end  71  of the channel  70  so as to facilitate the denaturation process. 
     None of the foregoing vertical channel profiles are mutually exclusive. That is, a channel that has a first portion that is straight and second portion that is tapered (with respect to the channel axis  80 ) is within the scope of the present invention. 
     B. Horizontal Profiles 
     The invention is also compatible with a variety of horizontal channel profiles. An essentially symmetrical channel shape is generally preferred where ease of manufacture is a concern.  FIGS. 6A-J  show a few examples of acceptable horizontal channel profiles, each with a designated symmetry. For instance, the channel  70  may have its horizontal shape that is circular ( FIG. 6A ), square ( FIG. 6D ), rounded square ( FIG. 6G ) or hexagonal ( FIG. 6J ) with respect to the channel axis  80 . In other embodiments, the channel  70  may have a horizontal shape that has its width larger than its length (or vice versa). For instance, and as depicted in the middle column of  FIGS. 6B , E and H, the horizontal profile of the channel  70  may be shaped as an ellipsoid ( FIG. 6B ), rectangular ( FIG. 6E ), or rounded rectangular ( FIG. 6H ). This type of horizontal shape is useful when incorporating a convection flow pattern going upward on one side (e.g., on the left hand side) and going downward on the opposite side (e.g., on the right hand side). Due to the relatively larger width profile incorporated compared to the length, interference between the upward and downward convection flows can be reduced, leading to more smooth circulative flow. The channel may have a horizontal shape that has its one side narrower than the opposite side. A few examples are shown on the right column of  FIGS. 6C , F and I. The left side of the channel is depicted to be narrower than the right side for instance. This type of horizontal shape is also useful when incorporating a convection flow pattern going upward on one side (e.g., on the left hand side) and going downward on the opposite side (e.g., on the right hand side). Moreover, when this type of shape is incorporated, speed of the downward flow (e.g., on the right hand side) can be controlled (typically reduced) with respect to the upward flow. Since the convective flow must be continuous within the continuous medium of the sample, the flow speed should be reduced when cross-sectional area becomes larger (or vice versa). This feature is particularly important with regard to enhancing the polymerization efficiency. The polymerization step typically takes place during the downward flow (i.e., after the annealing step), and therefore time period for the polymerization step can be lengthened by making the downward flow slower as compared to that of the upward flow, leading to more efficient PCR amplification. 
     Thus in one invention embodiment, at least part of the channel  70  (including the entire channel) has a horizontal shape along a plane essentially perpendicular to the channel axis  80 . In one invention example, the horizontal shape has at least one reflection (σ) or rotation symmetry element (C x ) in which X is 1, 2, 3, 4, up to ∞ (infinity). Nearly any horizontal shape is acceptable provided it satisfies intended invention objectives. Further acceptable horizontal shapes include a circular, rhombus, square, rounded square, ellipsoid, rhomboid, rectangular, rounded rectangular, oval, semi-circular, trapezoid, or rounded trapezoid shape along the plane. If desired, the plane perpendicular to the channel axis  80  can be within the first  20 , second  30  or third  40  heat source. 
     None of the foregoing horizontal channel profiles are mutually exclusive. That is, a channel that has a first portion that is circular, for instance, and a second portion that is semi-circular (with respect to the channel axis  80 ) is within the scope of the present invention. 
     Horizontal Chamber Shape and Position 
     As discussed, an apparatus of the invention can include at least one chamber, preferably one, two or three chambers to help control the temperature distribution within the apparatus, for instance, within the transition region of the channel. The channel can have one or a combination of suitable shapes provided intended invention results are achieved. 
     For instance,  FIGS. 7A-I  show suitable horizontal profiles of a chamber (the first chamber  100  is used as an illustration only). In this invention embodiment, the horizontal profile of the chamber  100  may be made into various different shapes although shapes that are essentially symmetric will often be useful to facilitate the fabrication process. For instance, the first chamber  100  may have a horizontal shape that is circular, square, or rounded square as depicted in the left column. See  FIGS. 7A , D, and G. The first chamber  100  may have a horizontal shape that has its width larger than its length (or vice versa), for instance, an ellipsoid, rectangular, or rounded rectangular as depicted in the middle column. The first chamber  100  may have a horizontal shape that has its one side narrower than the opposite side as depicted in the right column. See  FIGS. 7C , F, and I. 
     As discussed, chamber structure is useful in controlling (typically reducing) the heat transfer from the heat source (typically the second heat source) to the channel or the reaction vessel. Therefore, it is important to change the position of the first chamber  100  relative to that of the channel  70  depending on the invention embodiment of interest. In one embodiment, the first chamber  100  is disposed symmetrically with respect to the position of the channel  70 , i.e., the chamber axis (an axis formed by the center points of the top and bottom end of the chamber,  106 ) coincides with the channel axis  80 . In this embodiment, the heat transfer from the heat source  20 ,  30  or  40  to the channel is intended to be constant in all directions across the horizontal profile of the channel (at certain vertical location). Therefore, it is preferred to use a horizontal shape of the first chamber  100  that is the same as that of the channel in such embodiments. See  FIGS. 7A-I . 
     However other embodiments of the chamber structure are within the scope of the present invention. For instance, one or more of the chambers within the apparatus may be disposed asymmetrically with respect to the position of the channel  70 . That is the chamber axis  106  formed between the top end and bottom end of a particular chamber may be off-centered, tilted or both off-centered and tilted with respect to the channel axis  80 . In this embodiment, one or more of the chamber gaps between the channel  70  and a wall of the chamber will be larger on one side and smaller on the opposite side of that chamber. Heat transfer in such embodiments will be higher in one side of the channel  70  and lower in the opposite side (while it is same or similar in the two opposite sides located along the direction perpendicular to the positions of above two sides). In a particular embodiment, it is preferred to use a horizontal shape of the first chamber  100  that is circular or rounded rectangular. A circular shape is generally more preferred. 
     Thus in one embodiment of the apparatus, at least part of the first chamber  100  (including the entire chamber) has a horizontal shape along a plane essentially perpendicular to the channel axis  80 . See  FIG. 7A  and  FIG. 2A-C , for instance. Typically, the horizontal shape has at least one reflection or rotation symmetry element. Preferred horizontal shapes for use with the invention include those that are circular, rhombus, square, rounded square, ellipsoid, rhomboid, rectangular, rounded rectangular, oval, semi-circular, trapezoid, or rounded trapezoid shape along a plane perpendicular to the channel axis  80 . In one embodiment, the plane perpendicular to the channel axis  80  is within the second  30  or third  40  heat source. 
     It will be appreciated that the foregoing discussion about chamber structure and position will be applicable to more chamber embodiments than the first chamber  100 . That is, in an invention embodiment with multiple chambers (e.g., one with the second chamber  110  and/or third chamber  120 ), these considerations may also apply. 
     Asymmetric and Symmetric Channel/Chamber Configurations 
     As mentioned, the invention is compatible with a wide variety of channel and chamber configurations. In one embodiment, a suitable channel is disposed asymmetrically with respect to the chamber.  FIGS. 8A-P  show some examples of this concept. 
     In particular,  FIGS. 8A-P  show horizontal sections of suitable channel and chamber structures with reference to location of the channel  70  within the chamber  100  (the first chamber  100  is used only for illustrative purposes). Horizontal shapes of the first chamber  100  and channel  70  are shown to be circular or rounded rectangular for instance. The first column ( FIGS. 8A , E, I and M) shows examples of symmetrically positioned structures. In these embodiments, the chamber axis coincides with the channel axis  70 . Therefore, the gap between the first chamber wall ( 103 , solid line) and the channel  70  (dotted line) is the same for the left and right sides, and also for the upper and lower sides, providing a heat transfer from the heat source to the channel that is symmetric in both directions. The second column ( FIGS. 8B , F, J and N) shows examples of asymmetrically positioned structures. The channel axis  80  is positioned off-centered (to the left hand side) from the chamber axis and the gap between the first chamber wall  103  and the channel  70  is smaller on the left side (while it is the same on the upper and lower sides), providing higher heat transfer from the left side. The third ( FIGS. 8C , G, K and O) and fourth ( FIGS. 8D , H, L, and P) columns show other examples of asymmetrically positioned structures that provide more asymmetric heat transfer. The third column ( FIGS. 8C , G, K and O) shows examples in which the chamber wall is in contact with the channel on one side (the left side). The fourth column ( FIGS. 8D , H, L, and P) shows examples in which one side (the right side) forms the first chamber  100  while the opposite side (the left side) forms the channel  70 . In both examples, heat transfer from the left side is much higher than from the right side. The physically contacting side shown in the third and fourth columns is intended to function as a thermal brake, particularly as an asymmetric thermal brake that provides thermal braking on one side only. 
     It is thus an object of the invention to provide an apparatus in which at least one of the chambers therein (e.g., one or more of the first chamber  100 , second chamber  110 , or the third chamber  120 ) is disposed essentially symmetrically about the channel along a plane that is essentially perpendicular to the channel axis. It is also an object to provide an apparatus in which at least one of the chambers is disposed asymmetrically about the channel and along the plane that is essentially perpendicular to the channel axis. All or part of a particular chamber(s) can be disposed about the channel axis either symmetrically or asymmetrically as needed. In embodiments in which at least one chamber is disposed asymmetrically about the channel axis, the chamber axis and the channel axis can be off-centered while essentially parallel to each other, tilted or both off-centered and tilted. In a more specific embodiment of the foregoing, at least part of a chamber including the entire chamber is disposed asymmetrically about the channel along a plane perpendicular to the channel axis. In other embodiments, at least part of the channel is located inside the chamber along the plane perpendicular to the channel axis. In one example of this embodiment, at least part of the channel is in contact with the chamber wall along the plane perpendicular to the channel axis. In another embodiment, at least part of the channel is located outside of the chamber along the plane perpendicular to the channel axis and contacting the second or third heat source. For some invention embodiments, the plane perpendicular to the channel axis contacts the second or third heat source. 
     Vertical Chamber Shape 
     It is also an object of the invention to provide an apparatus in which the second heat source includes at least one chamber, typically one, two or three of same to help control temperature distribution. Preferably, the chamber helps control the temperature gradient of the transition region from one heat source (e.g., the first heat source  20 ) within the apparatus to another heat source (e.g., the third heat source  40 ) therein. Various adaptations of the chamber are within the scope of the invention so long as it generates a temperature distribution suitable for the convection-based PCR process of the present invention. 
     It is an object of the invention to provide an apparatus in which at least part of a chamber (up to and including the entire chamber) is tapered along the channel axis. For instance, and in one embodiment, one or more of the chambers including all of the chambers therein are tapered along the channel axis. In one embodiment, at least part of one or all of the chambers is positioned within the second heat source and has a width (w) perpendicular to the channel axis that is greater towards the third heat source than the first heat source. In some embodiments, at least part of the chamber is positioned within the second heat source and has a width (w) perpendicular to the channel axis that is greater towards the first heat source than the third heat source. In one embodiment, the apparatus includes the first chamber and the second chamber positioned within the second heat source, the first chamber having a width (w) perpendicular to the channel axis that is larger (or smaller) than the width (w) of the second chamber. For some embodiments, the first chamber is facing the first or the third heat source. 
     Further Illustrative Apparatus Embodiments 
     Suitable heat source, insulator, channel, gap, chamber, receptor hole configurations and PCR conditions are described throughout the present application and may be used as needed with the following invention examples. 
     A. Tapered Chamber 
     Referring now to  FIGS. 9A-B , the apparatus embodiment features a first chamber  100  that is concentric with the channel. In this example of the invention, the chamber axis (i.e., an axis formed by the centers of the top and bottom end of the chamber) coincides with the channel axis  80 . The chamber wall  103  of the first chamber  100  has an angle with respect to the channel axis  80 . That is, the chamber wall  103  is tapered from the top end  101  to the bottom end  102  of the first chamber  100  ( FIG. 9A ). In  FIG. 9B , the chamber wall  103  is tapered from the bottom end  102  to the top end  101  of the first chamber  100 . Such a structure provides a narrow hole on the bottom and a wide hole on the top, or vice versa. For instance, if the bottom part is made narrower, as in  FIG. 9A , heat transfer from the bottom part  32  of the second heat source  30  to the channel  70  becomes larger than that from the top part  31  of the second heat source  30 . Moreover, the high denaturation temperature typical of the first heat source  20  is more preferentially blocked compared to that of the relatively low annealing temperature of the third heat source  40 . If the top part of the second heat source  31  is made narrower, as in  FIG. 9B , the effect of the third heat source will be more preferentially blocked. 
     In the examples shown in  FIGS. 9A-B , the temperature distribution of the channel  70  inside the second heat source  30  can be controlled with the tapered chamber structure. Depending on the temperature property of DNA polymerase used, the temperature conditions inside the second heat source  30  may need to be adjusted using such structure because the polymerization efficiency is sensitive to the temperature conditions inside the second heat source  30 . For most widely used Taq DNA polymerase or its derivatives, a first chamber wall  103  that is tapered from the top to the bottom is more preferred since optimum temperature of Taq DNA polymerase (around 70° C.) is closer to the annealing temperature compared to the denaturation temperature in typical operation conditions. 
     B. One or Two Chambers, One Thermal Brake 
     Referring now to  FIG. 10A , the apparatus  10  features the first chamber  100  and the second chamber  110  disposed in the second heat source  30  essentially symmetrically about the channel axis  80 . In this embodiment, the first chamber  100  is located on the bottom part of the second heat source  30  and the second chamber  110  is located on the top part of the second heat source  30 . The apparatus  10  includes the first thermal brake  130  to help provide more active control of the temperature distribution. In this embodiment, the width of the first chamber  100  and the second chamber  110  are about the same. However, the heights of the first chamber  100  and the second chamber  110  can be varied between about 0.2 mm to about 80% or 90% of the length of the second heat source  30  along the channel axis  80 , depending on the temperature property of DNA polymerase used as discussed below.  FIG. 10B  provides an expanded view of the first thermal brake  130  defined by the top end  131 , bottom end  132 , and wall  133  contacting the channel  70 . In this embodiment, the location and thickness of the first thermal brake  130  along the channel axis  80  will be defined by the heights of the first  100  and second  110  chambers along the channel axis  80 . The thickness of the thermal brake  130  along the channel axis  80  is between about 0.1 mm to about 80% of the height of the second heat source  30  along the channel axis  80 , preferably between about 0.5 mm to about 60% of the height of the second heat source  30 . The first thermal brake  130  can be located nearly anywhere inside the second heat source in between the first  100  and second  110  chambers, depending on temperature property of DNA polymerase used. It is preferred to locate the first thermal brake  130  closer to the bottom surface  32  of the second heat source  30  if optimum temperature of DNA polymerase used is closer to the annealing temperature of the third heat source  40  than the denaturation temperature of the first heat source  20 , or vice versa. 
       FIG. 10C  is an example in which the first chamber  100  has a smaller width than the second chamber  110 , for instance, about 0.9 to about 0.3 times smaller, preferably about 0.8 to about 0.4 times smaller. An opposite arrangement with the first chamber  100  having a larger width than the second chamber  110  can also be used depending on the temperature property of DNA polymerase used. An expanded view of the first thermal brake  130  is shown in  FIG. 10D . 
     In the embodiments shown in  FIGS. 10A-D , the apparatus features the first chamber and the second chamber that are not tapered. In these embodiments, the first chamber is spaced from the second chamber by a length (l) along the channel axis  80 . In one embodiment, the first chamber, the second chamber, and the second heat source define a first thermal brake contacting the channel between the first and second chambers with an area and a thickness (or a volume) sufficient to reduce heat transfer from the first heat source or to the third heat source. 
     Referring to  FIGS. 10E-F , the apparatus features the first chamber  100  disposed symmetrically about the channel axis  80 . The first thermal brake  130  is positioned on the bottom of the second heat source  30  between the first chamber  100  and the first insulator  50 . 
     The thickness of the first thermal brake  130  along the channel axis  80  shown in  FIGS. 10E-F  is defined by distance from the top end  131  to the bottom end  132  of the first thermal brake  130 . Preferably that distance is between from about 0.1 mm to about 80% of the height of the second heat source  30  along the channel axis  80 , more preferably about 0.5 mm to about 60% of the height of the second heat source  30 . 
     In this embodiment, the apparatus features the first chamber positioned on the bottom part of the second heat source and the first chamber and the first insulator define the first thermal brake. The first thermal brake contacts the channel between the first chamber and the first insulator with an area and a thickness (or a volume) sufficient to reduce heat transfer from the first heat source. In this embodiment, the first thermal brake comprises a top surface and a bottom surface in which the bottom surface of the first thermal brake is located at about the same height as the bottom surface of the second heat source. This embodiment is particularly useful when using DNA polymerase that has optimum temperature closer to the annealing temperature of the third heat source than the denaturation temperature of the first heat source (e.g., Taq DNA polymerase). 
     C. One, Two or Three Chambers, Two Thermal Brakes 
     As mentioned, it will be useful in some invention embodiments to reduce intrusion of the temperature profile from one or more of the heat sources within the apparatus, for instance from the first and third heat sources. In this embodiment, it will be generally useful to include two thermal brakes. 
     Referring now to  FIG. 11A , the apparatus  10  includes the first chamber  100 , the first thermal brake  130  and the second thermal brake  140 . In this example, the first thermal brake  130  is located on a lower part of the first chamber  100  to block or reduce the heat transfer from the first heat source  20 . The second thermal brake  140  is located on an upper part of the first chamber  100  to further block or reduce heat transfer from the third heat source  40 .  FIG. 11B  shows an expanded view of the first thermal brake  130  and the second thermal brake  140  within the apparatus. The thickness of each thermal brake along the channel axis  80  can be varied depending on use. However, each thermal brake  130  and  140  is preferably at least about 0.1 mm, more preferably at least about 0.2 mm. The sum of the thickness of the two thermal brakes  130 ,  140  is smaller than about 80% of the height of the second heat source along the channel axis, more preferably smaller than about 60% of same. Dimensions of each of thermal brakes  130  and  140  can be the same or different depending on intended use of the apparatus. 
       FIG. 4A  shows a related embodiment. In this embodiment, the apparatus  10  includes the first chamber  100 , the first thermal brake  130 , the second chamber  110 , the second thermal brake  140  and the third chamber  120 . In this example, the first thermal brake  130  is located on a lower part in between the first chamber  100  and the second chamber  110  to block or reduce the heat transfer from the first heat source  20 . The second thermal brake  140  is located on an upper part in between the second chamber  110  and the third chamber  120  to further block or reduce heat transfer from the third heat source  40 .  FIG. 4B  shows an expanded view of the first thermal brake  130  and the second thermal brake  140  within the apparatus. The thickness of each thermal brake along the channel axis  80  can be varied depending on use. However, each thermal brake  130  and  140  is preferably at least about 0.1 mm, more preferably at least about 0.2 mm. The sum of the thickness of the two thermal brakes  130 ,  140  is smaller than about 80% of the height of the second heat source along the channel axis, more preferably smaller than about 60% of same. Dimensions of each of thermal brakes  130  and  140  can be the same or different depending on intended use of the apparatus. 
     In other embodiments, the apparatus  10  can include two chambers and two thermal brakes in the second heat source. In one embodiment, the first thermal brake is located on the bottom of the second heat source in between the first chamber and the first insulator, and the second thermal brake is located in between the first and second chambers within the second heat source. In another embodiment, the first chamber is located on the bottom of the second heat source and the first thermal brake is located in between the first and second chambers. In this embodiment, the second thermal brake is located on the top of the second heat source in between the second chamber and the second insulator. 
     D. One Chamber, First and Second Heat Sources, Protrusion 
     In some invention embodiments, it will be useful to manipulate the structure of one or more of the chambers by changing the structure of at least one of the heat sources. For instance, at least one of the first, second and third heat sources can be adapted to include one or more protrusions that defines the gap or chamber and generally extends essentially parallel to the channel or chamber axis. A protrusion may be disposed symmetrically or asymmetrically about the channel or chamber axis. Significant protrusions extend away from one heat source to another heat source within the apparatus. For example, second heat source protrusions extend away from the second heat source in the direction toward the first heat source or the third heat source. In these embodiments, the protrusion contacts the chamber and defines a chamber gap or chamber wall. In a particular embodiment, the width or diameter of the second heat source protrusions along the channel axis is decreased as going away from the second heat source while the width of the first or second insulator adjacent to the protrusion along the channel axis is increased. Each chamber may have the same or different protrusion (including no protrusion). An important advantage of the protrusions is to help reduce the size of the heat sources and lengthen chamber dimensions and insulator or insulating gap dimensions along the channel axis. These and other benefits were found to assist thermal convection PCR in the apparatus while substantially reducing the power consumption of the apparatus. 
     A particular embodiment of an invention apparatus with protrusions is shown in  FIG. 12A . The apparatus includes protrusions ( 33 ,  34 ) of the second heat source  30  disposed essentially symmetrically about the channel axis  80 . Importantly, there is a gap between the bottom of the second heat source  32  and the top of the first heat source  21 . In this embodiment, the first heat source  20  also includes protrusions  23 ,  24  that are disposed symmetrically about the channel  70  and extending from the first heat source  20  to the second heat source  30  or away from the bottom surface of the first heat source  22 . Also in this embodiment, the width or diameter of the first heat source protrusions  23 ,  24  along the channel axis  80  is reduced as going away from the first heat source  20 . The apparatus also includes a thermal brake  130  positioned between the first chamber bottom end  102  and the bottom surface  32  of the second heat source  30 . As also shown in  FIG. 12A , the second heat source  30  includes a protrusion  34  that is disposed symmetrically about the channel  70  and extends from the second heat source  30  to the third heat source  40 . Also in this embodiment, there is a gap between the top of the first chamber  101  and the bottom of the third heat source  41 . 
     As is also shown in  FIG. 12A , the receptor hole  73  is disposed symmetrically about the channel axis  80 . In this embodiment, the receptor hole  73  has a width or diameter perpendicular to the channel axis  80  that is about the same as the width or diameter of the channel  70 . Alternatively, the receptor hole  73  may have a width or diameter perpendicular to the channel axis  80  that is somewhat larger (for example, about 0.01 mm to about 0.2 mm larger) than the width or diameter of the channel  70 . 
     As discussed, it is an object of the invention to provide an apparatus for performing thermal convection PCR which includes at least one temperature shaping element which in one embodiment can be a positional asymmetry imposed on the apparatus.  FIG. 12B  shows one important example of this embodiment. As shown, the apparatus is tilted at an angle θg (tilting angle) with respect to the direction of gravity. This type of embodiments is particularly useful in controlling (typically increasing) speed of the thermal convection PCR. As will be discussed below, increase of the tilting angle typically leads to faster and more robust thermal convection PCR. Other embodiments that include one or more positional asymmetries will be described in more detail below. 
     The embodiments shown in  FIGS. 12A-B  will be particularly suitable for many invention applications including amplification of “difficult” samples such as genomic or chromosomal target sequences or long-sequence target templates (e.g., longer than about 1.5 or 2 kbp). In particular,  FIG. 12A  shows heat sources with a symmetric chamber and channel configuration. The thermal brake  130  effectively blocks protrusion of the high temperature of the first heat source  20  toward inside the first chamber  100  as it is located on the bottom of the second heat source  32 . In use, the temperature drops down rapidly in the first insulator region  50  from the high denaturation temperature (about 92° C. to about 106° C.) of the first heat source  20  to the polymerization temperature (about 75° C. to about 65° C.) of the second heat source  30 . The temperature drop from the second heat source  30  to the third heat source (about 45° C. to about 65° C.) in the second insulator region  60  is relatively small in typical conditions. Hence, the temperature inside the second heat source  30  becomes more narrowly distributed around the polymerization temperature of the second heat source  30  (due to the early cut off of the high denaturation temperature by the first thermal brake) so that a large volume (and time) inside the second heat source  30  becomes available for the polymerization step. 
     A major difference between the embodiments shown in  FIGS. 12A and 12B  is that the apparatus of  FIG. 12B  has a tilting angle θg. The apparatus without the tilting angle ( FIG. 12A ) works well and takes about 15 to 25 min to amplify from a 1 ng plasmid sample and about 25 to 30 min to amplify from a 10 ng human genome sample (3,000 copies) when the structure of the apparatus is optimized. PCR amplification efficiency of the apparatus can be further enhanced if a tilting angle of about 2° to about 60° (more preferably about 5° to about 30°) is introduced as depicted in  FIG. 12B . With the gravity tilting angle introduced with this structure ( FIG. 12B ), PCR amplification from a 10 ng human genome sample can be completed in about 20 to 25 min. See Examples 1 and 2 below. 
     E. Asymmetric Receptor Hole 
     As mentioned, it is an object of the invention to provide an apparatus with at least one temperature shaping element that has horizontal asymmetry. By “horizontal asymmetry” is meant asymmetry along a direction or plane perpendicular to the channel and/or channel axis. It will be apparent that many of the apparatus examples provided herein can be adapted to have a horizontal asymmetry. In one embodiment, the receptor hole is placed asymmetrically in the first heat source with respect to the channel axis sufficient to generate a horizontally asymmetric temperature distribution suitable for inducing a stable, directed convection flow. Without wishing to be bound to theory, it is believed that the region between the receptor hole and the bottom end of the chamber is a location where a major driving force for thermal convection flow can be generated. As will be readily apparent, this region is where initial heating to the highest temperature (i.e., the denaturation temperature) and transition toward a lower temperature (i.e., the polymerization temperature) take place, and thus the largest driving force can originate from this region. 
     It is thus an object of the invention to provide an apparatus with at least one horizontal asymmetry in which at least one of the receptor holes (for instance, all of them) in the first heat source has a width or diameter larger than the channel in the first heat source. Preferably, the width disparity allows the receptor hole to be off-centered from the channel axis. In this example of the invention, the receptor hole asymmetry produces a gap in which one side of the receptor hole is located closer to the channel compared to the opposite side. It is believed that in this embodiment, the apparatus will exhibit horizontally asymmetric heating from the first heat source to the channel. 
     An example of such an invention apparatus is shown in  FIG. 13 . As shown, the receptor hole  73  is disposed asymmetrically with respect to the channel axis  80  to form a receptor hole gap  74 . That is, the receptor hole  73  is slightly off-centered with respect to the channel axis  80 , for instance, by about 0.02 mm to about 0.5 mm. In this example, the receptor hole  73  has a width or diameter perpendicular to the channel axis  80  that is larger than the width or diameter of the channel  70 . For example, the width or diameter of the receptor hole  73  can be about 0.04 mm to about 1 mm larger than the width or diameter of the channel  70 . 
     Turning again to the embodiment shown in  FIG. 13 , one side (the left side) of the channel  70  is in contact with the first heat source  20  and the opposite side (the right side) is not in contact with the first heat source  20 , to form a receptor hole gap  74 . While the invention is compatible with several gap sizes, a typical receptor hole gap can be as small as about 0.04 mm, particularly if the other side is contacted to the channel. In other words, one side is formed as a channel and the opposite side as a small space. In this embodiment, it is believed that one side (the left side) is heated preferentially over the opposite side (the right side), providing a horizontally asymmetric heating directing the upward flow to the preferentially heated side (the left side). A similar effect can be obtained with a receptor hole having a gap from the wall of the receptor hole that is smaller on one side than the opposite side. 
     As shown in  FIG. 13 , the first protrusion  33  of the second heat source  30  defines a portion  51  of the first insulator  50  (called a first insulator chamber) and the second heat source  30 . As shown, the first protrusion  33  also separates the first insulator  50  from the chamber  100  and the channel  70 . The second protrusion  34  of the second heat source  30  also defines a portion of the first chamber  100  or the channel  70 . In this embodiment, the second protrusion  34  also defines a portion  61  of the second insulator  60  (called a second insulator chamber) and the second heat source  30 . In addition, the second protrusion  34  of the second heat source  30  separates the second insulator  60  from the first chamber  100  and the channel  70 . 
     F. Multiple Chambers, Second and Third Heat Sources 
     As discussed, the invention provides an apparatus for performing thermal convection PCR which includes at least one, two or three chambers up to about four or five of such chambers. In one embodiment, one, two or three of such chambers can be symmetrically positioned partially or entirely within the second heat source, the third heat source or both the second and third heat sources. Examples are provided in  FIGS. 14A-C . 
     In particular,  FIG. 14A  shows an apparatus in which the first chamber  100  is disposed symmetrically within the second heat source  30  and a second chamber  110  is disposed symmetrically within the third heat source  40  (with respect to the channel axis  80 ). The bottom end  102  of the first chamber  100  contacts the bottom  32  of the second heat source  30 . Turning to  FIG. 14C , the apparatus also shows the first chamber  100  disposed symmetrically within the second heat source  30  and a second chamber  110  is disposed symmetrically within the third heat source  40  (with respect to the channel axis  80 ). However, the first chamber  100  does not contact the bottom  32  of the second heat source  30 . Instead, it has a shorter length with respect to the channel axis  80  i.e., the bottom end  102  of the first heat source  100  contacts the interior of the second heat source  30 . In both the embodiments of  FIGS. 14A and 14C , the receptor hole  73  is disposed symmetrically about the channel axis  80 . However unlike the embodiment shown in  FIG. 14A , the apparatus of  FIG. 14C  includes the first thermal brake  130  positioned between the bottom  102  of the first chamber  100  and the bottom  32  of the second heat source. This position of the first thermal brake  130  will be useful for many invention embodiments to reduce or block undesired heat flow from the first heat source  20 . 
       FIG. 14B  shows an invention embodiment in which the first chamber  100  and the second chamber  110  are disposed symmetrically within the second heat source  30  (with respect to the channel axis  80 ). This apparatus further includes the third chamber  120  disposed symmetrically within the third heat source  40  (also with respect to the channel axis  80 ). In this embodiment, the receptor hole  73  is disposed symmetrically about the channel axis  80 . In this embodiment, the first thermal brake  130  is positioned between the first chamber  100  and the second chamber  110  to help reduce or block undesired heat flow from the first heat source  20  and/or to the third heat source  40  depending on its thickness and position along the channel axis  80 . 
     G. One Chamber, Second or Third Heat Source 
     Also provided by the invention is an apparatus in which at least one chamber (e.g., one, two or three chambers) is positioned within the third heat source. If desired, the length of at least one of the heat sources along the channel axis can be reduced when compared to the embodiment shown in  FIG. 2A . Alternatively, and in addition, the length of at least one of the heat sources along the channel axis can be increased. 
     Turning now to  FIG. 15A , the first chamber  100  is positioned entirely within the third heat source  40  and it is disposed symmetrically with respect to the channel axis  80 . In the embodiment shown in  FIG. 15B , the first heat source  20  includes a protrusion  23  that is disposed symmetrically about the channel  70 , thereby forming a larger insulating gap between the first heat source  20  and the second heat source  30  in the regions between adjacent protrusions  23 . 
     If desired, the third heat source  40  can also include a protrusion  43  that is disposed symmetrically about the channel  70  and extending toward the top  31  of the second heat source  30 . In such embodiment, a larger insulating gap can be formed between the second heat source  30  and the third heat source  40  in the regions between adjacent protrusions  43 . In these embodiments, the length of the second heat source  30  along the channel axis  80  is larger than about 1 mm, preferably between about 2 mm to about 6 mm, and the length of the third heat source  40  along the channel axis  80  is between about 2 mm to 20 mm, preferably between about 3 mm to about 10 mm. The receptor hole  73  is preferably disposed symmetrically about the channel in  FIG. 15A . Preferred lengths of the first and second insulators have already been described. 
     In the embodiment shown in  FIGS. 16A-C , the second heat source  30  includes a protrusion  33  that extends away from the second heat source  20  toward the first heat source  20 . The second heat source  20  further includes a protrusion  34  that extends toward the third heat source  40 . In this example of the invention, each of the protrusions ( 33 ,  34 ) is disposed symmetrically about the first chamber  100  and channel axis  80 . In this embodiment, the protrusion  33  helps define the first chamber  100  or the channel  70 , the first insulator  50 , and the second heat source  30 , and separate the first insulator  50  from the first chamber  100  or the channel  70 . The protrusion  34  helps define the first chamber  100  or the channel  80 , the second insulator  60  and the second heat source  30 , and separate the second insulator  60  from the first chamber  100  or the channel  70 . 
     In the embodiment shown, the top  101  and bottom  102  ends of the first chamber  100  are essentially perpendicular to the channel axis  80 . The length of the first chamber  100  is between about 1 mm to about 25 mm, preferably between about 2 mm to about 15 mm. Additionally, the receptor hole  73  is symmetrically disposed about the channel  70  and channel axis  80 . 
     Referring to the embodiment shown in  FIGS. 17A-C , the first heat source  20  includes a protrusion  23  extending away from the first heat source  20  and toward the second heat source  30 . Protrusion  23  and receptor hole  73  are each disposed symmetrically about the channel axis  80 . Also in this embodiment, the apparatus  10  features protrusions  33 ,  34  that extend from the second heat source  30  toward the first heat source  20  or the third heat source  40  and disposed symmetrically about the first chamber  100  and channel axis  80 . The apparatus  10  also features a third heat source protrusion  43  that is symmetrically disposed about the first chamber  100  and the channel axis  80 . The protrusion  43  extends from the third heat source  40  toward the second heat source  30 . In this embodiment, the protrusion  23  helps define the channel  70 , the first insulator  50  and the first heat source  20 , and separate the first insulator  50  from the channel  70 . The protrusion  43  helps define the channel  80 , the second insulator  60  and the third heat source  40 , and separate the second insulator  60  from the channel  70 . The top end of the first chamber  101  and the bottom end of the first chamber  102  are essentially perpendicular to the channel axis  80 . A gap separates the protrusion  23  from the bottom end of the first chamber  102 . Another gap separates the top end of the first chamber  101  from the protrusion  43 . Additionally, the receptor hole  73  is symmetrically disposed about the channel  70  and channel axis  80 . 
     H. One Chamber in Second Heat Source, Tilted 
     As mentioned, it is an object of the invention to provide an apparatus in which various temperature shaping elements such as one or more of the channel, receptor hole, protrusion (if present), gap such as a chamber, insulators or insulating gaps, and thermal brake are each disposed symmetrically about the channel axis. In use, the apparatus will often be placed on a flat, horizontal surface so that the channel axis will be substantially aligned with the direction of gravity. In such an orientation, it is believed that a buoyancy force is generated by the temperature gradient inside the channel and that the buoyancy force also becomes aligned parallel to the channel axis. It is also believed that the buoyancy force will have its direction opposite to the direction of gravity with a magnitude proportional to the temperature gradient (along the vertical direction). Since the channel and the one or more chambers are symmetrically disposed about the channel axis in this embodiment, it is believed that the temperature distribution (i.e., distribution of the temperature gradient) generated inside the channel should also be symmetric with respect to the channel axis. Therefore, distribution of the buoyancy force should also be symmetric with respect to the channel axis with its direction parallel to the channel axis. 
     It is possible to introduce a horizontal asymmetry into the apparatus by moving the channel axis away from the direction of gravity. In these embodiments, it is possible to further enhance the efficiency and speed of convection-based PCR within the apparatus. Thus it is an object of the invention to provide an apparatus featuring one or more horizontal asymmetries. 
     Examples of an invention apparatus with positional horizontal asymmetry are provided by  FIGS. 18A-B . 
     In  FIG. 18A , the channel axis  80  is offset with respect to the direction of gravity to give the apparatus a positional horizontal asymmetry. In particular, the channel and chamber are formed symmetrically with respect to the channel axis. However the whole apparatus is rotated (or tilted) by an angle θ g  with respect to the direction of gravity. In this tilted structure, the channel axis  80  is no longer parallel to the direction of gravity, and thus the buoyancy force generated by the temperature gradient on the bottom of the channel becomes tilted with respect to the channel axis  80  since it is supposed to have a direction opposite to the direction of gravity. Without wishing to be bound to theory, the direction of the buoyancy force makes an angle θ g  with the channel axis  80  even if the channel/chamber structure is symmetric with respect to the channel axis  80 . In this structural arrangement, the upward convection flow will take a route on one side of the channel or the reaction vessel (the left side in the case of  FIG. 18A ) and the downward flow will take a route on the opposite side (i.e., the right side in the case of  FIG. 18A ). Hence, the route or pattern of the convection flow is believed to become substantially locked to one determined by such structural arrangement, therefore the convective flow becomes more stable and not sensitive to small perturbations from environment or small structural defects, leading to more stable convection flow and enhanced PCR amplification. It has been found that introduction of the gravity tilting angle helps enhancing the speed of the thermal convection, thereby supporting faster and more robust convection PCR amplification. The tilt angle θ g  can be varied between from about 2° to about 60°, preferably between about 5° to about 30°. This tilted structure can be used in combination with all the symmetric or asymmetric channel/chamber structures provided in the present invention. 
     The tilt angle θ g  shown in  FIG. 18A  can be introduced by one or a combination of different element. In one embodiment, the tilt is introduced manually. However it will often be more convenient to introduce the tilt angle θ g  by placing the apparatus  10  on an incline, for instance, by placing apparatus  10  on a wedge or similar shaped base. 
     However for some invention embodiments, it will not be useful to tilt the apparatus  10 .  FIG. 18B  shows another approach for introducing the horizontal asymmetry. As shown, one or more of the channel and chambers is tilted with respect to the direction of gravity. That is, the channel axis  80  (and the chamber axis) are offset (by θ g ) with respect to an axis perpendicular to the horizontal surface of the heat sources. In this invention embodiment, the channel axis  80  makes an angle θ g  with respect to the direction of gravity when the apparatus is placed on a flat, horizontal surface to have its bottom opposite from and parallel to that surface (as would be typical). According to this embodiment, and without wishing to be bound to theory, the buoyancy force generated by the temperature gradient on the bottom of the channel (that is supposed to have a direction opposite to the direction of gravity) will make an angle θ g  with respect to the channel axis as in the case of the embodiments described above. Such a structural arrangement will make the convection flow going upward on one side (i.e., the left side in the case of  FIG. 18B ) and going downward on the opposite side (i.e., the right side in the case of  FIG. 18B ). The tilt angle θ g  can be varied preferably between from about 2° to about 60°, more preferably between about 5° to about 30°. This tilted structure can also be used in combination with all the structural features of the channel and the chamber provided in the present invention. 
     Nearly any of the apparatus embodiment disclosed herein can be tilted by placing it on a structure capable of offsetting the channel axis  80  between from about 2° to about 60° with respect to the direction of gravity. As mentioned, an example of an acceptable structure is a surface capable of producing an incline such as a wedge or related shape. 
     I. One Chamber, Asymmetric Receptor Hole 
     As discussed, it is within the scope of the present invention to introduce one or more asymmetries within the first heat source to assist thermal convection PCR. In one embodiment, the receptor hole of the first heat source includes one or more structural asymmetries to achieve this objective. 
     Referring now to invention apparatus of  FIG. 19 , the receptor hole  73  is disposed asymmetrically about the channel axis  80  to form the receptor hole gap  74 . Preferably, the asymmetry is sufficient to cause uneven heat transfer in a horizontal direction from the first heat source  20  to the channel  70 . The receptor hole  73  is thus off-centered with respect to the channel axis  80  (by about 0.02 mm to about 0.5 mm). A further preferred receptor hole  73  has a width or diameter perpendicular to the channel axis  80  that is preferably larger than the width or diameter of the channel  70 , for example, about 0.04 mm to about 1 mm larger than the width (w 1  or w 2 ) or diameter of the channel  70 . As shown, the second heat source  30  of the apparatus has a constant height along the channel axis  80  in the region around the channel  70 . 
     An even larger asymmetry can be obtained when, as shown in  FIG. 19 , one side of the receptor hole is in contact with the channel. In this embodiment, the asymmetry introduced into the apparatus by the receptor hole  73  helps to drive thermal convection although receptor hole configurations with different gap structures, for instance on two opposing sides of the receptor hole  73  are also within the scope of the present invention. In the particular embodiment shown in  FIG. 19 , one side of the channel  70  (e.g., the left side in the case of  FIG. 19 ) is heated preferentially over the opposite side due to a better thermal contact with the first heat source  20 , and thus a larger driving force is generated on that side, thereby assisting the upward convection flow to go that route. Width or diameter of the receptor hole  73  in this embodiment may be made at least about 0.04 mm up to about 1 mm larger than the channel  70  and the center of the receptor hole may be positioned off-centered at least about 0.02 mm up to about 0.5 mm. 
     To enhance asymmetry, it is possible to make one side of the receptor hole deeper than the other with respect to the first heat source (and also closer to the chamber and the second heat source). Referring now to the apparatus shown in  FIGS. 20A-B , the receptor hole  73  has a larger depth on one side of the hole (left side) compared to the side opposite to the channel  70  (right side). In this embodiment, both sides of the receptor hole  73  remain in contact with the channel  70 . As shown in  FIG. 20A , the top portion of the side wall of the receptor hole  73  is removed to form a receptor hole gap  74  defined roughly by the channel  70  and the first heat source  20 . The bottom of the receptor hole gap  74  may be perpendicular to the channel axis  80  ( FIG. 20A ) or it may be disposed at an angle thereto ( FIG. 20B ). A side wall of the receptor hole gap  74  may be parallel to the channel axis  80  ( FIG. 20A ) or it may be at an angle thereto ( FIG. 20B ). In both the embodiments shown in  FIGS. 20A-B , one side of the channel  70  has a larger depth with respect to the first heat source  20  than the other side with the receptor hole gap  74 . Without wishing to be bound to theory, it is believed that the channel side with the larger depth in the embodiments shown in  FIGS. 20A-B  is heated preferentially due to more heat transfer from the first heat source, generating a larger buoyancy force on that side. It is further believed that by adding such an asymmetric receptor hole  73  and receptor hole gap  74  to the apparatus, there is an increase of the temperature gradient on one side of the channel  70  compared to the opposite side (the temperature gradient is typically inversely proportional to the distance). It is also believed that these features create a larger driving force on one side (e.g., the left side in  FIGS. 20A  and B) and support upward thermal convective flow along that side. It will be appreciated that one or a combination of different adaptations of the receptor hole  73  and receptor hole gap  74  are possible to achieve this goal. However, for many invention embodiments, it will be generally useful to make difference in the receptor hole depth on two opposing sides in the range of between from about 0.1 mm up to about 40 to 50% of the receptor hole depth. 
     J. One Chamber, Asymmetric or Symmetric Receptor Hole, Protrusions 
       FIGS. 21A-B  show further examples of suitable apparatus embodiments in which the receptor hole  73  is disposed about the channel asymmetrically. Portions of the receptor hole are deeper in the first heat source and closer to the chamber or the second heat source than other portions, thereby providing uneven thermal flow toward the second heat source. 
     In the apparatus shown in  FIG. 21A , the receptor hole  73  has two surfaces coincident with the top  21  of the first heat source  20 . Each surface faces the second heat source  30  and one of the surfaces (the one on the right side in  FIG. 21A ) has a larger gap on one side of the channel  70  compared to the surface opposite the channel  70  (the one on the left side) with respect to the bottom surface  32  of the second heat source  30 . That is, one of the surfaces is closer to the bottom  102  of the first chamber  100  or the bottom surface  32  of the second heat source  30  than the other. In this embodiment, both sides of the receptor hole  73  remain in contact with the channel  70 . The difference of the receptor hole depth between the two surfaces is preferably in the range of between from about 0.1 mm up to about 40 to 50% of the receptor hole depth. The second heat source  30  features protrusions  33 ,  34  that are each disposed symmetrically about the channel axis  80 . Also in this embodiment, the third heat source  40  includes protrusions  43 ,  44  disposed symmetrically about the channel axis  80 . 
     Turning to  FIG. 21B , the receptor hole  73  has a single inclined surface coincident with the top  21  of the first heat source  20 . The incline angle is between about 2° to about 45° with respect to an axis perpendicular to the channel axis  80 . In this embodiment, the apex of the inclined surface is relatively close to the bottom  102  of the first chamber  100 . The second heat source  30  features protrusions  33 ,  34  that are each disposed symmetrically about the channel axis  80 . Also in this embodiment, the third heat source includes protrusions  43 ,  44  that are each disposed symmetrically about the channel axis  80 . 
     In the embodiment shown in  FIG. 22A-B , the first chamber  100  is disposed asymmetrically about the channel axis  80  sufficient to cause horizontally uneven heat transfer from the second heat source  20  to the channel  70 . The receptor hole  73  may also be disposed asymmetrically about the channel  70  as in  FIGS. 21A-B . In the embodiment shown in  FIG. 22A , the first chamber  100  is positioned within the second heat source  30  and has a greater height on one side of the chamber than the other side opposite the channel axis  80 . That is, the length between one surface of the top end of the first chamber  101  and one surface of the bottom end of the first chamber  102  is greater (left side of  FIG. 22A ) along the channel axis  80  than the length between another surface of the top end of the first chamber  101  and another surface of the bottom end of the first chamber  102  (right side of  FIG. 22A ). The difference of the chamber height between the two opposing sides is preferably in the range of between from about 0.1 mm up to about 5 mm. There is gap between the bottom  101  of the first chamber  100  (or the bottom surface of the second heat source) and the top end of the receptor hole  73  that is smaller on the left side of the channel  70  than the other side. 
     Turning to  FIG. 22B , the bottom end  102  of the first chamber  100  is inclined with respect to an axis perpendicular the channel axis  80  by from about 2° to about 45°. In the example, the apex of the incline is further closer to the receptor hole  73 . The top of the receptor hole  73  coincident with the top surface  21  of the first heat source  20  is inclined with respect to the channel axis  80 . In this embodiment, the apex of the receptor hole incline is closer to the bottom end of the first chamber  102 . That is, there is gap between the bottom of the first chamber  100  (or the bottom surface of the second heat source) and the top end of the receptor hole  73  that is smaller on the left side of the channel  70  than the other side. 
     The configurations shown in  FIGS. 22A-B  provide preferential heating on one side of the channel  70  (i.e., the left side) in the receptor hole  73 , and thus initial upward convective flow can start preferentially on that side. However, the second heat source  30  provides preferential cooling on the same side due to the longer chamber length on that side. Therefore, the upward flow can change its path to the other side depending on the extent of the first chamber asymmetry. 
     Turning to  FIGS. 22C-D , the length between the top end  101  and the bottom end  102  is greater on one side of the first chamber  100  (the right side) than the other side with respect to the channel axis  80 . Here, preferential cooling from the second heat source will be on the right side of the chamber shown in  FIGS. 22C-D . Further asymmetry is provided by the larger depth of the receptor hole  73  on one side of the channel  70  (i.e., the left side of  FIGS. 22C-D ) than the other side. In the receptor hole  73 , preferential heating will be on the left side of the channel  70 . In this embodiment, a gap between the bottom  102  of the chamber  100  and the top of the receptor hole  73  is essentially constant around the channel  70 . 
     The configurations shown in  FIGS. 22C-D  support preferential heating on one side of the channel  70  (i.e., the left side) in the receptor hole  73  and preferential cooling on the opposite side in the first chamber  100 , and thus upward convective flow will stay preferentially on the left side. 
     In the embodiments shown in  FIGS. 22A-D , asymmetry introduced by the chamber configurations is sufficient to cause horizontally uneven heat transfer from the second heat source to the channel. Also in these embodiments, the protrusions  23 ,  33  are disposed asymmetrically with respect to the channel axis  80  and the protrusion  43  is disposed symmetrically about the channel axis  80 . Also in these embodiments, the apparatus includes a first insulator  50  and a second insulator  60  in which the length of the first insulator  50  along the channel axis  80  is greater than the length of the second insulator  60  along the channel axis  80 . 
     Other apparatus embodiments with at least one structural asymmetry are within the scope of the present invention. 
     For example, and as shown in  FIGS. 23A-B , the bottom end of the first chamber  102 , is asymmetrically disposed with respect to the channel axis  80 . The length between the top end  101  and the bottom end  102  is greater on one side of the first chamber  100  (the left side of the  FIGS. 23A-B ) than the other side with respect to the channel axis  80 . A gap between the bottom of the first chamber  102  and the top of the receptor hole  73  is smaller on one side of the channel  70  (the left side of  FIGS. 23A-B ) than the other side. In these embodiments, the protrusion  23  is disposed symmetrically about the channel axis  80 . Also in these embodiments, there is preferential heating on the right side of the receptor hole  73  (with respect to the channel axis  80 ) due to the larger gap on that side (since cooling by the second heat source is less significant on that side due to the larger gap) and thus a larger driving force is generated on the right side of the channel  70  and more pronounced upward flow on that side. In addition, the second heat source  30  features a protrusion  33  disposed asymmetrically about the channel axis  80 . In this embodiment, the second heat source features a protrusion  34  that is disposed asymmetrically about the channel axis  80 . The third heat source includes protrusions  43 ,  44  that are disposed symmetrically about the channel axis  80 . Also in the embodiments shown in  FIGS. 23A-B , the apparatus includes a first insulator  50  and a second insulator  60  in which the length of the first insulator  50  along the channel axis  80  is greater than the length of the second insulator  60  along the channel axis  80 . 
     Other apparatus embodiments with at least one structural asymmetry are within the scope of the present invention. 
     In the apparatus embodiments shown in  FIG. 24A-B , the second heat source  30  features protrusions ( 33 ,  34 ) that are each disposed asymmetrically around the channel axis  80 . In the embodiment shown in  FIG. 24A , the bottom end  102  of the first chamber  100  is inclined by between from about 2° to about 45° with respect to an axis perpendicular to the channel axis  80  so that a portion of the bottom end  102  is closer to the first heat source  20  than another portion opposite the channel axis  80 . In this embodiment, a gap between the bottom end  102  and the first heat source  20  is smaller on one side of the channel axis  80  than the other side. In this embodiment, none of the first  20  and third  40  heat sources includes a protrusion extending toward the second heat source  30 . Additionally, the top end of the first chamber  101  is inclined by between about 2° to about 30° with respect to an axis perpendicular to the channel axis  80 . 
     In  FIG. 24B , a surface of the bottom end of the first chamber  102  is positioned closer to the first heat source protrusion  23  than another surface of the bottom end  102 . In this embodiment, a gap is smaller between the bottom end  102  of the first chamber  100  and the top of the receptor hole  73  on one side (on left side). Also in  FIG. 24B , the third heat source  40  features a protrusion  43  disposed symmetrically about the channel  70 . The first chamber  100  features a top end  101  with two surfaces in which one surface is positioned closer to the third heat source protrusion  43  (left side) than the other surface. 
     In the apparatus embodiments shown in  FIGS. 24A-B , initial upward convective flow is favored along the right side of the channel  70  as a result of preferential heating from the receptor hole  73  on that side (due to less significant cooling by the second heat source as a result of the larger insulating gap on that side). Depending on the extent of the asymmetry on the top part of the first chamber, the upward flow can change its path to the opposite side (i.e., the left side) since preferential cooling from the first heat source  40  takes place on the right side due to the larger second insulating gap on that side. In both embodiments, the length of the first insulator  50  parallel to the channel axis  80  is longer than the length of the second insulator  60  parallel to the channel axis  80 . 
     K. Asymmetric Chambers 
     As discussed, it is an object of the present invention to provide an apparatus within one, two or three chambers in the second heat source, for example. In one embodiment, at least one of the chambers has a horizontal asymmetry. The asymmetry helps create a horizontally asymmetric driving force within the apparatus. For example, and in the embodiment shown in  FIG. 25 , the first chamber  100  and the second chamber  110  are each off-centered from the channel axis  80  along opposite directions. In particular, the top end of the first chamber  101  is positioned at essentially at the same height as the bottom end of the second chamber  112 . The first and second chambers may have different width or diameter. Difference of the chamber gap  105 ,  115  on two opposite sides may be at least about 0.2 mm up to about 4 to 6 mm. 
     In addition to the off-centered chamber structures exemplified in  FIG. 25 , one or more of the chambers may be made horizontally asymmetric by including structures that are tilted (skewed) with respect to the channel axis  80 . For instance, and as shown in  FIG. 26 , the first chamber  100  may be tilted with respect to the channel axis  80 . In this embodiment, the first wall of the first chamber  103  is tilted with respect to the channel axis  80  (e.g., at an angle less than about 30° with respect to the channel axis  80 ). Tilt angle as defined by an angle between the center axis of the chamber (or the chamber wall  103 ) and the channel axis may be between from about 2° to about 30°, more preferably between from about 5° to about 20°. 
     In the apparatus embodiments shown in  FIGS. 25 and 26 , upward convective flow from the bottom of the channel  70  is favored along the right side of the channel  70  as a result of preferential heating from the receptor hole  73  on that side (due to less significant cooling by the second heat source as a result of the larger chamber gap on that side). Similarly, downward flow from the top of the channel  70  is favored along the left side of the channel  70  as a result of preferential cooling from the third heat source  40  or the through hole  71  (due to less significant heating by the second heat source  30  as a result of the larger chamber gap on that side). 
     Referring now to the apparatus embodiments shown in  FIG. 27A-B , the top end  101  and/or bottom end  102  of the first chamber  100  may be structured to provide different gaps (from the third or first heat source) on two opposite sides of the channel axis  80 . For instance, and referring to  FIG. 27A , the top  101  and/or bottom end  102  of the first chamber  100  may be inclined from about 2° to about 30° with respect to an axis perpendicular to the chamber axis (or the channel axis  80 ). Alternatively, the first chamber  100  can have multiple top and bottom end surfaces as shown in  FIG. 27B . 
     In the embodiments shown in  FIGS. 27A-B , a gap between the bottom end of the first chamber  102  and the top end of the first heat source  21 , and between the top end of the first chamber  101  and the bottom end of the third heat source  42  is different on two opposite sides (i.e., the left and right sides in  FIGS. 27A-B ). Hence, similar to the embodiments shown in  FIGS. 25 and 26 , upward convective flow from the bottom of the channel  70  is favored along the right side of the channel  70  as a result of preferential heating from the receptor hole  73  on that side (due to less significant cooling by the second heat source as a result of the larger insulating gap on that side). Downward flow from the top of the channel  70  is favored along the left side of the channel  70  as a result of preferential cooling from the third heat source  40  or the through hole  71  (due to less significant heating by the second heat source  30  as a result of the larger insulating gap on that side). 
     In the embodiments shown in  FIGS. 27A-B , protrusions  33 ,  34  are disposed asymmetrically about the first chamber  100  with respect to the channel axis  80 . Additionally, the receptor hole  73  is disposed symmetrically about the channel axis  80 . The embodiment shown in  FIG. 27B  further includes protrusions  23  and  43  disposed symmetrically about the channel axis  80 . 
     L. Two Chambers, Asymmetric Thermal Brake(s) 
     It is an object of the invention to provide an apparatus with one or more thermal brakes, e.g., one, two or three thermal brakes in which one or more of them have horizontal asymmetry. Referring to the apparatus shown in  FIGS. 28A-B , the first thermal brake  130  has horizontal asymmetry. In this embodiment, the through hole formed in the first thermal brake  130  (that typically is made to fit with the channel) is larger than the channel  70  and off-centered from the channel axis  80  to provide a smaller (or no) gap on one side and a larger gap on the opposite side. Temperature distribution is found to be more sensitive to the asymmetry in the thermal brake compared to the asymmetry in the chamber (i.e., asymmetry in the first chamber wall  103 ). Preferably, the through hole in the thermal brake may be made at least about 0.1 mm up to about 2 mm larger, and off-centered from the channel axis by at least about 0.05 mm up to about 1 mm. 
     In embodiments in which the structural asymmetry resides in the first thermal brake  130  or the second thermal brake  140  (or both the first  130  and second  140  thermal brakes), the apparatus can include at least one chamber that is disposed symmetrically or asymmetrically about the channel axis  80 . In the embodiment shown in  FIG. 28A , the first chamber  100  and the second chamber  110  are positioned within the second heat source  30  and disposed symmetrically about the channel axis  80 . In this embodiment, the first chamber  100  is spaced from the second chamber  110  by a length  1  along the channel axis  80 . A portion of the second heat source  30  contacts the channel  70  to form the first thermal brake  130  sufficient to reduce heat transfer from the first heat source  20  or to the third heat source  40 . The first thermal brake  130  is disposed asymmetrically about the channel  70 . The first thermal brake  130  contacts one side of the channel  70  between the first  100  and second  110  chambers, the other side of the channel  70  being spaced from the second heat source  30 .  FIG. 28B  shows an expanded view of the first thermal brake  130  showing wall  133  contacting the channel  70  on the left side. When the structural asymmetry is associated with one or more of the thermal brakes, the upward and downward convective flow can be favored on one side of the channel or the opposite side with respect to the channel axis depending on the position and thickness of the thermal brakes along the channel axis. 
     M. One or Two Asymmetric Chambers with and without Thermal Brake(s) 
     Referring to  FIG. 29A , the first chamber  100  is off-centered with respect to the channel axis  80 . In this embodiment, the receptor hole  73  is disposed symmetrically about the channel axis  80  and is of constant depth. The first chamber  100  is off-centered from the channel  70  so that the chamber gap  105  is smaller on one side compared to the opposite side. As shown in  FIG. 29B , the chamber  100  can be further off-centered from the channel  70  so that one side or wall of the channel  70  makes contact with the chamber wall. In this embodiment, the channel-forming side (e.g., the left side in  FIG. 29B ) functions as a first thermal brake  130  having its top  131  and bottom  132  ends coincide with the top  101  and bottom  102  end of the first chamber  100 . In such an embodiment, heat transfer between the second heat source  30  and the channel  70  is larger on the side where the chamber gap  105  is smaller or does not exist (i.e., the left side in  FIGS. 29A and 29B ), thus producing a horizontally asymmetric temperature distribution.  FIG. 29C  provides an expanded view of the first thermal brake  130 . An acceptable difference between the chamber gaps on two opposite sides is preferably in the range between from about 0.2 mm to about 4 to 6 mm, and hence the chamber axis is off-centered from the channel axis by at least about 0.1 mm up to about 2 to 3 mm. 
     It will be appreciated that all or part of a chamber can be made asymmetric with respect to the channel axis  80 , for example, all or part of the chamber may be off-centered. For most invention applications, it will be useful to off-center an entire chamber. 
     It will sometimes be useful to have an invention apparatus with one, two, or three chambers disposed in the second heat source either symmetrically or asymmetrically about the channel axis  80 . In one embodiment, the apparatus has a first, second, and third chamber in which one or two of the chambers is disposed asymmetrically about the channel axis  80  and the other chamber is disposed symmetrically about the same axis. In an embodiment in which the apparatus includes a first chamber and second chamber that are each disposed asymmetrically about the channel axis  80 , those chambers can reside completely or partially within the second heat source. 
     Particular examples of this invention embodiment are shown in  FIGS. 30A-D . 
     In  FIG. 30A , the first thermal brake  130  contacts part of the height of the channel  70  within the second heat source  30 . The first chamber  100  and the second chamber  110  are each positioned in the second heat source  30  and the first chamber  100  is spaced from the second chamber  110  by a length (l) along the channel axis  80 . In this embodiment, the thermal brake  130  contacts the whole circumference of the channel  70  on the length (l) between the first  100  and second  110  chambers. The first chamber  100  and the second chamber  110  are each off-centered from the channel axis  80  in the same horizontal direction.  FIG. 30B  provides an expanded view of the first thermal brake  130  in which wall  133  contacts the channel  70 . 
     Turning to  FIG. 30C , the first chamber  100  and the second chamber  110  are each off-centered from the channel axis in the same horizontal direction. The first  100  and second  110  chambers can have the same or different width or diameter. In this embodiment, the first thermal brake  130  contacts one side of the channel  70  (i.e., the left side) within the first chamber  100  on a length from the bottom end  132  to the top end  131  of the first thermal brake  130  that is the same as the length of the first chamber  100  along the channel axis  80  in the embodiment shown in FIG.  30 C.  FIG. 30D  provides an expanded view of the first thermal brake  130  showing wall  133  contacting the channel  70 . 
     In each of the embodiments shown in  FIGS. 30A-D , the receptor hole  73  is disposed symmetrically about the channel  70 . 
       FIG. 31A  shows an invention embodiment in which the first chamber  100  and the second chamber  110  are each off-centered in opposite directions with respect to the channel axis  80  by about 0.1 mm up to about 2 to 3 mm. The first thermal brake  130  is symmetrically disposed with respect to the channel axis  80 . In this embodiment, a portion of the second heat source  30  contacts the channel  70  to form a first thermal brake  130  sufficient to reduce heat transfer from the first heat source  20  or to the third heat source  40 . In this example of the invention, the first thermal brake  130  contacts the whole circumference of the channel  70  on a length (l) between the first  100  and second  110  chambers. In other embodiments, the first thermal brake  130  can contact the channel  70  on one side, the other side being spaced from the second heat source  30 .  FIG. 31B  provides an expanded view of the first thermal brake  130  showing wall  133  contacting the channel  70 . 
     Referring to the embodiment shown in  FIG. 32A , the first chamber  100  and second chamber  110  are each off-centered with respect to the channel axis  80  in the same horizontal direction (e.g., by about 0.1 mm up to about 2 to 3 mm). In this embodiment, the first thermal brake  130  is asymmetrically disposed with respect to the channel axis  80 . The first thermal brake  130  and the chamber wall  103  are off-centered to the same direction. In this embodiment, the first thermal brake  130  contacts the channel  70  on one side (i.e., the left side), the other side being spaced from the second heat source  30 .  FIG. 32B  shows an expanded view of the first thermal brake  130 . 
     In  FIG. 32C , the first chamber  100  and the second chamber  110  are each off-centered with respect to the channel axis  80  in the same horizontal direction and the first thermal brake  130  is off-centered to the opposite direction. In this embodiment, the first thermal brake  130  contacts the channel  70  on one side (i.e., the right side), the other side being spaced from the second heat source  30 .  FIG. 32D  shows an expanded view of the first thermal brake  130 . 
     In another invention embodiment, the apparatus has two chambers in the second heat source  30  in which each chamber is off-set from the other in different horizontal directions.  FIG. 33A  shows an example. Here, the first chamber  100  and second chamber  110  within the second heat source  30  are each off-set with respect to the channel axis  80  in opposite horizontal directions (e.g., by about 0.5 mm to about 2 to 2.5 mm). The wall of the first chamber  103  is disposed lower along the channel axis  80  than the wall of the second chamber  113 . The wall of the first thermal brake  133  contacts one side of the channel  70  (i.e., the left side) on the lower part of the channel  70  within the first chamber  100 , and the wall of the second thermal brake  143  contacts the other side of the channel (i.e., the right side) on the upper part of the channel  70  within the second chamber  110 . The top end of the first thermal brake  131  is positioned essentially at the same height as the bottom end of the second thermal brake  142 . This arrangement is generally sufficient to cause horizontally uneven heat transfer between the second heat source  30  and the channel  70 .  FIG. 33B  shows an expanded view of the first thermal brake  130  and the second thermal brake  140 . 
       FIG. 33C  shows an invention embodiment in which the top end of the first thermal brake  131  is positioned higher than the bottom end of the second thermal brake  142 . The wall of the first thermal brake  133  and the wall of the second thermal brake  143  each contact the channel  70  on one side.  FIG. 33D  shows an expanded view of the first thermal brake  130  and the second thermal brake  140 . 
       FIG. 33E  shows an embodiment in which the top end of the first thermal brake  131  is positioned lower than the bottom end of the second thermal brake  142 . The wall of the first thermal brake  133  and the wall of the second thermal brake  143  each contact the channel  70  on one side.  FIG. 33F  shows an expanded view of the first thermal brake  130  and the second thermal brake  140 . 
     The invention provides other embodiments in which an asymmetry is introduced into the apparatus by tilting (skewing) one or more of the thermal brakes or the chamber with respect to the channel axis. Referring now to  FIG. 34A , the top end of the first chamber  101  and the bottom end of the second chamber  112  are each inclined between about 2° to about 45° with respect to an axis perpendicular to the channel axis  80 . In this embodiment, the distance between the top end of the first heat source  21  and the bottom end of the first thermal brake  132  is smaller on one side (i.e., the left side) with respect to the channel axis  80 , resulting in a temperature gradient that is biased to be larger on that side of the first chamber  100 . A similar effect can be expected on the opposite side (i.e., the right side) of the second chamber  110  due to the smaller distance on that side between the bottom end of the third heat source  42  and the top end of the first thermal brake  131 . The thermal brake  130  contacts the whole circumference of the channel  70  between the first chamber  100  and the second chamber  110  and at a higher location on one side than the other side.  FIG. 34B  shows an expanded view of the first chamber  100 , first thermal brake  130  and the second chamber  110  in which wall  133  contacts the channel  70 . 
     In some invention embodiments, it will be useful to tilt at least one of the chambers with respect to the channel axis (e.g., one, two, or three of the chambers). Indeed, different combinations of the tilted or skewed structures may be adopted to achieve the intended horizontally asymmetric temperature distribution. A few examples are shown in  FIGS. 35A-D . 
     In particular,  FIG. 35A  shows a case in which the first chamber  100  and the second chamber  110  are each tilted or skewed with respect to the channel axis  80  between about 2° to about 30°. In this embodiment, the first thermal brake  130  is not tilted.  FIG. 35B  shows an expanded view of the first chamber  100 , the first thermal brake  130  and the second chamber  110  in which wall  133  contacts the channel  70 . 
       FIG. 35C  shows an example in which both of the first chamber  100 , the second chamber  110 , and the first thermal brake  130  are each tilted with respect to the channel axis  80 . Each of the first chamber  100  and the second chamber  110  can be tilted or skewed with respect to the channel axis  80  by between about 2° to about 30°. The top end  131  and bottom end  132  of the first thermal brake  130  can be each inclined or tilted by between about 2° to about 45° with respect to an axis perpendicular to the channel axis  80 . In this embodiment, the first thermal brake  130  contacts the whole circumference of the channel between the first chamber and the second chamber and at a higher location on one side than the other side. 
     In the embodiments shown in  FIGS. 31A-B ,  32 A-D,  33 A-F,  34 A-B, and  35 A-D, the receptor hole  73  is disposed symmetrically about the channel axis  80 . 
     N. Additional Embodiments 
     Additional apparatus embodiments are shown in  FIGS. 36A-C ,  FIGS. 37A-C , and  FIG. 38A-C . 
     Turning to  FIG. 36A , the first chamber  100  of the apparatus  10  is within the second heat source  30  and the second chamber  110  is within the third heat source  40 . A second heat source protrusion  33  is disposed symmetrically about the channel axis  80 . The apparatus  10  further includes a first heat source protrusion  23  disposed symmetrically about the channel axis  80 . In this embodiment, the receptor hole  73  is disposed symmetrically about the channel axis  80 . 
     In embodiment shown in  FIG. 36B , the first chamber  100  of the apparatus  10  and the second chamber  110  are within the second heat source  30 . The apparatus further includes a third chamber  120  within the third heat source  40 . The apparatus also includes the first thermal brake  130  disposed between the first  100  and second  110  chambers within the second heat source  30 . A second heat source protrusion  33  is disposed symmetrically about the channel axis  80 . The apparatus further includes a first heat source protrusion  23  disposed symmetrically about the channel axis  80 . In this embodiment, the receptor hole  73  is disposed symmetrically about the channel axis  80 . 
     Turning to the embodiment shown in  FIG. 36C , the bottom of the first chamber  102  is within the second heat source  30 . However in the apparatus embodiment shown in  FIG. 36A , the bottom of the first chamber  102  is coincident with the bottom surface of the second heat source  32 . The apparatus shown in  FIG. 36C  includes the first chamber  100  within the second heat source  30  and the second chamber  110  within the third heat source  40 . The apparatus further includes the first thermal brake  130  that is disposed on the bottom of the second heat source  30  in between the bottom end of the first chamber  102  and the bottom of the second heat source  32 . The receptor hole  73  is disposed symmetrically with respect to the channel axis  80 . 
     In the embodiments shown in  FIGS. 36A-C , each apparatus further includes a first insulator chamber  51  defined by at least the first heat source  20 , the first protrusion of the first heat source  23 , the second heat source  30 , and the first protrusion of the second heat source  33 . 
     The apparatuses shown in  FIGS. 37A-C  further includes a second protrusion of the second heat source  34  disposed symmetrically about the channel axis  80  and a second insulator chamber  61  defined by at least the third heat source  40 , the second heat source  30 , and the second protrusion of the second heat source  34 . In the embodiment shown in  FIG. 37A , the apparatus includes the first chamber  100  within the second heat source  30  and the second chamber  110  within the third heat source  40 . The receptor hole  73  is disposed symmetrically with respect to the channel axis  80 . 
     Turning to  FIG. 37B , the apparatus shown features the first chamber  100  and the second chamber  110  positioned within the second heat source  30 . The third chamber  120  is within the third heat source  40 . The apparatus further includes the first thermal brake  130  located between the first  100  and second  110  chambers within the second heat source  30 . In this embodiment, the apparatus  10  includes protrusions ( 23 ,  33 ,  34 ) that are each disposed symmetrically with respect to the channel axis  80 . The receptor hole  73  is disposed symmetrically with respect to the channel axis  80 . 
     In the embodiments shown in  FIGS. 37A-B , the bottom end of the first chamber  102  contacts the first insulator  50 . However in the embodiment shown in  FIG. 37C , the bottom end of the first chamber  102  is within the second heat source  20  and the first thermal brake  130  is located on the bottom of the second heat source  30  in between the bottom end of the first chamber  102  and the bottom of the second heat source  32 . The apparatus shown in  FIG. 37C  also includes protrusions  23 ,  33 ,  34  that are each disposed symmetrically about the channel axis  80 . Also in the embodiments shown in  FIGS. 37B-C , the first thermal brake  130  is disposed symmetrically with respect to the channel axis  80 . 
     The apparatuses shown in  FIGS. 38A-C  further includes a first protrusion of the third heat source  43  disposed symmetrically about the channel axis  80  and a second insulator chamber  61  defined by at least the third heat source  40 , the third heat source protrusion  43 , the second heat source  30 , and the second protrusion of the second heat source  34 . In the embodiment shown in  FIG. 38A , the apparatus includes the first chamber  100  within the second heat source  30  and the second chamber  110  within the third heat source  40 . The receptor hole  73  is disposed symmetrically with respect to the channel axis  80 . 
     In the apparatus embodiment shown in  FIG. 38B , the first chamber  100  and second chamber  110  are each positioned in the second heat source  30 . The third chamber  120  is positioned in the third heat source  40 . The apparatus further includes the first thermal brake  130  located between the first  100  and second  110  chambers within the second heat source  30 . In this embodiment, the apparatus  10  includes protrusions ( 23 ,  33 ,  34 ,  43 ) that are each disposed symmetrically with respect to the channel axis  80 . The receptor hole  73  is disposed symmetrically with respect to the channel axis  80 . 
     In the embodiment shown in  FIG. 38C , the bottom end of the first chamber  102  is within the second heat source  20  and the first thermal brake  130  is located on the bottom of the second heat source  30  in between the bottom end of the first chamber  102  and the bottom of the second heat source  32 . The apparatus shown in  FIG. 37C  also includes protrusions  23 ,  33 ,  34 ,  43  that are each disposed symmetrically about the channel axis  80 . The receptor hole  73  is disposed symmetrically with respect to the channel axis  80 . 
     Manufacture, Use and Temperature Shaping Element Selection 
     A. Heat Sources 
     For most invention embodiments, one or more of the heat sources can be made with materials having a relatively low thermal conductivity as compared to materials used for other thermal cycling type apparatuses. Rapid temperature changing process can be usually avoided in the present invention. Therefore, a high temperature uniformity across each of the heat sources (e.g., with a temperature variation smaller than about 0.1° C.) can be readily achieved using a material having a relatively low thermal conductivity. The heat sources can be made of any solid material that has a thermal conductivity sufficiently larger than that of the sample or the reaction vessel, for instance, preferably at least about 10 times larger, more preferably at least about 100 times larger. The sample to be heated is mostly water that has a thermal conductivity of 0.58 W·m −1 ·K −1  at room temperature, and the reaction vessel is typically made of a plastic that has a thermal conductivity typically about a few tenths of W·m −1 ·K −1 . Therefore, the thermal conductivity of a suitable material is at least about 5 W·m −1 ·K −1  or larger, more preferably at least about 50 W·m −1 ·K −1  or larger. If the reaction vessel is made of a glass or ceramic that has a thermal conductivity larger than that of a plastic, it is preferred to use a material having somewhat larger thermal conductivity, for instance one having a thermal conductivity larger than about 80 or about 100 W·m −1 ·K −1 . Most metals and metal alloys as well as some high thermal conductivity ceramics fulfill such requirement. Although materials having a higher thermal conductivity will generally provide better temperature uniformity across each of the heat sources, aluminum alloys and copper alloys are typically useful materials since they are relatively cheap and easy to fabricate while possessing high thermal conductivity. 
     The following specifications will be generally useful for making and using apparatus embodiments described herein. The width and length dimensions of the first, second and third heat sources along an axis perpendicular to the channel axis can be selected as any values depending on intended use, for instance, depending on spacing between adjacent channel/chamber structures. The spacing between the adjacent channel/chamber structures can be at least about 2 to 3 mm, preferably between about 4 mm to about 15 mm. It will be generally preferred to use the industry standards, i.e., 4.5 mm or 9 mm spacing. In typical embodiments, the channel/chamber structures are arranged in equally spaced rows and/or columns. In such embodiments, it is preferred to make the width or length (along an axis perpendicular to the channel axis) of each of the heat sources that is at least about the value corresponding to the spacing times the number of rows or columns up to about one to about three spacing larger than this value. In other embodiments, the channel/chamber structures may be arranged in a circular pattern and preferably equally spaced. The spacing in such embodiments is also at least about 2 to 3 mm, preferably about 4 mm to about 15 mm with the industry standards of 4.5 mm or 9 mm spacing more preferred. In these embodiments, it is preferred to have the shape of the heat sources as a donut-like shape typically having a hole in the center. The channel/chamber structures may be positioned on one, two, three, up to about ten concentric circles. Diameter of each concentric circle can be determined by a geometric requirement for intended use, e.g., depending on number of the channel/chamber structures, spacing between adjacent channel/chamber structures in that circle, etc. Outer diameter of the heat sources is preferably at least about one spacing larger than diameter of the largest concentric circle, and inner diameter of the heat sources is preferably at least about one spacing smaller than diameter of the smallest concentric circle. 
     Length or thickness of the first, second and third heat sources along the channel axis has been already discussed. In the embodiments comprising at least one chamber in the second heat source, the thickness of the first heat source is larger than about 1 mm along the channel axis, preferably from about 2 mm to about 10 mm. Thickness of the second heat source along the channel axis is between about 2 mm to about 25 mm, preferably between 3 mm to about 15 mm. Thickness of the third heat source along the channel axis is larger than about 1 mm, preferably between about 2 mm to about 10 mm. In other embodiments that include only one chamber that is disposed in the third heat source, the second and third heat sources may have different thickness along the channel axis as compared to the embodiments comprising at least one chamber in the second heat source. For instance, the second heat source has a thickness larger than 1 mm along the channel axis, preferably between about 2 mm to about 6 mm. In these embodiments, thickness of the third heat source along the channel axis is between about 2 to about 20 mm, preferably between about 3 mm to about 10 mm. The first heat source can have a thickness along the channel axis that is within the same range as other embodiments, e.g., larger than about 1 mm, preferably between about 2 mm to about 10 mm. 
     The channel dimensions can be defined by a few parameters as denoted in  FIGS. 5A-D  and  6 A-J. The height (h) of the channel along the channel axis is at least about 5 mm to about 25 mm, preferably 8 mm to about 16 mm for a sample volume of about 20 microliters. The taper angle (θ) is between from about 0° to about 15°, preferably from about 2° to about 10°. The width (w 1 ) or diameter of the channel (or its average) along an axis perpendicular to the channel axis is at least about 1 mm to about 5 mm. The vertical aspect ratio as defined by the ratio of the height (h) to the width (w 1 ) is between about 4 to about 15, preferably from about 5 to about 10. The horizontal aspect ratio as defined by the ratio of the first width (w 1 ) to the second width (w 2 ) along first and second directions, respectively, that are mutually perpendicular to each other and aligned perpendicular to the channel axis, is typically between about 1 to about 4. 
     The receptor hole has a width or diameter that is in the same range as the channel, i.e., at least about 1 mm to about 5 mm. When the channel is tapered, the width or diameter of the receptor hole is smaller or larger than that of the channel depending on the tapering direction. Depth of the receptor hole is typically at least about 0.5 mm up to about 8 mm, preferably between about 1 mm to about 5 mm. 
     The chamber typically has a width or diameter along an axis perpendicular to the channel axis that is at least about 1 mm to about 10 or 12 mm, preferably between about 2 mm to about 8 mm. Presence of the chamber structure provide the chamber gap between the channel and the chamber wall that is typically between about 0.1 mm to about 6 mm, more preferably about 0.2 mm to about 4 mm. Length or height of the chamber along the channel axis can vary depending on different embodiments. For instance, if the apparatus comprises one chamber in the second heat source, that chamber can have a height along the channel axis between about 1 mm to about 25 mm, preferably between about 2 mm to about 15 mm. In the embodiments having two or more chambers in the second heat source, the height of each chamber is between about 0.2 mm to about 80% or 90% of the thickness of the second heat source along the channel axis, with the sum of the height of the two or more chambers can be as large as the thickness of the second heat source. In the embodiments having only one chamber that is disposed in the third heat source, the chamber height along the channel axis is in the range between about 0.2 mm up to about 60% or 70% of the thickness of the third heat source along the channel axis. 
     Dimensions of the thermal brake and the insulators (or insulating gaps) are also very important. Please refer to the general specifications as already provided above. 
     Although not generally required for optimal use of the invention, it is within the scope of the present invention to provide an apparatus with protrusions  24 ,  44 , or both. See  FIG. 22C , for example. 
     It will be appreciated that there usually exists certain tolerance in machining or fabricating mechanical structures. Therefore, in actual practice, the physically contacting holes (e.g., the through hole in the third heat source or the receptor hole in the first heat source in particular embodiments) must be designed to have a positive tolerance with respect to the size of the reaction vessel. Otherwise, the through hole or the channel could be made smaller or equal to the size of the reaction vessel, not allowing proper installation of the reaction vessel to the channel. Practically reliable tolerance for the physically contacting hole is about +0.05 mm in standard fabrication process. Therefore, if two objects are said to be “in physical contact”, it should be interpreted as having a gap between the two contacting objects that is smaller than or equal to about 0.05 mm. If two objects are said to be “not in physical contact”, or “spaced”, it should be interpreted as having a gap between the two objects that is larger than about 0.05 or 0.1 mm. 
     B. Use 
     Nearly any thermal convection PCR apparatus described herein can be used to perform one or a combination of different PCR amplification techniques. One suitable method includes at least one of and preferably all of the following steps:
         (a) maintaining a first heat source comprising a receptor hole at a temperature range suitable for denaturing a double-stranded nucleic acid molecule and forming a single-stranded template,   (b) maintaining a third heat source at a temperature range suitable for annealing at least one oligonucleotide primer to the single-stranded template,   (c) maintaining a second heat source at a temperature suitable for supporting polymerization of the primer along the single-stranded template; and   (d) producing thermal convection between the receptor hole and third heat source under conditions sufficient to produce the primer extension product.       

     In one embodiment, the method further includes the step of providing a reaction vessel comprising the double-stranded nucleic acid and the oligonucleotide primer(s) in aqueous buffer solution. Typically, the reaction vessel further includes one or more DNA polymerases. If desired, the enzyme may be immobilized. In a more particular embodiment of the reaction method, the method includes a step of contacting (either directly or indirectly) the reaction vessel to the receptor hole, the through hole, and at least one temperature shaping element (typically at least one chamber) disposed within at least one of the second or third heat sources. In this embodiment, the contacting is sufficient to support the thermal convection within the reaction vessel. Preferably, the method further includes a step of contacting the reaction vessel to a first insulator between the first and second heat sources and a second insulator between the second and third heat sources. In one embodiment, the first, second and third heat sources have a thermal conductivity at least about tenfold, preferably about one hundred fold greater than the reaction vessel or aqueous solution therein. The first and second insulators may have a thermal conductivity at least about five fold smaller than the reaction vessel or aqueous solution therein in which the thermal conductivity of the first and second insulators is sufficient to reduce heat transfer between the first, second and third heat sources. 
     In the step (c) of the foregoing method, the thermal convection fluid flow is produced essentially symmetrically or asymmetrically about the channel axis within the reaction vessel. Preferably, the steps (a)-(d) of the method described above consume less than about 1 W, preferably less than about 0.5 W of power per reaction vessel to produce the primer extension product. If desired, the power for performing the method is supplied by a battery. In typical embodiments, the PCR extension product is produced in about 15 to about 30 minutes or shorter and the reaction vessel can have a volume of less than about 50 or 100 microliters, for example, less than or equal to about 20 microliters. 
     In embodiments in which the method is used with a thermal convection PCR centrifuge of the invention, the method further includes the step of applying or impressing a centrifugal force to the reaction vessel conducive to performing the PCR. 
     In a more specific embodiment of the method for performing PCR by thermal convection, the method includes the steps of adding an oligonucleotide primer, nucleic acid template, and buffer to a reaction vessel received by any of the apparatuses disclosed herein under conditions sufficient to produce a primer extension product. In one embodiment, the method further comprises a step of adding a DNA polymerase to the reaction vessel. 
     In another embodiment of a method for performing PCR by thermal convection, the method comprising the steps of adding an oligonucleotide primer, nucleic acid template, and buffer to a reaction vessel received by any PCR centrifuge disclosed herein and applying a centrifugal force to the reaction vessel under conditions sufficient to produce a primer extension product. In one embodiment, the method includes the step of adding a DNA polymerase to the reaction vessel. 
     Practice of the invention is compatible with one or a combination of PCR techniques including quantitative PCR (qPCR), multiplex PCR, ligation-mediated PCR, hot-start PCR, allele-specific PCR among other variations of the amplification technique. The following particular use of the invention is with reference to the embodiment shown in  FIGS. 1 and 2A . As will be appreciated however, the methodology is generally applicable to other embodiments referred to herein. 
     Referring to  FIGS. 1 and 2A , the first heat source  20  generates a temperature distribution suitable for the denaturation process on the bottom or lower portion of the channel (sometimes referred herein to as a denaturation region). The first heat source  20  is typically maintained at a temperature useful to melt the nucleic acid template of interest (e.g., about 1 fg to about 100 ng of a DNA-based template). In this embodiment, the first heat source  20  should be maintained at between about 92° C. to about 106° C., preferably between about 94° C. to about 104° C., and more preferably between about 96° C. to about 102° C. As will be appreciated, other temperature profiles may be better suited for optimal practice of the invention depending on recognized parameters such as the nucleic acid of interest, the sensitivity desired, and the speed of which the PCR process should be conducted. 
     The third heat source  40  generates a temperature distribution suitable for the annealing process on the top or upper portion of the channel (sometimes referred herein to as an annealing region). The third heat source is typically maintained at a temperature between about 45° C. to about 65° C., depending, for instance, on the melting temperatures of the oligonucleotide primers used and other parameters known to those with experience in PCR reactions. 
     The second heat source  30  generates a temperature distribution suitable for the polymerization process in the intermediate region of the channel  70  (sometimes referred herein to as a polymerization region). For many invention applications, the second heat source  30  is typically maintained at a temperature between about 65° C. to about 75° C., more preferably between about 68° C. to about 72° C., in cases in which Taq DNA polymerase or a relatively heat stable derivative thereof is used. If a DNA polymerase that has a different temperature profile of its activity is used, the temperature range of the second heat source can be changed to match with the temperature profile of the polymerase used. See U.S. Pat. No. 7,238,505 and references disclosed therein regarding use of heat sensitive and heat stable polymerases in the PCR process. 
     See the Examples section for information about use of additional apparatus embodiments. 
     C. Selection of Temperature Shaping Elements 
     The following section is intended to provide further guidance on the selection and use of temperature shaping elements. It is not intended to limit the invention to a particular apparatus design or use. 
     Choice of one or a combination of temperature shaping elements for use with an invention apparatus will be guided by the particular PCR application of interest. For instance, properties of the target template are important for selecting temperature shaping element(s) that is/are best suited for a particular PCR application. For instance, the target sequence may be relatively short or long; and/or the target sequence may have a relatively simple structure (such as in plasmid or bacterial DNA, viral DNA, phage DNA, or cDNA) or a complex structure (such as in genomic or chromosomal DNA). In general, target sequences having longer sequences and/or complex structures are more difficult to amplify and typically require a longer polymerization time. Additionally, longer times for annealing and denaturation are often required. Moreover, the target sequence may be available in a large or small amount. Target sequences in smaller amounts are more difficult to amplify and generally require more PCR reaction time (i.e., more PCR cycles). Other considerations may also be important depending on particular uses. For instance, the PCR apparatus may be used to produce a certain amount of a target sequence for subsequent applications, experiments, or analyses, or else to detect or identify a target sequence from a sample. In further considerations, the PCR apparatus may be used in the laboratory or in the field, or in certain extraordinary environments, for instance, inside a car, a ship, a submarine, or a spaceship; under severe weather conditions, etc. 
     As discussed, the thermal convection PCR apparatus of the present invention generally provides faster and more efficient PCR amplification than prior PCR apparatuses. Moreover, the invention apparatus has a substantially lower power requirement and a much smaller size than prior PCR apparatuses. For instance, the thermal convection PCR apparatus is typically at least about 1.5 to 2 times faster (preferably about 3 to 4 times faster) and requires at least about 5 times (preferably about ten times to several tens of times) less power for operation with its size or weight at least about 5 to 10 times smaller. Hence, if a suitable design can be selected, users can have an apparatus that can cost much less time, energy, and space. 
     In order to select a suitable apparatus design, it is important to appreciate the key functions of an intended temperature shaping element. As summarized in Table 1 below, each temperature shaping element has specific functions with regard to the performance of the thermal convection PCR apparatus. For instance, the chamber structure generally increases the speed of the thermal convection within a heat source in which a chamber resides as compared to the structures without the chamber, and the thermal brake generally decreases the speed of the thermal convection as compared to the structures having the chamber structure without the thermal brake. Importantly, however, incorporation of the thermal brake structure in addition to the chamber structure within the second heat source makes the time length or volume of the sample available for the polymerization step larger so that efficiency of the PCR amplification can be increased for target sequences that require a longer polymerization time. Hence, the chamber structure can be used with or without the thermal brake depending on particular applications as discussed below. As also summarized in Table 1, any one or a combination of the convection accelerating elements (e.g., the positional asymmetry, the structural asymmetry, and the centrifugal acceleration) can be used to increase the speed of the thermal convection regardless of other heat source structures including the channel alone structure (i.e., a structure without the chamber). Hence, at least one or a combination of these convection accelerating elements can be combined with nearly all of the heat source structures in order to enhance the thermal convection speed as needed. As discussed, the invention apparatus requires much less power than prior PCR apparatuses, mainly as a result of eliminating necessity for the thermal cycling process (i.e., the process that changes the temperature of the heat source). As also discussed, a suitable combination of the first and second insulators (i.e., the thickness of the insulating gaps as well as use of a proper thermal insulator) can make the power consumption of the invention apparatus further reduced. Moreover, use of the protrusion structure(s) can still further reduce the power consumption of the invention apparatus substantially (see Examples 1 and 3, for instance) and also to increase the chamber length and thus to increase the polymerization time. Other parameters such as the receptor hole depth and the temperatures of the first, second and third heat sources can also be used to modulate the thermal convection speed and also the time period available for each of the polymerization, annealing and denaturation steps. As discussed below, each of these temperature shaping elements can be used alone or in combination with one or more other elements to construct a particular thermal convection PCR apparatus that is suitable for a particular application. 
     
       
         
           
               
             
               
                 TABLE 1 
               
             
            
               
                   
               
               
                 Key Functions of Temperature Shaping Elements 
               
            
           
           
               
               
            
               
                 Temperature Shaping 
                   
               
               
                 Element 
                 Key Functions 
               
               
                   
               
               
                 Chamber 
                 Increases the thermal convection speed within the heat source in 
               
               
                   
                 which the chamber resides as compared to the channel alone 
               
               
                   
                 structure. The smaller the chamber diameter or the chamber gap, 
               
               
                   
                 the slower is the thermal convection speed. 
               
               
                 Thermal Brake 
                 Decreases the thermal convection speed when combined with the 
               
               
                   
                 chamber structure. Typically positioned within the second heat 
               
               
                   
                 source in combination with at least one chamber and make the time 
               
               
                   
                 length and volume of the sample available for the polymerization 
               
               
                   
                 step increase as compared to the chamber only structure. The larger 
               
               
                   
                 the length of the thermal brake along the channel axis, the slower is 
               
               
                   
                 the thermal convection speed and the larger time and sample 
               
               
                   
                 volume becomes available for the polymerization step. 
               
               
                 Insulator/Insulating gap 
                 Generally required for the multi-stage thermal convection 
               
               
                   
                 apparatus. Useful to control the thermal convection speed and to 
               
               
                   
                 reduce power consumption. The smaller the length of the insulator 
               
               
                   
                 along the channel axis, the larger are the power consumption and 
               
               
                   
                 the driving force for the thermal convection. 
               
               
                 Protrusion 
                 Useful to reduce power consumption substantially and also to 
               
               
                   
                 lengthen the chamber length along the channel axis (and thus to 
               
               
                   
                 increase the time and sample volume available for the 
               
               
                   
                 polymerization step). 
               
               
                 Positional Asymmetry 
                 Increases the thermal convection speed and can be incorporated 
               
               
                   
                 into the invention apparatus as an adjustable structural element so 
               
               
                   
                 as to provide freedom to control the thermal convection speed 
               
               
                   
                 within a given design. When used with a structural asymmetry, an 
               
               
                   
                 adjustable positional asymmetry element can be used as both an 
               
               
                   
                 accelerating and a decelerating element. 
               
               
                 Structural Asymmetry 
                 Increases the thermal convection speed. 
               
               
                 Centrifugal Acceleration 
                 Increases the thermal convection speed while providing freedom to 
               
               
                   
                 control the thermal convection speed within a given design. 
               
               
                   
                 Typically used with the positional asymmetry. 
               
               
                   
               
            
           
         
       
     
     Although many useful apparatus embodiments are provided by the invention, the following combinations are particularly useful and easy to predict the performance of the invention apparatus. 
     An acceptable thermal convection PCR apparatus for many applications typically includes the channel and the first and second insulators (or the first and second insulating gaps) as basic elements. One or more other temperature shaping elements can be combined to use with these basic elements. An apparatus that uses the channel and the insulators only may not be optimal for some PCR applications. With the channel structure alone, the temperature gradient inside the sample within each heat source may be too small due to efficient heat transfer from the heat sources, and thus thermal convection becomes either too slow or not properly occurring. Use of the chamber structure can remedy this deficiency. As discussed, the speed of the thermal convection within each heat source can be increased by incorporating a chamber structure in that heat source. Thermal convection PCR apparatuses that use the chamber as an additional temperature shaping element are best suited for fast amplification of relatively short target sequences (e.g., shorter than about 1 kbp, preferably shorter than about 500 or 600 bp) having simple structures such as plasmid or bacterial DNA, viral DNA, phage DNA, cDNA, etc. For instance, an apparatus design having a straight chamber in the second heat source with its width or diameter about 3 to 6 mm can deliver PCR amplification of such samples within less than about 25 or 30 min, preferably within less than about 10 to 20 min depending on the amount and size of the target sequence (see Examples 1 and 3, for instance). Further increase of the speed of the thermal convection PCR could be achieved by incorporating at least one of the convection accelerating elements (e.g., see Examples 2 and 7). 
     An invention apparatus that includes the chamber (without the thermal brake) is also useful to amplify longer target sequences (e.g., longer than about 1 kbp up to about 2 or 3 kbp) or target sequences having complex structures (e.g., genomic or chromosomal DNAs) as well as the shorter sequences having simple structures. In one type of such embodiments, the chamber(s) resides in the second heat source only or both in the second and third heat sources, and the width or diameter of the chamber located in the second heat source could be reduced (either partially or completely) or an additional chamber having a reduced width or diameter could be incorporated within the second heat source. The reduced chamber width or diameter is typically in the range less than about 3 mm. In such designs, enhanced heat transfer from the second heat source (in the chamber region having the reduced width or diameter) leads to increase of the time length available for the polymerization step, and thus amplification of longer sequences and/or sequences having complex structures becomes efficient. However, use of a reduced chamber width or diameter typically results in decrease of the thermal convection speed. If the convection speed becomes too slow for user&#39;s applications, at least one of the convection accelerating elements can be combined to increase the convection speed. In another type of embodiments, the chamber could reside in the third heat source only. In this type of embodiments, use of primers having relatively high melting points (e.g., higher than about 60° C.) is typically recommended in order to amplify the different types of the target sequences mentioned above. 
     As discussed above, the thermal brake is a convection decelerating element and typically makes the polymerization time period longer when combined with the chamber structure typically within the second heat source. Hence, a combination of a thermal brake and the chamber structure within the second heat source is a good design example that can provide a thermal convection speed that is appropriately slow to provide a sufficient polymerization time and also sufficiently fast to deliver fast PCR amplification. As demonstrated in Example 1, a combination of a large width chamber (e.g., the width or diameter of the chamber larger than about 3 mm) and a thin thermal brake (e.g., the length of the thermal brake along the channel axis being less than about 2 mm) is a good example of an apparatus design that can deliver sufficiently fast amplification for both short and long target sequence (e.g., up to about 2 or 3 kbp of plasmid targets) as well as target sequences having complex structures (e.g., up to about 1 kbp or about 800 bp of human genome targets). Importantly, such design provides substantially fast amplification (i.e., within less than about 25 or 30 min, preferably within less than about 10 to 20 min) for the different types of the target sequences without using any of the convection accelerating elements. As also demonstrated, incorporation of a convection accelerating element (e.g., the positional asymmetry in Example 2) can provide further accelerated thermal convection PCR. 
     Further enhancement of the dynamic range of the thermal convection PCR apparatus can be achieved by incorporating a narrower chamber (e.g., smaller than about 3 mm of the chamber width or diameter) and/or a thermal brake within the second heat source. Use of a chamber having a reduced width or diameter (either partially completely) or a thermal brake within the second heat source leads to enhanced heat transfer from the second heat source to the channel, and hence the thermal convection becomes decelerated. In such decelerated heat source structures, the polymerization time period can be increased so as to amplify longer sequences, for instance, up to about 5 or 6 kbp. However, the total PCR reaction time could be inevitably increased due to a slow thermal convection speed, for instance, about 35 min to up to about 1 hour or longer depending on the size and structure of the target sequence. Any one or more of the convection accelerating elements can also be combined with this type of apparatus designs to increase the speed of the thermal convection PCR as desired. 
     The convection accelerating elements mentioned above (i.e., the positional asymmetry, the structural asymmetry, and the centrifugal acceleration) can affect the speed of the thermal convection in different degrees. The positional or structural asymmetry can typically enhance the thermal convection speed from about 10% or 20% up to about 3 to 4 times. In the case of the centrifugal acceleration, the enhancement can be made as large as possible, for instance, about 11,200 times at 10,000 rpm when R=10 cm as discussed. A practically useful range would be up to about 10 to about 20 times enhancement. When any one of these convection accelerating elements is used, the speed of the thermal convection can be increased. Hence, whenever a further increase of the thermal convection speed is needed for the user&#39;s applications, such feature can be conveniently incorporated. One particular design that includes at least one of the convection accelerating elements is a heat source structure that does not include the chamber (i.e., the channel only). As demonstrated in Example 6 (see  FIG. 76E  in comparison with  FIG. 75E ), use of a convection accelerating element can make the channel alone design operable. Such channel alone design is advantageous since it can provide the time period and volume of the sample available for the polymerization step that is as largest as possible. However, as discussed, such design delivers a thermal convection speed that is typically too slow. Use of any one or more of the convection accelerating elements can remedy such deficiency by increasing the thermal convection speed as user&#39;s demand. 
     All of the apparatus examples discussed above require much less power than prior PCR apparatuses and can be made as portable devices, i.e., operable with a battery, even without the protrusion structure. As discussed, use of the protrusion structure can reduce the power consumption substantially and thus more recommended if a portable PCR apparatus is essential for the user&#39;s applications. 
     Also, the apparatus designs discussed above can amplify from very low copy number samples (when optimized). For instance, as demonstrated in Examples 1, 2, and 3, target sequences even much less than about 100 copies can be amplified in about 25 min or about 30 min. 
     Moreover, the apparatus designs discussed above can be used in the laboratory or in the field, or in certain extraordinary conditions, not like many prior PCR apparatuses that can be used only under controlled conditions such as inside a laboratory. For instance, we have tested a few invention apparatuses inside a car while driving and confirmed that fast and efficient PCR amplification can be achieved as inside a laboratory. Furthermore, we also tested a few invention apparatuses under extraordinary temperature conditions (from below about −20° C. to above about 40° C.) and confirmed fast and efficient PCR amplification regardless of the outside temperatures. 
     Finally, as exemplified throughout the Examples, the thermal convection PCR apparatuses of the present invention can deliver PCR amplification that is not only fast but also very efficient. Hence, it is demonstrated that the invention apparatuses are generally suitable for nearly all of the diverse different applications of the PCR apparatus while providing enhanced performance with a new feature of a palm-size portable PCR device. 
     Apparatus with Housing and Temperature Control Elements 
     The invention apparatus referred to above can be used alone or in combination with suitable housing, temperature sensing, and heating and/or cooling elements. In one embodiment shown in  FIG. 39 , the first heat source  20 , second heat source  30 , and third heat source  40  features at least one first securing element  200  (typically a screw hole) and a second securing element  210  in which each of the elements are adapted to secure the heat sources, the first insulator  50  and second insulator  60  together as a single operable unit. The second securing element  210  is preferably “wing-shaped” to help provide a boundary for additional insulating spaces (see below). Heating and/or cooling elements  160   a ,  160   b , and  160   c  are each positioned in the first  20 , second  30  and third heat sources  40 , respectively. Each of the heat sources is typically equipped with at least one heating element. Typically useful heating elements are of resistive heating or inductive heating types. Depending on intended use, one or more of the heat sources can be further equipped with one or more of cooling elements and/or one or more of heating elements. Typically preferred cooling elements are a fan or a Peltier cooler. As well known, the Peltier cooler can function as both a heating and cooling element. It is particularly preferred to use more than one heating elements or both heating and cooling elements in different locations of one or more of the heat sources when a temperature gradient operation is required to provide different temperatures across that heat source. The first  20 , second  30  and third heat sources  40  further include temperature sensors  170   a ,  170   b  and  170   c  disposed in each of the heat sources, respectively. For most of the embodiments, each of the heat sources is typically equipped with one temperature sensor. However, in some embodiments such as those with a temperature gradient operation capability in one or more of the heat sources, two or more temperature sensors can be located at different positions of that heat source. 
       FIGS. 40A-B  provide cross-sectional views of the embodiment shown in  FIG. 39 . In addition to the cross sectional views of the channel and chamber structures, locations of the heating and/or cooling elements are shown as one example. As shown in this example, it is preferred to position the heating and/or cooling elements evenly to each of the heat sources to provide a uniform heating and/or cooling across each of the heat sources. For instance as depicted in  FIG. 40B , the heating and/or cooling elements are positioned in between each of the channel and chamber structures and equally spaced from each other (see also  FIG. 42  for instance). The cross-sectional view depicted in  FIG. 40A , for instance, shows connections (i.e., the circles) between the heating and/or cooling elements from one position in between each of the channel and chamber structures to another. In other types of embodiments such as those with a temperature gradient operation option, two or more of the heating or cooling elements can be used in one or more of the heat sources and positioned to different locations of that heat source to provide a biased heating and/or cooling across that heat source. 
     In  FIG. 41 , the plane of section is through one of the second securing elements  210  and a first securing element  200 . As shown, the first securing element  200  includes a screw  201 , washer  202   a , securing element of the first heat source  203   a , spacer  202   b , securing element of the second heat source  203   b , spacer  202   c , and securing element of the third heat source  203   c . Preferably, at least one of and more preferably all of the screw  201 , the washer  202   a  and spacers  202   b  and  202   c  are made from a thermal insulator material. Examples include plastics, ceramics, and plastic composites (such as those with carbon or glass fiber). Materials having a high mechanical strength, high melting and/or deflection temperature (e.g., about 100° C. or higher, more preferably about 120° C. or higher), and low thermal conductivity (e.g., plastics with thermal conductivity smaller than about a few tenths of W·m −1 ·l 1  or ceramics with thermal conductivity smaller than about a few W·m −1 ·K −1 ) are more preferred. More specific examples include plastics such as PPS (polyphenylene sulfide), PEEK (polyetherehterketone), Vesper (polyimide), RENY (polyamide), etc. or their carbon or glass composites, and low thermal conductivity ceramics such as Macor, fused silica, zirconium oxide, Mullite, Accuflect, etc. 
       FIG. 42  provides an expanded view of an apparatus embodiment with various securing element and temperature control elements. It will be apparent that in addition to the particular securing structures shown in  FIG. 42 , others are possible. Thus in one embodiment, at least one of the first and/or second securing elements ( 200 ,  210 ) is located in other region(s) of at least one, and preferably all of the first heat source  20 , second heat source  30 , third heat source  40 , first insulator  50 , and second insulator  60 . That is, although the third heat source  40  is shown to include the second securing element  210 , any other or all of the heat sources and/or the insulators could include the second securing element  210 . In another embodiment, at least one of the first and/or second securing elements ( 200 ,  210 ) is located in an inner region of at least one, and preferably all of the first heat source  20 , second heat source  30 , third heat source  40 , first insulator  50 , and second insulator  60 . 
     Although the forgoing invention embodiments will be generally useful for many PCR applications, it will often be desirable to add protective housing. One embodiment is shown in  FIGS. 43A-B . As shown, the apparatus  10  features a first housing element  300  that surrounds the first heat source  20 , the second heat source  30 , the third heat source  40 , the first insulator  50 , and the second insulator  60 . In this embodiment, each of the second securing elements  210  has a wing-shaped structure that cooperates with other structural elements of the apparatus  10  to form at least one insulating gap, for example, one, two, three, four, five, six, seven or eight of such gaps. Each of the gaps can be filled with a suitable insulating material such as those disclosed herein such as a gas or solid insulator. Air will be a preferred insulating material for many applications. Presence of the insulating gap(s) provides advantages such as reducing heat loss from the apparatus  10 , thereby lowering power consumption. 
     Thus in the embodiment shown in  FIG. 43A-B , the third heat source  40  comprises four second securing elements  210  in which each pair of second securing elements defines a third insulating gap  310 . In particular,  FIG. 43A  shows four parts of the third insulating gaps  310  each defined by a first housing element  300  and a pair of the second securing element  210 .  FIG. 43A  also shows a fourth insulating gap  320  located between the bottom of the first heat source  20  and the first housing element  300 . Also shown is a support  330  for suspending the secured heat sources inside the first housing element  300 , thereby helping form the third insulating gap  310  and the fourth insulating gap  320 . 
     It will often be desirable to further house the invention apparatus, for example to provide further protection and insulating gaps. Referring now to  FIG. 44A-B , the apparatus further includes a second housing element  400  that surrounds the first housing element  300 . In this embodiment, the apparatus  10  further includes a fifth insulating gap  410  defined by the first housing element  300  and the second housing element  400 . The apparatus  10  can also include a sixth insulating gap  420  located between the bottom of the first housing element  300  and the bottom of the second housing element  400 . 
     If desired, the invention apparatus may further include at least one fan unit to remove heat from the apparatus. In one embodiment, the apparatus comprises a first fan unit positioned above the third heat source  40  to remove heat from the third heat source  40 . If desired, the apparatus may further include a second fan unit positioned below the first heat source  20  to remove heat from the first heat source  20 . 
     Convection PCR Apparatus Incorporating Centrifugal Acceleration 
     It is an object of the invention to provide “centrifugal acceleration” as an optional additional feature of the apparatus embodiments described herein. As discussed above, it is believed that thermal convection can be made optimal when a vertical temperature gradient (and optionally or in addition, a horizontally asymmetric temperature distribution when the positional or structural asymmetry is used) is generated inside a fluid. Proportional to the magnitude of vertical temperature gradient, a buoyancy force is generated that drives a convection flow inside the fluid. Thermal convection generated by an invention apparatus must typically fulfill various conditions for inducing a PCR reaction. For instance, the thermal convection must flow through a plurality of spatial regions sequentially and repeatedly, while maintaining each of the spatial regions at a temperature range suitable for each step of the PCR reaction (i.e., the denaturation, annealing, and polymerization steps). Moreover, the thermal convection must be controlled to have a suitable speed so as to allow suitable time period for each of the three PCR reaction steps. 
     Without wishing to be bound to any theory, it is believed that thermal convection can be controlled by controlling the temperature gradient, more precisely distribution of the temperature gradient inside the fluid. The temperature gradient (dT/dS) depends on temperature difference (dT) and distance (dS) between two reference positions. Therefore, the temperature difference or distance may be changed to control the temperature gradient. However, in the convection PCR apparatus, neither the temperature (or its difference) nor the distance may be changed easily. The temperature of different spatial regions inside the sample fluid is subject to a specific range as defined by the temperature suitable for each of the three PCR reaction steps. There are not many opportunities to change the temperature of different (typically at least vertically different) spatial regions inside the sample. Furthermore, vertical positions of the different spatial regions (in order to generate a vertical temperature gradient for inducing a buoyant driving force) are usually restricted due to a small volume of the sample fluid. For instance, a typical volume of PCR sample is only about 20 to 50 microliters and sometimes smaller. Such small volumes and space limitations do not allow much freedom to change the vertical positions of the different spatial regions for the PCR reaction. 
     As discussed, the buoyancy force is proportional to the vertical temperature gradient that in turn depends on temperature difference and distance between two reference points. Further to such dependence, however, the buoyancy force is also proportional to the gravitational acceleration (g=9.8 m/sec 2  on Earth). This force field parameter is a constant, a variable that cannot be controlled or changed, but can be only defined by the law of universal gravitation. Therefore, nearly all of the thermal convection based PCR apparatuses rely upon highly restricted special structures, inevitably adapted to gravitational forces. 
     Use of centrifugal acceleration in accord with the present invention provides a solution for this problem. By making a convection based PCR apparatus subject to a centrifugal acceleration force field, one can control the magnitude of the buoyant driving force regardless of the structure that defines the magnitude of the temperature gradient, thereby controlling the convection speed without much limitation. 
       FIGS. 45A-B  shows one embodiment of a PCR centrifuge  500  according to the invention. In this example, the apparatus  10  is attached to a rotation arm  520  rotatably attached to motor  501 . In this embodiment, the rotation arm  520  includes a tilt shaft  530  for providing freedom of changing the angle between the axis of rotation  510  and the channel axis  80 . The PCR centrifuge may include any number of the apparatus  10  provided intended results are achieved, for example, 2, 4, 6, 8, 10 or even 12. The apparatus  10  may or may not include protective housing as discussed above, although having some protective housing will be generally useful. 
     The tilt shaft  530  is preferably configured to be an angle inducing element capable of tilting the angle of the heat source (more particularly the angle of the channel axis  80 ) with respect to the rotation axis. Tilt angle can be adjusted depending on the rotation speed (i.e., depending on the magnitude of the centrifugal acceleration) so that the tilt angle between the channel axis  80  and the net acceleration vector depicted in  FIG. 46  can be adjusted in the range between from about 0° to about 60°. In one embodiment, the angle inducing element in  FIG. 45A  is a rotation shaft (depicted as a circle) in the center of the joint region between the horizontal arm and an arm on which the heat source assembly is located. 
     In the embodiment shown in  FIGS. 45A-B , the sample fluid inside the reaction vessel placed inside the apparatus  10  is subject to a centrifugal acceleration force in addition to the gravitational acceleration force. See  FIG. 46 . As will be appreciated, the direction of the centrifugal acceleration g c  is perpendicular to (and outward from) the axis of the centrifugal rotation, and its magnitude is given by an equation g c =R ω 2 , where R is the distance from the axis of the centrifugal rotation to the sample fluid and w is angular velocity in radian/sec. For instance, when R=10 cm and speed of the centrifugal rotation is 100 rpm (corresponding to ω=about 10.5 radian/sec), magnitude of the centrifugal acceleration is about 11 m/sec 2 , similar to the gravitational acceleration on Earth. Since the centrifugal acceleration is proportional to square of the rotation speed (or square of the angular velocity), the centrifugal acceleration increases quadratically with increase of the rotation speed, for instance, about 4.5 times of the gravitational acceleration at 200 rpm, about 112 times at 1,000 rpm, and about 11,200 times at 10,000 rpm when R=10 cm. The magnitude of the net force field that acts on the sample fluid can be controlled freely by adopting such centrifugal acceleration. Therefore, the buoyancy force can be controlled (typically increased) as needed so as to make the convection speed as fast as needed. Practically, there are few limitations for inducing the thermal convection to very high flow speed sufficient for very high speed PCR reaction, provided a small vertical temperature gradient can be generated in the sample fluid. Therefore, prior limitations regarding heat source assembly and use can be minimized or avoided when combined with centrifugal acceleration in accord with the invention. 
     As depicted in  FIG. 46 , the sample fluid is subject to the net force field generated by addition of the centrifugal acceleration and the gravitational acceleration. In a typical embodiment, the channel axis  80  is aligned parallel to the net force field or made to have a tilt angle θ c  with respect to the net force field. As discussed, presence of the tilt angle is generally preferred in order to make the convection flow stay in a stable route. The tilt angle θ c  ranges from about 2° to about 60°, more preferably about 5° to about 30°. 
     It will be appreciated that the apparatus embodiment used to exemplify the PCR centrifuge  500  is shown in  FIGS. 1 and 2A -C. However, the PCR centrifuge  500  is compatible with use of one or a combination of different invention apparatuses as described herein. In particular, the PCR centrifuge  500  can also be used with nearly any type of heat source structure and reaction vessel described herein provided that a small vertical temperature gradient can be generated inside the sample. For example, nearly any of the heat source structures described above and elsewhere (e.g., WO02/072267 to Benett et al. and U.S. Pat. No. 6,783,993 to Malmquist et al.) may be combined with the centrifugal element of the present invention so as to enhance the amplification speed and performance of the apparatus. Moreover, other heat source structures that cannot be made operable (or that cannot be made to provide a high PCR amplification speed) in typical gravitationally driven mode can be made operable when combined with the centrifugal acceleration structure. For instance, a heat source structure that does not include a chamber as described herein but only comprises the channel structure may also be made operable. See PCT/KR02/01900, PCT/KR02/01728 and U.S. Pat. No. 7,238,505, for example. In this embodiment, the prior heat source structures without the chamber provides a temperature distribution inside the second heat source that changes slowly, presumably due to a high heat transfer from the second heat source. A result is a small temperature gradient within the second heat source. With only gravity, thermal convection will be unsatisfactory or too slow for many PCR applications. However, introduction of centrifugal acceleration in accord with the invention can make thermal convection sufficiently fast and stable so as to induce the PCR reaction successfully and efficiently. 
     In typical operation of the thermal convection PCR centrifuge  500 , the axis of rotation  510  is essentially parallel to the direction of gravity. See  FIG. 46 . In this embodiment, the channel axis  80  is essentially parallel to, or tilted with respect to the direction of net force generated by the gravitational force and the centrifugal force. That is, the channel axis  80  can be tilted with respect to the direction of net force generated by the gravitational force and the centrifugal force. For most embodiments, the tilt angle θ c  between the channel axis  80  and the direction of the net force is between about 2° to about 60°. The tilt shaft  530  is adapted to control the angle between the channel axis  80  and the net force. In operation, the axis of rotation  510  is usually located outside of the first  20 , second  30 , and third  40  heat sources. Alternatively, the axis of rotation  510  is located essentially at or near the center of the first  20 , second  30 , and third  40  heat sources. In these embodiments, the apparatus  10  includes a plurality of channels  70  that are located concentrically with respect to the axis of rotation  510 . 
     Circular-Shaped Heat Sources 
     In another embodiment of the thermal convection PCR centrifuge, one or more of the heat sources has a circular or semi-circular shape.  FIGS. 47A-B ,  48 A-C,  49 A-B, and  50 A-C show particular embodiments of such a heat source structure. 
       FIGS. 47A-B  show vertical sections of a particular embodiment of a centrifugally accelerated convection PCR apparatus. In particular,  FIGS. 47A and 47B  show cross-sections along the channel and securing element regions, respectively. The two sections are defined in  FIGS. 48A-C  which depict horizontal top view of the first  20 , second  30  and third  40  heat sources, respectively. As depicted in  FIGS. 47A-B , the three circular shape heat sources are assembled to form an apparatus embodiment rotatably attached to the rotation axis  510  of a PCR centrifuge  500  through a rotation arm  520 . The center of the heat source assembly is positioned concentric with respect to the rotation axis  510  so that the radius of centrifugal rotation is defined by the horizontal length of the rotation arm from the rotation axis to the center of the channel  70 . The three heat sources  20 ,  30  and  40  are assembled essentially parallel to each other with the top of one heat source facing the bottom of an adjacent heat source. As also depicted, the heat source assembly is oriented with respect to the rotation axis such that the channel axis  80  is aligned either parallel to, or tilted from the net acceleration vector depicted in  FIG. 46 . 
     The three heat sources depicted in  FIGS. 48A-C  are assembled using a set of first securing element comprising a screw  201 , spacers or washers  202   a - c , and securing apertures  203   a - c  formed in the heat sources as depicted in  FIG. 47B . A second securing element  210  formed in the third heat source  40  shown in  FIGS. 47B and 48C  is used to install the apparatus within the first housing element  300 . 
     Nearly any of the apparatus embodiments disclosed in the present application (including various channel and chamber structures) can be used with the centrifugally accelerated thermal convection PCR apparatus described herein. However, an apparatus without any chamber structure can also be used.  FIGS. 49A and 50A -C show an example in which each of the heat sources are adapted to provide a channel only, i.e., channel  70  formed as a hole having a closed bottom end in the first heat source  20 , and extending through the second heat source  30  to the third heat source  40 . As another embodiment,  FIG. 47A  shows a vertical section of an example in which a chamber structure  100  having a first thermal brake  130  on the bottom of the second heat source is used in combination with the channel structure.  FIG. 48B  shows a horizontal top view of the second heat source comprising the chamber  100  and the first thermal brake  130  as used in the example of  FIG. 47A . The first and third heat sources have the same structures as  FIGS. 50A and 50C , respectively. 
     In one embodiment of the forgoing thermal convection PCR centrifuge, the device is made portable and preferably operated with a battery. The embodiment shown in  FIGS. 45A-B  can be used for high throughput large scale PCR amplification, for example. In this embodiment, the apparatus can be used as a separable module and thus can be easily loaded and unloaded to the centrifuge unit. 
     Reaction Vessels 
     A suitable channel of the apparatus is adapted to hold a reaction vessel within the apparatus so that intended results can be achieved. In most cases, the channel will have a configuration that is essentially the same as that of a lower part of the reaction vessel. In this embodiment, the outer profile of the reaction vessel, particularly the lower part, will be essentially identical to the vertical and horizontal profiles of the channel. The upper part of the reaction vessel (i.e., toward the top end) may have nearly any shape depending on intended use. For instance, the reaction vessel may have a larger width or diameter on the upper part to facilitate introduction of a sample and may include a cap to seal the reaction vessel after introduction of a sample to be subjected to thermal convection PCR. 
     In one embodiment of a suitable reaction vessel, and referring again to  FIG. 5A-D , the outer profile of the reaction vessel can be identical to the profile of the channel  70  up to the top end  71  of the channel  70 . The shape or profile of inside of the reaction vessel may have a shape different from that of outside of the reaction vessel (if wall thickness of the reaction vessel is made to vary). For instance, the outer profile of the horizontal section may be circular while the inner profile is ellipsoidal, or vice versa. Different combinations of outer and inner profiles are possible as far as the outer profile is suitably selected to provide proper thermal contact with the heat sources, and the inner profile is suitably selected for an intended thermal convection pattern. In typical embodiments, however, the reaction vessel has a wall thickness that is about constant or does not vary much, i.e., the inner profile is typically identical or similar to the outer profile of the reaction vessel. Typical wall thickness ranges between from about 0.1 mm to about 0.5 mm, more preferably between from about 0.2 mm to about 0.4 mm, although it can vary depending on the material used. 
     If desired, the vertical profile of the reaction vessel may also be shaped to form a linear or tapered tube to fit with the channel as shown in  FIGS. 5A-D . When tapered, the reaction vessel may be tapered either from the top to the bottom or from the bottom to the top, although a reaction vessel that is (linearly) tapered from the top to the bottom is generally preferred as in the case of the channel. Typical taper angle θ of the reaction vessel is in the range between from about 0° to about 15°, more preferably from about 2° to about 10°. 
     The bottom end of the reaction vessel may also be made flat, rounded, or curved as for the bottom end of the channel depicted in  FIGS. 5A-D . When the bottom end is rounded or curved, it can have a convex or concave shape with its radius of curvature equal to or larger than the radius or half width of the horizontal profile of the bottom end. Flat or near flat bottom end is more preferred over other shapes since it can provide an enhanced heat transfer so as to facilitate the denaturation process. In such preferred embodiments, the flat or near flat bottom end has a radius of curvature that is at least two times larger than the radius or half width of the horizontal profile of the bottom end. 
     Also if desired, horizontal profile of the reaction vessel may also be made into various different shapes although a shape having certain symmetry is generally preferred.  FIGS. 6A-J  shows a few examples of the horizontal profile of the channel having certain symmetry. An acceptable reaction vessel may be made to fit these shapes. For instance, the reaction vessel may have its horizontal shape that is circular (top, left), square (middle, left), or rounded square (bottom, left) generally the same as that shown for the channel  70  in  FIGS. 6A , D, G, and J. Thus, the reaction vessel may have a horizontal shape that has its width larger than its length (or vice versa), for instance, an ellipsoid (top, middle), rectangular (middle, middle), or rounded rectangular (bottom, middle) that is generally the same as that depicted in the middle column of  FIGS. 6B , E, and H for the channel  70 . This type of horizontal shape for the reaction vessel is useful when incorporating a convection flow pattern going upward on one side (e.g., on the left hand side) and going downward on the opposite side (e.g., on the right hand side). Due to the relatively larger width profile incorporated compared to the length, interference between the upward and downward convection flows can be reduced, leading to more smooth circulative flow. The reaction vessel may have a horizontal shape that has its one side narrower than the opposite side. A few examples are shown on the right column of  FIGS. 6A-J  for the shape of the channel. In particular, the reaction vessel may be made so that the left side of the reaction vessel is narrower than the right side for instance, as shown in  FIGS. 6C , F and I for the channel  70 . This type of horizontal shape is also useful when incorporating a convection flow pattern going upward on one side (e.g., on the left hand side) and going downward on the opposite side (e.g., on the right hand side). Moreover, when this type of shape is incorporated, speed of the downward flow (e.g., on the right hand side) can be controlled (typically reduced) with respect to the upward flow. Since the convective flow must be continuous within the continuous medium of the sample, the flow speed should be reduced when cross-sectional area becomes larger (or vice versa). This feature is particularly important with regard to enhancing the polymerization efficiency. The polymerization step typically takes place during the downward flow (i.e., after the annealing step), and therefore time period for the polymerization step can be lengthened by making the downward flow slower as compared to that of the upward flow, leading to more efficient PCR amplification. 
     Further examples of suitable reaction vessels are provided in  FIGS. 51A-D . As shown, the reaction vessel  90  includes a top end  91  and a bottom end  92  which ends include center points that define a central reaction vessel axis  95 . The reaction vessel  90  is further defined by an outer wall  93  and an inner wall  94  which surround a region for holding a PCR reaction mixture. In  FIGS. 51A-B , the reaction vessel  90  is tapered from the top end  91  to the bottom end  92 . A generally useful taper angle (θ) is in the range between from about 0° to about 15°, preferably from about 2° to about 10°. In the embodiment shown in  FIG. 51A , the reaction vessel  90  has a flat or near flat bottom end  92  while in the example shown in  FIG. 52B , the bottom end is curved or rounded. The top  71  and bottom  72  ends of the channel are marked in  FIGS. 51A-D . 
       FIGS. 51C-D  provide examples of suitable reaction vessels with straight walls from the top end  91  to the bottom end  92 . The reaction vessel  90  shown in  FIG. 51C  has a flat or near flat bottom end  92  while in the example shown in  FIG. 51D , the bottom end is curved or rounded. 
     Preferably, the vertical aspect ratio of the outer wall  93  of the reaction vessel  90  shown in  FIGS. 51A-D  is at least about 4 to about 15, preferably from about 5 to about 10. The horizontal aspect ratio of the reaction vessel is defined by the ratio of the height (h) to the width (w 1 ) up to the position corresponding to the top end  71  of the channel  70  as in the case of the channel. The horizontal aspect ratio of the outer wall  93  is typically about 1 to about 4. The horizontal aspect ratio is defined by the ratio of the first width (w 1 ) to the second width (w 2 ) of the reaction vessel along first and second directions, respectively, that are mutually perpendicular to each other and aligned perpendicular to the channel axis. Preferably, the height of the reaction vessel  90  along the reaction vessel axis  95  is at least between about 6 mm to about 35 mm. In this embodiment, the average of the width of the outer wall is between about 1 mm to about 5 mm, and that of the inner wall of the reaction vessel is between about 0.5 mm to about 4.5 mm. 
       FIGS. 52A-J  show horizontal cross-sectional views of suitable reaction vessels for use with the invention. The invention is compatible with other reaction vessel configurations provided intended results are achieved. Accordingly, the horizontal shape of an acceptable reaction vessel can be one or a combination of circle, semi-circle, rhombus, square, rounded square, ellipsoidal, rhomboid, rectangular, rounded rectangular, oval, triangular, rounded triangular, trapezoidal, rounded trapezoidal or oblong shape. In many embodiments, the inner wall is disposed essentially symmetrically with respect to the reaction vessel axis. For example, the thickness of the reaction vessel wall can be between about 0.1 mm to about 0.5 mm. Preferably, the thickness of the reaction vessel wall is essentially unchanged along the reaction vessel axis  95 . 
     In one embodiment of the reaction vessel  90 , the inner wall  94  is disposed off-centered with respect to the reaction vessel axis  95 . For instance, the thickness of the reaction vessel wall is between about 0.1 mm to about 1 mm. Preferably, the thickness of the reaction vessel wall is thinner on one side than the other side by at least about 0.05 or 0.1 mm. 
     As discussed, bottom end of a suitable reaction vessel can be flat, curved or rounded. In one embodiment, the bottom end is disposed essentially symmetrically with respect to the reaction vessel axis. In another embodiment, the bottom end is disposed asymmetrically with respect to the reaction vessel axis. The bottom end may be closed and can include or consist of a plastic, ceramic or a glass. For some reactions, the reaction vessel may further include an immobilized DNA polymerase. Nearly any reaction vessel described herein can include a cap in sealing contact with the reaction vessel. 
     In embodiments where a reaction vessel is used with a thermal convection PCR centrifuge of the invention, relatively large forces will be generated by centrifugal rotation. Preferably, the channel and the reaction vessel will have a smaller diameter or width thus having a large vertical profile can be used. The diameter or width of the channel and the outer wall of the reaction vessel is at least about 0.4 mm to up to about 4 to 5 mm, and that of the inner wall of the reaction vessel is at least about 0.1 mm to up to about 3.5 to 4.5 mm. 
     Convection PCR Apparatus Comprising an Optical Detection Unit 
     It is objective of the invention to provide “optical detection” as an additional feature of the apparatus embodiments described herein. It is important to detect progress or results of the polymerase chain reaction (PCR) during or after the PCR reaction with speed and accuracy. The optical detection feature can be useful for such needs by providing apparatuses and methods for simultaneous amplification and detection of the PCR reaction. 
     In typical embodiments, a detectable probe that can generates an optical signal as a function of the amount of the amplified PCR product is introduced to the sample, and the optical signal from the detectable probe is monitored or detected during or after the PCR reaction without opening the reaction vessel. The detectable probe is typically a detectable DNA binding agent that changes its optical property depending on its binding or non-binding to DNA molecules or interaction with the PCR reaction and/or the PCR product. Useful examples of the detectable probe include, but not limited to, intercalating dyes having a property of binding to double-stranded DNA and various oligonucleotide probes having detectable label(s). 
     The detectable probe that can be used with the invention typically changes its fluorescence property such as its fluorescence intensity, wavelength or polarization, depending on the PCR amplification. For instance, intercalating dyes such as SYBR green 1, YO-PRO 1, ethidium bromide, and similar dyes generate fluorescence signal that is enhanced or activated when the dye binds to double-stranded DNA. Hence, fluorescence signal from such intercalating dyes can be detected to monitor the amount of the amplified PCR product. Detection using the intercalating dye is non-specific with regard to the sequence of the double-stranded DNA. Various oligonucleotide probes that can be used with the invention are known in the field. Such oligonucleotide probes typically have at least one detectable label and a nucleic acid sequence that can specifically hybridize to the amplified PCR product or the template. Hence, sequence-specific detection of the amplified PCR product, including allelic discrimination, is possible. The oligonucleotide probes are typically labeled with an interactive label pair such as a pair of two fluorescers or a pair of a fluorescer and a quencher whose interaction (such as “fluorescent resonance energy transfer” or “non-fluorescent energy transfer”) is enhanced as the distance between the two labels becomes shorter. Most of the oligonucleotide probes are designed such that the distance between the two interactive labels is modulated depending on its binding (typically a longer distance) or non-binding (typically a shorter distance) to a target DNA sequence. Such hybridization-dependent distance modulation results in change of the fluorescence intensity or change (increase or decrease) of the fluorescence wavelength depending on the amount of the amplified PCR product. In other types of the oligonucleotide probes, the probes are designed to undergo certain chemical reactions during the extension step of the PCR reaction, such as hydrolysis of the fluorescer label due to the 5′-3′ nuclease activity of a DNA polymerase or extension of the probe sequence. Such PCR reaction dependent changes of the probes lead to activation or enhancement of a fluorescence signal from the fluorescer so as to signal the change of the amount of the PCR product. 
     A variety of suitable detectable probes and devices for detecting such probes are described in the following U.S. Pat. Nos. 5,210,015; 5,487,972; 5,538,838; 5,716,784; 5,804,375; 5,925,517; 5,994,056; 5,475,610; 5,602,756; 6,028,190; 6,030,787; 6,103,476; 6,150,097; 6,171,785; 6,174,670; 6,258,569; 6,326,145; 6,365,729; 6,703,236; 6,814,934; 7,238,517, 7,504,241; 7,537,377; as well as non-US counterpart applications and patents. 
     As used herein, the phrase “optical detection unit” including plural forms means a device(s) for detecting PCR amplification that is compatible with one or more of the PCR thermal convection apparatuses and PCR methods disclosed herein. A preferred optical detection unit is configured to detect a fluorescence optical signal such as when a PCR amplification reaction is in progress. Typically, the device will provide for detection of the signal and preferably quantification thereof without opening at least one reaction vessel of the apparatus to which it is operably attached. If desired, the optical detection unit and one or more of the PCR thermal convection apparatuses of the invention can be configured to relate the amount of amplified nucleic acid in the reaction vessel (i.e., real-time or quantitative PCR amplification). A typical optical detection unit for use with the invention includes one or more of the following components in an operable combination: an appropriate light source(s), lenses, filters, mirrors, and beam-splitter(s) for detecting fluorescence typically in the visible region between from about 400 to about 750 nm. A preferred optical detection unit is positioned below, above and/or to the side of a reaction vessel sufficient to receive and output light for detecting PCR amplification within the reaction vessel. 
     An optical detection unit is compatible with a thermal convection PCR apparatus of the invention if it supports robust, sensitive and rapid detection of the PCR amplification for which the apparatus is intended. In one embodiment, the thermal convection PCR apparatus includes an optical detection unit that enables detection of an optical property of the sample in the reaction vessel. The optical property to be detected is preferably fluorescence at one or more wavelengths depending on the detectable probe used, although absorbance of the sample is sometimes useful to detect. When fluorescence from the sample is detected, the optical detection unit irradiates the sample (either a portion of, or entire sample) with an excitation light and detects a fluorescence signal from the sample. The wavelength of the excitation light is typically shorter than the fluorescence light. In the case of detecting absorbance, the optical detection unit irradiates the sample with a light (typically at a selected wavelength or with scanning the wavelength) and the intensity of the light before and after passing through the sample is measured. Fluorescence detection is generally preferred because it is more sensitive and specific to the target molecule to be detected. 
     Reference to the following figures and descriptions is intended to provide greater understanding of the thermal convection PCR apparatus comprising an optical detection unit for fluorescence detection. It is not intended and should not be read as limiting the scope of the present invention. 
     Referring to  FIGS. 80A-B , the apparatus embodiments feature one or more optical detection units  600 - 603  operable to detect a fluorescence signal from the sample in the reaction vessel  90  from the bottom end  92  of the reaction vessel  90  or the bottom end  72  of the channel  70 . Shown in  FIG. 80A  is an embodiment in which single optical detection unit  600  is used to detect fluorescence from multiple reaction vessels  90 . In this embodiment, a broad excitation beam (shown as upward arrows) is generated to irradiate multiple reaction vessels and a fluorescence signal (shown as downward arrows) from multiple reaction vessels  90  is detected. In this embodiment, a detector  650  (see  FIG. 83 , for instance) to be used for the fluorescence detection is preferably one that has an imaging capability so that the fluorescence signal from different reaction vessels can be distinguished from the fluorescence image. Alternatively, multiple detectors  650  each of which detects the fluorescence signal from each reaction vessel can be incorporated. 
     In the embodiment shown in  FIG. 80B , multiple optical detection units  601 - 603  are incorporated. In this embodiment, each optical detection unit irradiates the sample in each reaction vessel  90  with an excitation light and detects a fluorescence signal from each sample. This embodiment is advantageous in controlling the profile of the excitation beam for each reaction vessel more precisely and also measuring different fluorescence signal from different reaction vessels independently and simultaneously. This type of embodiment is also advantageous in constructing miniaturized apparatuses since larger optical elements and greater optical paths required for generating a broad excitation beam in the single optical detection unit embodiment can be avoided. 
     Again referring to  FIGS. 80A-B , when the optical detection unit  600 - 603  is located on the bottom end  92  of the reaction vessel  90 , the first heat source  20  comprises an optical port  610  for each channel  70  to provide a path for the excitation and emission light to the reaction vessel  70 . The optical port  610  may be a through hole or an optical element made of (partially or entirely) an optically transparent or semitransparent material such as glass, quartz or polymer materials having such optical property. If the optical port  610  is made as a though hole, the diameter or width of the optical port is typically smaller than that of the bottom end  72  of the channel  70  or the bottom end  92  of the reaction vessel  90 . In the embodiments shown in  FIGS. 80A-B , the bottom end  92  of the reaction vessel  90  also works as an optical port. Therefore, it is generally desirable to have all or at least the bottom end  92  of the reaction vessel  90  made of an optically transparent or semitransparent material. 
     Turning now to  FIGS. 81A-B , the apparatus embodiments feature single optical detection unit  600  ( FIG. 81A ) or multiple optical detection units  601 - 603  ( FIG. 81B ) that are located above the top end  91  of the reaction vessel  90 . Again, when a single optical detection unit  600  is incorporated ( FIG. 81A ), a broad excitation beam (shown as downward arrows) is generated to irradiate the multiple reaction vessels and a fluorescence signal (shown as upward arrows) from the multiple reaction vessels  90  is detected. When multiple optical detection units  601 - 603  ( FIG. 81B ) are incorporated, each optical detection unit irradiates the sample in each reaction vessel  90  with an excitation light and detects a fluorescence signal from each sample. 
     In the embodiments shown in  FIGS. 81A-B , a center part of a reaction vessel cap (not shown) that typically fits to the top end (opening)  91  of the reaction vessel  90  functions as an optical port for the excitation and emission light. Therefore, all or at least the center part of the reaction vessel cap is made of an optically transparent or semitransparent material. 
       FIG. 82  shows an apparatus embodiment that features optical detection units  600  that are located on the side of the reaction vessel  90 . In this particular embodiment, the optical port  610  is formed on the side of the second heat source  30 . Alternatively, the optical port  610  can be formed any one or more of the first  20 , second  30 , and third  40  heat sources, and the first  50  and second  60  insulators depending on the position of the fluorescence detection as required by particular application purposes. In this embodiment, a side part of the reaction vessel  90  and a portion of the first chamber  100  along the light path also function as optical port, and thus all or at least the parts of the reaction vessel  90  and the first chamber  100  are made of an optically transparent or semitransparent material. When the optical detection unit  600  is located on the side of the reaction vessel  90 , the channels  90  are typically formed in one or two arrays that are linearly or circularly arranged. Such arrangement of the channels  70  enables to detect a fluorescence signal from every channel  70  or reaction vessel  90  without interference by other channels. 
     In the embodiments described above, both excitation and fluorescence detection are performed from the same side with respect to the reaction vessel  90 , and thus both an excitation part and a fluorescence detection part are located on the same side, typically within a same compartment of an optical detection unit  600 - 603 . For instance, in the embodiments shown in  FIGS. 80A-B , the optical detection unit  600 - 603  that contains both parts is located on the bottom end  92  of the reaction vessel  90 . Similarly, entire optical detection unit is located above the top end  91  of the reaction vessel  90  in the embodiments shown in  FIGS. 81A-B , and on the side part of the reaction vessel  90  in the embodiment shown in  FIG. 82 . Alternatively, the optical detection unit  600 - 603  may be modified so that the excitation part and the fluorescence detection part are located separately. For instance, the excitation part is located on the bottom (or top) of the reaction vessel  90  and the fluorescence detection part is located on the top (bottom) or side part of the reaction vessel  90 . In other embodiments, the excitation part may be located on one side (e.g., left side) of the reaction vessel  90  and the fluorescence detection part may be located another side (e.g., top, bottom, right, front or back side; or a side part other than the excitation side). 
     The optical detection unit  600 - 603  typically comprises an excitation part that generates an excitation light with a selected wavelength and a fluorescence detection part that detects a fluorescence signal from the sample in the reaction vessel  90 . The excitation part typically comprises a combination of light sources, wavelength selection elements, and/or beam shaping elements. Examples of the light source include, but not limited to, arc lamps such as mercury arc lamps, xenon arc lamps, and metal-halide arc lamps, lasers, and light-emitting diodes (LED). The arc lamps typically generate multiple bands or broad bands of light, and the lasers and LEDs typically generate a monochromatic light or a narrow band light. The wavelength selection element is used to select an excitation wavelength from the light generated by the light source. Examples of the wavelength selection element includes a grating or a prism (for dispersing the light) combined with a slit or an aperture (for selecting a wavelength), and an optical filter (for transmitting a selected wavelength). The optical filter is generally preferred because it can effectively select specific wavelength with compact size and it is relatively cheap. Preferred optical filter is an interference filter having a thin-film coating that can transmit certain band of light (band-pass filter) or light having wavelength longer (long-pass filter) or shorter (short-pass filter) than certain cut-on value. Acoustic optical filters and liquid crystal tunable filters can be an excellent wavelength selection element since these types of filters can be electronically controlled to change the transmission wavelength with speed and accuracy in a compact size although relatively expensive. A colored filter glass can also be used as a wavelength selection element as a cheap replacement of, or in combination with other types of the wavelength selection element to enhance rejection of undesired light (e.g., IR, UV, or other stray light). Choice of the optical filter depends on the characteristics of the light generated by the light source and the wavelength of the excitation light as well as other geometric requirement of the apparatus such as the size. The beam shaping element is used to shape and guide the excitation beam. The beam shaping element can be any one or combination of lenses (convex or concave), mirrors (convex, concave, or elliptical), and prisms. 
     The fluorescence detection part typically comprises a combination of detectors, wavelength selection elements, and/or beam shaping elements. Examples of the detector include, but not limited to, photomultiplier tubes (PMT), photodiodes, charge-coupled devices (CCD), and video camera. The photomultiplier tubes are typically most sensitive. Therefore, when the sensitivity is the key issue due to very weak fluorescence signal, the photomultiplier tube can be a suitable choice. However, the photomultiplier tubes are not suitable if a compact size or an imaging capability is required (due to its large size). CCDs, silicon photodiodes, or video cameras intensified with, for example, a microchannel plate can have sensitivity similar to the photomultiplier tubes. If imaging of the fluorescence signal is not required and miniaturization is important as in the embodiments having an optical detection unit for each reaction vessel, photodiodes or CCDs with or without an intensifier can be a good choice since these elements are compact and relatively cheap. If imaging is required as in the embodiments having single optical detection unit for multiple reaction vessels, CCD arrays, photodiode arrays, or video cameras (also with or without an intensifier) can be incorporated. Similar to the excitation part, the wavelength selection element is used to select an emission wavelength from the light collected from the sample and the beam shaping element is used to shape and guide the emission light for efficient detection. Examples of the wavelength selection element and the beam shaping element are the same as those described for the excitation part. 
     In addition to the optical elements described above, the optical detection unit can comprise a beam-splitter. The beam-splitter is particularly useful if the excitation part and the fluorescence detection part are located on the same side with respect to the reaction vessel  90 . In such embodiments, the paths of the excitation and emission beams (along opposite directions) coincide with each other and thus it becomes necessary to separate the beam paths using a beam-splitter. Typically useful beam-splitters are dichroic beam-splitters or dichroic mirrors that have a thin-film interference coating similar to the thin-film optical filters. Typical beam-splitters reflect the excitation light and transmit the fluorescence light (a long-pass type), or vice versa (a short-pass type). 
     Referring now to  FIGS. 83-84, 85A -B, and  86 , a few design examples of structure of the optical detection unit  600  are described. 
     In  FIG. 83 , one embodiment of the optical detection unit  600  is illustrated. In this embodiment, excitation optical elements ( 620 ,  630 , and  640 ) are located along a direction at a right angle with respect to the channel axis  80 , and fluorescence detection optical elements ( 650 ,  655 ,  660 , and  670 ) are located along the channel axis  80 . A dichrocic beam-splitter  680  that transmits the fluorescence emission and reflects the excitation light (i.e., a long-pass type) is located around the middle. As typical, a light generated by the light source  620  is collected by an excitation lens  630  and filtered with an excitation filter  640  to select an excitation light with a desired wavelength. The selected excitation light is then reflected by a dichroic beam-splitter and irradiated to the sample. Fluorescence emission from the sample is collected by an emission lens  660  after passing through the dichroic beam-splitter  680  and an emission filter  670  to select an emission light with a desired wavelength. The fluorescence light thus collected is then focused to an aperture or slit  655  or to a detector  650  to measure the fluorescence signal. The function of the aperture or slit  655  is “spatial filtering” of the emission. Typically, the fluorescence light is focused on or near the aperture or slit  655  and thus a fluorescence image from certain (vertical) location of the sample is formed on the aperture or slit  655 . Such optical arrangement enables to collect a fluorescence signal efficiently from a certain limited location inside the sample (e.g., the annealing, extension or denaturation region) while rejecting light from other locations. Use of the aperture or slit  655  is optional depending on the type of the detectable probe used. If the fluorescence signal is subject to be generated from a specific region inside the sample, use of one or more of the aperture or slit  655  is preferred. If the fluorescence signal is subject to be generated regardless of the location inside the sample, use of the aperture or slit  655  may not be necessary or one having a larger opening may be used. 
     As shown in the embodiment depicted in  FIG. 84 , the optical detection unit  600  may be modified to position the excitation optical elements ( 620 ,  630 ,  640 ) along the channel axis  80  and the fluorescence detection optical elements ( 650 ,  655 ,  660 , and  670 ) along a direction at a right angle to the channel axis  80 . A dichrocic beam-splitter  680  useful for this type of embodiment is a short-pass type that transmits the excitation light and reflects the emission light. 
     The excitation lens  630  used in the embodiments shown in  FIGS. 83-84  can be replaced with a combination of more than one lenses or a combination of lenses and mirrors. When a combination of such optical elements is used, the first lens (typically a convex lens) is preferably located close to and in front of the light source in order to collect the excitation light efficiently. To further enhance the collection efficiency of the excitation light, a mirror (typically concave or elliptic) may be placed on the back side of the light source. When it is required to make the excitation beam large as in the embodiments having a single optical detection unit  600  for irradiating multiple reaction vessels  90 , a concave lens or a convex mirror may be used additionally to expand the excitation beam. In some embodiments, one or more of the optical elements (e.g., one or more of lenses or mirrors) may be placed other locations, e.g., between the reaction vessel  90  and the dichroic beam-splitter  680  or the excitation filter  640 . In other aspect, the excitation light is typically shaped to an essentially collinear beam so as to irradiate a larger volume of the sample(s). In some special applications such as when using a multi-photon excitation scheme, the excitation light may be tightly focused to a certain position inside the sample. 
     The emission lens  660  used in the embodiments shown in  FIGS. 83-84  can also be replaced with a combination of more than one lenses or a combination of lenses and mirrors. When a combination of such optical elements is used, the first lens (typically a convex lens) is preferably located close to the reaction vessel  90  (for instance, between the reaction vessel  90  and the dichroic beam-splitter  680  or the emission filter  670 ) in order to collect the fluorescence light more efficiently. In some embodiments, one or more of the optical elements (e.g., a lens or a mirror) may be placed other locations, e.g., between the reaction vessel  90  and the dichroic beam-splitter  680  or the emission filter  670 . 
       FIGS. 85A-B  show embodiments in which one lens  635  is used to shape both the excitation beam and the emission beam. Two examples of arranging the excitation optical elements ( 620  and  640 ) and the fluorescence detection optical elements ( 650 ,  655 , and  670 ) are shown. The excitation optical elements ( 620  and  640 ) are located along a direction at a right angle to the channel axis  80  in  FIG. 85A  and along the channel axis  80  in  FIG. 85B . This type of embodiments using a single lens is useful in miniaturizing the optical detection unit  600  such as in the embodiments of incorporating multiple optical detection units shown in  FIGS. 80B, 81B and 82 . 
       FIG. 86  shows one apparatus embodiment in which the optical detection unit  600  is located on the top side of the reaction vessel  90 . The arrangement of the optical elements depicted is the same as the embodiment shown in  FIG. 83 . Other types of the optical arrangements (e.g., those shown  FIGS. 84 and 85A -B) can also be incorporated. When the optical detection unit  600  (or the excitation or fluorescence detection part) is located on the top side of the reaction vessel  90 , the center part of the reaction vessel cap  690  functions as an optical port  610 . Therefore, as discussed, the reaction vessel cap  690  or at least the center part is preferably made of an optically transparent or semitransparent material in this type of embodiments. 
     Again referring to  FIG. 86 , the reaction vessel  90  and the reaction vessel cap  690  typically has a sealing relationship with each other in order to avoid an evaporative loss of the sample during the PCR reaction. In the reaction vessel embodiment shown in  FIG. 86 , the sealing relationship is made between an inner wall of the reaction vessel  90  and an outer wall of the reaction vessel cap  690 . Alternatively, the sealing relationship may be made between an outer wall of the reaction vessel  90  and an inner wall of the reaction vessel cap  690  or between a top surface of the reaction vessel  90  and a bottom surface of the reaction vessel cap  690 . In some embodiments, the reaction vessel cap  690  may be a thin-film adhesive tape that is optically transparent or semitransparent. In such embodiments, the sealing relationship is made between a top surface of the reaction vessel  90  and a bottom surface of the reaction vessel cap  690 . 
     The reaction vessel embodiments described above may not be optimal for all uses of the invention. For instance, and as shown in  FIG. 86 , it is typical that the sample meniscus (i.e., a water-air interface) is formed between the sample and the reaction vessel cap  690  (or an optical port part of the reaction vessel cap  690 ). In operation, water in the sample evaporates and condenses to the inner surface of the reaction vessel cap  690  (or an optical port part of the reaction vessel cap  690 ) due to the PCR reaction that involves a high temperature process. Such condensed water may, for some applications, interfere somewhat with the excitation beam and the fluorescence beam, particularly when the optical detection unit is positioned on the top side of the reaction vessel  90 . 
     The reaction vessel embodiments exemplified in  FIGS. 87A-B  provide another approach. As shown, a reaction vessel  90  and a reaction vessel cap  690  are designed to have an optical port  695  to contact the sample. A sample meniscus is formed higher than, or about the same height as the bottom surface  696  of the optical port  695 . Unlike the typical reaction vessel embodiments described above, the excitation beam and the fluorescence beam are transmitted directly from the optical port  695  to the sample or vice versa without passing through the air or any condensed water inside the reaction vessel  90 . Structural requirements for such embodiments are as follows: 
     Firstly, as shown  FIGS. 87A-B , the reaction vessel cap  690  has a sealing relationship with the upper part of the reaction vessel  90  and also with the optical port  695 . As discussed, the sealing between the reaction vessel  90  and the reaction vessel cap  690  can be made at an inner wall of the reaction vessel (as in  FIGS. 87A-B ) or at an outer wall or a top end  91  of the reaction vessel  90 . The sealing between the reaction vessel cap  690  and the optical port  695  can be made at a top surface  697  ( FIG. 87A ) or a side wall  699  ( FIG. 87B ) of the optical port  695 . Alternatively the reaction vessel cap  690  and the optical port  695  may be made as one body, preferably using a same or similar optically transparent or semitransparent material. 
     Additionally, the diameter or width of the optical port  695  (and also that of a wall of the reaction vessel cap  690  if that wall is located near or about the same height as the bottom surface  696  of the optical port  695 ) is made smaller than the diameter or width of a portion of the inner wall of the reaction vessel  90  that is located near or about the same height as the bottom surface  696  of the optical port  695 . Moreover, the bottom surface  696  of the optical port  695  is located lower than, or about the same height as the bottom of the inner part of the reaction vessel cap  690 . When these structural requirements are met, an open space  698  is provided between the inner wall of the reaction vessel  90  and the side part of the optical port  695 . Therefore, the sample can fill up a portion of the open space to form a sample meniscus above the bottom part  696  of the optical port  695  when the reaction vessel  90  is sealed with the reaction vessel cap  690  to make the bottom of the optical port contact the sample. 
     In  FIG. 88 , use of the optically non-interfering reaction vessel discussed above is exemplified. As discussed, the bottom  696  of the optical port  695  contacts the sample and the sample meniscus is formed above the bottom  696  of the optical port  695 . With an optical detection unit  600  located on the top end  91  of the reaction vessel  90 , the excitation beam and the fluorescence beam are transmitted directly from the optical port  695  to the sample or vice versa without passing through the air or any condensed water inside the reaction vessel  90 . Such optical structure can greatly facilitate the optical detection feature of the invention. 
     Convection PCR Apparatus Comprising a Nucleic Acid Separation Unit 
     It is a further object of the invention to provide at least one “nucleic acid separation” unit operably linked to the multi-stage thermal convection apparatus invention described herein (e.g., one, two, three or more of such units). As will be appreciated, it will often be important to separate the PCR amplified product(s) produced by the apparatus during or after the PCR reaction. In such embodiments, the additional feature of having the operably linked nucleic acid separation unit will assist identification, analysis and/or utilization of the amplified PCR product. Preferably, the nucleic acid separation can be performed as a function of size or size to charge ratio and/or in combination with optional optical detection of the separated product(s). The nucleic acid separation feature can be useful in embodiments that require simultaneous amplification and separation as well as identification of the PCR product(s). 
     In one embodiment, the multi-stage thermal convection PCR apparatus is a three-stage apparatus as described herein that includes an operably linked nucleic acid separation unit that can separate the amplified PCR product(s). Preferably, the nucleic acid separation unit separates the PCR product(s) as a function of size or size to charge ratio. Examples of the size-dependent nucleic acid separation unit include, but not limited to, a capillary electrophoresis unit, a gel electrophoresis unit, and other types of electrophoresis or chromatography units known in the field. 
     In another embodiment, the multi-stage thermal convection PCR apparatus is a three-stage apparatus as described herein that further comprises at least one operably linked optical detection unit for detecting the separated PCR product (e.g., one, two, three or more of such units). For most applications, the optical detection unit typically detects fluorescence, absorbance, or chemiluminescence from the PCR product as a function of elution time and/or as a function of position within the separation unit. 
     Examples of suitable nucleic acid separation units and/or optical detection units include, but not limited to those described in the following references: U.S. Pat. Nos. 4,865,707; 5,147,517; 5,384,024; 5,582,705; 5,597,468; 5,790,727; 6,017,434; and 7,361,259; as well as non-US counterpart applications and patents. See also Felhofer, J. L., et al., Electrophoresis, 31(15), pp. 2469-2486 (2010); Terabe, S., et al., Analytical Chemistry, 56, pp. 111-113 (1984); Jorgenson, J. W. and Lukacs, K. D., Science, 222, pp. 266-272 (1983); Hjerten, S., Journal of Chromatography 270, pp. 1-6 (1983); and Jorgenson, J. W. and Lukacs, K. D., Analytical Chemistry, 53(8), pp. 1298-1302 (1981). 
     In one embodiment in which the three-stage apparatus includes an operably linked optical detection unit, at least one detectable probe (e.g., one, two, three or more of such probes) that can generate an optical signal as a function of the amount of the PCR product is introduced to the sample during or after the PCR reaction, and the optical signal from the detectable probe is monitored or detected during or after the nucleic acid separation. The detectable probe is typically a detectable label that generates a fluorescence, absorbance or chemiluminescence signal, or a detectable DNA binding agent that generates an optical signal or changes its optical property depending on its binding or non-binding to, or interaction with the PCR product. Useful examples of the detectable probe include, but not limited to, detectable labels that can be incorporated into the primers or PCR products, intercalating dyes having a property of binding to double-stranded DNA, and various oligonucleotide probes having detectable label(s). Suitable detectable probes include, but are not limited to the following U.S. Pat. Nos. 5,210,015; 5,487,972; 5,538,838; 5,716,784; 5,804,375; 5,925,517; 5,994,056; 5,475,610; 5,602,756; 6,028,190; 6,030,787; 6,103,476; 6,150,097; 6,171,785; 6,174,670; 6,258,569; 6,326,145; 6,365,729; 6,703,236; 6,814,934; 7,238,517; 7,504,241; and 7,537,377; as well as non-US counterpart applications and patents. 
     The optical detection unit may be used to determine the size of one or more of the PCR products or in some embodiments to determine a partial or whole nucleic acid sequence of the PCR product. When the sequence of the PCR product is to be determined, the PCR reaction may be terminated by adding a termination agent such as dideoxynucleotide triphosphates (ddNTPs). 
     Thus in a particular invention embodiment, the multi-stage thermal convention apparatus is a three-stage apparatus as described herein that further includes as operably linked components, a suitable nucleic acid separation unit and an optical detection unit. In use, the three-stage apparatus with the operably linked nucleic acid separation and optical detection units may be used in conjunction with an appropriate detectable probe for monitoring or detecting amplification during or after the PCR reaction. 
     Convection PCR Apparatus Comprising a Sequence-Specific Detection Unit 
     It is a further object of the invention to provide “sequence-specific detection” as an additional feature of the multi-stage thermal convection apparatus embodiments described herein such as the three-stage apparatus. For some applications, it will be important to detect the PCR product(s) in a sequence-specific manner, for instance, in embodiments in which a user wishes to have accurate identification of target amplicon(s) and/or elimination of false amplicon(s) during or after a PCR reaction. The sequence-specific detection feature can be useful for such needs by providing apparatuses and methods for simultaneous amplification and sequence-specific detection of the PCR product(s) during or after the PCR reaction. 
     In one embodiment, the multi-stage thermal convection PCR apparatus is a three-stage apparatus as described herein that includes at least one operably linked sequence-specific detection unit (e.g., one, two, three or more of such units). The sequence-specific detection unit typically comprises one or more hybridization chips such as DNA chip, for example, one, two, three, four or more of such hybridization chips. The hybridization chip typically comprises at least one oligonucleotide probe that is immobilized on a solid substrate (e.g., less than several hundreds of such oligonucleotide probes such as one, two, three, four or more of such oligonucleotide probes). In preferred embodiments, the hybridization chip comprises two or more oligonucleotide probes with each probe immobilized at a different location on a suitable solid substrate. The oligonucleotide probe typically has a nucleic acid sequence that can specifically hybridize to at least one of the PCR products. Hence, sequence-specific detection of the amplified PCR product, including allelic discrimination, is possible. 
     In some embodiments, the hybridization chip may be located inside of the reaction vessel described above, preferably in contact with the PCR reaction mixture. In such embodiments, the hybridization chip may be a separate unit that can be introduced into the reaction vessel, or it can be a part of the reaction vessel. The hybridization chip may be located anywhere inside of the reaction vessel, for instance, the side, bottom or top part of the reaction vessel. In preferred embodiments, the hybridization chip is located at the bottom of the inside of the reaction vessel or at the bottom side of the reaction vessel cap  690 , e.g., the bottom end  696  of the optical port  695  as shown in  FIGS. 87A-B  and  88 . 
     In other embodiments, the sequence-specific detection unit including the hybridization chip may be located outside the reaction vessel as a separate unit. 
     In other embodiments, the multi-stage thermal convection PCR apparatus is a three-stage apparatus that further includes the operably linked optical detection unit for detecting hybridization of the PCR product on the hybridization chip. The optical detection unit typically detects a fluorescence, absorbance or chemiluminescence signal from the hybridized PCR product as a function of position within the hybridization chip. In a particular embodiment, the optical detection unit has a capability of capturing an image of the hybridization chip. 
     Examples of suitable hybridization chips and/or optical detection units include, but not limited to those described in the following references: U.S. Pat. Nos. 5,445,934; 5,545,531; 5,744,305; 5,837,832; 5,861,242; 6,579,680; and 7,879,541; as well as non-US counterpart applications and patents. See also PCT Publication Nos. WO 2006/082035; and WO 2012/080339; and Maskos, U. and Southern, E. M., Nucleic Acids Research, 20(7), pp. 1679-1684 (1992). 
     In one embodiment, a detectable probe that can generate an optical signal as a function of the amount of the hybridized PCR product is introduced to the sample during or after the PCR reaction, and the optical signal from the detectable probe is monitored or detected after hybridization to the hybridization chip. The detectable probe is typically a detectable label that generates a fluorescence, absorbance or chemiluminescence signal, or a detectable DNA binding agent that generates an optical signal or changes its optical property depending on its binding or non-binding to, or interaction with the hybridized PCR product. Useful examples of the detectable probe include, but not limited to, detectable labels that can be incorporated into the primers or PCR products, intercalating dyes having a property of binding to double-stranded DNA, and various oligonucleotide probes having detectable label(s). Suitable detectable probes and labels have been described above. 
     In a particular embodiment, the structure of the optical detection unit can be the same as or operably similar to any one of the structures depicted in  FIGS. 80A-B ,  81 A-B,  82 - 84 ,  85 A-B, and  88 . In another particular embodiment, the detector  650  has an imaging capability. 
     The following examples are given for purposes of illustration only in order that the present invention may be more fully understood. These examples are not intended to limit in any way the scope of the invention unless otherwise specifically indicated. 
     EXAMPLES 
     Materials and Methods 
     Three different DNA polymerases purchased from Takara Bio (Japan), Finnzymes (Finland), and Kapa Biosystems (South Africa) were used to test PCR amplification performance of various invention apparatuses. Plasmid DNAs comprising various insert sequences, human genome DNA, and cDNA were used as template DNAs. The plasmid DNAs were prepared by cloning insert sequences with different size into pcDNA3.1 vector. The human genome DNA was prepared from a human embryonic kidney cell (293, ATCC CRL-1573). The cDNA was prepared by reverse transcription of mRNA extracts from HOS or SV-OV-3 cells. 
     Composition of the PCR mixture was as follows: a template DNA with different amount depending on experiments, about 0.4 μM each of a forward and reverse primer, about 0.2 mM each of dNTPs, about 0.5 to 1 units of DNA polymerase depending on DNA polymerase used, about 1.5 mM to 2 mM of MgCl 2  mixed in a total volume of 20 μL using a buffer solution supplied by each manufacturer. 
     The reaction vessel was made of polypropylene and had structural features as depicted in  FIG. 51A . The reaction vessel had a tapered cylindrical shape with its bottom end closed and comprised a cap that fits with the inner diameter of the top end of the reaction vessel so as to seal the reaction vessel after introduction of a PCR mixture. The reaction vessel was (linearly) tapered from the top to the bottom end so that the upper part had a larger diameter. The taper angle as defined in  FIG. 51A  was about 4°. The bottom end of the reaction vessel was made flat in order to facilitate heat transfer from the receptor hole in the first heat source. The reaction vessel had a length from the top end to the bottom end of about 22 mm to about 24 mm, an outer diameter at the bottom end of about 1.5 mm, an inner diameter at the bottom end of about 1 mm, and a wall thickness of about 0.25 mm to about 0.3 mm. 
     Volume of the PCR mixture used for each reaction was 20 μL. The PCR mixture with 20 μL volume produced a height of about 12 to 13 mm inside the reaction vessel. 
     All the apparatuses used in the examples below were made operable with a DC power. A rechargeable Li +  polymer battery (12.6 V) or a DC power supply was used to operate the apparatus. The apparatuses used in the examples had 12 (3×4), 24 (4×6), or 48 (6×8) channels that were arranged in an array format with multiple rows and columns as exemplified in  FIG. 39 . The spacing between adjacent channels was made as 9 mm. In the experiments, the reaction vessel(s) containing the PCR mixture sample was introduced into the channel(s) after the three heat sources of the apparatus were heated to desired temperatures. The PCR mixture sample was removed from the apparatus after a desired PCR reaction time and analyzed with agarose gel electrophoresis using ethidium bromide (EtBr) as a fluorescent dye for visualizing amplified DNA bands. 
     Example 1. Thermal Convection PCR Using the Apparatus of FIG.  12 A 
     The apparatus used in this example had the structure shown in  FIG. 12A  comprising a channel  70 , a first chamber  100 , a first thermal brake  130 , a receptor hole  73 , a through hole  71 , protrusions  33 ,  34  of the second heat source  30 , and protrusions  23 ,  24  of the first heat source  20 . The length of the first, second and third heat sources along the channel axis  80  were about 4 mm, about 5.5 mm, and about 4 mm, respectively. The first and second insulators (or insulating gaps) had a length along the channel axis  80  near the channel region (i.e., within the protrusion region) of about 2 mm and about 0.5 mm, respectively. The length of the first and second insulators along the channel axis  80  outside the channel region (i.e., outside the protrusion region) was about 6 mm to about 3 mm (depending on position) and about 1 mm, respectively. The first chamber  100  was located on the upper part of the second heat source  30  and had a cylindrical shape with a length along the channel axis  80  of about 4.5 mm and a diameter of about 4 mm. The first thermal brake  130  was located on the bottom of the second heat source  30  and had a length or thickness along the channel axis  80  of about 1 mm with the wall  133  of the first thermal brake contacting the whole circumference of the channel  70  or the reaction vessel  90 . The depth of the receptor hole  73  along the channel axis  80  was varied between from about 1.5 mm to about 3 mm. In this apparatus, the channel  70  was defined by the through hole  71  in the third heat source  40 , the wall  133  of the first thermal brake  130  in the second heat source  30 , and the receptor hole  73  in the first heat source  20 . The channel  70  had a tapered cylinder shape. Average diameter of the channel was about 2 mm with the diameter at the bottom end (in the receptor hole) being about 1.5 mm. In this apparatus, all the temperature shaping elements including the first chamber, the first thermal brake, the receptor hole, the first and second insulators, and the protrusions were disposed symmetrically with respect to the channel axis. 
     As presented below, the apparatus used in this example having the structure shown in  FIG. 12A  was found to be efficient enough to amplify from a 10 ng human genome sample (about 3,000 copies) in about 25 to about 30 min without the gravity tilting angle. For a 1 ng plasmid sample, PCR amplification resulted in a detectable amplification in as little as about 6 or 8 min. Hence, this is a good demonstrating example of a symmetric heating structure that can provide an efficient PCR amplification without using the gravity tilting angle. As presented in Example 2, this structure also works better when the gravity tilting angle is introduced. However, a small tilting angle (about 10° to 20° or smaller) can be sufficient for most applications. 
     1.1. PCR Amplification from Plasmid Samples 
       FIGS. 53A-C  show PCR amplification results obtained from a 1 ng plasmid DNA template using the three different DNA polymerases (from Takara Bio, Finnzymes, and Kapa Biosystems, respectively) described above. The expected size of the amplicon was 373 bp. The forward and reverse primers used were 5′-TAATACGACTCACTATAGGGAGACC-3′ (SEQ ID NO: 1) and 5′-TAGAAGGCACAGTCGAGGCT-3′ (SEQ ID NO: 2), respectively. In  FIGS. 53A-C , the left most lane shows DNA size marker (2-Log DNA Ladder (0.1-10.0 kb) from New England BioLabs) and lanes 1 to 5 are results obtained with the thermal convection PCR apparatus at PCR reaction time of 10, 15, 20, 25, and 30 min, respectively, as denoted on the bottom of each Figure. The temperatures of the first, second and third heat sources of the invention apparatus were set to 98° C., 70° C., and 54° C., respectively. Depth of the receptor hole along the channel axis was about 2.8 mm. Lane 6 (denoted as C on the bottom) is a result from a control experiment obtained using T1 Thermocycler from Biometra. The same PCR mixture containing the same amount of the plasmid template was used in the control experiment. Total PCR reaction time of the control experiment including pre-heating (5 min) for hot starting and final extension (10 min) was about 1 hour and 30 min. As shown in  FIGS. 53A-C , the thermal convection apparatus yielded an amplified product at the same size as the control experiment, but in much shorter PCR reaction time (i.e., about 3 to 4 times shorter). PCR amplification reached a detectable level at about 10 to 15 min and became saturated in about 20 or 25 min. As manifested, the three DNA polymerases were found to be nearly equivalent to use with the thermal convection PCR apparatus. 
       FIGS. 54A-C  show further examples of thermal convection PCR. The temperatures of the first, second and third heat sources were set to 98° C., 70° C., and 54° C., respectively. Depth of the receptor hole along the channel axis was about 2.8 mm.  FIGS. 54A-C  are results obtained for amplification from three different plasmid DNA templates with amplicon size of 177 bp, 960 bp, and 1,608 bp, respectively. Amount of the template plasmid used for each reaction was 1 ng. The forward and reverse primers used had the sequences as set forth in SEQ ID NOs: 1 and 2, respectively. As shown, even larger amplicons (about 1 kbp and 1.6 kbp) were amplified in very short reaction time, i.e., to a detectable level in about 20 min and to a saturation level in about 30 min. The short amplicon (177 bp) was amplified in a much shorter reaction time, i.e., to a detectable level in about 10 min and to a saturation level in about 20 min. 
       FIG. 55  shows results of thermal convection PCR amplification obtained from various different plasmid templates with amplicon size between about 200 bp to about 2 kbp. The temperatures of the first, second and third heat sources were set to 98° C., 70° C., and 54° C., respectively. Depth of the receptor hole along the channel axis was about 2.8 mm. Amount of the template plasmid used for each reaction was 1 ng. The forward and reverse primers used had the sequences as set forth in SEQ ID NOs: 1 and 2, respectively. The expected size of the amplicon was 177 bp for lane 1; 373 bp for lane 2; 601 bp for lane 3; 733 bp for lane 4; 960 bp for lane 5; 1,608 bp for lane 6; and 1,966 bp for lane 7. PCR reaction time was 25 min for lanes 1-6 and 30 min for lane 7. As shown, nearly saturated product bands were observed for all amplicons in a short reaction time. This result demonstrates that thermal convection PCR is not only fast and efficient, but also has a wide dynamic range. 
     1.2. Acceleration of PCR Amplification at Elevated Denaturation Temperature 
     The results shown in  FIGS. 56A-C  demonstrate acceleration of the thermal convection PCR at elevated denaturation temperatures. The template used was 1 ng plasmid that can yield a 373 bp amplicon. Except for the denaturation temperature, all other experimental conditions including the template and primers used were the same as those used for the experiments presented in  FIGS. 53A-C . While the temperatures of the second and third heat sources were set to 70° C. and 54° C., respectively, the temperature of the first heat source was increased to 100° C. ( FIG. 56A ), 102° C. ( FIG. 56B ), and 104° C. ( FIG. 56C ). As shown in  FIGS. 56A-C , increase of the denaturation temperature (i.e., the temperature of the first heat source) resulted in acceleration of PCR amplification. The 373 bp product was barely observable at 8 min reaction time when the denaturation temperature was 100° C. ( FIG. 56A ), and it became stronger at the same 8 min reaction time when the denaturation temperature was increased to 102° C. ( FIG. 56B ). When the denaturation temperature was further increased to 104° C. ( FIG. 56C ), the 373 bp product became observable even at 6 min reaction time. 
     1.3. PCR Amplification from Human Genome and cDNA Samples 
       FIGS. 57A-C  show three examples of thermal convection PCR for amplification from a human genome sample. The temperatures of the first, second and third heat sources were set to 98° C., 70° C., and 54° C., respectively. Depth of the receptor hole along the channel axis was about 2.8 mm. Amount of the human genome template used for each reaction was 10 ng corresponding to about 3,000 copies only.  FIG. 57A  shows results for amplification of a 363 bp segment of β-globin gene. The forward and reverse primers used for this sequence were 5′-GCATCAGGAGTGGACAGAT-3′ (SEQ ID NO: 3) and 5′-AGGGCAGAGCCATCTATTG-3′ (SEQ ID NO: 4), respectively.  FIG. 57B  shows results for amplification of a 469 bp segment of GAPDH gene. The forward and reverse primers used in this experiment were 5′-GCTTGCCCTGTCCAGTTAA-3′ (SEQ ID NO: 5) and 5′-TGACCAGGCGCCCAATA-3′ (SEQ ID NO: 6), respectively.  FIG. 57C  shows results for amplification of a 514 bp segment of β-globin gene. The forward and reverse primers used in this experiment were 5′-TGAAGTCCAACTCCTAAGCCA-3′ (SEQ ID NO: 7) and 5′-AGCATCAGGAGTGGACAGATC-3′ (SEQ ID NO: 8), respectively. 
     As shown in  FIGS. 57A-C , the thermal convection PCR from about 3,000 copies of human genome samples yielded amplicons with correct size in very short reaction time. The PCR amplification reached a detectable level in about 20 or 25 min and became saturated in about 25 or 30 min. These results demonstrate that the thermal convection PCR is fast and very efficient for amplifying from low copy number samples. 
       FIG. 58  shows further examples of thermal convection PCR amplification from 10 ng human genome or cDNA samples. PCR reaction time was 30 min. All other experimental conditions were the same as those used for the experiments presented in  FIGS. 57A-C . As shown, all fourteen gene segments with their size ranging from about 100 bp to about 800 bp were successfully amplified in 30 min reaction time. Target genes and corresponding primer sequences are summarized in Table 2 below. Templates used were human genome DNA (10 ng) for lanes 1, 3-5, and 9-14; and cDNA (10 ng) for lanes 2, 6, 7, and 8. The cDNA samples were prepared by reverse transcription of mRNA extracts from HOS (lanes 2 and 7) or SK-OV-3 (lanes 6 and 8) cells. 
     
       
         
           
               
             
               
                 TABLE 2 
               
             
            
               
                   
               
               
                 Primer Sequences and Target Genes Used for the Experiments in FIG. 58 
               
            
           
           
               
               
               
               
               
            
               
                 Lane 
                 Target 
                 Amplicon 
                 SEQ ID 
                   
               
               
                 No. 
                 Gene 
                 Size 
                 NO 
                 Primer Sequence 
               
               
                   
               
            
           
           
               
               
               
               
               
            
               
                 1 
                 PRPS1 
                  99 bp 
                 9 
                 5′-GATCTATTTGGCCTCTCAAA-3′ 
               
               
                   
                   
                   
                 10 
                 5′-CACACAGGTACACACACTTTATT-3′ 
               
               
                   
               
               
                 2 
                 p53 
                 123 bp 
                 11 
                 5′-TGCCCAACAACACCAGC-3′ 
               
               
                   
                   
                   
                 12 
                 5′-CCAAGGCCTCATTCAGCTC-3′ 
               
               
                   
               
               
                 3 
                 NAIP 
                 132 bp 
                 13 
                 5′-TGCCACTGCCAGGCAATCTAA-3′ 
               
               
                   
                 Exon5 
                   
                 14 
                 5′-CATTTGGCATGTTCCTTCCAAG-3′ 
               
               
                   
               
               
                 4 
                 p53 
                 152 bp 
                 15 
                 5′-GAAGACCCAGGTCCAGAT-3′ 
               
               
                   
                   
                   
                 16 
                 5′-CTGCCCTGGTAGGTTTTC-3′ 
               
               
                   
               
               
                 5 
                 CYP27B1 
                 168 bp 
                 17 
                 5′-GACAAGGTGAGAGGAGC-3′ 
               
               
                   
                   
                   
                 18 
                 5′-TTAGCTGGACCTCGTCTC-3′ 
               
               
                   
               
               
                 6 
                 HER2 
                 192 bp 
                 19 
                 5′-AGCACTGGGGAGTCTTTGT-3′ 
               
               
                   
                   
                   
                 20 
                 5′-GGGACAGTCTCTGAATGGGT-3′ 
               
               
                   
               
               
                 7 
                 CDK4 
                 284 bp 
                 21 
                 5′-GGTGTTTGAGCATGTAGACCA-3′ 
               
               
                   
                   
                   
                 22 
                 5′-GAACTTCGGGAGCTCGGTA-3 
               
               
                   
               
               
                 8 
                 CD24 
                 330 bp 
                 23 
                 5′-TCCAAGCACCCAGCATC-3′ 
               
               
                   
                   
                   
                 24 
                 5′-TGGGGAAATTTAGAAGACGTTTCTTG-3′ 
               
               
                   
               
               
                 9 
                 β-globin 
                 363 bp 
                 3 
                 5′-GCATCAGGAGTGGACAGAT-3′ 
               
               
                   
                   
                   
                 4 
                 5′-AGGGCAGAGCCATCTATTG-3′ 
               
               
                   
               
               
                 10 
                 CR2 
                 402 bp 
                 25 
                 5′-AGGTTGGGGTCTTGCCT-3′ 
               
               
                   
                   
                   
                 26 
                 5′-CACCTGTGCTAGACGGTG-3′ 
               
               
                   
               
               
                 11 
                 PIGR 
                 433 bp 
                 27 
                 5′-GCCACCTACTACCCAGAGG-3′ 
               
               
                   
                   
                   
                 28 
                 5′-TGATGGTCACCGTTCTGC-3′ 
               
               
                   
               
               
                 12 
                 GAPDH 
                 469 bp 
                 5 
                 5′-GCTTGCCCTGTCCAGTTAA-3′ 
               
               
                   
                   
                   
                 6 
                 5′-TGACCAGGCGCCCAATA-3′ 
               
               
                   
               
               
                 13 
                 β-globin 
                 514 bp 
                 7 
                 5′-TGAAGTCCAACTCCTAAGCCA-3′ 
               
               
                   
                   
                   
                 8 
                 5′-AGCATCAGGAGTGGACAGATC-3′ 
               
               
                   
               
               
                 14 
                 β-globin 
                 830 bp 
                 3 
                 5′-GCATCAGGAGTGGACAGAT-3′ 
               
               
                   
                   
                   
                 29 
                 5′-GGAGAAGATATGCTTAGAACCGA-3′ 
               
               
                   
               
               
                 Abbreviations used in Table 2 are as follows. PRPS1: phosphoribosyl pyrophosphate synthetase 1; NAIP: NLR family, apoptosis inhibitory protein; CYP27B1: cytochrome P450, family 27, subfamily B, polypeptide 1; HER2: ERBB2, v-erb-b2 erythroblastic leukemia viral oncogene homolog 2; CDK4: cyclin-dependent kinase 4; CR2: complement receptor 2; PIGR: polymeric 
               
               
                 immunoglobulin receptor; GAPDH: glyceraldehydes 3-phosphate dehydrogenase. 
               
            
           
         
       
     
     1.4. PCR Amplification from Very Low Copies of Human Genome Sample 
       FIG. 59  shows PCR amplification from very low copy number samples using the invention apparatus. Template sample used was human genome DNA extracted from 293 cells. Primers used for this experiment had the sequences as set forth in SEQ ID NOs: 3 and 4. Target sequence was a 363 bp segment of β-globin. PCR reaction time was 30 min. All other experimental conditions including the temperatures of the three heat sources and the depth of the receptor hole were the same as those used for the experiments presented in  FIGS. 57A-C  and  58 . As denoted on the bottom of  FIG. 59 , amount of the human genome sample used for each reaction was decreased consecutively, starting from 10 ng (about 3,000 copies) to 1 ng (about 300 copies), 0.3 ng (about 100 copies), and 0.1 ng (about 30 copies). As manifested, the thermal convection PCR yielded successful PCR amplification from as little as a 30 copy sample. Single copy samples were also examined for thermal convection PCR amplification. It was found that amplification from a single copy sample was successful with about 30 to 40% probability, likely due to statistical probability associated with chance of sampling a single copy. 
     1.5. Temperature Stability and Power Consumption of the Invention Apparatus 
     Temperature stability and power consumption of the invention apparatus having the structure shown in  FIG. 12A  were tested. The apparatus used in this experiment had 12 channels (3×4) disposed 9 mm apart from each other as shown in  FIGS. 39 and 42 . The first, second and third heat sources were each equipped with a NiCr heating wire ( 160   a - c ) that was disposed in between the channels as shown in  FIG. 42 . The apparatus also comprised a fan above the third heat source to provide cooling to the third heat source when needed. DC power from a rechargeable Li +  polymer battery (12.6 V) was supplied to each heating wire and controlled by PID (proportional-integral-derivative) control algorism so as to maintain the temperature of each of the three heat sources at a pre-set target value. 
       FIG. 60  shows temperature variations of the first, second and third heat sources when target temperatures were set to 98° C., 70° C., and 54° C., respectively. The ambient temperature was about 25° C. As shown, the three heat sources reached the target temperatures within less than about 2 min. During about 40 min time span after reaching the target temperatures, the temperatures of the three heat sources were maintained stably and accurately at the target temperatures. Average of the temperature of each heat source during the 40 min time span was within about ±0.05° C. with respect to each target temperature. Temperature fluctuations were also very small, i.e., standard deviation of the temperature of each heat source was within about ±0.05° C. 
       FIG. 61  shows power consumption of the invention apparatus having 12 channels. As shown, the power consumption was high in the initial time period (i.e., up to about 2 min) in which rapid heating to the target temperatures took place. After the three heat sources reached the target temperatures (i.e., after about 2 min), the power consumption was reduced to lower values. The large fluctuations observed after about 2 min are result of active control of the power supply to each heat source. Due to such active power control, the temperatures of the three heat sources can be maintained stably and accurately at the target temperatures as shown in  FIG. 60 . Average of the power consumption in the temperature maintaining region (i.e., after about 2 min) was about 4.3 W as denoted in  FIG. 61 . Therefore, power consumption per each channel or each reaction was less than about 0.4 W. Since about 30 min or less time is sufficient for PCR amplification in the invention apparatus, energy cost for completion of one PCR reaction is only about 700 J or less as is equivalent to energy needed to heat up about 2 mL water from room temperature to about 100° C. one time. 
     Invention apparatuses having 24 and 48 channels were also tested. Average power consumption was about 7 to 8 W for the 24 channel apparatus and about 9 to 10 W for the 48 channel apparatus. Hence, power consumption per each PCR reaction was found to be even less for lager apparatuses, i.e., about 0.3 W for the 24 channel apparatus and about 0.2 W for the 48 channel apparatus. 
     Example 2. Thermal Convection PCR Using the Apparatus of FIG.  12 B 
     In this example, effect of the gravity tilting angle θ g  to the thermal convection PCR was examined. The apparatus used in this example had the same structure and dimensions as that used in Example 1 except for incorporation of the gravity tilting angle θ g  as defined in  FIG. 12B . The apparatus was equipped with an inclined wedge on the bottom so that the channel axis was tilted by θ g  with respect to the direction of gravity. 
     As presented below, introduction of the gravity tilting angle caused the convective flow faster and thus accelerated the thermal convection PCR. It was therefore confirmed that a structural element such as a wedge or leg, or an inclined or tilted channel that can impose a gravity tilting angle to the apparatus or the channel is a useful structural element in constructing an efficient and fast thermal convection PCR apparatus. 
     2.1. PCR Amplification from Plasmid Sample 
       FIGS. 62A-E  show results of thermal convection PCR as a function of the gravity tilting angle for amplification from a plasmid sample. The temperatures of the first, second and third heat sources were set to 98° C., 70° C., and 54° C., respectively. Depth of the receptor hole along the channel axis was about 2.8 mm. Amount of the template plasmid used for each reaction was 1 ng. The primers used had the sequences as set forth in SEQ ID NOs: 1 and 2. The expected size of the amplicon was 373 bp.  FIG. 62A  shows results obtained at zero gravity tilting angle.  FIGS. 62B-E  show results obtained at θ g  equal to 10°, 20°, 30°, and 45°, respectively. At zero gravity tilting angle ( FIG. 62A ), the amplified product was barely observable at 15 min reaction time and became strong at 20 min. In contrast, the amplified product was observable with a significant intensity at 10 min reaction time when the gravity tilting angle of 10° was introduced ( FIG. 62B ). Further increase of the product band intensity at 10 and/or 15 min reaction time was observed as the gravity tilting angle was increased to 20° ( FIG. 62C ). Above 20° tilting angle ( FIGS. 62D-E ), amplification speed was observed to be similar to that observed at 20°. 
     2.2. PCR Amplification from Human Genome Sample 
       FIGS. 63A-D  show another example that demonstrates the effect of the gravity tilting angle. In this experiment, a 10 ng human genome sample (about 3,000 copies) was used as a template DNA and primers having the sequences as set forth in SEQ ID NOs: 3 and 4 were used. A 363 bp segment of β-globin gene was the target. Other experimental conditions were the same as those used for the experiment presented in  FIGS. 62A-E  above.  FIGS. 63A-D  show results obtained when θ g  was set to 0°, 10°, 20°, and 30°, respectively. As shown, the thermal convection PCR was accelerated when the gravity tilting angle was introduced (i.e.,  FIGS. 63B-D  as compared to  FIG. 63A ). Speed of the PCR amplification was observed to increase as the gravity tilting angle increased. Similar amplification speed was observed at 20° ( FIG. 63C ) and 30° ( FIG. 63D ). 
       FIGS. 64A-B  show a further example in which primers having high melting temperatures (above 60° C.) were used. In this experiment, a 10 ng human genome sample (about 3,000 copies) was used as a template DNA. The forward and reverse primers used had sequences 5′-GCTTCTAGGCGGACTATGACTTAGTTGCG-3′ (SEQ ID NO: 30) and 5′-CCAAAAGCCTTCATACATCTCAAGTTGGGGG-3′ (SEQ ID NO: 31), respectively. The amplification target was a 521 bp segment of β-actin gene. The temperatures of the first, second and third heat sources were set to 98° C., 74° C., and 64° C., respectively. Depth of the receptor hole along the channel axis was about 2.8 mm. The PCR reaction time was set to 30 min and experiment was performed with duplicate samples (lanes 1 and 2) for each tilting angle.  FIGS. 64A  and B show results obtained at θ g =0° and 20°, respectively. As shown, no significant amplification was observed at 0° for both PCR samples ( FIG. 64A ). In contrast, strong product bands were observed when 20° tilting angle was introduced ( FIG. 64B ). Compared to the experiments presented in  FIGS. 63A-D , the temperatures of the third and second heat sources were increased by 10° C. and 4° C., respectively, while the temperature of the first heat source was the same. Hence, the thermal convection was slowed down due to the reduced temperature difference between the heat sources. Without using the gravity tilting angle ( FIG. 64A ), the thermal convection PCR became too slow, not enabling fast PCR amplification. However, by introducing the gravity tilting angle ( FIG. 64B ), the thermal convection PCR became sufficiently fast and efficient to yield strong product bands from a low copy human genome sample (about 3,000 copies) in a short reaction time. 
     2.3. PCR Amplification from Very Low Copies of Human Genome Sample 
       FIG. 65  shows results of thermal convection PCR amplification from very low copy human genome samples when the gravity tilting angle was used. The primers used were the same as those used for the experiments presented in  FIGS. 64A-B . Hence, the amplification target was a 521 bp segment of β-actin gene. The temperatures of the first, second and third heat sources were set to 98° C., 74° C., and 60° C., respectively. Depth of the receptor hole along the channel axis was about 2.5 mm. The gravity tilting angle was set to 10° and the PCR reaction time was set to 30 min. As shown in  FIG. 65 , the thermal convection PCR yielded successful PCR amplification from as little as a 30 copy sample. 
     Example 3. Thermal Convection PCR Using the Apparatus of FIG.  14 C 
     The apparatus used in this example had the structure shown in  FIG. 14C  comprising a channel  70 , a first chamber  100 , a second chamber  110 , a first thermal brake  130 , a receptor hole  73 , and a through hole  71 . No protrusion structures were used in this apparatus. The length of the first, second and third heat sources along the channel axis  80  were about 5 mm, about 4 mm, and about 5 mm, respectively. The first and second insulators (or insulating gaps) had a length along the channel axis  80  of about 2 mm and about 1 mm, respectively. The first chamber  100  was located on the upper part of the second heat source  30  and had a cylindrical shape with a length along the channel axis  80  of about 3 mm and a diameter of about 4 mm. The first thermal brake  130  was located on the bottom of the second heat source  30  and had a length or thickness along the channel axis  80  of about 1 mm with the wall  133  of the first thermal brake  130  contacting the whole circumference of the channel  70  or the reaction vessel  90 . The second chamber  110  was located on the bottom part of the third heat source  40  and had a cylindrical shape with a diameter of about 4 mm. The length of the second chamber  110  along the channel axis  80  was varied between from about 1.5 mm to about 0.5 mm depending on the depth of the receptor hole  73 . The depth of the receptor hole  73  along the channel axis  80  was varied between from about 2 mm to about 3 mm. In this apparatus, the channel was defined by the through hole  71  in the third heat source  40 , the wall  133  of the first thermal brake  130  in the second heat source  30 , and the receptor hole  73  in the first heat source  20 . The channel  70  had a tapered cylinder shape. Average diameter of the channel was about 2 mm with the diameter at the bottom end (in the receptor hole) being about 1.5 mm. In this apparatus, all the temperature shaping elements including the first and second chambers, the first thermal brake, the receptor hole, and the first and second insulators were disposed symmetrically with respect to the channel axis. 
     3.1. PCR Amplification from Plasmid Samples 
       FIG. 66  shows PCR amplification results obtained from a 1 ng plasmid sample using two primers having sequences: 5′-AAGGTGAGATGAAGCTGTAGTCTC-3′ (SEQ ID NO: 32) and 5′-CATTCCATTTTCTGGCGTTCT-3′ (SEQ ID NO: 33). The expected size of the amplicon was 152 bp. The temperatures of the first, second and third heat sources were set to 98° C., 70° C., and 56° C., respectively. The length of the second chamber along the channel axis was about 1 mm and the depth of the receptor hole along the channel axis was about 2.5 mm. As shown in  FIG. 66 , the thermal convection PCR yielded successful amplification in as little as 10 min, demonstrating fast and efficient PCR amplification in this type of invention apparatuses. 
       FIG. 67  shows results of thermal convection PCR amplification from various different plasmid templates with amplicon size between about 200 bp to about 2 kbp. The temperatures of the first, second and third heat sources were set to 98° C., 70° C., and 56° C., respectively. The length of the second chamber along the channel axis was about 1.5 mm and depth of the receptor hole along the channel axis was about 2 mm. Amount of the template plasmid used for each reaction was 1 ng. The primers having the sequences as set forth in SEQ ID NOs: 1 and 2 were used. The expected size of the amplicon was 177 bp for lane 1; 373 bp for lane 2; 601 bp for lane 3; 733 bp for lane 4; 960 bp for lane 5; 1,608 bp for lane 6; and 1,966 bp for lane 7. PCR reaction time was 30 min for lanes 1-6 and 35 min for lane 7. As shown, nearly saturated product bands were observed for all amplicons in a short reaction time. These results demonstrate that thermal convection PCR is not only fast and efficient, but also has a wide dynamic range. 
     3.2. PCR Amplification from Human Genome Sample 
       FIGS. 68A-B  show two examples of thermal convection PCR for amplification from a human genome sample. The temperatures of the first, second and third heat sources were set to 98° C., 70° C., and 56° C., respectively. The length of the second chamber along the channel axis was about 1 mm and the depth of the receptor hole along the channel axis was about 2.5 mm. Amount of the human genome template used for each reaction was 10 ng corresponding to about 3,000 copies.  FIG. 68A  shows results for amplification of a 500 bp segment of β-globin gene. The forward and reverse primers used for this sequence were 5′-GCATCAGGAGTGGACAGAT-3′ (SEQ ID NO: 3) and 5′-CTAAGCCAGTGCCAGAAGA-3′ (SEQ ID NO: 34), respectively.  FIG. 68B  shows results for amplification of a 500 bp segment of β-actin gene. The forward and reverse primers used for this sequence had sequences 5′-CGGACTATGACTTAGTTGCG-3′ (SEQ ID NO: 35) and 5′-ATACATCTCAAGTTGGGGGA-3′ (SEQ ID NO: 36), respectively. 
     As shown in  FIGS. 68A-B , the thermal convection PCR from about 3,000 copies of human genome samples yielded amplicons with correct size in a short reaction time. Significant amplification was observed in about 20 or 25 min with saturated amplification reached in about 30 min. These results demonstrate high speed and efficiency of the thermal convection PCR for amplification from low copy number samples. 
     3.3. PCR Amplification from Very Low Copies of Plasmid Sample 
       FIG. 69  shows PCR amplification from very low copy number plasmid samples using the invention apparatus. Except for the amount of the plasmid sample, all other experimental conditions including the temperatures of the three heat sources and the depth of the receptor hole were the same as those used for the experiments presented in  FIG. 66 . The template plasmid and the primers used were also the same. The PCR reaction time was 30 min. As denoted on the bottom of  FIG. 69 , amount of the plasmid sample used for each reaction was decreased consecutively, starting from about 10,000 copies (lane 1) to about 1,000 copies (lane 2), 100 copies (lane 3) and 10 copies (lane 4). As manifested, the thermal convection PCR yielded successful PCR amplification from as little as a 10 copy sample. Single copy samples were also examined. It was found that amplification from a single copy sample was successful with about 30 to 40% probability. 
     3.4. Temperature Stability and Power Consumption of the Invention Apparatus 
     Temperature stability and power consumption of the invention apparatus having the structure shown in  FIG. 14C  were also tested. The apparatus used in this experiment had 48 channels (6×8) disposed 9 mm apart from each other. Temperature variations observed for this invention apparatus was slightly larger than the apparatus having the structure shown in  FIG. 12A  that was used for the experiments presented in Example 1 (see Section 1.5 above). Average temperature of each heat source during the temperature maintaining time was within about ±0.1° C. with respect to each of the target temperatures. Temperature fluctuation (i.e., standard deviation) of each heat source was within about ±0.1° C. Average of the power consumption during the temperature maintaining time was between about 15 W to about 20 W depending on the ambient temperature. Compared to the apparatus having the structure shown in  FIG. 12A , the power consumption was about 1.5 to about 2 times larger as a result of reduced insulating gaps in the absence of the protrusion structures used in the  FIG. 12A  apparatus. These results demonstrate that use of the protrusion structures is efficient in reducing power consumption of the invention apparatus. 
     Example 4. Thermal Convection PCR Using the Apparatus of FIG.  17 A 
     The apparatus used in this example had the structure shown in  FIG. 17A , but without the protrusions  43 ,  44  of the third heat source  40 . The apparatus comprised a channel  70 , a first chamber  100 , a receptor hole  73 , a through hole  71 , protrusions  33 ,  34  of the second heat source  30 , and protrusions  23 ,  24  of the first heat source  20 . The first chamber  100  was disposed in the second heat source  30  and no thermal brake structure was used. The length of the first, second and third heat sources along the channel axis  80  were about 4 mm, about 6.5 mm, and about 4 mm, respectively. The first and second insulators (or insulating gaps) had a length along the channel axis  80  near the channel region (i.e., within the protrusion region) of about 1 mm and about 0.5 mm, respectively. The length of the first and second insulators outside the channel region (i.e., outside the protrusion region) was about 6 mm to about 3 mm (depending on position) and about 1 mm, respectively. The first chamber  100  had a cylindrical shape with a length along the channel axis  80  equal to the length of the second heat source along the channel axis  80  (i.e., about 6.5 mm). Diameter of the first chamber  100  was varied from about 4 mm to about 2.5 mm. Depth of the receptor hole  73  along the channel axis was varied between from about 2 mm to about 3 mm. In this apparatus, the channel  70  was defined by the through hole  71  in the third heat source  40  and the receptor hole  73  in the first heat source  20 . The channel  70  had a tapered cylinder shape with average diameter of about 2 mm and the diameter at the bottom end (in the receptor hole) of about 1.5 mm. In this apparatus, all the temperature shaping elements including the first chamber, the receptor hole, and the first and second insulators were disposed symmetrically with respect to the channel axis. 
     In this example, effects of the chamber diameter, the receptor hole depth, and the gravity tilting angle were examined with regard to the speed of the thermal convection PCR. 
     4.1. Effects of the Chamber Diameter and the Receptor Hole Depth 
     In this example, the thermal convection PCR was examined as a function of the chamber diameter at different receptor hole depths. Template DNA used was a 1 ng plasmid. Two primers having the sequences as set forth in SEQ ID NOs: 1 and 2 were used and the size of the amplicon was 373 bp. The temperatures of the first, second and third heat sources were set to 98° C., 70° C., and 54° C., respectively. 
       FIGS. 70A-D  show results obtained when the diameter of the first chamber was about 4 mm ( FIG. 70A ), about 3.5 mm ( FIG. 70B ), about 3 mm ( FIG. 70C ), and about 2.5 mm ( FIG. 70D ). The depth of the receptor hole along the channel axis was about 2 mm. As shown, the convection PCR was found to slow down as the diameter of the first chamber was reduced. When the diameter of the first chamber was about 4.0 mm, the PCR product was amplified to a significant level even in 10 min reaction time ( FIG. 70A ). However, more reaction time was needed to reach similar band intensity when the chamber diameter was reduced to about 3.5 mm ( FIG. 70B ) and about 3 mm ( FIG. 70C ). When it was reduced to about 2.5 mm ( FIG. 70D ), no detectable PCR band was observed even after 30 min reaction time. Decrease of the chamber gap between the second heat source and the channel caused more efficient heat transfer between the second heat source and the channel. Thus, temperature gradient inside the channel became smaller at smaller chamber diameter, leading to decrease in the thermal convection speed. 
       FIG. 71A-D  show results obtained when the depth of the receptor hole was increased to about 2.5 mm while the diameters of the first chamber remained the same, i.e., about 4 mm ( FIG. 71A ), about 3.5 mm ( FIG. 71B ), about 3 mm ( FIG. 71C ), and about 2.5 mm ( FIG. 71D ). Due to increased heating from the deeper receptor hole, the thermal convection became faster for all different diameters of the first chamber as compared to the results shown in  FIGS. 70A-D . Even when the diameter of the first chamber was the smallest (i.e., about 2.5 mm), the thermal convection PCR became sufficiently fast and efficient to yield a detectable product band in about 15 min reaction time. 
     The results of this example demonstrate that the chamber diameter or the chamber gap is an important structural element that can be used to control the speed of the thermal convection PCR. It was found that lager chamber diameter leads to faster thermal convection PCR, or vice versa. While it is generally preferred to make the convective flow as fast as possible, it is sometimes preferred to reduce the speed of the convective flow. For instance, some template samples such as templates having long target sequences or certain target genes of genomic DNAs may not be successfully PCR amplified if the convection speed is too fast (due to the large size or certain complex structural limitations). For another instance, DNA polymerase used may have its polymerization speed that is too slow as compared to the speed of the thermal convection PCR. In such cases, use of the chamber structure with different (typically smaller) diameter or chamber gap can be very useful in controlling (typically reducing) the speed of the thermal convection PCR. 
     4.2. Effects of the Gravity Tilting Angle 
     In this example, the thermal convection PCR of the invention apparatus was further examined by introducing the gravity tilting angle θ g . Except for the gravity tilting angle, all other experimental conditions including the template DNA and primers used were the same as those used for the example presented in  FIGS. 70A-D  and  71 A-D. 
       FIGS. 72A-D  and  73 A-D show results obtained when a gravity tilting angle of 10° was introduced. The depth of the receptor hole was about 2.0 mm in  FIGS. 72A-D  and about 2.5 mm in  FIGS. 73A-D . As in  FIGS. 70A-D  and  71 A-D, the diameter of the first chamber was about 4 mm ( FIGS. 72A and 73A ), about 3.5 mm ( FIGS. 72B and 73B ), about 3 mm ( FIGS. 72C and 73C ), and about 2.5 mm ( FIGS. 72D and 73D ). As shown, acceleration of the thermal convection PCR was found to be evident when the gravity tilting angle was introduced. However, increase of the thermal convection PCR speed is more pronounced when the depth of the receptor hole was about 2 mm ( FIGS. 72A-D  as compared to  FIGS. 70A-D ). As compared to the results shown in  FIGS. 70A-D , about 5 min reduction of the PCR reaction time was observed when the chamber diameter was about 4 mm ( FIG. 72A ) and about 3.5 mm ( FIG. 72B ), and about at least 10 to 15 min reduction of the PCR time was observed when the chamber diameter was about 3 mm ( FIG. 72C ) and about 2.5 mm ( FIG. 72D ). When the depth of the receptor hole was about 2.5 mm, only slight increase of the thermal convection PCR speed was observed when the chamber diameter was about 4 mm ( FIG. 73A  as compared to  FIG. 71A ), about 3.5 mm ( FIG. 73B  as compared to  FIG. 71B ), and about 3 mm ( FIG. 73C  as compared to  FIG. 71C ). When the chamber diameter was about 2.5 mm ( FIG. 73D  as compared to  FIG. 71D ), a large reduction (about 10 min reduction) of the PCR reaction time was observed. 
     The results of this example demonstrate that the gravity tilting angle is an important structural element that can be used to increase the speed of the thermal convection PCR. Moreover, the results suggest that there may be certain limitations (other than the apparatus itself) in speeding up the thermal convection PCR. For instance, the speed of the thermal convection PCR was observed to be about the same in the results shown in  FIGS. 73A-C  although the chamber diameter (that was found to affect the convection speed significantly) was changed. Similarly, the results shown in  FIGS. 73A-C  were not much different from those shown in  FIGS. 71A-C  irrespective of presence or absence of the gravity tilting angle. These results demonstrate that the ultimate speed of the thermal convection PCR can be limited by the polymerization speed of the DNA polymerase used although the convection speed of the invention apparatus can be increased as fast as desired. 
     Example 5. Effects of Position of the First Thermal Brake 
     Two types of apparatuses were used in this example. The first apparatus used had the structure shown in  FIG. 12A  comprising a channel  70 , a first chamber  100 , a first thermal brake  130 , a receptor hole  73 , a through hole  71 , protrusions  33 ,  34  of the second heat source  30 , and protrusions  23 ,  24  of the first heat source  20 . Hence, the first thermal brake  130  was located on the bottom of the second heat source  30  with the first chamber  100  located on the upper part of the second heat source  30  as shown in  FIG. 12A . The thickness of the first thermal brake  130  along the channel axis  80  was about 1 mm. 
     The second apparatus used had a structure identical to the structure shown in  FIG. 12A  except for the chamber/thermal brake structure. The second apparatus comprised a first  100  and second  110  chambers located on the bottom and top part of the second heat source  30  and the first thermal brake  130  was located in between the first  100  and second  110  chambers as in the structure shown in  FIG. 10A . The thickness of the first thermal brake  130  along the channel axis  80  was about 1 mm. The position of the first thermal brake  130  was varied along the channel axis  80 . 
     In both apparatuses, the length of the first, second and third heat sources along the channel axis  80  were about 4 mm, about 6.5 mm, and about 4 mm, respectively. The first and second insulators (or insulating gaps) had a length along the channel axis  80  near the channel region (i.e., within the protrusion region) of about 1 mm and about 0.5 mm, respectively. The length of the first and second insulators outside the channel region (i.e., outside the protrusion region) was about 6 mm to about 3 mm (depending on position) and about 1 mm, respectively. Both the first  100  and second  110  chambers had a cylindrical shape with a diameter of about 4 mm. The first thermal brake  130  had a length or thickness along the channel axis  80  of about 1 mm with the wall  133  of the first thermal brake  130  contacting the whole circumference of the channel  70 . Depth of the receptor hole  73  along the channel axis was about 2.8 mm. The channel  70  had a tapered cylinder shape. Average diameter of the channel was about 2 mm with the diameter at the bottom end (in the receptor hole) being about 1.5 mm. In this apparatus, all the temperature shaping elements including the first chamber, the second chamber, the first thermal brake, the receptor hole, and the first and second insulators were disposed symmetrically with respect to the channel axis. 
     Template DNA used in this example was a 1 ng plasmid DNA. Two primers having the sequences as set forth in SEQ ID NOs: 1 and 2 were used and the size of the amplicon was 373 bp. The temperatures of the first, second and third heat sources were set to 98° C., 70° C., and 54° C., respectively. 
       FIGS. 74A-F  show results obtained when the position of the first thermal brake was varied along the channel axis. Position of the bottom end  132  of the first thermal brake was varied from the bottom of the second heat source ( FIG. 74A ) to about 1 mm ( FIG. 74B ), about 2.5 mm ( FIG. 74C ), about 3.5 mm ( FIG. 74D ), about 4.5 mm ( FIG. 74E ), or about 5.5 mm ( FIG. 74F ) above the bottom of the second heat source. As shown in  FIGS. 74A-F , the speed of the thermal convection PCR was modulated depending on the position of the first thermal brake along the channel axis. When the first thermal brake was located on the bottom of the second heat source ( FIG. 74A ), the thermal convection PCR yielded relatively slow PCR amplification as compared to other positions. As the first thermal brake was moved up by about up to 3.5 mm ( FIGS. 74B-D ), the PCR amplification speed was increased. At the higher positions ( FIGS. 74E-F ), a slight decrease of the amplification speed was observed. 
     The results of this example demonstrate that the position of the thermal brake is a useful structural element that can be used to adjust or control the speed of the thermal convection PCR. 
     Example 6. Effects of Thickness of the First Thermal Brake and the Gravity Tilting Angle 
     Three types of apparatuses were used in this example. The first apparatus used had the structure shown in  FIG. 12A  comprising a channel  70 , a first chamber  100 , a first thermal brake  130 , a receptor hole  73 , a through hole  71 , protrusions  33 ,  34  of the second heat source  30 , and protrusions  23 ,  24  of the first heat source  20 . Hence, the first thermal brake  130  was located on the bottom of the second heat source  30  with the first chamber  100  located on the upper part of the second heat source  30  as shown in  FIG. 12A . The thickness of the first thermal brake along the channel axis was varied. 
     The second apparatus used had the first chamber only (without the first thermal brake) that is disposed in the second heat source as in the structure shown in  FIG. 17A . Other structures were identical to those of the first apparatus. 
     The third apparatus used had no chamber structure with other structures identical to the first apparatus. Hence, the third apparatus had the channel structure only (that works as a thermal brake) without the chamber. 
     In the three apparatuses, the length of the first, second and third heat sources along the channel axis  80  were about 4 mm, about 5.5 mm, and about 4 mm, respectively. The first and second insulators (or insulating gaps) had a length along the channel axis  80  near the channel region (i.e., within the protrusion region) of about 2 mm and about 0.5 mm, respectively. The length of the first and second insulators outside the channel region (i.e., outside the protrusion region) was about 6 mm to about 3 mm (depending on position) and about 1 mm, respectively. The first chamber  100  had a cylindrical shape with a diameter of about 4 mm. The thermal brake  130  had a length or thickness along the channel axis  80  between about 1 mm to about 5.5 mm (when no chamber was present) with the wall  133  of the first thermal brake  130  contacting the whole circumference of the channel  70 . Depth of the receptor hole  73  along the channel axis was about 2.8 mm. The channel  70  had a tapered cylinder shape. Average diameter of the channel was about 2 mm with the diameter at the bottom end (in the receptor hole) being about 1.5 mm. In these apparatuses, all the temperature shaping elements including the first chamber, the first thermal brake, the receptor hole, and the first and second insulators were disposed symmetrically with respect to the channel axis. 
     Template DNA used in this example was a 1 ng plasmid DNA. Two primers having the sequences as set forth in SEQ ID NOs: 1 and 2 were used and the size of the amplicon was 373 bp. The temperatures of the first, second and third heat sources were set to 98° C., 70° C., and 54° C., respectively. 
       FIGS. 75A-E  show results obtained when the thickness of the first thermal brake along the channel axis was varied.  FIG. 75A  shows the results obtained when no thermal brake was present (i.e., the first chamber only).  FIGS. 75B-E  show the results obtained when the thickness of the first thermal brake was about 1 mm ( FIG. 75B ), about 2 mm ( FIG. 75C ), about 4 mm ( FIG. 75D ), and about 5.5 mm ( FIG. 75E , i.e., channel only without the chamber structure). As shown, the PCR amplification speed was reduced as the thickness of the first thermal brake was increased. Highest amplification speed was observed when there is no thermal brake ( FIG. 75A ). With the first thermal brake present, the amplification speed was reduced ( FIGS. 75B-E ) as compared to the structure without the thermal brake ( FIG. 75A ). As shown, thicker thermal brake imposed “stronger thermal braking”, leading to slower PCR amplification. When there was no chamber structure ( FIG. 75E ), no significant PCR amplification was observed as due to the very strong thermal braking by the channel alone structure. 
       FIGS. 76A-E  show the results obtained when the gravity tilting angle of 10° was introduced. Except for the gravity tilting angle, all other experimental conditions were the same as those used for the results presented in  FIGS. 75A-E .  FIG. 76A  shows the results obtained when no thermal brake was present (i.e., the first chamber only).  FIGS. 76B-E  show the results obtained when the thickness of the first thermal brake was about 1 mm ( FIG. 76B ), about 2 mm (FIG.  76 C), about 4 mm ( FIG. 76D ), and about 5.5 mm ( FIG. 76E , i.e., channel only without the chamber structure). As compared to the results shown in  FIGS. 75A-E  in which no gravity tilting angle was introduced, the PCR amplification was accelerated by use of the gravity tilting angle. Even when there is no chamber structure (i.e., the channel structure only,  FIG. 76E ), introduction of the gravity tilting angle enabled successful PCR amplification in about 30 min reaction time. Without the gravity tilting angle, no significant PCR amplification was observed when there is no chamber structure ( FIG. 75E ). 
     The results of this example demonstrate that the thermal brake, the chamber, and the gravity tilting angle are useful structural elements that can be used to adjust or control the speed of the thermal convection PCR depending on different applications. It was found that the chamber structure and the gravity tilting angle are useful to accelerate the thermal convection PCR while the thermal brake (including its thickness) is useful to decelerate the thermal convection PCR. It was confirmed that the speed of the thermal convection PCR can be modulated as desired by using one or more of such temperature shaping elements. 
     Example 7. Thermal Convection PCR Using Apparatuses Having Structural Asymmetry 
     Three types of apparatuses were used in this example. The first apparatus used had the structure shown in  FIG. 12A  comprising a channel  70 , a first chamber  100 , a first thermal brake  130 , a receptor hole  73 , a through hole  71 , protrusions  33 ,  34  of the second heat source  30 , and protrusions  23 ,  24  of the first heat source  20 . The first thermal brake  130  was located on the bottom of the second heat source  30  with the first chamber  100  located on the upper part of the second heat source  30  as shown in  FIG. 12A . The thickness of the first thermal brake along the channel axis was about 1 mm. In this apparatus, all the temperature shaping elements including the first chamber, the first thermal brake, the receptor hole, and the first and second insulators were disposed symmetrically with respect to the channel axis. 
     The second apparatus used had an asymmetric receptor hole having a structure shown in  FIG. 21A . Half of the receptor hole was made deeper in the first heat source and close to the second heat source compared to the other half opposite to the channel axis. The difference of the receptor hole depth on the two opposite sides was varied to be about 0.2 mm and about 0.4 mm. Other structures of the second apparatus were identical to those of the first apparatus. 
     The third apparatus used had the first thermal brake that was made asymmetric. The first thermal brake in this apparatus was made to have the structure shown in  FIG. 28A  so that one side of the thermal brake contacted the channel and the opposite side was spaced from the channel. The through hole formed in the first thermal brake was made larger than the diameter of the channel by about 0.4 mm and disposed off-centered with respect to the channel axis by about 0.2 mm. Other structures of the third apparatus including the thickness and position of the first thermal brake along the channel axis were identical to those of the first apparatus. 
     In the three apparatuses, the length of the first, second and third heat sources along the channel axis  80  were about 4 mm, about 6.5 mm, and about 4 mm, respectively. The first and second insulators (or insulating gaps) had a length along the channel axis  80  near the channel region (i.e., within the protrusion region) of about 1 mm and about 0.5 mm, respectively. The length of the first and second insulators outside the channel region (i.e., outside the protrusion region) was about 6 mm to about 3 mm (depending on position) and about 1 mm, respectively. The first chamber  100  had a cylindrical shape with a diameter of about 4 mm. The thermal brake  130  had a length or thickness along the channel axis  80  of about 1 mm. The depth of the receptor hole  73  along the channel axis was about 2.8 mm. The channel  70  had a tapered cylinder shape. Average diameter of the channel was about 2 mm with the diameter at the bottom end (in the receptor hole) being about 1.5 mm. 
     Template DNA used in this example was a 1 ng plasmid DNA. Two primers having the sequences as set forth in SEQ ID NOs: 1 and 2 were used and the size of the amplicon was 373 bp. The temperatures of the first, second and third heat sources were set to 98° C., 70° C., and 54° C., respectively. 
       FIG. 77  shows the results obtained with the first apparatus having all the temperature shaping elements that are disposed symmetrically with respect to the channel axis. As shown, a weak product band was observed in 20 min reaction time and nearly saturated strong band was observed after 25 min. 
       FIGS. 78A-B  show the results obtained with the second apparatus that had the asymmetric receptor hole structure. Difference of the receptor hole depths on the two opposite sides was about 0.2 mm for  FIG. 78A  and about 0.4 mm for  FIG. 78B . As shown in  FIGS. 78A-B , the PCR amplification became almost two times faster (and efficient) as compared to the results obtained with the symmetric apparatus ( FIG. 77 ). As manifested, the small horizontal asymmetry in the receptor hole was sufficient to accelerate the thermal convection PCR dramatically. 
       FIG. 79  shows the results obtained with the third apparatus that had the asymmetric first thermal brake. As shown in  FIG. 79 , the PCR amplification became more than two times faster (and efficient) as compared to the results obtained with the symmetric apparatus ( FIG. 77 ). In accord with the results obtained with the second apparatus, the small horizontal asymmetry in the first thermal brake was sufficient to accelerate the thermal convection PCR dramatically. 
     The results of this example demonstrate that the asymmetric structural elements such as asymmetric receptor hole, asymmetric thermal brake, asymmetric chamber, asymmetric insulators, etc. are useful structural elements. Such asymmetric structural elements can be used alone or in combination with other temperature shaping elements to modulate (typically to increase) the speed of the thermal convection PCR as desired. 
     The disclosures of all references mentioned herein (including all patent and scientific documents) are incorporated herein by reference. The invention has been described in detail with reference to particular embodiments thereof. However, it will be appreciated that those skilled in the art, upon consideration of this disclosure, may make modifications and improvements within the spirit and scope of the invention.