Patent Application: US-59476608-A

Abstract:
system for trapping and stretching biomolecules . a microfluidic device includes a symmetric channel forming a t - shaped junction at a narrow center region and three wider portions outside the center region . at least one power supply is provided to generate an electric potential across the t - shaped junction to create a local planar extensional field having a stagnation point in the junction whereby a biomolecule introduced into the microfluidic device is trapped at the stagnation point and stretched by the extensional field .

Description:
we have investigated the stretching of dna molecules in a symmetric channel 10 comprising a narrow t - shaped part 12 in the center and the three identical wide parts 14 , 16 , and 18 outside as shown in fig1 ( a ). the vertical part and horizontal part of the t - junction have the same length l 2 while the width of the vertical part is twice the width of the horizontal part : w 2 = 2w 3 . hence the t - junction is equivalent to half of a cross - slot channel . the dimensions used in this investigation were : l 1 = 1 mm , l 2 = 3 mm , w i = 80 μm , w 2 = 40 μm , and w 3 = 20 μm . in order to suppress the local electric field strength maximum , the two corners 20 and 22 of the t - junction 12 were rounded using an arc with radius r = 5 μm ( fig1 ( c )). when symmetric potentials are applied to the channel 10 in a manner as shown in fig1 ( b ), a local planar elongational electric field with a stagnation point 24 can be obtained within the t - junction 12 and uniform fields in the three straight arms . we use e 1 and e 2 to represent the uniform electric field obtained in uniform region 1 and uniform region 2 , respectively . because l 1 , l 2 & gt ;& gt ; w 3 , a simple circuit 26 as shown in fig1 ( d ) can be used to analogize this channel . the center t - junction region 12 is neglected and each straight part of the channel is represented with a resistor with resistance proportional to l / w . the potential at each point indicated in fig1 ( d ) can be solved analytically . the resulting field strengths in uniform region 1 and 2 are given by : as a result , the resulting extensional field in the t - junction 12 is nearly homogeneous . the electrophoretic strain rate is approximately given by { dot over ( ε )}≈ μ | e 1 | w 3 where μ is the electrophoretic mobility . for the remaining analysis , we non - dimensionalize the variables : in fig2 ( a ), we show a finite element calculation of the dimensionless electric field strength | ê | in the region around the t - junction 12 . we assume insulating boundary conditions for the channel walls . the white lines are the electric field lines . although the corners have been rounded , there is still a small local maximum in field strength at the corners . fig2 ( b ) shows the dimensionless electric field strength and strain rate in the junction 12 . due to symmetry , the data along ŷ = 0 and { circumflex over ( x )}= 0 overlap . the electric field and strain rate for an idealized t channel without any end effects are indicated by the dotted lines . the entrance ( or exit ) region starts at about 30 % of the length w 3 before the entrance ( or exit ) of the t - junction and extends a full length of w 3 into the uniform straight region . within the t - junction 12 , there is a homogeneous elongational field , but the strain rate is ≈ 0 . 74μ | e 1 |/ w 3 due to entrance / exit effects . the field kinematics was experimentally verified using particle tracking 17 . we use soft lithography 18 to construct 2 μm - high pdms ( polydimethylsiloxane ) microchannels . t4 dna ( 165 . 6 kilobasepairs , nippon gene ) and λ - dna concatomers ( integer multiples of 48 . 5 kilobasepairs from end - to - end ligation , new england biolabs ) were used in this study . dna were stained with yoyo - 1 ( molecular probes ) at 4 : 1 bp : dye molecule and diluted in 5 × tbe ( 0 . 45 m tris - borate , 10 mm edta ) with 4 vol % β - mercaptoethanol . the stained contour lengths are 70 μm for t4 dna and integer multiples of 21 μm for λ - dna concatomers . the bottom two electrodes were connected to two separate dc power supplies and the top electrode was grounded . molecules were observed using fluorescent video microscopy 13 . in a typical experiment , we first applied symmetric potentials to electrophoretically drive dna molecules into the t - junction region and then trapped one molecule of interest at the stagnation point of the local extensional field ( fig3 ( a )). with the application of two power supplies we were able to adjust the two potentials individually and therefore freely move the position of the stagnation point . this capability of stagnation point control allowed us to trap any dna molecules in the field of view even if it initially did not move toward the stagnation point . furthermore , we could also overcome fluctuations of a trapped molecule . for example , if a trapped dna begins to drift toward the right reservoir , the potential applied in the left reservoir can be increased so that the position of the stagnation point would reverse the direction of the drifting molecule ( fig3 ( b )). the t4 - dna in fig3 has a maximum stretch of ≈ 50 μm and extends just slightly beyond the region in the t - junction where homogenous electrophoretic elongation is generated . the dimensionless group which determines the extent of stretching in this region is the deborah number de = τ { dot over ( ε )} where τ is the longest relaxation time of the dna ( measured 17 to be 1 . 3 ± 0 . 2 s ). in fig3 ( c ) we see that strong stretching occurs once de & gt ; 0 . 5 , similar to what is observed in hydrodynamic flows 8 . each point in fig3 ( c ) represents the average of 15 to 30 molecules . we next tried to stretch molecules which have contour lengths much larger than 2 × w 3 ( 40 μm ). in fig4 we show the stretching of a concatomer of λ - dna which has a contour length of 210 μm ( 10 - mer , 485 kilobasepairs ). as the molecule enters the t - junction it is in a coiled state with mean radius of gyration ≈ 2 . 7 μm 19 . initially the stretching is governed by de due to the small coil size . however , as the arms of the dna begin to extent into regions of constant electric field , stretching occurs due to a different mechanism . for stretched lengths & gt ;& gt ; 2 × w 3 , the chain resembles a set of symmetrically tethered chains ( with contour lengths one - half that of the original chain ) in a homogeneous electric field . stretching still occurs , but is now governed by the pe = μel p / d 1 / 2 where μ is the electrophoretic mobility ( 1 . 35 ± 0 . 14 × 10 − 4 cm 2 /( sv )), l p is the persistence length (≈ 53 nm ) and d 1 / 2 is the diffusivity of a chain with a contour length half that of the original chain (≈ 0 . 062 μm 2 / s for this 10 - mer 19 ). the molecule in fig4 reaches a final steady state extension which is 94 % of the full contour length . the electric field generated in the t - junction was verified by tracking the center of mass of dna under conditions in which they do not appreciably deform . we chose to use λ - dna ( 48 . 5 kbp ) since it is large enough to easily track , but small enough to not appreciably deform at the conditions used below . tracking was performed at an applied electric field | e 1 |=| e 2 |= 30 v / cm . the center of mass positions of 34 λ - dna molecules were tracked using nih software . fig5 ( a ) shows the trajectories of these molecules in the t - junction vicinity . we first determined the ensemble average electrophoretic velocity in the two uniform regions to be μ | e 1 | = 40 ± 4 μm / s . the electrophoretic mobility of λ - dna can be then determined to be μ = 1 . 35 ± 0 . 14 × 10 − 4 cm 2 /( sv ). according to the results of the finite element calculation , the strain rate in the extensional region should be { dot over ( ε )}≈ 0 . 74 μ | e 1 | / w 3 = 1 . 48 ± 0 . 15 s − 1 . the relaxation time of λ - dna in the experimental buffer ( 5 × tbe with 4 vol % β - mercaptoethanol , viscosity η = 1 . 3 cp ) has been previously measured 20 to be τ = 0 . 19 s . therefore , the deborah number for the λ - dna is de = τ { dot over ( ε )}= 0 . 3 , smaller than 0 . 5 . hence , λ - dna did not deform significantly in the extensional field and sufficed to serve as tracers . an experimentally observable strain rate was extracted from the data independently . fifteen molecules which have experienced the extensional field were selected , and the portion of their trajectories located in the homogeneous extensional region was cropped and the { circumflex over ( x )} ( t ) and ŷ ( t ) data were fit to the exponential functions { circumflex over ( x )} ( t )={ circumflex over ( x )} ( 0 ) exp ({ dot over ( ε )} obs t ) and ŷ ( t )= ŷ ( 0 ) exp (−{ dot over ( ε )} obs t ), respectively . based on the results of the finite element calculation , we only selected the portion of the trajectory with both |{ circumflex over ( x )}| and ŷ ; in the range of [ 0 , 0 . 8 ] for the fitting . in fig5 we showed an example of the fitting using open circles to indicate a qualified dna trajectory and filled circles to indicate the part used for the fitting . the fitted ensemble average strain rate is { dot over ( ε )} obs = 1 . 49 ± 0 . 4 s − 1 , comparable to the predicted value of 1 . 48 ± 0 . 4 s − 1 . this result confirms that the field within the t - junction is nearly homogeneous and the magnitude is in quantitative agreement with the prediction . fig5 ( b ) and ( c ) show the semi - log plots of the { circumflex over ( x )} and ŷ data of the 15 trajectories . the thick black line is the affine scaling using { dot over ( ε )}= 1 . 49 s − 1 . the relaxation time of t4 dna in the experimental buffer and in the 2 μm - high t channel was experimentally determined by electrophoretically stretching the dna at the stagnation point , turning off the field and tracking the extension x ex ( t ) for these relaxing molecules . the extension data were fit to a function x ex ( t ) x ex ( t ) = x i 2 − x ex 2 ) exp (− t / τ )+ x ex 2 in the linear force regime , where x i is the initial stretch ( about 30 % extended for linear regime ) and x ex 2 corresponds to the mean square coil size at equilibrium which was measured to be 21 μm 2 in the 2 μm - high channel . fig6 shows the mean squared fractional extension (( x ex ( t ) x ex ( t ) − x ex 2 )/ l 2 ) data for 16 t4 dna molecules ( lines ) and the ensemble average ( symbols ). the resulting relaxation time is τ = 1 . 3 ± 0 . 2 s . other embodiments of the invention will now be described in conjunction with fig7 - 10 . with reference first to fig7 , the channel 10 includes corners 20 and 22 rounded using various curves which result in different types of transition from the elongational field to uniform field . for example , a hyperbolic function xy = lw / 2 ( w and l are shown in the figure ) can be used to round the corners so that the resulting channel provides a homogeneous elongational electric field within the region − l ≦ x ≦ l and 0 ≦ y ≦ 1 . the field transition is immediate and the entrance effect is almost completely suppressed in this type of t channel . the stretching of dna with contour lengths less than 2l is purely governed by the deborah number de . as shown in fig8 , a full cross - slot channel 10 ( the t channel discussed above can be imagined as half of the cross - slot channel ) can also be used for biomolecule trapping and manipulation . the four straight arms have identical width and length , and the corners can be rounded in the same manner as for the t channel . the trapping still depends on the local planar elongational electric field with a stagnation point located in the center of the junction region . the operating principle of the cross - slot device is the same with that of the t channel embodiments described above . fig9 illustrates an embodiment of the invention in which the t channel has an extra side injection part . such a modification on the top arm of the t channel will allow more potential biological applications . one ( or more ) side injection channels can be added so that when a dna molecule ( or other biomolecule ) is trapped at the stagnation point , other biological molecules ( e . g ., proteins ) can be sent into the junction through these injection channels . as a result , the interaction between multiple molecules can be visualized and studied . fig9 shows a t channel with one injection channel added . dna molecules are loaded from terminal a and electrophoretically driven down into the junction and stretched . other molecules of interest can be injected from terminal b afterwards . yet another embodiment of the invention is shown in fig1 . two focusing channels 40 and 42 having identical lengths and widths are added upstream of the t junction . when symmetric potentials are applied , these two channels 40 and 42 help focus dna into the center line of the top arm . as a result , most of the dna molecules entering the junction will move straightly towards the stagnation point and thus can be easily trapped and stretched . the two focusing channels 40 and 42 reduce the amount of controlling required for the trapping process . this type of t channel has the potential for performing a continuous process wherein the molecules are fed into the junction , trapped , stretched , and released one by one , as demonstrated in fig1 . our dna trapping and stretching device has several advantages over other methods . electric fields are much easier to apply , control and their connections have smaller lag times than hydrodynamic fields in micro / nano channels . further , the purely elongational kinematics of electric fields are advantageous for molecular stretching . the field boundary conditions also allow for the use of only three connecting channels to generate a homogenous elongational region and straightforward capture of a molecule by adjusting the stagnation point . stretching can occur even beyond the elongational region due to a molecule straddling the t - 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