Abstract:
A method of determining a number of a solution constituent includes introducing a first number of solution constituents to a first test location, establishing a first binding environment for the introduced first number of solution constituents, creating a first residual number of solution constituents by binding a first plurality of solution constituents, establishing a second binding environment for the first residual number of solution constituents, creating a second residual number of solution constituents by binding a second plurality of solution constituents from the first residual number of solution constituents, obtaining a first signal associated with the bound first plurality of solution constituents, obtaining a second signal associated with the bound second plurality of solution constituents, and determining a second number of a constituent of interest based upon the obtained first signal and the obtained second signal.

Description:
FIELD 
       [0001]    This invention relates to diagnostic tests and more specifically to affinity based diagnostic tests. 
       BACKGROUND 
       [0002]    Extensive scientific research in the fields of biochemistry and medicine, particularly in recent decades, have revealed the fact that a wide range of diseases and physical conditions are expressed by molecular changes in the human body. In many cases, early detection of the molecular changes can enable earlier diagnosis of the condition which significantly increases the potential for effectively treating the condition. 
         [0003]    Many molecular changes are identified using assays for detecting and quantifying analyte molecules such as DNA, RNA or proteins. These assays are based on specific binding of the analyte molecules to capture molecules with the amount of bound analyte molecules typically being proportional to the total number of analyte molecules in the test solution. This type of detection method is described as “affinity assay” and usually begins with bringing a test solution containing the analyte to be detected or quantified into contact with a set of capture molecules (also referred to as probe spot). When the test solution is in contact with the capture molecules, a certain percentage of the analyte will bind to the capture molecules. After a sufficient amount of time, the test solution is removed and the presence (or quantity) of analyte molecules bound to the capture molecules is detected. 
         [0004]    Typically, affinity assays are limited by the fact that each set of capture molecules usually yields only a single data point. A single data point is generally insufficient for computing an accurate result, especially when there are unknowns in the system. Such unknowns can be the presence of cross reactive molecules, molecules different from the analyte of interest which nonetheless bind to the capture molecules, thus rendering quantitative results useless and causing false positives. 
         [0005]    Another unknown might be the ambient temperature or the density of capture molecules. By way of example, molecules are usually immobilized on a surface by capture molecules. One method of preparing a test site with capture molecules is contact printing. With contact printing, the density of the capture molecules deposited on the surface frequently varies from one batch to the next by a factor of 2. As reported by Peterson et al., “The effect of surface probe density on DNA hybridization”, Nucleic Acids Research, Vol 29, No 24, pp. 5163-5168, Oxford University Press, capture molecule density strongly influences the amount of analyte binding. Accordingly, assays using capture molecules which have been contact printed rely upon cumbersome external calibration methods (such as a standard curve) to provide valid and meaningful results. 
         [0006]    A need exists for a device and method of performing an affinity assay. A further need exists for low cost assays including multiplexed assays, protein arrays, lateral flow devices, sandwich assays, competitive assays, or bead based arrays, which provide accurate results and a method of using such arrays. A method and system for performing an affinity assay which allows the number of analytes within a test solution to be determined would be beneficial. 
       SUMMARY 
       [0007]    In accordance with one embodiment, a method of determining a number of a solution constituent includes introducing a first number of solution constituents to a first test location, establishing a first binding environment for the introduced first number of solution constituents, creating a first residual number of solution constituents by binding a first plurality of solution constituents, establishing a second binding environment for the first residual number of solution constituents, creating a second residual number of solution constituents by binding a second plurality of solution constituents from the first residual number of solution constituents, obtaining a first signal associated with the bound first plurality of solution constituents, obtaining a second signal associated with the bound second plurality of solution constituents, and determining a second number of a constituent of interest based upon the obtained first signal and the obtained second signal. 
         [0008]    In another embodiment, a method of determining the number of molecules involved in an analyte capture system includes introducing a first number of solution constituents to a first test location, creating a first residual number of solution constituents by binding a first plurality of solution constituents to a first percentage of a plurality of capture probes at the first test location, creating a second residual number of solution constituents by binding a second plurality of solution constituents from the first residual number of solution constituents to a second percentage of a plurality of capture probes at a second test location, obtaining a first signal associated with the bound first plurality of solution constituents, obtaining a second signal associated with the bound second plurality of solution constituents, and determining a second number of a molecule of interest based upon the obtained first signal and the obtained second signal. 
         [0009]    In yet another embodiment, a successive sampling system includes a plurality of first capture probes, a plurality of second capture probes, a transport system for moving a first number of analytes of interest in a solution from a location proximate the plurality of first capture probes to a location proximate the plurality of second capture probes, a memory in which command instructions are stored, and a processor configured to execute the command instructions to obtain a first signal associated with a first plurality of bound first capture probes, obtain a second signal associated with a second plurality of bound second capture probes, and determine a first number of a constituent of interest based upon the obtained first signal and the obtained second signal. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0010]      FIG. 1  depicts a successive sampling system configured to expose a single sample to successive sampling allowing determination of the number of a molecule of interest in a sample including other molecules which increase the detected signal; 
           [0011]      FIG. 2  depicts a platform for providing a number of different test sites in the form of a microarray; 
           [0012]      FIG. 3  depicts a procedure that can be used to successively sample a test solution at various test sites on a platform so as to expose a sample to multiple capture probe sites; 
           [0013]      FIG. 4  depicts a schematic of a test site on an array that has been charged to transport analytes of interest within a test solution to a location adjacent a first set of capture probes; 
           [0014]      FIG. 5  depicts a schematic of a second test site on the array of  FIG. 4  that has been charged to transport analytes of interest within the test solution that have not been bound at the first test site to a location adjacent a second set of capture probes; 
           [0015]      FIG. 6  depicts a schematic of a successive sampling system incorporating a lateral flow technology to capture analytes of interest from a test solution as the test solution flows past different capture probe sites; and 
           [0016]      FIGS. 7-11  depict a successive sampling system wherein captured analytes of interest in a test solution are used to provide a residual number of analytes which are sampled to provide data which can be used to determine the initial number of the analytes in the test solution. 
       
    
    
     DESCRIPTION 
       [0017]    For the purposes of promoting an understanding of the principles of the invention, reference will now be made to the embodiments illustrated in the drawings and described in the following written specification. It is understood that no limitation to the scope of the invention is thereby intended. It is further understood that the present invention includes any alterations and modifications to the illustrated embodiments and includes further applications of the principles of the invention as would normally occur to one skilled in the art to which this invention pertains. 
         [0018]    A wide range of affinity assays function in accordance with the mass action law which predicts that for a given affinity constant and probe density, the percentage of analyte which will bind to the probes is constant and not a function of analyte concentration. The mass action law is expressed as: 
         [0000]    
       
         
           
             
               
                 b 
                 analyte 
               
               
                 n 
                 analyte 
               
             
             = 
             
               
                 
                   
                     n 
                     probes 
                   
                    
                   
                     k 
                     a 
                   
                 
                 
                   
                     
                       n 
                       probes 
                     
                      
                     
                       k 
                       a 
                     
                   
                   + 
                   
                     
                       N 
                       A 
                     
                      
                     V 
                   
                 
               
               = 
               
                 a 
                 analyte 
               
             
           
         
       
     
         [0000]    wherein 
         [0019]    b analyte  is the number of bound analyte molecules, 
         [0020]    n analyte  is the number of total analyte molecules in the test solution, 
         [0021]    n probes  is the number of total probe molecules, 
         [0022]    k a  is the association constant between the analyte molecules and the probe molecules, 
         [0023]    N A  is Avogadro&#39;s number, 
         [0024]    V is the test solution volume, and 
         [0025]    a analyte  is the percentage of bound analyte. 
         [0026]    Referring to  FIG. 1 , there is depicted a representation of a successive sampling system generally designated  100 . The sampling system  100  includes an I/O device  102 , a processing circuit  104  and a memory  106 . The I/O device  102  may include a user interface, graphical user interface, keyboards, pointing devices, remote and/or local communication links, displays, and other devices that allow externally generated information to be provided to the sampling system  100 , and that allow internal information of the sampling system  100  to be communicated externally. 
         [0027]    The processing circuit  104  may suitably be a general purpose computer processing circuit such as a microprocessor and its associated circuitry. The processing circuit  104  is operable to carry out the operations attributed to it herein. 
         [0028]    Within the memory  106  are various program instructions  108 . The program instructions  108 , some of which are described more fully below, are executable by the processing circuit  104  and/or any other components as appropriate. Association databases  110  are also located within the memory  106 . 
         [0029]    The sampling system  100  further includes a transport control system  112  and an environment detector suite  114 . The transport control system  112  is configured to move a test solution, in this example, about a microarray  120  depicted in  FIG. 2 . Various methods may be used to form the microarray platform  120 . By way of example, U.S. Pat. No. 5,807,522 discloses a method for forming microarrays. The microarray platform  120  includes a number of different subarrays  122 . The subarrays  122  include a number of test sites  124  consisting of analyte probes. The number of subarrays  122  as well as the number of test sites  124  within each of the subarrays  122  may be varied within the scope of the invention. The precise temperature of the test solution at the test sites  124  may be detected, in this embodiment, by the detector suite  114 . 
         [0030]    The system  100  further includes a sensor  116 . The sensor  116  may be included in a single device along with the other components of the system  100 . Alternatively, one or more of the components of the system  100  may be provided as a separate device which may be remotely located from the other components of the system  100 . 
         [0031]    The test sites  124  are prepared with a capturing agent or analyte probes effective for capturing an analyte of interest. Further details regarding the sampling system  100  are provided with reference to the procedure  130  of  FIG. 3 . The processor  104  executes the program instructions  108  to execute at least some of the procedure  130  of  FIG. 3 . In different embodiments, the procedure  130  may be modified to include more or fewer steps depending upon the specific criterion. 
         [0032]    At block  132 , an analyte of interest is identified and the k a  for the analyte of interest and the probe molecules on the microarray  120  is obtained (block  134 ) and stored in the association database  110  (block  136 ). Potential sources of interference or noise likely to be present in a tested sample are then identified (block  138 ). The identification of signal interference may include, for example, an identification of likely or potential molecules within a sample that also have an affinity for the identified probe molecules. The k a  for each source of noise with the probe molecules is then identified (block  140 ) and stored in one of the affinity databases  110  (block  142 ). 
         [0033]    At block  144 , the microarray platform  120  is prepared by depositing the desired amount of the selected probe molecules in each of the test sites  124 . In alternative embodiments, a subset of the test sites  124  may be prepared with a first probe molecule while another subset of the test sites  124  may be prepared with a second probe molecule so as to allow two separate tests to be conducted within a single microarray platform  120 . Additional configurations within a single microarray platform  120  may also be used. By way of example, each of the test sites within one of the subarrays  122  may be prepared with the same probe molecule while another of the subarrays  122  includes a different probe molecule. The number of test sites  124  prepared with a particular probe molecule in this embodiment is selected to be at least the same as the number of potentially interfering molecule types identified above plus the analyte of interest. 
         [0034]    Once the microarray platform  120  is prepared, a test sample is introduced into the selected set of test sites  124  (block  146 ). The test sample includes a number of the analyte of interest as well as a number of interfering analytes. If not already established, the environment within each of the selected set of test sites  124  is controlled to localize the analyte of interest within the sample at a desired test site  124  or set of test sites  124  (block  148 ). In this example, the analyte of interest is electrically charged and the transport control system  112  is used to establish electrical forces within the test sample. The transport control system thus transports the molecules of interest within the test sample to a desired test site  124  as depicted in  FIG. 4 . 
         [0035]      FIG. 4  depicts a test site  124   1  and a test site  124   2  which are covered by a test sample  150 . The analytes of interest  152  are negatively charged, as are the interfering analytes  154 . The transport control system  112  applies a positive charge to the test site  124   1  which causes the negatively charged analytes of interest  152  and interfering analytes  154  to move away from the test site  124   2  and be concentrated above the test site  124   1 . 
         [0036]    The test sample  150  is then incubated for a predetermined time (block  156 ). During the incubation, the actual test environment within each of the selected set of test sites  124  is monitored by the environment detector suite  114  and data indicative of the established test environment is provided to the processing circuit  104  (block  158 ). In some embodiments, the environment may not be monitored. The environment data may include temperature, and the difference in potential between the test sites  124   1  and  124   2 . During incubation, some of the analytes of interest  152  and some of the interfering analytes  154  are bound by the test probes  160  at the test site  124   1 . 
         [0037]    When the sample  150  has been sufficiently incubated, the transport control system  112  applies a positive charge to the test site  124   2  which causes the negatively charged analytes of interest  152  and interfering analytes  154  which have not been bound to move away from the test site  124   1  and be concentrated above the test site  124   2  (block  160 ) as depicted in  FIG. 5 . The test sample  150  is then incubated for a predetermined time (block  162 ). During the incubation, the actual test environment within each of the selected set of test sites  124  is monitored by the environment detector suite  114  and data indicative of the established test environment is provided to the processing circuit  104  (block  164 ). The environment data may include temperature, and the difference in potential between the test sites  124   1  and  124   2 . During incubation, some of the analytes of interest  152  and some of the interfering analytes  154  are bound by the test probes  160  at the test site  124   2 . 
         [0038]    When the sample  150  has been sufficiently incubated, the test sites  124  are washed (block  166 ) and the sensor  116  is used to detect the bound analytes of interest  152  and the bound interfering analytes  154  (block  168 ). A variety of sensing methods may used for quantifying analyte binding in affinity assays. Such sensing methods include luminescence, fluorescence, colorimetric, electrochemical, impedance, and magnetic readout. The sensing method preferably provides high precision indications of the number of bound probes. Based upon the signals associated with the number of bound probes in the test sites  124   1  and  124   2 , the number of one or more analytes of interest within the sample is calculated by the processing circuit  104  (block  170 ). 
         [0039]    Calculation of the number of one or more analytes of interest is possible since the signal obtained by the sensor  116  for a particular one of the selected set of test sites  124  is the summation of the contributors to the signal including the molecule of interest, and each of the noise sources such as interfering molecules. The relative proportion of the signal attributable to each of the contributors is dependent upon the amount of the particular contributor, the amount of the other contributors, and the relative affinity to the initially deposited capturing probes of each of the contributors. The relationship is reflected in the following equation: 
         [0000]    
       
      
       S 
       1 
       =a 
       1-1 
       n 
       1-1 
       +a 
       1-2 
       n 
       1-2 
       + . . . a 
       1-x 
       n 
       1-x  
      
     
         [0000]    wherein 
         [0040]    S 1  is the signal associated with the bound probes  160  in the test site  124   1 , 
         [0041]    a 1-1  is the percentage of an analyte (1 through x) which binds to the probes  160  in the test site  124   1 , and 
         [0042]    n 1-1  is the number in the sample of the identified analyte (1 through x) at the test site  124   1 . 
         [0043]    Similarly, the relationship of the signal at the test site  124   2  is reflected in the following equation: 
         [0000]    
       
      
       S 
       2 
       =a 
       2-1 
       n 
       2-1 
       +a 
       2-2 
       n 
       2-2 
       + . . . a 
       2-x 
       n 
       2-x  
      
     
         [0000]    wherein 
         [0044]    S 2  is the signal associated with the bound probes  160  in the test site  124   2 , 
         [0045]    a 2-1  is the percentage of an analyte (1 through x) which binds to the probes  160  in the test site  124   2 , and 
         [0046]    n 2-1  is the number in the sample of the identified analyte (1 through x) at the test site  124   2 . 
         [0047]    Since the number of the analytes at the test site  124   2  is equal to the original number of analytes in the test sample less the number of analytes that were bound at the test site  124   1 , the equation for the signal at the test site  124   2  may be rewritten as: 
         [0000]        S   2   =a   2-1 (1− a   1-1 ) n   1-1   +a   2-2 (1 −a   1-2 ) n   1-2   + . . . a   2-x (1 −a   1-x ) n   1-x  
 
         [0048]    The foregoing equations, for the case of two analytes, can be resolved to: 
         [0000]    
       
         
           
             
               n 
               
                 1 
                  
                 
                   - 
                 
                  
                 1 
               
             
             = 
             
               
                 ( 
                 
                   
                     S 
                     1 
                   
                   - 
                   
                     
                       a 
                       
                         1 
                          
                         
                           - 
                         
                          
                         2 
                       
                     
                      
                     
                       S 
                       1 
                     
                   
                   - 
                   
                     S 
                     2 
                   
                 
                 ) 
               
               
                 
                   a 
                   
                     1 
                      
                     
                       - 
                     
                      
                     1 
                   
                 
                  
                 
                   ( 
                   
                     
                       a 
                       
                         1 
                          
                         
                           - 
                         
                          
                         1 
                       
                     
                     - 
                     
                       a 
                       
                         1 
                          
                         
                           - 
                         
                          
                         2 
                       
                     
                   
                   ) 
                 
               
             
           
         
       
     
         [0049]    Accordingly, because the number of probe molecules is controlled, the percentage of bound analytes can be determined for each of the analytes as a function of the affinity constant and probe density. Thus, the number of each of the analytes in the initial test solution  150  can be determined. 
         [0050]    By way of example, the test sample  150  in one scenario includes a number of 10 6  molecules of an analyte of interest and 10 6  molecules of another analyte which is very similar to the analyte of interest and thus features cross reactivity. The affinity constant (k a ) and probe density predict that 40% of the molecules of the analyte of interest and 60% of the other analyte will bind to the capture molecules. Accordingly, 400,000 molecules of the analyte of interest and 600,000 of the other analyte molecules will be captured at test site  124   1  and yield a signal corresponding to 1,000,000 bound probes (S i ). 
         [0051]    Upon moving the residual number of the analyte of interest and the other analyte to the test site  124   1  there will be 400,000 molecules of the analyte of interest and 600,000 molecules of the analyte of interest left in the test solution  150 . Accordingly, after incubation, 240,000 molecules of the analyte of interest and 240,000 molecules of the other analyte will be bound at the test site  124   2 . The signal S 2  will then correspond to 480,000 bound probes. Substituting the calculated binding percentages and the obtained signals in the equation above yields: 
         [0000]    
       
         
           
             
               n 
               
                 1 
                  
                 
                   - 
                 
                  
                 1 
               
             
             = 
             
               
                 
                   ( 
                   
                     
                       1 
                       , 
                       000 
                       , 
                       000 
                     
                     - 
                     
                       0.60 
                        
                       
                         ( 
                         
                           1 
                           , 
                           000 
                           , 
                           000 
                         
                         ) 
                       
                     
                     - 
                     
                       480 
                       , 
                       000 
                     
                   
                   ) 
                 
                 
                   0.40 
                    
                   
                     ( 
                     
                       0.40 
                       - 
                       0.60 
                     
                     ) 
                   
                 
               
               = 
               
                 10 
                 6 
               
             
           
         
       
     
         [0052]    A multisite successive sampling system can thus be implemented on a printed circuit board, glass, plastic substrate, or on a CMOS chip with gold, glass, epoxy, polymer, or gel coating, or even in a well plate such as a 96 well plate. If desired, control, readout, and also sensing for the control can be provided in the printed circuit board or CMOS chip. CMOS technology allows multiple sensing sites to be fabricated in close proximity. This assists in maintaining uniformity of non-controlled environmental factors amongst the test sites. The signal estimation and the assay data can be hard coded on the CMOS chip if desired. 
         [0053]    The transport control system  112  in the embodiment described above incorporated an electric field to move analytes within the test sample. Electric fields are useful for transporting analytes which possess a net charge when in solution such as proteins or DNA strands (see, e.g., Dalibor Hodko et al., “CMOS Electronic Microarrays in Diagnostics and Nanotechnology”, CMOS Biotechnology 2007). 
         [0054]    Electrically charged and electrically neutral analytes may also be moved in bulk using a pipette or liquid handling machine. For both electrically neutral analytes and charged analytes, other transport control systems can be used to successively sample a test solution. Technologies which may be particularly useful in a transport control system include microfluidics wherein the entire test solution is moved on chip level from one probe spot to another probe spot. Microfluidics approaches include continuous-flow microfluidics which enable the control of liquid flow through micro fabricated channels by external or internal micro pumps and valves as reported by A J Tüd         s, “Trends in miniaturized total analysis systems for point-of-care testing in clinical chemistry”, Lab on a Chip, 2001. A continuous flow system  200  is depicted in  FIG. 6 . 
         [0055]    With reference to  FIG. 6 , the test sample  202  is caused to flow past capture probes  204  by the continuous-flow transport system. Sensors  206   1-3  are positioned along the flow path and configured to detect the number of probes  204  which have captured an analyte  208 . Since the capture of analytes is a function of the number of the analytes within the test solution, the rate of capture decreases as the number of analytes within the test solution is reduced. Accordingly, the signal obtained by the sensor  206   1  is larger than the signal produced by the sensor  206   2 . Thus, calculation of the number of analyte molecules in the embodiment of  FIG. 6  is calculated in a manner similar to the calculation of the number of analyte molecules in the example set forth above. 
         [0056]    Other technologies which may be used in a transport system include discrete microfluidics such as electrowetting on dielectric (EWOD) as reported by Vijay Srinivasan, “An integrated digital microfluidic lab-on-a-chip for clinical diagnostics on human physiological fluids”, Lab Chip, 2004, 4, 310-315, or surface acoustic Waves as reported by Achim Wixforth, “Flat Fluidics: Acoustically driven planar microfluidic devices for biological and chemical application”, Transducers 05. Lateral flow systems may also be incorporated wherein a liquid test solution is transferred through a porous membrane, containing several zones of reporter or capture molecules. In addition to electric fields, magnetic fields may be used to transport analytes within a solution. Analyte molecules may be labeled with a magnetic bead or charged label to assist in transportation of the analyte. 
         [0057]    While the embodiment of  FIG. 4  creates a residual number of solution constituents wherein the analytes in the residual number are those analytes that have not been bound, a residual number of solution constituents may also be generated using the analytes that have been bound such as is accomplished by the sampling system  220  of  FIGS. 7-11 . 
         [0058]      FIG. 7  depicts a test solution  222  which includes a number of analytes  224 . A residual number of solution constituents is generated by placing a test strip  226  with a number of probes  228  into the solution  222  as indicated by the arrow  230 . The test strip  226  is then removed with a number of analytes  224  bound to the probes  228  ( FIG. 8 ). A first signal may be obtained from the test strip  226  indicative of the number of analytes bound to the probes  228 . Prior to obtaining a signal, the test strip  226  may be washed to remove analytes which have become attached to the test strip  226  but not bound to a probe  228 . 
         [0059]    The test strip  226  is then immersed into a solution  232  shown in  FIG. 9 . The solution  232  may be selected to dislodge the analytes  224  from the probes  228  or the environment within the solution  232  may be controlled to break the bonds between the analytes  224  and the probes  228 . The analytes  224  within the solution  232  thus form a residual number of solution constituents. 
         [0060]    A second test strip  240  with a number of probes  242  is then exposed to the solution  232  as indicated by the arrow  244  in  FIG. 10 . The test strip  240  is then removed with a number of analytes  224  bound to the probes  242  ( FIG. 11 ). A second signal may be obtained from the test strip  240  indicative of the number of analytes bound to the probes  242 . Prior to obtaining a signal, the test strip  240  may be washed to remove analytes which have become attached to the test strip  240  but not bound to a probe  242 . Determination of the number of analytes in the test solution  222  may be calculated using the affinity constants of the probe and the analytes along with probe density and the obtained signals. 
         [0061]    In embodiments of the sampling system  220  wherein the environment is controlled to break the bonds between the between the analytes  224  and the probes  228 , the test strip  226  may be removed after the bonds have been broken. The environment in the solution  232  may then be controlled to allow binding and the test strip  226  may be re-introduced. Binding of the analytes  224  in the solution  230  to the probes  228  would be a function of the number of analytes  224  in the solution  230 . Thus, the number of analytes  224  which are bound from the solution  230  would be less than the number of analytes  224  which are bound from the solution  232 . 
         [0062]    The procedure of  FIG. 3  may be modified to accommodate a variety of scenarios. By way of example, the system may transport liquids rather than probes. In this scenario, a test solution is transferred into contact with a probe spot and incubated. The initial solution is then removed and a measurement of the bound analytes is obtained. A fluid without analytes or interfering constituents is then brought into contact with the probe spot and incubated, allowing some of the bound analytes to go into solution. The fluid is then removed and the probe spot is measured with the reduced number of bound analytes. 
         [0063]    In another scenario, a solution with a number of interfering analytes that is much greater than the number of the analytes of interest can be determined even if the binding efficiency of the interfering analytes is not known. Specifically, as long as the binding efficiency is small, the number of interfering analyte molecules can be assumed to be constant even when some of the interfering analytes have been bound to capture probes. Thus, the decrease in signal between the first and second signals in successive samples is attributed solely to the change in the number of the analyte of interest. Accordingly, the number of analytes in the test solution is determined according the following formula: 
         [0000]    
       
         
           
             
               n 
               analyte 
             
             = 
             
               
                 ( 
                 
                   
                     S 
                     1 
                   
                   - 
                   
                     S 
                     2 
                   
                 
                 ) 
               
               
                 a 
                 analtye 
                 2 
               
             
           
         
       
     
         [0064]    The procedure of  FIG. 3  may further be modified to calibrate different batches of test platforms. By using a test solution with a single binding analyte, a residual number of the analyte may be obtained in a manner such as the procedure of  FIG. 3 . Signals associated with the bound analytes from the initial solution and from the residual solution may then be used to ascertain the number of analytes in the original solution according to the equation: 
         [0000]    
       
         
           
             
               n 
               analyte 
             
             = 
             
               
                 S 
                 1 
                 2 
               
               
                 
                   S 
                   1 
                 
                 - 
                 
                   S 
                   2 
                 
               
             
           
         
       
     
         [0000]    In this equation, binding efficiency is not required. Accordingly, this equation may be used in scenarios wherein the binding efficiency is not known. 
         [0065]    Additionally, using, e.g., the equation set forth above in paragraph 44, the signals obtained from a test solution (S 1 ) and a residual solution (S 2 ) are determined according to the following equations: 
         [0000]      S 1 =a 1 n 1    
         [0000]      S 1 =a 1   2 n 1    
         [0066]    wherein n 1 =n analyte . 
         [0000]    Thus, for scenarios wherein the percentage of analyte molecules which bind to capture molecules is not known, the number of analytes in a solution can be determined according to the equation: 
         [0000]    
       
         
           
             
               n 
               1 
             
             = 
             
               
                 S 
                 1 
                 2 
               
               
                 S 
                 2 
               
             
           
         
       
     
         [0067]    The equation set forth above in paragraph 44 is also useful in scenarios wherein an interfering analyte is present in the solution. In this scenario, the signals obtained from a test solution (S 1 ) and a residual solution (S 2 ) are determined according to the following equations: 
         [0000]    
       
      
       S 
       1 
       =a 
       1 
       n 
       1 
       +a 
       2 
       n 
       2  
      
     
         [0000]    
       
      
       S 
       2 
       =a 
       1 
       2 
       n 
       1 
       +a 
       2 
       2 
       n 
       2  
      
     
         [0000]    Thus, for scenarios wherein the percentage of analyte molecules which bind to capture molecules is not known, the number of analytes in a solution including an interfering species can be determined according to the equation: 
         [0000]    
       
         
           
             
               n 
               1 
             
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         [0068]    Once the number of analytes in the original solution is ascertained, the number of capture probe molecules may be determined using the mass action law described above. This approach may be modified to compensate for other unknowns affecting binding efficiencies for a particular combination of analytes and capture probes such as temperature. 
         [0069]    While the invention has been illustrated and described in detail in the drawings and foregoing description, the same should be considered as illustrative and not restrictive in character. It is understood that only the preferred embodiments have been presented and that all changes, modifications and further applications that come within the spirit of the invention are desired to be protected.