Methods for determining the kinetic parameters of a reaction

Abstract

According to the present invention, there is provided a method for determining the kinetic parameters of a reaction between an analyte and a ligand attached to a test surface of a flow cell, comprising the steps of: (a) flowing a first volume (V1) of sample fluid containing the analyte over a test surface between a first time point (t1) and a second time point (t2); (b) flowing a first volume (Vb1) of analyte-free buffer fluid over the test surface between a third time point (t3) and a fourth time point (t4); (c) flowing at least a second volume (V2) of sample fluid containing the analyte over the test surface between a fifth time point (t2) and a sixth time point (t6); (d) flowing at least a second volume (Vb2) of analyte-free buffer fluid over the test surface between a seventh time point (t7) and an eighth time point (t8); (e) using the sensor to measure binding of the analyte to the ligand on the test surface to obtain a binding curve; (f) determining kinetic parameters using only the portion of the binding curve at a predetermined time interval without using other portions of the binding curve; A method is provided which includes:

Description

[Technical field]

[0001] The present invention relates to a method for determining the kinetic parameters of a reaction between an analyte and a ligand attached to a test surface of a flow cell; in particular to a method which involves substantially less use of the portion of the binding curve which describes the association of the analyte to the ligand, but rather primarily use of the portion of the binding curve which describes the dissociation of the analyte from the ligand, to determine the kinetic parameters. [Background technology]

[0002] 2. Background of the Invention In existing methods for determining the kinetic parameters of a reaction between an analyte and a ligand attached to a test surface of a flow cell, a volume of sample fluid containing the analyte is continuously flowed over the test surface. As the volume of sample fluid containing the analyte is continuously flowed over the test surface, a sensor is used to measure the amount of analyte bound to the ligand on the test surface; a curve representing the amount of analyte bound to the ligand on the test surface, known as a binding curve, is output by the sensor. The binding curve includes association phases and dissociation phases. The association phase occurs when a volume of sample fluid passes over the test surface and the analyte in the sample fluid binds to the ligand; the binding curve shows an increase in the amount of analyte bound to the ligand on the test surface during the association phase. The dissociation phase occurs after a volume of sample fluid passes over the test surface and before the next volume of sample fluid flows over the test surface; the binding curve shows a decrease in the amount of analyte bound to the ligand on the test surface during the dissociation phase, as the previously bound analyte dissociates (or desorbs) from the ligand.

[0003] The entire binding curve (i.e., all of the association and dissociation phases) is then used to determine the kinetic parameters of the reaction between the analyte and the ligand on the test surface; this is typically done by identifying a pre-defined model, with known kinetic parameters, that best fits the binding curve; the kinetic parameters of the model that best fits the binding curve are then considered to be the kinetic parameters of the reaction.

[0004] However, a problem with using the entire binding curve to determine the kinetic parameters of the reaction between an analyte and a ligand on a test surface is that it can result in an inaccurate determination of the kinetic parameters of the reaction: existing sensors used to measure the amount of analyte bound to a ligand on a test surface and output a binding curve are sensitive to changes in the refractive index of the volume of sample fluid; when a volume of sample fluid containing the analyte flows over the test surface, changes in the refractive index of the volume of sample fluid can introduce artifacts into the binding curve; these artifacts are present in the association phase of the binding curve; and since the entire binding curve (i.e. all of the association and dissociation phases) is then used to determine the kinetic parameters of the reaction between an analyte and a ligand on a test surface, these artifacts result in an inaccurate determination of the kinetic parameters of the reaction. Summary of the Invention [Problem to be solved by the invention]

[0005] It is an object of the present invention to obviate or mitigate at least some of the disadvantages associated with existing methods in the art. In particular, it is an object of the present invention to provide an improved method for determining kinetic parameters of a reaction that is less vulnerable to artifacts in the binding curves generated by refractive index changes that occur as a volume of sample fluid flows over a test surface of a flow cell. [Means for solving the problem]

[0006] According to the present invention, this object is achieved by a method comprising at least the steps as set out in claim 1. The dependent claims describe preferred, optional steps which may be implemented in various embodiments of the invention.

[0007] Advantageously, in the methods of the invention, primarily the dissociation phase of the binding curve (i.e. the portion of the binding curve corresponding to the time after a volume of sample fluid has flowed over the test surface and before the next volume of sample fluid flows over the test surface) is used to determine the kinetic parameters of the reaction, rather than the association phase of the binding curve (i.e. the portion of the binding curve corresponding to when a volume of sample fluid has flowed over the test surface and the analyte in the sample fluid is binding to the ligand).

[0008] In particular, in the first embodiment, only the dissociation phase of the binding curve is used to determine kinetic parameters, without using the association phase of the binding curve; in the second embodiment, only the dissociation phase of the binding curve and a very small portion of the association phase of the binding curve are used to determine kinetic parameters. In the second embodiment, said small portion of the association phase of the binding curve can be so small that artifacts in those portions of the binding curve have negligible effect on the determination of kinetic parameters. In both embodiments, the amount of the association phase of the binding curve used to determine kinetic parameters is reduced compared to the prior art.

[0009] Thus, in the present invention, artifacts in the binding curves generated by refractive index changes that occur as a volume of sample fluid flows over the test surface of the flow cell have a lesser effect on the determination of kinetic parameters.

[0010] Exemplary embodiments of the present invention are disclosed herein and illustrated in the figures: [Brief description of the drawings]

[0011] [Figure 1]FIG. 1 is a complete binding curve, including six association phases and six dissociation phases, resulting from sequentially flowing six volumes each of analyte-containing sample fluid over the test surface of a flow cell; [Diagram 2] FIG. 2 shows portions of the binding curves of FIG. 1 at several selected intervals of time; [Diagram 3] FIG. 3 shows the normalized concentration curve used to determine the plurality of predetermined interval times.

[0012] DETAILED DESCRIPTION OF EMBODIMENTS OF THE PRESENTINVENTION According to the present invention, there is provided a method for determining the kinetic parameters of a reaction between an analyte and a ligand attached to a test surface of a flow cell, said method comprising the steps of:

[0013] (a) flowing a first volume (V1) of sample fluid containing the analyte over a test surface between a first time point (t1) and a second time point (t2).

[0014] (b) flowing a first volume (Vb1) of buffer fluid (which does not contain analyte) over the test surface between a third time point (t3) and a fourth time point (t4), which may be equal to the second time point (t2); most preferably, dissociation of at least a portion of the analyte from the first volume (V1) of sample fluid that was bound to the ligand on the test surface occurs between the third time point (t3) and the fourth time point (t4). In one embodiment, the buffer fluid is configured to promote dissociation of the bound analyte from the ligand.

[0015] (c) flowing at least a second volume (V2) of sample fluid containing said analyte over the test surface between a fifth time point (t2) and a sixth time point (t6), where the fifth time point (t5) may be equal to the fourth time point (t4);

[0016] (d) flowing a second volume (Vb2) of buffer fluid (which does not contain analyte) over the test surface between a seventh time point (t7) and an eighth time point (t8), which may be equal to the sixth time point (t6); most preferably, dissociation of at least a portion of the analyte from the second volume (V2) of sample fluid that was bound to the ligand on the test surface occurs between the seventh time point (t7) and the eighth time point (t8). In one embodiment, the buffer fluid is configured to promote dissociation of the bound analyte from the ligand.

[0017] (e) Using the sensor to measure binding of the analyte to the ligand on the test surface to obtain a binding curve.

[0018] (f) determining kinetic parameters using only that portion of the binding curve at the predetermined time interval without using other portions of the binding curve;

[0019] To determine the kinetic parameters using only the portion of the binding curve that falls within a given time interval, the following steps are performed: constructing a normalized concentration curve (c(t)) that depicts the concentration of analyte at the test surface over time; determining the kinetic parameters Rmax, k a , k d where Rmax is a predetermined theoretical maximum binding curve value corresponding to saturation of the ligand (e.g., when all binding sites of the ligand are occupied by analyte bound to the ligand), and k a is the association rate constant, and k d is the dissociation rate constant; the normalized concentration curve (c(t)), and the kinetic parameters Rmax, k a , k d Using the above estimates for , we solve the differential reaction equation:

number

[0020] Once the differential reaction equation is obtained, the portion of the simulated binding curve at said predetermined time interval (tjΔ) is then extracted to provide each partial simulated binding curve (sbcj).

[0021] Subsequently, the partial chi-squared (χ 2 ) is determined according to the following formula:

number

[0022] where dmbj is the portion of the binding curve at the jth predetermined interval (tjΔ), sbcj is the jth partial simulated binding curve, and N dmbj is the number of data points in the portion of the binding curve at the jth given time interval (tjΔ).

[0023] The partial chi-squared (χ 2 After the partial chi-square (χ 2 ) is minimized, where the determined partial chi-square (χ 2 ) to minimize the kinetic parameters Rmax, k a , k d The value of defines the kinetic parameters of the reaction between the analyte and the ligand attached to the test surface of the flow cell.

[0024] In a preferred embodiment, the kinetic parameters Rmax, k a , k d The step of estimating values ​​for partial chi-square (χ 2 The objective of the present invention is to find the kinetic parameters that minimize

[0025] In a further preferred embodiment, the kinetic parameters Rmax, k a , k d The step of estimating values ​​for partial chi-square (χ 2 The objective of the present invention is to find the kinetic parameters that minimize

[0026] In a preferred embodiment, the method comprises the steps of measuring binding of an analyte to a ligand on a test surface continuously from a first time point (t1) to a ninth time point (t9) using a sensor, and then extracting portions of the binding curve at said predetermined intervals; and determining kinetic parameters using only said extracted portions of the binding curve.

[0027] In another embodiment, the method comprises the steps of measuring binding of an analyte to a ligand on a test surface continuously from a first time point (t1) to a ninth time point (t9) using a sensor; zeroing the portion of the binding curve outside the predetermined time interval; and determining kinetic parameters using only the non-zeroed portion of the binding curve.

[0028] Exemplary embodiment 1: In a first embodiment, the predetermined intervals are a first and a second interval (t1Δ, t2Δ); where the first interval (t1Δ) occurs between the second time point (t2) and the fifth time point (t5); and the second interval (t2Δ) occurs between the sixth time point (t6) and the ninth time point (t9), the ninth time point (t9) occurring some time after the eighth time point (t8) (or in another embodiment, the ninth time point (t9) is equal to the eighth time point (t8)). Advantageously, in this embodiment, only the part of the binding curve corresponding to the dissociation phase is used to determine the kinetic parameters.

[0029] In one embodiment, the first interval time (t1Δ) is a portion of the period between the second time point (t2) and the fifth time point (t5); and the second interval time (t2Δ) is a portion of the period between the sixth time point (t6) and the ninth time point (t9), the ninth time point (t9) occurring some time after the eighth time point (t8) (or in another embodiment, the ninth time point (t9) is equal to the eighth time point (t8)). For example, the first interval time (t1Δ) may be for a predetermined time after the second time point (t2), until the fifth time point (t5), or until a predetermined time before the fifth time point (t5); and the second interval time (t2Δ) may be for a predetermined time after the sixth time point (t6), until the eighth time point (t8), or until a predetermined time before the eighth time point (t8). In another embodiment, the first interval time (t1Δ) is defined by the entire time interval between the second time point (t2) and the fifth time point (t5); and the second interval time (t2Δ) is defined by the entire time interval between the sixth time point (t6) and the ninth time point (t9), the ninth time point (t9) occurring some time after the eighth time point (t8) (or in another embodiment, the ninth time point (t9) is equal to the eighth time point (t8)).

[0030] This first embodiment includes the following steps:

[0031] (a) flowing a first volume (V1) of sample fluid containing the analyte over a test surface between a first time point (t1) and a second time point (t2).

[0032] (b) flowing a first volume (Vb1) of buffer fluid (which does not contain analyte) over the test surface between a third time point (t3) and a fourth time point (t4), which may be equal to the second time point (t2); most preferably, dissociation of at least a portion of the analyte from the first volume (V1) of sample fluid that was bound to the ligand on the test surface occurs between the third time point (t3) and the fourth time point (t4). In one embodiment, the buffer fluid is configured to promote dissociation of the bound analyte from the ligand.

[0033] (c) flowing at least a second volume (V2) of sample fluid containing said analyte over the test surface between a fifth time point (t2) and a sixth time point (t6), where the fifth time point (t5) may be equal to the fourth time point (t4);

[0034] (d) flowing a second volume (Vb2) of buffer fluid (which does not contain analyte) over the test surface between a seventh time point (t7) and an eighth time point (t8), which may be equal to the sixth time point (t6); most preferably, dissociation of at least a portion of the analyte from the second volume (V2) of sample fluid that was bound to the ligand on the test surface occurs between the seventh time point (t7) and the eighth time point (t8). In one embodiment, the buffer fluid is configured to promote dissociation of the bound analyte from the ligand.

[0035] (e) using the sensor to measure binding of the analyte to the ligand on the test surface for at least a first and a second interval period (t1Δ, t2Δ) to obtain a binding curve, wherein the first interval time (t1Δ) occurs between the second time point (t2) and the fifth time point (t5), and the second interval time (t2Δ) occurs between the sixth time point (t6) and the ninth time point (t9), the ninth time point (t9) occurring some time after the eighth time point (t8) (or in another embodiment, the ninth time point (t9) is equal to the eighth time point (t8)). In one embodiment, the first interval time (t1Δ) is a portion of the period between the second time point (t2) and the fifth time point (t5); and the second interval time (t2Δ) is a portion of the period between the sixth time point (t6) and the ninth time point (t9), the ninth time point (t9) occurring some time after the eighth time point (t8) (or in another embodiment, the ninth time point (t9) is equal to the eighth time point (t8)). For example, the first interval time (t1Δ) may be for a predetermined time after the second time point (t2), until the fifth time point (t5), or until a predetermined time before the fifth time point (t5); and the second interval time (t2Δ) may be for a predetermined time after the sixth time point (t6), until the eighth time point (t8), or until a predetermined time before the eighth time point (t8). In another embodiment, the first interval time (t1Δ) is defined by the entire time interval between the second time point (t2) and the fifth time point (t5); and the second interval time (t2Δ) is defined by the entire time interval between the sixth time point (t6) and the ninth time point (t9), the ninth time point (t9) occurring some time after the eighth time point (t8) (or in another embodiment, the ninth time point (t9) is equal to the eighth time point (t8)).

[0036] (f) The portions of the binding curve at the first and second interval times (t1Δ, t2Δ) are divided into a first time point (t1) and a second time point (t 2a ) and without the portion between the fifth time point (t5) and the sixth time point (t6), determining kinetic parameters.

[0037] In this first embodiment, substantially none of the binding curves between the first time point (t1) and the second time point (t2) and between the fifth time point (t5) and the sixth time point (t6) are used to determine the kinetic parameters. Therefore, artifacts in the binding curves generated by refractive index changes that occur when a volume of sample fluid flows over the test surface of the flow cell have less impact on the determination of the kinetic parameters.

[0038] In one embodiment, the method comprises measuring binding of an analyte to a ligand on a test surface continuously from a first time point (t1) to a ninth time point (t9) using a sensor, then extracting portions of the binding curve at said first and second interval times (t1Δ, t2Δ); and determining kinetic parameters using only said extracted portions of the binding curve.

[0039] In another embodiment, the method comprises the steps of measuring binding of an analyte to a ligand on a test surface continuously from a first time point (t1) to a ninth time point (t9) using a sensor; zeroing the portion of the binding curve outside the first and second interval times (t1Δ, t2Δ); and determining kinetic parameters using only the portion of the binding curve that has not been zeroed.

[0040] The step of determining kinetic parameters using the portions of the binding curve in the first and second intervals (t1Δ, t2Δ) without using the portions of the binding curve between the first time point (t1) and the second time point (t2) and between the fifth time point (t5) and the sixth time point (t6) can be carried out using any known technique for determining kinetic parameters using a binding curve; those very same techniques can be used in the present invention to determine kinetic parameters, the difference being that the techniques are applied to the portions of the binding curve in the first and second intervals (t1Δ, t2Δ) and not to the portions of the binding curve between the first time point (t1) and the second time point (t2) and between the fifth time point (t5) and the sixth time point (t6).

[0041] In a most preferred embodiment, the step of determining kinetic parameters using the portions of the binding curve at the first and second interval times (t1Δ, t2Δ) without using the portions of the binding curve between the first time point (t1) and the second time point (t2) and between the fifth time point (t5) and the sixth time point (t6) preferably comprises the steps of: generating a normalized concentration curve (c(t)) depicting the concentration of the analyte at the test surface over time (preferably, a concentration curve is first generated and then normalized to yield said normalized concentration curve (c(t)); a , k d where Rmax is a predetermined theoretical maximum binding curve value corresponding to saturation of the ligand (e.g., when all binding sites of the ligand are occupied by analyte bound to the ligand), and k a is the binding rate constant, and k d is the dissociation rate constant; the normalized concentration curve (c(t)), and the kinetic parameters Rmax, k a , k d Using the above estimates for , we solve the differential reaction equation:

number

[0042] Once the differential reaction equation is obtained, the portion of the simulated binding curve in the first time interval (tΔ) is then extracted to provide a first partial simulated binding curve (sbc1); and the portion of the simulated binding curve in the second time interval (tΔ) is extracted to provide a second partial simulated binding curve (sbc2); and the partial chi-squared (χ 2 ) to determine:

number

[0043] The partial chi-squared (χ 2 After the partial chi-square (χ 2 ) is minimized, where the determined partial chi-square (χ 2 ) to minimize the kinetic parameters Rmax, k a , k d The value of defines the kinetic parameters of the reaction between the analyte and the ligand attached to the test surface of the flow cell.

[0044] In a preferred embodiment, the kinetic parameters Rmax, k a, k d The step of estimating values ​​for partial chi-square (χ 2 The objective of the present invention is to find the kinetic parameters that minimize

[0045] In a further preferred embodiment, the step of estimating values ​​for the kinetic parameters Rmax, ka, kd comprises using Estimators to estimate partial chi-squared (χ 2 The objective of the present invention is to find the kinetic parameters that minimize

[0046] Exemplary embodiment 2: In the first embodiment above, the predetermined interval time includes a first and a second interval time (t1Δ, t2Δ); where the first interval time (t1Δ) occurs between the second time point (t2) and the fifth time point (t5); and the second interval time (t2Δ) occurs between the sixth time point (t6) and the ninth time point (t9), where the ninth time point (t9) occurs sometime after the eighth time point (t8) (or in another embodiment, the ninth time point (t9) is equal to the eighth time point (t8)). However, in this second embodiment, the predetermined interval time is determined from the concentration curve (or from the normalized concentration curve). The second embodiment includes the following steps:

[0047] (a) flowing a first volume (V1) of sample fluid containing the analyte over a test surface between a first time point (t1) and a second time point (t2).

[0048] (b) flowing a first volume (Vb1) of buffer fluid (which does not contain analyte) over the test surface between a third time point (t3) and a fourth time point (t4), which may be equal to the second time point (t2); most preferably, dissociation of at least a portion of the analyte from the first volume (V1) of sample fluid that was bound to the ligand on the test surface occurs between the third time point (t3) and the fourth time point (t4). In one embodiment, the buffer fluid is configured to promote dissociation of the bound analyte from the ligand.

[0049] (c) flowing at least a second volume (V2) of sample fluid containing said analyte over the test surface between a fifth time point (t2) and a sixth time point (t6), where the fifth time point (t5) may be equal to the fourth time point (t4);

[0050] (d) flowing a second volume (Vb2) of buffer fluid (which does not contain analyte) over the test surface between a seventh time point (t7) and an eighth time point (t8), which may be equal to the sixth time point (t6); most preferably, dissociation of at least a portion of the analyte from the second volume (V2) of sample fluid that was bound to the ligand on the test surface occurs between the seventh time point (t7) and the eighth time point (t8). In one embodiment, the buffer fluid is configured to promote dissociation of the bound analyte from the ligand.

[0051] (e) Using the sensor to measure binding of the analyte to the ligand on the test surface to obtain a binding curve.

[0052] (f) determining kinetic parameters using portions of the binding curve at predetermined first (t1Δ) and second (t2Δ) time intervals;

[0053] In this second embodiment, substantially less of the portion of the binding curve between the first time point (t1) and the second time point (t2) and between the fifth time point (t5) and the sixth time point (t6) is used to determine the kinetic parameters, and therefore artifacts in the binding curve generated by refractive index changes that occur as the volume of sample fluid flows over the test surface of the flow cell have less impact on the determination of the kinetic parameters.

[0054] In one embodiment, the method comprises measuring binding of an analyte to a ligand on a test surface continuously from a first time point (t1) to a ninth time point (t9) using a sensor, then extracting portions of the binding curve at said first and second interval times (t1Δ, t2Δ); and determining kinetic parameters using only said extracted portions of the binding curve.

[0055] In another embodiment, the method comprises the steps of measuring binding of an analyte to a ligand on a test surface continuously from a first time point (t1) to a ninth time point (t9) using a sensor; zeroing the portion of the binding curve outside the first and second time intervals (t1Δ, t2Δ); and determining kinetic parameters using only the portion of the binding curve within the first and second time intervals (t1Δ, t2Δ) (i.e., the portion of the binding curve that is not zeroed).

[0056] The second embodiment further includes a calibration step, which may be performed before steps (a)-(f) or after steps (a)-(e) (before step (f) is performed), to determine the first and second interval times (t1Δ, t2Δ).

[0057] In one embodiment, the calibration step involves generating a concentration curve depicting the concentration of the analyte at the test surface over time and then normalizing the concentration curve to obtain a normalized concentration curve and then providing the normalized concentration curve In another embodiment, the calibration step includes generating a concentration curve depicting the concentration of the analyte at the test surface over time; then using the concentration curve to determine the first and second interval times (t1Δ, t2Δ). Also, the normalized concentration curve To determine the first and second interval times (t1Δ, t2Δ), curve It should be noted that the same steps are performed to determine the first and second interval times (t1Δ, t2Δ) from curve is used to determine the kinetic parameters.

[0058] In a second exemplary embodiment of the present application, a concentration curve depicting the concentration of an analyte at a test surface over time is generated, and then the concentration curve is normalized to provide a normalized concentration curve (c(t)); and then the normalized concentration curve (c(t)) is used to determine first and second interval times (t1Δ, t2Δ):

[0059] In a second exemplary embodiment of the present application, in which a first and second volume (V1, V2) of sample fluid is flowed over a test surface of a flow cell to generate a binding curve, a first volume (V1') of a refractive index standard fluid containing a known concentration of a reference molecule is flowed over the test surface from a first reference time (t'1) to a second reference time (t'2).

[0060] Importantly, the rate (i.e., flow rate) at which the first volume (V1') of refractive index standard fluid flows over the test surface is equal to the rate at which the first volume (V1) of sample fluid flows over the test surface; and the time period between the first reference time (t'1) and the second reference time (t'2) is equal to the time period between the first time point (t1) and the second time point (t2).

[0061] After a first volume (V1') of refractive index standard fluid containing a known concentration of reference molecule is flowed over the test surface, a first volume (Vb1') of buffer fluid (which does not contain the reference molecule) is flowed over the test surface from a third reference time point (t'3) to a fourth time point (t'4) (the third reference time point (t'3) may be equal to the second reference time point (t'2)).

[0062] A second volume (V2') of refractive index standard fluid containing a known concentration of the reference molecule is then flowed over the test surface from a fifth reference time point (t'5) to a sixth reference time point (t'6).

[0063] Importantly, the rate at which the second volume (V2') of refractive index standard fluid flows over the test surface (i.e., the flow rate) is equal to the rate at which the second volume (V2) of the sample fluid flows over the test surface; and the time period between the fifth reference time point (t'5) and the sixth reference time point (t'6) is equal to the time period between the fifth time point (t5) and the sixth time point (t6); and the ratio of the concentration of the second volume (V2') of refractive index standard fluid to the concentration of the first volume (V1') of the refractive index standard fluid is equal to the ratio of the concentration of the second volume (V2) of the sample fluid to the first volume (V1) of the sample fluid; and the time period between the second reference time point (t'2) and the fifth reference time point (t'5) is equal to the time period between the second time point (t2) and the fifth reference time point (t'5).

[0064] After a second volume (V2') of refractive index standard fluid containing a known concentration of the reference molecule is flowed over the test surface, a second volume (Vb2') of buffer fluid (which does not contain the reference molecule) is flowed over the test surface from a seventh reference time point (t7) to an eighth reference time point (t8) (the seventh time point (t7) may be equal to the sixth reference time point (t'6)).

[0065] To obtain a concentration curve (cmc), the concentration of the reference molecule on the test surface is continuously measured over time from a first reference time point (t'1) to a ninth reference time point (t'9), where the ninth reference time point (t'9) occurs some time after the eighth reference time point (t'8) (or in another embodiment, the ninth reference time point (t'9) is equal to the eighth reference time point (t'8)).

[0066] The concentration curve (cmc) is then divided by the maximum value of the concentration curve (max(cmc)) and the result is the maximum known concentration (c) of the analyte in the first and second volumes (V1, V2) of the sample fluid, as shown in the following formula: max ) to obtain the normalized concentration curve (c(t)): c(t)=((cmc) / max(cmc))*c max

[0067] In this example, the concentration (c(V1)) of the analyte in the first volume (V1) of sample fluid is equal to the concentration (c(V2)) of the analyte in the second volume (V2) of sample fluid (i.e., both the first and second volumes (V1, V2) of sample fluid have the same concentration of the analyte); however, if one of the volumes (V1, V2) of sample fluid contains a higher concentration of the analyte than the other, then this higher concentration value will be equal to c(V2) max Define (i.e. (c max =max(c(V1),c(V2)). It will be appreciated that the concentration of an analyte in a volume of sample fluid may be determined using any suitable technique known in the art.

[0068] A threshold concentration is selected to determine the first and second interval times (t1Δ, t2Δ) using the normalized concentration curve (c(t)). Most preferably, the threshold concentration is determined as a predetermined percentage of the maximum value of the normalized concentration curve (c(t)); for example, if the maximum value of the normalized concentration curve (c(t)) is "200", the threshold concentration can be selected to be 5% of the maximum value, in this example 5%*200=10; therefore, the threshold concentration in this example is "10"; in another example, the threshold concentration can be 2% of the maximum value, in this example 2%*200=4, therefore, the threshold concentration in this example is "4".

[0069] The earliest time interval on the normalized concentration curve (c(t)) from the time the normalized concentration curve (c(t)) falls below the threshold concentration to the time the normalized concentration curve (c(t)) is equal to the threshold concentration defines a first interval time (t1Δ). The next time interval on the normalized concentration curve (c(t)) from the time the normalized concentration curve (c(t)) falls below the threshold concentration to a ninth reference time point (t'9), which occurs sometime after the first interval time (t1Δ), defines a second interval time (t2Δ).

[0070] In a variation of this embodiment, the concentration curve (not normalized) may alternatively be used to determine the first and second interval periods (t1Δ, t2Δ); it should be understood that, again, in this variation of the embodiment, the threshold concentration is selected. Most preferably, the threshold concentration is determined as a predefined percentage of the maximum value of the concentration curve; for example, if the maximum value of the concentration curve is "2000", the threshold concentration may be selected to be 5% of the maximum value, in this example 5%*2000=100; thus, the threshold concentration in this example is "100"; in another example, the threshold concentration may be 2% of the maximum value, in this example 2%*2000=40, thus, the threshold concentration in this example is "40". The earliest time interval on the concentration curve from the time when the concentration curve falls below the threshold concentration to the time when the concentration curve is equal to the threshold concentration defines the first interval time (t1Δ). The next time interval on the concentration curve from the time the concentration curve falls below the threshold concentration to the ninth reference time point (t'9), which occurs sometime after the first interval time (t1Δ), defines the second interval time (t2Δ).

[0071] In the above example, most preferably, the refractive index standard fluid preferably comprises a buffer fluid containing a known concentration of a reference molecule; and the reference molecule (which is present in the refractive index standard fluid at a known concentration) may comprise, for example, DMSO or glucose. Most preferably, the concentration of the reference molecule in the refractive index standard fluid (and therefore the concentration of the reference molecule in the first volume (V1') of the refractive index standard fluid, and also the concentration of the reference molecule in the second volume (V2') of the refractive index standard fluid) is preferably 0.1% v / v, or 0.5% v / v, or 1% v / v, and therefore the refractive index of the refractive index standard fluid is different from the refractive index of the first and second volumes (Vb1', Vb2') of the buffer fluid that do not contain the reference molecule.

[0072] Step (f) of determining kinetic parameters using the portions of the binding curve in the first and second time intervals (t1Δ, t2Δ) can be carried out using any known technique for determining kinetic parameters using a binding curve; those very same techniques can be used in the present invention to determine kinetic parameters, the difference being that the technique is applied to the portions of the binding curve in the first and second time intervals (t1Δ, t2Δ).

[0073] In a most preferred embodiment, the step of determining the kinetic parameters using the portions of the binding curve in said first and second interval periods (t1Δ, t2Δ) preferably includes the steps of generating a normalized concentration curve (c(t)) depicting the concentration of analyte at the test surface over time (if a normalized concentration curve (c(t)) has not already been generated; for example, the normalized concentration curve (c(t)) generated in the calibration step may be used) (using any of the steps described herein for obtaining a normalized concentration curve (c(t))); and determining the kinetic parameters Rmax, k a , k d where Rmax is a predetermined theoretical maximum binding curve value corresponding to saturation of the ligand (e.g., when all binding sites of the ligand are occupied by analyte bound to the ligand), and k a is the binding rate constant, and k d is the dissociation rate constant; the normalized concentration curve (c(t)) determined in the calibration step, and the kinetic parameters Rmax, k a , k d Using the above estimates for , we solve the differential reaction equation:

number

[0074] Once the differential reaction equation is obtained, the portion of the simulated binding curve in the first time interval (t1Δ) is then extracted to provide a first partial simulated binding curve (sbc1); and the portion of the simulated binding curve in the second time interval (t2Δ) is extracted to provide a second partial simulated binding curve (sbc2); and the partial chi-square (χ 2 ) to determine:

number

[0075] The partial chi-squared (χ 2 After the partial chi-square (χ 2 ) is minimized, where the determined partial chi-square (χ 2 ) to minimize the kinetic parameters Rmax, k a , k d The value of defines the kinetic parameters of the reaction between the analyte and the ligand attached to the test surface of the flow cell.

[0076] In a preferred embodiment, the kinetic parameters Rmax, k a , k d The step of estimating values ​​for partial chi-square (χ 2 The objective of the present invention is to find the kinetic parameters that minimize

[0077] In a further preferred embodiment, the kinetic parameters Rmax, k a , k d The step of estimating values ​​for partial chi-square (χ 2 The objective of the present invention is to find the kinetic parameters that minimize

[0078] Creating a normalized concentration curve: Each of the embodiments of the present invention includes the step of generating a concentration curve that depicts the concentration of analyte at the test surface over time, It should be noted that the concentration curve can be generated using any suitable method known in the art.

[0079] In the present invention, the step of generating a concentration curve may be performed using a volume of refractive index standard fluid containing a known concentration of a reference molecule, as described in the second embodiment above.

[0080] In another embodiment, a concentration curve depicting the concentration of analyte at the test surface over time can be generated using a mathematical model of convection and diffusion fluid dynamics transport phenomena.

[0081] In yet another embodiment, a concentration curve depicting the concentration of an analyte at a test surface over time can be generated using a simplified model that does not consider transport phenomenology: in this embodiment, the concentration curve is formed by setting the concentration curve to a "zero" value for the time before a first time point (t1), during a first interval time (t1Δ), and during a second interval time (t2Δ); the concentration curve is set to a constant value of c1 between the first time point (t1) and the second time point (t2), where c1 is the time when a first volume (V1) of sample fluid is placed on the test surface. C1 is the concentration of the analyte at the test surface between a first time point (t1) and a second time point (t2) as the second volume of sample fluid (V2) flows over the test surface (i.e., C1 is the concentration of the analyte in the first volume of sample fluid); the concentration curve is set to a constant value of c2 between a fifth time point (t5) and a sixth time point (t6), where c2 is the average concentration of the analyte at the test surface between the fifth time point (t5) and the sixth time point (t6) as the second volume of sample fluid (V2) flows over the test surface (i.e., C2 is the concentration of the analyte in the first volume of sample fluid).

[0082] Regardless of what steps are taken to generate the concentration curve, in each embodiment of the present invention, after the concentration curve is generated, the concentration curve is subsequently normalized to provide a normalized concentration curve (c(t)); the normalized concentration curve (c(t)) is then used to determine the kinetic parameters in a manner similar to that described in the above embodiments.

[0083] It should be appreciated that in some embodiments (e.g., the second embodiment), the concentration curve or normalized concentration curve can further be used to determine the predetermined interval time on the binding curve that is used to determine the kinetic parameters.

[0084] Exemplary embodiments using multiple volumes of sample fluid: Importantly, the above examples (particularly the first and second embodiments) describe flowing a first and second volume (V1, V2) of sample fluid containing an analyte over the test surface of the flow cell. However, it should be understood that any number of volumes of sample fluid can be flowed over the test surface of the flow cell (each volume of buffer fluid is flowed over the test surface between the volumes of sample fluid); the same principles of the invention apply when multiple volumes of sample fluid (e.g., more than two) are flowed over the surface of the flow cell. With respect to the second embodiment, the number of volumes of refractive index standard fluid flowing over the test surface of the flow cell during the calibration step corresponds to the number of volumes of analyte-containing sample fluid that have flowed or should flow over the test surface of the flow cell.

[0085] Thus, the method of the invention may comprise the steps of: sequentially flowing multiple volumes of sample fluid, each containing the analyte, over the test surface, with time intervals between each respective volume of sample fluid flowing over the test surface; and flowing respective volumes of buffer fluid (which does not contain analyte) over the test surface during each respective time interval; measuring binding of the analyte to the ligand on the test surface using a sensor to obtain a binding curve; and determining kinetic parameters using only portions of the binding curve at multiple predetermined time intervals.

[0086] The plurality of predetermined interval times can be determined as described in the first and second embodiments.

[0087] As mentioned with respect to the first and second embodiments, the method can include using a sensor to measure binding of the analyte to the ligand on the test surface continuously during the time that the first volume of sample fluid flows over the test surface until the time that the last volume of buffer fluid flows over the test surface; extracting portions of the binding curve at said plurality of predetermined time intervals; and determining kinetic parameters using only said extracted portions of the binding curve. In a further embodiment, the method includes extracting portions of the binding curve at said plurality of predetermined time intervals and portions of the binding curve after the last volume of sample fluid flows over the test surface until the level of binding falls to a predetermined threshold level; and determining kinetic parameters using only said extracted portions of the binding curve.

[0088] Alternatively, the method may include using a sensor to measure binding of analyte to the ligand on the test surface continuously during the time that the first volume of sample fluid flows over the test surface until the time that the last volume of buffer fluid flows over the test surface; zeroing the portion of the binding curve that is not at said plurality of predetermined intervals; and determining kinetic parameters using only said non-zeroed portion of the binding curve. Optionally, the portion of the binding curve after the last volume of sample fluid flows over the test surface until the level of binding falls to a predetermined threshold level may not be zeroed.

[0089] As mentioned in relation to the first and second embodiments, preferably the buffer fluid has a composition that allows the buffer to promote dissociation of analyte bound to a ligand on the test surface from said ligand. Most preferably, each respective volume of sample fluid is preferably composed of a buffer fluid that contains the analyte; and each respective volume of buffer fluid is preferably composed of the same buffer fluid as in the volume of sample fluid, but does not contain the analyte.

[0090] The step of determining the kinetic parameters using only the portion of the binding curve at said multiple predetermined intervals (and optionally also the portion of the binding curve after the last volume of sample fluid has flowed over the test surface until the level of binding falls to a predetermined threshold level) can be performed in the same manner as described above in the first or second embodiment, the only difference being that in the first and second embodiments, only two volumes of sample fluid (first and second volumes of sample fluid (V1, V2)) and only two intervals (first interval (t1Δ) and second interval (t2Δ)) are used, whereas in this second embodiment, this concept is extended to multiple volumes of sample fluid and multiple predetermined intervals.

[0091] The step of determining kinetic parameters using only the portion of the binding curve at said multiple predetermined time intervals (and optionally also the portion of the binding curve after the last volume of sample fluid has flowed over the test surface until the level of binding has fallen to a predetermined threshold level) can be carried out using any known technique for determining kinetic parameters using a binding curve; those very same techniques can be used in the present invention to determine kinetic parameters, the difference being that the technique is applied exclusively to only the portion of the binding curve at said multiple predetermined time intervals (and optionally also the portion of the binding curve after the last volume of sample fluid has flowed over the test surface until the level of binding has fallen to a predetermined threshold level).

[0092] Most preferably, to determine the kinetic parameters using only the portion of the binding curve at said multiple predetermined time intervals (and optionally also the portion of the binding curve after the last volume of sample fluid has flowed over the test surface until the level of binding has fallen to a predetermined threshold level), the following steps are performed: generating a normalized concentration curve (c(t)) depicting the concentration of analyte at the test surface over time (using any of the techniques described herein); determining the kinetic parameters Rmax, k(t) and the binding curve (using any of the techniques described herein);a , k d where Rmax is a predetermined theoretical maximum binding curve value corresponding to saturation of the ligand (e.g., when all binding sites of the ligand are occupied by analyte bound to the ligand), and k a is the association rate constant, and k d is the dissociation rate constant; the normalized concentration curve (c(t)) determined in the calibration step, and the kinetic parameters Rmax, k a , k d Using the above estimates for , we solve the differential reaction equation:

number

[0093] Once the differential reaction equation is obtained, portions of the simulated binding curve at said plurality of predetermined time intervals (tjΔ) are then extracted to provide respective partial simulated binding curves (sbcj).

[0094] Subsequently, the partial chi-squared (χ 2 ) is determined according to the following formula:

number

[0095] where dmbj is the portion of the binding curve at the jth time interval (tjΔ), sbcj is the jth partial simulated binding curve, and N dmbj is the number of data points in the jth predetermined time interval (tjΔ) of the binding curve.

[0096] The partial chi-squared (χ 2 After the partial chi-square (χ 2) is minimized, where the determined partial chi-square (χ 2 ) to minimize the kinetic parameters Rmax, k a , k d The value of defines the kinetic parameters of the reaction between the analyte and the ligand attached to the test surface of the flow cell.

[0097] In a preferred embodiment, the kinetic parameters Rmax, k a , k d The step of estimating values ​​for partial chi-square (χ 2 The objective of the present invention is to find the kinetic parameters that minimize

[0098] In a further preferred embodiment, the kinetic parameters Rmax, k a , k d The step of estimating values ​​for partial chi-square (χ 2 The objective of the present invention is to find the kinetic parameters that minimize

[0099] Description of Figure 1-3: 1-3 can be used to illustrate the principles outlined in the second embodiment above, applied where multiple volumes of sample fluid are flowed over the test surface of a flow cell.

[0100] FIG. 1 shows an example of a complete binding curve obtained when six volumes of sample fluid (V1-V6) are flowed consecutively over the test surface of a flow cell. The complete binding curve includes the following binding curves: when the first volume of sample fluid (V1) containing the analyte flows over the test surface (T1-T2); after the first volume of sample fluid containing the analyte flows over the test surface and before the second volume of sample fluid flows over the test surface (T2-T3) (during time T2-T3, a first volume of buffer fluid (V'1), which does not contain analyte, flows over the test surface); when the second volume of sample fluid containing the analyte (V2) flows over the test surface (T3-T4); after the second volume of sample fluid containing analytes has flowed over the test surface and before the third volume of sample fluid has flowed over the test surface (T4-T5) (during time T4-T5, a second volume of buffer fluid (V'2), which does not contain analyte, flows over the test surface); when the third volume of sample fluid containing analyte (V3) flows over the test surface (T5-T6); after the third volume of sample fluid containing analyte has flowed over the test surface and before the fourth volume of sample fluid flows over the test surface (T during time T6-T7 (during time T6-T7, a third volume (V'3) of buffer fluid (which does not contain analyte) flows over the test surface); when a fourth volume (V4) of sample fluid containing analyte flows over the test surface (T7-T8); after the fourth volume of sample fluid containing analyte flows over the test surface and before a fifth volume of sample fluid flows over the test surface (T8-T9) (during time T8-T9, a fourth volume (V'4) of buffer fluid (which does not contain analyte) flows over the test surface). flow; when the fifth volume (V5) of sample fluid containing analyte flows over the test surface (T9-T10); after the fifth volume of sample fluid containing analyte flows over the test surface and before the sixth volume of sample fluid flows over the test surface (T10-T11) (during time T10-T11, a fifth volume (V'5) of buffer fluid (which does not contain analyte) flows over the test surface); when the sixth volume (V6) of sample fluid containing analyte flows over the test surface (T11-T12);indicates the amount of analyte bound to the ligand on the test surface after a sixth volume of sample fluid containing the analyte has flowed over the test surface, until the amount of analyte bound to the ligand has decreased to a predetermined threshold level or until a predetermined time has elapsed (T12-T13) (preferably during time T12-T13, a sixth volume (V'6) of buffer fluid (which does not contain analyte) is flowed over the test surface);

[0101] Preferably, the volumes of buffer fluid (V'1 to V'6) preferably have a composition that enables the buffer fluid to promote dissociation of analyte bound to ligands on the test surface from said analyte. Most preferably, each of the volumes of sample fluid (V1 to V6) consists of buffer fluid mixed with analyte; each of the volumes of buffer fluid (V'1 to V'6) consists of buffer fluid only (i.e. no analyte), and most preferably the buffer fluid in each of the volumes of buffer fluid (V'1 to V'6) is the same as the buffer fluid in the volumes of sample fluid (V1 to V6).

[0102] Each of the six volumes (V1-V6) of sample fluid has a known concentration of analyte. The concentration of analyte in each volume can be determined using any means known in the art. Thus, the concentration of analyte in each of the six volumes (V1-V6) of sample fluid is known. The volume (V1-V6) of sample fluid having the greatest concentration of analyte is the volume with the greatest concentration (c max In this example, each of the six volumes (V1-V6) of sample fluid happens to have the same concentration of analyte (so each volume of sample fluid has the maximum concentration (c max )); however, in another embodiment, the six volumes (V1 to V6) of sample fluid have different concentrations of analyte, in which case the maximum concentration (c max ) is the concentration of the analyte in the volume (V1-V6) of sample fluid having the greatest concentration.

[0103] Figure 2 shows a number of predetermined intervals of the extracted binding curve of Figure 1. It should be understood that Figure 2 may alternatively show a number of predetermined intervals of the binding curve of Figure 1, with other portions of the binding curve being considered to be "zeroed". In any event, in the present invention, Figure 2 shows the portion of the binding curve that is exclusively used in the present invention (e.g., in step (e) of the first embodiment) to determine kinetic parameters.

[0104] It should be understood that the predetermined interval times are preferably determined from a concentration curve or from a normalized concentration curve. Figure 3 shows the normalized concentration curve used to determine the predetermined interval times; these predetermined interval times need to be determined in order to know which portion of the binding curve of Figure 1 to extract to form the curve shown in Figure 2.

[0105] In this case, six volumes (V1-V6) of sample fluid are flowed sequentially over the test surface of the flow cell to generate the binding curve (Figure 1), and six volumes of corresponding refractive index standard fluids containing known concentrations of the reference molecule are flowed over the test surface to obtain the normalized concentration curve in Figure 3.

[0106] after the first volume of refractive index standard fluid (V''1) has flowed over the test surface; after the first volume of refractive index standard fluid has flowed over the test surface and before the second volume of refractive index standard fluid has flowed over the test surface (during this time a first volume of buffer fluid (V'1), which does not contain the reference molecule, flows over the test surface); when the second volume of refractive index standard fluid (V''2) flows over the test surface; after the second volume of refractive index standard fluid has flowed over the test surface and before the third volume of refractive index standard fluid has flowed over the test surface. before the second volume of the buffer fluid (V'2), which does not contain the reference molecules, flows over the test surface; when the third volume of the refractive index standard fluid (V''3) flows over the test surface; after the third volume of the refractive index standard fluid flows over the test surface and before the fourth volume of the refractive index standard fluid flows over the test surface (during this time, the third volume of the buffer fluid (V'3), which does not contain the reference molecules, flows over the test surface); when the fourth volume of the refractive index standard fluid (V''4) flows over the test surface. when the fourth volume of the refractive index standard fluid flows over the test surface; after the fourth volume of the refractive index standard fluid has flowed over the test surface and before the fifth volume of the refractive index standard fluid flows over the test surface (during this time, a fourth volume of buffer fluid (V'4), which does not contain the reference molecule, flows over the test surface); when the fifth volume of the refractive index standard fluid (V''5) flows over the test surface; after the fifth volume of the refractive index standard fluid has flowed over the test surface and before the sixth volume of the refractive index standard fluid flows over the test surface (during this time, a fifth volume of buffer fluid (V'5), which does not contain the reference molecule, flows over the test surface); when the sixth volume of the refractive index standard fluid (V''6) flows over the test surface; after the sixth volume of the refractive index standard fluid has flowed over the test surface, until the concentration of the reference molecule at the test surface decreases to a predetermined threshold level or until a predetermined time has elapsed (preferably during this time, a sixth volume of buffer fluid (V'6), which does not contain the reference molecule, flows over the test surface). The normalized concentration curve in FIG. 3 is obtained.A concentration curve (cmc) is generated by measuring the concentration of the reference molecule at the test surface while each of the above steps is performed (preferably from before the first volume (V1) of sample fluid flows over the test surface until the concentration of the reference molecule at the test surface is reduced to a predetermined threshold level or until a predetermined time has elapsed, at the end of the last step, in which a sixth volume (V'6) of buffer fluid flows over the test surface).

[0107] Importantly, the rate at which each volume of the refractive index standard fluid flows over the test surface (i.e., the flow rate) is equal to the rate at which each of the six volumes of the sample fluid (V1-V6) flows over the test surface, and the ratio of concentrations of the volumes of the refractive index standard fluid (V1''-V''6) is equal to the ratio of concentrations of the volumes of the sample fluid (V1-V6).

[0108] The concentration curve (cmc) is then divided by the maximum value of the concentration curve (max(cmc)) and the result is the maximum known concentration (c max ) to obtain the normalized concentration curve (c(t)) shown in Figure 3: c(t)=((cmc) / max(cmc))*c max

[0109] To determine each of the plurality of predetermined interval times from the normalized concentration curve (c(t)) shown in Figure 3, a threshold concentration is selected; in this example, the threshold concentration is 5% of the maximum value of the normalized concentration curve (c(t)); since the maximum value of the normalized concentration curve (c(t)) is "200", in this example the threshold concentration is "10" (i.e., 5% * 200 = 10). The time intervals from when the normalized concentration curve (c(t)) falls below the level of "10" to when it rises again above "10" define the plurality of predetermined interval times. Referring to the normalized concentration curve (c(t)) shown in FIG. 3, at time T'2, the normalized concentration curve (c(t)) falls below the level of "10", and at time T'3, the normalized concentration curve (c(t)) rises to "10", so T'2-T'3 defines one of the predetermined intervals; at time T'4, the normalized concentration curve (c(t)) falls below the level of "10", and at time T'5, the normalized concentration curve (c(t)) rises to "10", so T'4-T'5 defines one of the predetermined intervals. at time T'6, the normalized concentration curve (c(t)) falls below the level of "10", and at time T'7, the normalized concentration curve (c(t)) rises to "10", so that T'6-T'7 defines another of the predetermined intervals; at time T'8, the normalized concentration curve (c(t)) falls below the level of "10", and at time T'9, the normalized concentration curve (c(t)) rises to "10", so that T'8-T'9 defines another of the predetermined intervals; 10 At time T', the normalized concentration curve (c(t)) falls below the level of "10". 11 The normalized concentration curve (c(t)) rises to 10, so T' 10 -T' 11 defines another one of the predetermined interval times; time T' 12 At time T', the normalized concentration curve (c(t)) falls below the level of "10". 13 Now that the specified time has elapsed, T' 12 -T' 13 defines the end of said predetermined interval.

[0110] Predetermined interval times T'2-T'3, T'4-T'5, T'6-T'7, T'8-T'9, T' 10 -T' 11 , T' 12 -T' 13 The portion of the binding curve shown in FIG. 1 occurring at a time corresponding to is then extracted to produce the binding curve shown in FIG. 2, which is used to calculate the kinetic parameters Rmax, k a , k d Determine.

[0111] Various modifications and variations to the described embodiments of the invention will be apparent to those of ordinary skill in the art without departing from the scope of the invention, which is defined in the appended claims. Although the invention has been described in connection with specific preferred embodiments, it should be understood that the invention as claimed should not be unduly limited to such specific embodiments. In addition, the present application relates to the invention described in the claims, but may also include the following as other aspects. 1. A method for determining kinetic parameters of a reaction between an analyte and a ligand attached to a test surface of a flow cell, comprising the steps of: (a) A first volume (V1) of sample fluid containing the analyte is measured at a first time point (t 1 ) and the second time point (t 2 ) over the test surface; (b) A first volume of analyte-free buffer fluid (Vb1) is added at a third time point (t 3 ) and the fourth time point (t 4 ) over the test surface; (c) measuring at least a second volume (V2) of sample fluid containing the analyte at a fifth time point (t 2 ) and the sixth time point (t 6 ) over the test surface; (d) adding at least a second volume (Vb2) of analyte-free buffer fluid to the sample at a seventh time point (t 7 ) and the eighth time point (t 8 ) over the test surface; (e) measuring binding of the analyte to the ligand on the test surface using the sensor to obtain a binding curve; (f) determining kinetic parameters using only the portion of the binding curve at a given time interval without using other portions of the binding curve; The method includes: 2. The predetermined interval time includes a first and a second interval time (t1Δ, t2Δ); The first interval time (t1Δ) is the second time point (t 2 ) and the fifth time point (t 5 ) and the second interval time (t2Δ) occurs between the sixth time point (t 6 ) and the ninth time point (t 9 ) and at the ninth time point (t 9 ) is the eighth time point (t 8 ) or at some time after the ninth time point (t 9 ) is the eighth time point (t 8 ), The method according to claim 1. 3. The first interval time (t1Δ) is the second time point (t 2 ) and the fifth time point (t 5 ) and the second interval time (t2Δ) is a portion of the period between the sixth time point (t 6 ) and the ninth time point (t 9 ) is part of the period between The first interval time (t1Δ) is the second time point (t 2 ) and the fifth time point (t 5 ) and the second interval time (t2Δ) is defined by the entire time interval between the sixth time point (t 6 ) and the ninth time point (t 9 ), defined by the entire time interval between The method described in 2 above. 4. The method of claim 1, further comprising a calibration step for determining said predetermined interval time, said calibration step comprising the steps of: creating a concentration curve; and determining said predetermined interval time using said concentration curve. 5. The step of determining the predetermined interval time using the concentration curve, Selecting a threshold concentration; identifying a moment when said concentration curve is equal to said threshold concentration; Including, each respective predetermined interval time being defined by the time between an instant at which the concentration curve is at the threshold concentration (wherein said concentration curve exhibits a decrease in concentration prior to said instant) and a next instant at which the concentration curve is at the threshold concentration (wherein said concentration curve exhibits an increase in concentration prior to said next instant); The method according to claim 4. 6. The step of selecting a threshold concentration comprises: identifying a maximum of said concentration curve; Selecting a percentage value; wherein the threshold concentration is defined by a maximum value of the concentration curve multiplied by the percentage value. The method according to item 5 above. 7. Further comprising a calibration step for determining said predetermined interval time; the calibrating step comprises: generating a concentration curve; normalizing the concentration curve to provide a normalized concentration curve (c(t)); and then determining the predetermined interval time using the normalized concentration curve (c(t)). The method according to claim 1. 8. The step of determining the predetermined interval time using the normalized concentration curve comprises: Selecting a threshold concentration; identifying an instant at which the normalized concentration curve is equal to the threshold concentration; Including, each respective predetermined interval time is defined by the time between an instant at which the normalized concentration curve is at the threshold concentration (wherein the normalized concentration curve shows a decrease in concentration prior to said instant) and a next instant at which the normalized concentration curve is at the threshold concentration (wherein the normalized concentration curve shows an increase in concentration prior to said next instant); The method according to claim 7. 9. The step of selecting a threshold concentration comprises: identifying a maximum of said normalized concentration curve; Selecting a percentage value; wherein the threshold concentration is defined by the maximum of the normalized concentration curve multiplied by the percentage value. 9. The method according to claim 8. 10. Using the sensor, continuously measure the first time point (t 1 ) or from the first time point (t 1 ) from the eighth time point (t 8 ) or until the eighth time point (t 8 measuring binding of the analyte to the ligand on the test surface until after said predetermined time interval; extracting a portion of the binding curve at said predetermined time interval; determining kinetic parameters using only said extracted portion of the binding curve; 10. The method according to any one of 1 to 9 above, comprising: 11. Using the sensor, continuously measure the first time point (t 1 ) or from the first time point (t 1 ) from the eighth time point (t 8 ) or until the eighth time point (t 8 measuring binding of the analyte to the ligand on the test surface until after said predetermined time interval; zeroing the portion of the binding curve that is outside said predetermined time interval; determining kinetic parameters using only said non-zeroed portion of the binding curve; The method according to any one of 1 to 10 above, comprising: 12. sequentially flowing a plurality of volumes of sample fluid, each containing the analyte, over the test surface, with a time interval between each respective volume of sample fluid flowing over the test surface; flowing respective volumes of analyte-free buffer fluid over the test surface for each respective interval time; measuring binding of the analyte to the ligand on the test surface using the sensor to obtain a binding curve; determining kinetic parameters using only portions of the binding curve at multiple predetermined time intervals; The method according to any one of 1 to 11 above, comprising: 13. A step of determining kinetic parameters using only a portion of the binding curve at a predetermined time interval without using other portions of the binding curve, creating a normalized concentration function c(t) that describes the concentration of the analyte at the test surface over time; Kinetic parameters Rmax, k a 、k d where Rmax is a predetermined maximum response value corresponding to saturation of the ligand on the test surface, and k a is the binding rate constant, and k d is the dissociation rate constant; To obtain the simulated binding curve, the normalized concentration curve (c(t)) and the kinetic parameters Rmax, k a 、k d Using the above estimates for , we solve the differential reaction equation:

number

number

Claims

1. 1. A method for determining kinetic parameters of a reaction between an analyte and a ligand attached to a test surface of a flow cell, comprising the steps of: (a) a first volume (V1) of sample fluid containing the analyte is measured at a first time (t １ ) and the second time point (t ２ ) over a test surface; (b) A first volume (Vb1) of analyte-free buffer fluid is added at a third time point (t ３ ) and the fourth time point (t ４ ) over a test surface; (c) measuring at least a second volume (V2) of sample fluid containing the analyte at a fifth time point (t5) and a sixth time point (t ６ ) over a test surface; (d) adding at least a second volume (Vb2) of analyte-free buffer fluid to the sample at a seventh time point (t ７ ) and the eighth time point (t ８ ) over a test surface; (e) using the sensor to measure binding of the analyte to the ligand on the test surface to obtain a binding curve; (f) determining kinetic parameters using only the portion of the binding curve at a given time interval without using other portions of the binding curve; Including, the predetermined interval time includes a first and a second interval time (t1Δ, t2Δ); a first interval time (t1Δ) occurs between the second time point (t2) and the fifth time point (t5); and a second interval time (t2Δ) occurs between the sixth time point (t6) and the ninth time point (t9), the ninth time point (t9) occurring some time after or equal to the eighth time point (t8); Neither the binding curves between the first time point (t 1 ) and the second time point (t 2 ) nor between the fifth time point (t 5 ) and the sixth time point (t 6 ) are used to determine kinetic parameters; The method.

2. The first interval time (t1Δ) is a second time point (t ２ ) and the fifth time point (t ５ ) and the second interval time (t2Δ) is a portion of the period between the sixth time point (t ６ ) and the ninth time point (t ９ ) is part of the period between The first interval time (t1Δ) is a second time point (t ２ ) and the fifth time point (t ５ ) and the second interval time (t2Δ) is defined by the entire time interval between the sixth time point (t ６ ) and the ninth time point (t ９ ), defined by the entire time interval between The method of claim 1.

3. 2. The method of claim 1, further comprising a calibration step for determining said predetermined interval time, said calibration step comprising: generating a concentration curve depicting the concentration of analyte on the test surface over time; and determining said predetermined interval time using said concentration curve.

4. determining said predetermined interval time using said concentration curve, Selecting a threshold concentration; identifying a moment when said concentration curve is equal to said threshold concentration; Including, each respective predetermined interval time being defined by the time between an instant at which the concentration curve is at the threshold concentration (wherein said concentration curve exhibits a decrease in concentration prior to said instant) and a next instant at which the concentration curve is at the threshold concentration (wherein said concentration curve exhibits an increase in concentration prior to said next instant); The method according to claim 3.

5. The step of selecting a threshold concentration comprises: identifying a maximum of said concentration curve; Selecting a percentage value; wherein the threshold concentration is defined by a maximum value of the concentration curve multiplied by the percentage value. The method according to claim 4.

6. a calibration step for determining said predetermined interval time; the calibration step comprises: generating a concentration curve depicting the concentration of the analyte at the test surface over time; normalizing the concentration curve to provide a normalized concentration curve (c(t)) depicting the concentration of the analyte at the test surface over time; and then determining the predetermined interval time using the normalized concentration curve (c(t)). The method of claim 1.

7. The step of determining the predetermined interval time using the normalized concentration curve comprises: selecting a threshold concentration; identifying an instant at which the normalized concentration curve is equal to the threshold concentration; Including, each respective predetermined interval time being defined by the time between a moment at which the normalized concentration curve is at a threshold concentration, where said normalized concentration curve exhibits a decrease in concentration prior to said moment, and a next moment at which the normalized concentration curve is at the threshold concentration, where said normalized concentration curve exhibits an increase in concentration prior to said next moment; The method according to claim 6.

8. The step of selecting a threshold concentration comprises: identifying a maximum of said normalized concentration curve; Selecting a percentage value; wherein the threshold concentration is defined by the maximum of the normalized concentration curve multiplied by the percentage value. The method according to claim 7.

9. Using the sensor, at a first time point (t １ ) or from the first time point (t １ ) from the eighth time point (t ８ ) or until the eighth time point (t ８ measuring binding of the analyte to the ligand on the test surface continuously after the predetermined time interval; extracting a portion of the binding curve at said predetermined time interval; determining kinetic parameters using only said extracted portion of the binding curve; The method according to any one of claims 1 to 8, comprising:

10. Using the sensor, at a first time point (t １ ) or from the first time point (t １ ) from the eighth time point (t ８ ) or until the eighth time point (t ８ measuring binding of the analyte to the ligand on the test surface continuously until after said predetermined time interval; zeroing the portion of the binding curve that is outside said predetermined time interval; determining kinetic parameters using only said non-zeroed portion of the binding curve; The method according to any one of claims 1 to 9, comprising:

11. sequentially flowing a plurality of volumes of sample fluid, each containing the analyte, over the test surface, with a time interval between each respective volume of sample fluid flowing over the test surface; flowing respective volumes of analyte-free buffer fluid over the test surface for each respective time interval; measuring binding of the analyte to the ligand on the test surface using the sensor to obtain a binding curve; determining kinetic parameters using only portions of the binding curve at multiple predetermined time intervals; The method according to any one of claims 1 to 10, comprising:

12. determining kinetic parameters using only a portion of the binding curve at a predetermined time interval without using other portions of the binding curve; generating a normalized concentration curve depicting the concentration of the analyte at the test surface over time; Kinetic parameters Rmax, k ａ , k ｄ where Rmax is a predetermined maximum response value corresponding to saturation of the ligand on the test surface, and k ａ is the binding rate constant, and k ｄ is the dissociation rate constant; obtaining a simulated binding curve using said estimates for the kinetic parameters Rmax, k a , and k d ; extracting portions of the simulated binding curve at said plurality of predetermined time intervals (tjΔ) to provide respective partial simulated binding curves (sbcj); The partial chi-square (χ ２ ) determining: [0025] where d is the portion of the binding curve at the jth predetermined interval (tΔ), s is the jth partial simulated binding curve, and N ｄｍｂｊ is the number of data points in the jth predetermined time interval (tjΔ) of the binding curve; The determined partial chi-square (χ ２ ), Including, The determined partial chi-square (χ ２ The kinetic parameters Rmax, k ａ , k ｄ defines the kinetic parameters of the reaction between the analyte and the ligand attached to the test surface of the flow cell. The method according to any one of claims 1 to 11.

13. Constructing a concentration curve depicting the concentration of analyte at the test surface over time may be accomplished using a Levenberg-Marquard algorithm to obtain a partial chi-squared (χ ２ 13. The method of claim 12, comprising finding the kinetic parameters that minimize

14. Kinetic parameters Rmax, k ａ , k ｄ The step of estimating values ​​for ２ 13. The method of claim 12, comprising finding the kinetic parameters that minimize

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