Method for determining dissociation constant of two binding molecules

Abstract

The present invention related to methods for determining and correcting the dissociation constant KD of a binding pair of two molecules. The method measures of the binding of two biomolecules at 4 or more different absolute temperatures (T) between 4- 40ºC and then calculating and correcting the dissociation constants (KD).

Description

METHOD FOR DETERMINING DISSOCIATION CONSTANT OF TWO BINDING MOLECULESFIELD OF THE INVENTIONThe present invention related to methods for determining and correcting the dissociation constant KD of a binding pair of two molecules.BACKGROUND OF THE INVENTIONThe constant of dissociation, or dissociation constant, is a kinetic parameter used when measuring intermolecular interactions and binding events between two or more molecules. There are methods to measure the association rate of a complex formation of two molecules that bind to each other, followed by monitoring the dissociation rate of the complex, and then derive an overall equilibrium binding constant.Label-free analytical methods such as BioLayer Interferometry (BLI, Comb Chem High Throughput Screen, 2009 Sep;12(8):791-800) offers an advantage of determining the association and dissociation of two molecules without the use of labels that could perturb the immune binding. Ylera et al. (Analytical Biochemistry 441 (2013) 208-213) report off-rate screening for selection of high-affinity anti-drug antibodies using BLI method. These methods have become the accepted gold standard for affinity measurements. BLI has been widely used in biotherapeutic development, however, the lack of sensitivity’ and potential interference by crude biological samples have restricted clinical applications.BRIEF DESCERIPTION OF THE DRAWINGSFIG. 1 A depicts a biosensor interferometer that includes a light source, a detector, a waveguide, and an optical assembly (also referred to as a ‘"probe”).FIG. I B depicts an example of a conventional probe.FIG. 2 depicts another configuration of a probe.FIGs. 3A-3B illustrate the principles of detection in a thin-film interferometer.FIGs. 4A-4G show the wavelength shift vs. time of association and dissociation, at different temperatures. The dashed line represents the time when the probe moves from PD-1 sample to buffer for dissociation.FIG. 5 plots R*Ln(Ko) vs. 1 / T (°K). FIG. 5 shows that the five points on the right fit in a linear line, but the two points on the left contribute to a poor linear fitting (the dash line) with R2being 0.96.FIG. 6 adjusts the two points of FIG. 5 to fit a straignt line.DETAILED DESCRIPTION OF THE INVENTIONDefinitionsUnless specifically defined in this section, serms used in the claims and specification are to be construed in accordance with their usual meaning as understood by one skilled in the art.‘‘About,” as used herein, refers to within ± 10% of the recited value.“Absolute temperature, also called thermodynamic temperature, is the temperature of an object on a scale where 0 is taken as absolute zero. Absolute temperature scales are Kelvin. Celsius to Kelvin: K=C+273.15 conversion.“Antibody affinity" describes the strength of an antibody binds to an antigen.A “binding molecule.” refers to a molecule that is capable to bind another molecule of interest.“A binding pair,” as used herein, refers to two molecules that are attracted to each other and specifically bind to each other. Examples of binding pairs include, but not limited to, an antigen and an antibody against the antigen, a ligand and its receptor, complementary strands of nucleic acids, biotin and avidin, biotin and streptavidin, lectin and carbohydrates.“Immobilized,” as used herein, refers to reagents being fixed to a solid surface. When a reagent is immobilized to a solid surface, it is either be non-covalently bound or covalently bound to the surface.A “probe.” as used herein, refers to a substrate coated with a thin-film layer of binding molecules at the sensing side. A probe has a distal end and a proximal end. The proximal end (also refers to probe tip in the application) has a sensing surface coated with a thin layer of analyte-binding molecules. Probe can be made of glass or quartz of any other suitable materials such as plastic, optical fiber, metal, or ceramic. In one example, a “probe” can be a pin, in a slender elongated form.Equilibrium Dissociation ConstantBinding kinetics describes the dynamic binding interaction between two molecules.kon (also called ka) is the rate constant of association of the two molecules, which describes the rate at which the studied molecules form a complex. koff (also called kd) is the rate constant of dissociation of the two molecules.Dissociation constant (KD ) is the rate constant of dissociation at equilibrium, defined as the ratio koff / kon.In equilibrim, the forward binding transition of two molecules A and B: A+B >AB should be balanced by the backward unbinding transition (dissociation): AB^A + B. That is, kon [A] [B] = koff [AB]Where [A] and [B] represent the concentration of unbound free molecules, and [AB] represent the concentration of the complex.KD= koff / kon = [A] [B] / [AB]Binding affinity is the strength of the binding interaction between a molecule to its ligand or binding partner. Binding affinity is typically measured and reported by the equilibrium dissociation constant (KD), which is used to evaluate and rank order strengths of bimolecular interactions. The smaller the KD value, the greater the binding affinity of the ligand for its target. The larger the KD value, the weaker the two binding molecules are attracted to and bind to one another.Calculation of Kobs from Experimental Results-kobs*tY = YQ+ Rgq(l -e ) Equation A kobs is the rate constant that is observed in an experiment. It can be the rate constant of association of the two molecules or the the rate constant of the dissociation of the two molecules. In this example, kobs is the the rate constant of association.In equation A, R eq and k o ,bs are unknown,To expalin how to calculation kobs from Equation I from experimental results, we illustrate herewith a solid phase binding, where molecule A is immobilized to a solid pase, and its binding partner molecule B is in a liquid phase, in contact with the solid phase. The association and dissociation can be measured by different methods, In one embodiment, the association and dissociation can be measured by a biolayer interferometry (BLI) method, which measures the wavelength shift when two molecules are associated or dissociated.Y is the wavelength shift at time 0 when two molecules start to associate, i.e., when molecule B starts to bind to molecule A on the solid phase.Y is wavelength shift observed at a given time t during the association. kobs is unknown and is calculated from equation A.By curve fitting putting wavelength shift (Y) vs. time (t) into Equation A, kobs is calculated.Calculation of kofrThe following equation calculates koff.-koff*tDissociation: Z = ZQ+ A^ Equation BZ(jis the wavelength shift at time 0 when two molecules start to dissociate.Z is wavelength shift observed at a given time t during the dissociation.By putting in numbers of wavelength shift (Z) vs. time (t) into Equation II, koff is calculated.Calculation of konkon = (kobs -koff) / starting molecule B concentration. Equation CTo calculate kon, we subtract koff from kobs, and divide it by the starting concentration of molecule B in the liquid phase when the association startsCalculation of KDKD = koff / kon (Equation D)Relation of KD and TemperatureA spontaneous reaction takes place in the direction of a decrease in Gibbs (G) free energy under constant temperature and pressure conditions.AGO = AH - TAS Equation E where GO represents the Gibbs free energy, T represents absolute temperature (K), S is the entropy and H is the enthalpy.If the reaction is in equilibrium, at the equilibrium, based on the Van't Hoff isotherm equation:AGO = -RT InKo Equation FWhere R is the ideal gas constant (8.314 J / (mol»K) or 1.987 cal / (mol»K)).Substitute Equation E into Equation F and divide by T to obtain- R lnKD= AH / T - AS Equation GDetermining Equibrilium Dissociation Constant KDThe present invention is directed to a method for determining and correcting the dissociation constant KD of a binding pair of two molecules. The method comprises: (a) measuring of the binding of two biomolecules at 4 or more different absolute temperatures (T) between 4- 40°C and calculating the dissociation constants (KD); (b) plotting R*1U(KD) VS. 1 / T; wherein R is ideal gas constant. In is nature log, and T is absolute temperate; (c) curvefitting the plot to a linear line; and (dl) determining that the measured KD at each of the measured temperatures is accurate if its R*ln(Ko) value results in the coefficient of determination r2> 0.98 of the fitted linear line, or (d2) determining that the measured KD at the measured temperature is inaccurate if its R*1U(KD) value is not on the fitted linear line, and (e) correcting the inaccurate R*ln(Ko) value to a corrected R*ln(Ko) value that is the fitted linear line; and calculating a corrected KD from the corrected R*ln(Ko) value.In step (a), the binding and dissociation of two biomolecules can be measured by methods known to a person skilled in the art. For example, it can be measured by end point assays or kinetic assays. End point assays include spectroscopy assays such as UV-visible, fluorescence, and NMR; separation methods such as FIPLC, GC, and CE even centrifuge. Kinetic assays include continuous real time monitoring methods such as bio-layer interferometry' (BLI), grating coupled interferometry (GCI), Kinexa, and surface plasmon resonance (SPR).In one embodiment, the binding and dissociation can be measured by fluorescent detection as described in WO2021 / 0247838, which is incorporated herein in its entirety7.In one embodiment, the binding and dissociation can be measured by BLI method as described in W02023 / 019107, which is incorporated herein in its entirety.In one embodiment, the binding and dissociation can be measured by surface plasmon resonance (SPR) method, which is an optical technique for detecting molecular interactions in real time. SPR can occur when plane-polarized light hits a metal film under total internal reflection conditions. SPR signal is directly dependent on the refractive index of the medium on the sensor chip. The binding of biomolecules results in changes in the refractive index on the sensor surface. In an SPR experiment, one molecule is immobilized on a sensor chip and its binding to a second molecule is measured under flow. Response is measured in resonance units (RU) and is proportional to the mass on the surface. For a binding reaction, the responseis proportional to the number of molecules bound to the surface.The KD (koff / kon) value is calculated from the experimental data according to the description above.In step (b), R*ln(Kn) and 1 / T values are mathetically calculated and R*ln(Ko) vs. 1 / T is plotted. T is an absolute temperature using the Kelvin scale where zero is absolute zero. The zero point is the temperature at which particles of matter have their minimum motion, After data collating, analysis and computation according to the calculation described in Detailed Description of the Invention, the KD and R*ln(Kn) values were calculatedIn step (c), the plot is fitted into a linear trend line with least squares. The line is described by a linear equation and the coefficient of determination r2. If the fitted linear equation has r2equal to or greater than 0.98, it is considered as an accurate fitting. If r2is less than 0.98, the fitting is poor.In step (dl) and (d2), if the R*ln(Kn) value accurately fits the linear line, then the measured KD at the measured temperature is determined to be accurate. However, if the R*ln(Ko) value poorly fits the linear line, then the measured KD at the measured temperature is inaccurate and further step needs to be taken in order to determine a correct KD value. In step (e), the one or more R*ln(Kn) values of the inaccurate KD in step (d2) are moved to fit them into a straight line with the other R*ln(Ko) values of the accurate KD. Based on the corrected value of R*ln(Ko) on the linear line, the KD values are then calculated as the corrected KD values.There are several benefits to employing the aforementioned method. For example, by calculating and then plotting the dissociation constants at several different absolute temperatures, instances of inaccuracy can be discovered in a more consistent, efficient manner. In response to a determination that a given KD is incorrect, rather than remeasure binding and recalculate a correct KD. step (e) can instead be employed. This approach not only ensures that significant time and physical resources are not expended on addressing inaccurate dissociation constants, but does so in a computationally ‘lightweight” manner by relying on a linear model rather than more computationally “heavyweight” approaches, such as linear regression or polynomial regression, that are generally not necessary to achieve sufficient accuracy.Biosensor Interferometer SystemsSeveral biosensor interferometer systems can be used for measuring the binding anddissociation of two molecules. FIGs. 1 A-B illustrate examples of a system in which a solid support is a probe. FIG. 1A depicts a biosensor interferometer 100 (or simply “interferometer') that includes a light source 102, a detector 104, a waveguide 106. and an optical assembly 108 (also referred to as a “probe’’). The probe 108 may be connected to the waveguide 106 via a coupling medium.The light source 102 may emit white light that is guided toward the probe 108 by the waveguide 106. For example, the light source 102 may be a light-emitting diode (LED) that is configured to produce light over a range of at least 50 nanometers (nm), 100 nm, or 150 nm within a given spectrum (e.g., 400 nm or less to 700 nm or greater). Alternatively, the interferometer 100 may employ a plurality of light sources having different characteristic wavelengths, such as LEDs designed to emit light at different wavelengths in the visible range. The same function could be achieved by a single light source with suitable filters for directing light with different wavelengths onto the probe 108.The detector 104 is preferably a spectrometer, such as an Ocean Optics USB4000, that is capable of recording the spectrum of interfering light received from the probe 108. Alternatively, if the light source 102 operates to direct different wavelengths onto the probe 108, then the detector 104 can be a simple photodetector capable of recording intensity at each wavelength. In another embodiment, the detector 104 can include multiple filters that permit detection of intensity7at each of multiple w avelengths.The waveguide 106 can be configured to transport light emitted by the light source 102 to the probe 108. and then transport light reflected by surfaces within the probe 108 to the detector 104. In some embodiments the waveguide 106 is a bundle of optical fibers (e g., single-mode fiber optic cables), while in other embodiments the waveguide 106 is a multimode fiber optic cable.As shown in FIG. IB, the probe 108 includes a monolithic substrate 114, a thin-film layer (also referred to as an “interference layer”), and a biomolecular layer (also referred to as a “biolayer”) comprised of analyte molecules 122 that have bound to analyte-binding molecules 120. The monolithic substrate 114 is comprised of a transparent material through which light can travel. The interference layer is also comprised of a transparent material. When light is shone on the probe 108, the proximal surface of the interference layer may act as a first reflecting surface and the biolayer may act as a second reflecting surface. As further described below, light reflected by the first and second reflecting surfaces may form an interference pattern that can be monitored by the interferometer 100.The interference layer normally includes multiple layers that are combined in such a manner to improve the detectabi lily of the interference pattern. Here, for example, the interference layer is comprised of a tantalum pentoxide (Ta20s) layer 116 and a silicon dioxide (SiO2) layer 118. The tantalum pentoxide layer 1 16 may be thin (e.g., on the order of 10-40 nm) since its main purpose is to improve reflectivity at the proximal surface of the interference layer. Meanwhile, the silicon dioxide layer 118 may be comparatively thick (e.g., on the order of 650-900 nm) since its main purpose is to increase the distance between the first and second reflecting surfaces.To perform a test, the probe 108 can be suspended in a microwell 110 (or simply “well'’) that includes a sample 112. Analyte molecules 122 will bind to the analyte-binding molecules 120 along the distal end of the probe 108 over the course of the diagnostic test, and these binding events will result in an interference pattern that can be observed by the detector 104. The interferometer 100 can monitor the thickness of the biolayer formed along the distal end of the probe 108 by detecting shifts in a phase characteristic of the interference pattern.FIG. 2 illustrates another biosensor interferometer probe. The probe includes a monolithic substrate that has a first and a second surfaces arranged substantially parallel to one another at opposite ends of the monolithic substrate, an interference layer coated on the second surface of the monolithic substrate, and a layer of analyte-binding molecules coated on the interference layer. The interference layer will generally be comprised of magnesium fluoride (MgF2). A first interface between the monolithic substrate and the interference layer acts as a first reflecting surface when light is shone on the interferometric sensor, while a second interface between a biolayer formed by analyte molecules in a sample binding to the analyte-binding molecules and a solution containing the sample acts as a second reflecting surface when the light is shone on the probe. As described above, the thickness of the biolayer can be estimated based on the interference pattern of light reflected by the first and second reflecting surfaces.The probe 200 includes an interference layer 204 that is secured along the distal end of a monolithic substrate 202. Analyte-binding molecules 206 can be deposited along the distal surface of the interference layer 204. Over the course of a biochemical test, a biolayer will form as analyte molecules 208 in a sample bind to the analyte-binding molecules 206.

[0035] As shown in Figure 2, the monolithic substrate 202 has a proximal surface (also referred to as a “coupling side") that can be coupled to, for example, a waveguide of an interferometer and a distal surface (also referred to as a “sensing side'’) on which additionallayers are deposited. Generally, the monolithic substrate 202 has a length of at least 3 millimeters (mm), 5 mm, 10 mm, or 15 mm. In a preferred embodiment, the aspect ratio (length-to-width) of the monolithic substrate 202 is at least 5 to 1. In such embodiments, the monolithic substrate 202 may be said to have a columnar form. The cross section of the monolithic substrate 202 may a circle, oval, square, rectangle, triangle, pentagon, etc. The monolithic substrate 202 preferably has a refractive index that is substantially higher than the refractive index of the interference layer 204, such that the proximal surface of the interference layer 204 effectively reflects light directed onto the probe 200. The preferred refractive index of the monolithic substrate may be higher than 1.5, 1.8, or 2.0. Accordingly, the monolithic substrate 202 may be comprised of a high-refractive-index material such as glass (refractive index of 2.0) rather than a low-refractive-index material such as quartz (refractive index of 1.46) or plastic (refractive index of 1.32-1.49).The interference layer 204 is comprised of at least one transparent material that is coated on the distal surface of the monolithic substrate 202. These transparent material(s) are deposited on the distal surface of the monolithic substrate 202 in the form of thin films ranging in thickness from fractions of a nanometer (e.g.. a monolayer) to several micrometers. The interference layer 204 may have a thickness of at least 500 nm, 700 nm, or 900 nm. An exemplary thickness is between 500-5,000 nm (and preferably 800-1,200 nm). Here, for example, the interference layer 204 has a thickness of approximately 900-1,000 nm, or 940 nm.In contrast to conventional probes, the interference layer 204 has a substantially similar refractive index as the biolayer. This ensures that the reflection from the distal end of the probe 200 is predominantly due to the analyte molecules 208 rather than the interface between the interference layer 204 and the analyte-binding molecules 206. In some embodiments the interference layer 204 is comprised of magnesium fluoride (MgF2), while in other embodiments the interference layer 204 is comprised of potassium fluoride (KF), lithium fluoride (LiF), sodium fluoride (NaF), lithium calcium aluminum fluoride (LiCaAlFe), sodium aluminum fluoride (Na3AlFe), strontium fluoride (SrF2), aluminum fluoride (AlFs). sulphur hexafluoride (SFe), etc. Magnesium fluoride has a refractive index of 1.38, which is substantially identical to the refractive index of the biolayer formed along the distal end of the probe 200. For comparison, the interference layer of conventional probes is normally comprised of silicon dioxide, and the refractive index of silicon dioxide is approximately 1.4- 1.5 in the visible range. Because the interference layer 204 and biolay erhave similar refractive indexes, light will experience minimal scattering as it travels from the interference layer 204 into the biolayer and then returns from the biolayer into the interference layer 204.In one embodiment, the probe 200 includes an adhesion layer that is deposited along the distal surface of the interference layer 204 affixed to the monolithic substrate 202. The adhesion layer may be comprised of a material that promotes adhesion of the analyte-binding molecules 206. One example of such a material is silicon dioxide. The adhesion layer is generally very thin in comparison to the interference layer 204, so its impact on light traveling toward, or returning from, the biolayer will be minimal. For example, the adhesion layer 310 may have a thickness of approximately 3-10 nm, while the interference layer 304 may have a thickness of approximately 800-1,000 nm. The biolayer formed by the analytebinding molecules 306 and analyte molecules 308 will normally have a thickness of several nm.When light is shone on the probe 200, the proximal surface of the interference layer 204 may act as a first reflecting surface and the distal surface of the biolayer may act as a second reflecting surface. The presence, concentration, or binding rate of analyte molecules 208 to the probe 200 can be estimated based on the interference of beams of light reflected by these two reflecting surfaces. As analyte molecules 208 attach to (or detach from) the analyte-binding molecules 206, the distance between the first and second reflecting surfaces will change. Because the dimensions of all other components in the probe 200 remain the same, the interference pattern formed by the light reflected by the first and second reflecting surfaces is phase shifted in accordance with changes in biolayer thickness due to binding events.In operation, an incident light signal 210 emitted by a light source is transported through the monolithic substrate 202 toward the biolayer. Within the probe 200, light will be reflected at the first reflecting surface resulting in a first reflected light signal 212. Light will also be reflected at the second reflecting surface resulting in a second reflected light signal 214. The second reflecting surface initially corresponds to the interface between the analytebinding molecules 206 and the sample in which the probe 200 is immersed. As binding occurs during the biochemical test, the second reflecting surface becomes the interface between the analyte molecules 208 and the sample.The first and second reflected light signals 212, 214 form a spectral interference pattern, as shown in FIG. 3A. When analyte molecules 208 bind to the analyte-bindingmolecules 206 on the distal surface of the interference layer 204, the optical path of the second reflected light signal 214 will lengthen. As a result, the spectral interference pattern shifts from TO to T1 as shown in FIG. 3B. By measuring the phase shift continuously in real time, a kinetic binding curve can be plotted as the amount of shift versus the time. The association rate of an analyte molecule to an analyte-binding molecule immobilized on the distal surface of the interference layer 204 can be used to calculate analyte concentration in the sample. Hence, the measure of the phase shift is the detection principle of a thin-film interferometer.Fluorescent Detection SystemSeveral fluorescent detection systems can be used for measuring the binding and dissociation of two molecules. For example, a fluorescent detection system as described in U.S. Patent No. 8,309,369, which is incorporated herein by reference, can be used in the present invention. The system comprises: (a) a probe having an aspect ratio of length to width at least 5 to 1, the probe having a first end and a second end, the second end having a sensing surface bound with a fluorescent label; (b) a light source for emitting excitation light directly to the probe’s sensing surface; (c) a collecting lens pointed toward the sensing surface; and (d) an optical detector for detecting the emission fluorescent light; where the collecting lens collects and directs the emission fluorescent light to the optical detector.The probe can be a monolithic substrate or an optical fiber. The probe can be any shape such as rod, cylindrical, round, square, triangle, etc., with an aspect ratio of length to width of at least 5 to 1, preferably 10 to 1. Because the probe is dipped in a sample solution and one or more assay solutions during an immunoassay, it is desirable to have a long probe with an aspect ratio of at least 5 to 1 to enable the probe tip’s immersion into the solutions. Heterogeneous assays can be performed where the long probe is transferred to different reaction chambers. Dispensing and aspirating reagents and sample during the assay are avoided. The sensing surface of the probe is coated with analyte-binding molecules and bound with fluorescent labels.Any light source that can emit proper excitation light for the fluorescent label is suitable for the present invention. A prefer light source is a laser that can emit light with wavelengths suitable for fluorescent labels. For example, the laser center wavelength is preferred to be 649 nm for Cy5 fluorescent dye. A suitable optical detector for detecting emission light is a photomultiplier tube (PMT), a charge coupled device (CCD), or aphotodiode.The light source and the optical detector including the collecting lens are mounted on the same side of the probe tip surface (the sensing surface). If the sensing surface faces down, they are both mounted below the tip surface. If the sensing surface faces up, they are both mounted above the tip surface. They are closer to the sensing surface than the other end of the probe. The sensing surface is always within the numeric aperture of the collecting lens. The probe can be, but it does not have to be centrally aligned with the collecting lens.The invention is illustrated further by the following examples that are not to be construed as limiting the invention in scope to the specific procedures described in them.EXAMPLESExample 1.ObjectiveComparison of associatiation and dissociation of a pair of molecules (anti-PD 1 antibody and PD-1) at a temperature between 10°C and 40°C.EquipmentThe Gator® Pivot instrument (Gator Bio) was used to run the experiments at different temperatures (10, 15, 20, 25, 30, 35, or 40°C).BiosensorGator* Anti-Human IgG Fc Gen II (HFCII) probes (Gator Bio, Inc.) are high- performance nanobody -based biosensors that can detect and quantitate human IgG.ReagentsBuffer: PBST (PBS+0.02%Tween+0.2% BSA)Human anti-PD-1 antibody (Absolute Antibody Ab00791 -13.12). The anti-PD-1 antibody is diluted in PBST to 5 pg / mL in the wells. 1 is serial-diluted in PBST toExperiment Procedures(a) Immerse HFCII probe into anti-PDl solution to allow the anti-PDl binding to the probe. The affinity between HFCII probe (anti -human IgG Fc) and human anti-PDl is 2 orders of magnitude higher than the affinity of anti-PDl and PD1, therefore dissociation of the immunocomplex formed by anti-Fc / Anti-PDl / PDl is negligible compared to dissociation of PDl from anti-PDl.(b) Rinse the probe with buffer.(c) Immerse the probe into PD1 sample to bind PD1 to the anti-PD l immobilized probe for a period of time and measure the wavelength shift due to association of PD1 to the anti- PDl -immobilized probe vs. time.(d) Immerse the probe into PBST buffer (see dashed line in each figure below) and and measure the wavelength shift for a period of time due to dissociation of PD 1 from the anti- PDl -immobilized probeResultsThe wavelength shift vs. time of association and dissociation at different temperatures are plotted and shown in FIGs. 4A-4G. The dashed line represents the time when the probe moves from PD-1 sample to buffer for dissociation.By curve fitting putting wavelength shift (Y) vs. time (t) into Equation A according to FIGs. 4A-4G, Kobs is calculated.By putting in numbers of wavelength shift (Z) vs. time (t) into Equation B, Koff and Kon, and KD are then calculated. Tables 1-7 below show calculated Kob, Koff, Kon, and KD at different temperatures. Tables 1-7 correspond to FIGs 4A-4G.Table 1. Experimental temperature: 10°CTable 2. Experimental temperature: 15°CTable 3. Experiment temperature: 20°CTable 4. Experimental temperature: 25°CTable 5. Experimental temperature: 30°CTable 6. Experimental temperature: 35°CTable 7. Experimental temperature: 40°CExample 2. Calculation based on the Results of Example 1.(A) Plotting R*ln vs. 1 / T (K)After data collating, analysis and computation according to the calculation described in Detailed Description of the Invention, the R*ln(Ko) values were calculated and they are shown in Table 8 below.Table 8.Then the value of R*ln(Ko) is plotted against 1 / T (K). The scale of 1 / T is shown in 0.001 in FIG. 5. The results are shown in the solid line in FIG. 5.FIG. 5 shows that the five points on the right fit in a linear line, but the two points on the left contribute to a poor linear fitting (the dash line) with R2being 0.96. From FIG. 5, we conclude that the calculated KD values of the five points on the right (temperatures of 10, 15, 20, 25, and 30°C) shown in Table 8 are accurate, and the calculated KD values of the tw o points in the left (temperatures of 35 and 40°C) shown in Table 8 are inaccurate.(B) Adjusting R*ln(Kp) value to fit a straight lineAccording to the methods described in Detailed Description of the Invention, we then move the tw o points on the left in FIG. 5 to fit them into a straight line (see FIG. 6).(C) Recalculating KD valuesBased on the R*ln(Kn) value of FIG. 6, the KD value are re-calculated in Table 9. TheKD values at 35°C and 40°C are now accurate and different from those in Table 8.Table 9.The invention, and the manner and process of making and using it, are now described in such full, clear, concise and exact terms as to enable any person skilled in the art to which it pertains, to make and use the same. It is to be understood that the foregoing describes preferred embodiments of the present invention and that modifications may be made therein without departing from the scope of the present invention as set forth in the claims. To particularly point out and distinctly claim the subject matter regarded as invention, the following claims conclude this specification.

Claims

WHAT IS CLAIMED IS:

1. A method for determining and correcting the dissociation constant KD of a binding pair of two molecules, comprising:(a) measuring the binding of two molecules at 4 or more different absolute temperatures (T) between 4- 40°C and calculating the dissociation constants (KD);(b) plotting R*ln(Ko) vs. 1 / T; wherein R is ideal gas constant, In is nature log, and T is absolute temperate;(c) curve-fitting the plot to a fitted linear line;(dl) determining that the measured KD at each of the measured temperatures is accurate if its R*ln(Ko) value results in the coefficient of determination r2> 0.98 of the fitted linear line, or (d2) determining that the measured KD at the measured temperature is inaccurate if its R*ln(Ko) value causes the coefficient of determination r2<0.98 of the fitted linear line, and(e) correcting the inaccurate R*ln(Kn) value to a corrected R*ln(Ko) value that provides an accurate fitted linear line; and calculating a corrected KD from the corrected R*ln(Ko) value.

2. The method of claim 1, wherein the measurement of the binding of the two molecules are performed by kinetic or end point measurement.

3. The method of claim 2, wherein measurement is performed by spectroscopy measurement, biolayer interferometry, grating coupled inferferometry, or surface plasmon resonance.

4. The method of claim 3, wherein measurement is preformed by biolayer interferometry.

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