Titration methods to measure kinetic binding parameters and distinguish specific binding from background

Abstract

A method for determining kinetic binding parameters of a molecular binder conjugated to a fluorophore. Repeated staining of an antigen and detection of emitted radiation generates a titration series. By fitting the emitted radiation over the titration series, kinetic binding parameters can be determined. The emitted radiation is detected by a camera, and single-pixel fitting using global analysis allows for discrimination of specific binding signal from nonspecific background at each pixel.

Description

[Technical Field]

[0001] The present invention relates to a method for measuring the kinetic binding parameters of molecular binding agents with target epitopes and for distinguishing specific binding from background.

[0002] background Prior art approaches to measuring the kinetic binding parameters of molecular binders and their target epitopes are based on purifying the target epitope to isolate the interaction in vitro. Typically, binding of a molecule to a target epitope is monitored label-free by immobilizing the target epitope on a glass substrate, where the on-rate and off-rate constants of the molecular binder are measured via changes in surface plasmon resonance (SPR) at the glass substrate (e.g., Bakhtiar, J Chem Ed 90, 203, 2012). Specifically, an empty buffer solution is applied to the sample, followed by rapid exchange with a buffer solution containing the molecular binder at a specific concentration to determine the unbound molecular binder concentration A and the unbound target epitope concentration E: dB / dt = k on The on-rate constant k is defined as the proportionality constant connecting the rate of change B of the concentration of epitope bound to the molecular binder to the product of AE, depending on the mass action. on The sample is then typically allowed to reach equilibrium binding and the dissociation constant is determined. The buffer is then rapidly exchanged with empty buffer to determine the proportionality constant connecting the rate of change in concentration of the binding epitope to the concentration of the binding epitope, i.e., dB / dt=-k off The off-rate constant, defined as B, can then be determined independently.

[0003] While such in vitro approaches are routinely employed to determine the on- and off-rate constants of molecular binders, purification of the target epitope represents a complex and time-consuming step. For certain epitopes, purification may even be impossible. Attachment of the target epitope to glass represents an additional problematic step, as attachment can lead to misfolding and altered binding. Molecular binders may also additionally and nonspecifically bind to the glass substrate, generating background. Finally, kinetic parameters obtained by such in vitro approaches may not be transferable to other, more relevant contexts, such as to accurately predict the binding of dye-labeled versions of molecular binders to fixed biological samples for immunofluorescence.

[0004] In situ determination of the kinetic binding constants of fluorescent probes binding to epitope targets within biological samples has been reported, for example, at the cell population level (Bondza et al., Frontiers in Immunology 8, 455, 2017). Here, a LigandTracerGreen setup (Ridgeview Instruments) was used to obtain kinetic binding curves of immunofluorescent probes applied to cell populations. Specifically, the target cell population was briefly stained (30 seconds), washed (5 seconds), and imaged (30 seconds) under a microscope in multiple cycles. This allowed the kinetic binding curve of the cell population to be sampled at a fixed concentration of applied probe on a time scale of approximately 1 minute. After incubation with the probe at this fixed concentration, an additional incubation step at zero probe concentration allowed the off-rate constant to be determined. Background binding was corrected by obtaining a binding curve for control cells not expressing the target epitope and subtracting this control binding curve from the binding curve of the target cell population. Related approaches down to the level of single cells (May et al., Molecular Pharmacology 78, 511, 2010) or tissue regions (Dubois et al., BMC Research Notes 6, 542, 2013) have also reported that rely on separate measurements of control cells or regions to indirectly estimate the contribution of background binding in target cells or regions. A more precise determination of the actual contributions of specific and nonspecific binding in each region of interest, ideally down to the single pixel level, has not been achieved.

[0005] Immunofluorescence staining of cells has recently been extended from classical single-shot imaging to imaging of multiple different targets on the same tissue slice, allowing high-content insight into the target epitope and the cellular microenvironment of the tissue (Kinkhabwala et al., Sci Rep 12, 1911, 2022). The MACSima Imaging System (Miltenyi Biotec BV & Co.KG) is specifically designed for this technique.

[0006] The current solution for reducing background in immunofluorescence images is to "block" the sample before staining using specific (e.g., Fc domain to block Fc receptors) or nonspecific (e.g., whole serum, bovine serum albumin, or isotype antibody controls) blocking reagents. For a given antibody staining, it is difficult to predict the amount of blocking (blocking reagent concentration and incubation time) required to enhance signal-to-background. Blocking can improve the contrast of antibody staining by reducing background, but it does not completely eliminate the background. Blocking reagents may also block the targeted epitope in the sample, reducing the specific signal.

[0007] Background patterns in images can be visualized by using an isotype antibody control stain with a different fluorescent label. Scaling subtraction of the isotype control stain from the immunofluorescence stain can be used to remove background signals. However, the scaling factor to apply is not clearly defined. Color shifts or other imaging distortions caused by detection across two different fluorescent channels can also disrupt the final image. Furthermore, isotype control staining may not represent the actual nonspecific binding of antibodies due to inevitable differences in their recognition domains.

[0008] There are currently no sufficiently comprehensive methods available for accurately determining the kinetic binding parameters (specifically, on-rate and off-rate constants) that control in situ binding of molecular binders to target epitopes within fixed biological samples. A fundamental challenge here is the proper discrimination of a specific signal (target binding interaction) from multiple potential contaminating backgrounds (mainly due to nonspecific binding interactions).

[0009] Furthermore, there are currently no sufficiently comprehensive methods available to reliably extract specific staining signals from the background in each pixel of immunofluorescence images of fixed biological samples to enable truly background-free immunofluorescence imaging.

[0010] Object of the invention We propose a method based on repeated staining and imaging of a dye-labeled molecular binder on a fixed biological sample using an automated microscope for immunofluorescence imaging (the "titration method") that (1) enables accurate discrimination of the specific kinetics of molecular binding to a target epitope from background binding interactions, and (2) simultaneously enables accurate discrimination of specific binding signals from background in every pixel of the sample image. Specifically, a model is fitted across a stack of images corresponding to different titrations of the dye-labeled molecular binder to the sample. By fitting a model that describes both the specific binding interaction and the background binding interaction, kinetic binding parameters characterizing the specific interaction can be simultaneously extracted, as well as the signal-to-background ratio in every pixel (representing a 3D voxel) of the sample image. Thus, the primary output of the method of the present invention is the kinetic binding parameters of molecules binding to the target epitope, as well as pure signal and pure background images.

[0011] It is therefore an object of the present invention to provide a method for determining the on-rate constant for the specific binding of a conjugate comprising a fluorescent detection moiety and an antigen-binding moiety applied to a fixed biological sample expressing a corresponding antigen, as well as a method for determining the contribution of specific and background binding to the emitted radiation at each registered pixel of an image of the fixed biological sample, comprising: a. measuring the emitted radiation of the fixed biological sample as an image formed on a camera before delivering the conjugate; b. thereafter, providing the conjugate to the fixed biological sample at at least two different concentrations and for a specific time interval; c. detecting emitted radiation for each concentration as an image formed on a camera; d. Registering the images to each other; e. fitting a function that accounts for the amount of specific binding and background binding for each concentration to the emission radiation in each aligned pixel across the separate images; f. Obtaining the on-rate constants defining the specific binding function from step e). and The method is characterized by comprising:

[0012] Preferably, in addition to obtaining the on-rate that defines the specific binding function, the contributions of specific binding and background binding to the emitted radiation are determined at each registered pixel of the image of the fixed biological sample.

[0013] The method further comprises: g. creating an image of the specific binding by assigning the emission radiation contributed by the specific binding to each aligned pixel; h. creating an image of the background coupling by assigning the emission radiation contributed by the background coupling to each aligned pixel; The method can be characterized by including:

[0014] The fixed biological sample may represent one of the following: adherent cells, suspension cells, tissue or a smear (eg bone marrow). [Brief explanation of the drawings]

[0015] [Figure 1] 1A and 1B are diagrams illustrating the titration method of the present invention. [Figure 2] FIG. 1 shows an example of the titration method applied to fixed tissue slices.

[0016] Detailed Description of the Invention This paper details a method for measuring the kinetic binding parameters of a molecular binder to its target epitope located in a fixed biological sample. The method is based on applying a series of titrations of a molecular binder to a fixed biological sample, with the emission from the sample measured after each step. If the emission emission is detected as a microscopic image for each titration step, a global analysis across the aligned images (each corresponding to a different titration) can be used. In this case, the global analysis allows for the discrimination of the signal (specific binding of the molecular binder) from the background (non-specific binding of the molecular binder) at each pixel of the aligned image sequence. Thus, a new image can be constructed in which each pixel contains only the signal proportional to the concentration of the target epitope.

[0017] In the drawings, the following reference numbers are used to refer to the following features: Similar reference numbers are used in the various figures to denote components having similar or identical functions: 001 Fixed biological specimens 002 Cover slide 003 Microscope Objective Lens 004 Nuclear DAPI staining image 005 Image of dye-labeled molecular binder (compared to the same in other images in the row) 006 Image of dye-labeled molecular binder (compared to any other) 007 Extracted image of specific binding ("signal") 008 Extracted image of non-specific binding ("background").

[0018] The titration method is shown in Figure 1A. The titration method is characterized by a series of staining and washing of single molecule binders targeting specific antigens within a fixed biological sample, typically corresponding to a fixed tissue slice several microns thick. A series of images obtained for the various titration steps are shown in Figure 1A. m can be used, for example, to determine the on-rate constant for specific binding of a molecular binder. Image sequences can also be used to distinguish signal contributions from background binding. In FIG. 1B, an additional delayed image sequence consisting of at least one image B1 can be performed directly following the titration process shown in FIG. 1A for better determination and differentiation of the off-rate constants for specific and background binding.

[0019] By modifying standard instrument protocols, the titration method of the present invention can be performed using the MACSima Imaging System (Miltenyi Biotec BV & Co. KG), which allows automated sequential immunofluorescence staining of fixed biological samples.

[0020] The standard instrument protocol for MACSima consists of sequential staining and immunofluorescence imaging of fixed biological samples using an array of molecular binders. The standard protocol is typically characterized by repeated cycles of staining, washing, imaging, and clearing. Clearing of the fluorescent signal from a specific molecular binder is achieved by photodestruction of the fluorophore (photobleaching) or by enzymatic cleavage of the molecular binder (with an additional wash step applied to remove the solubilized fluorophore) to remove the fluorophore from the sample. For sequential staining of a given field of view, returning to the same z-position within the sample is ensured by detecting and adjusting the distance from the objective lens to the glass cover slide (using the glass position determined by detecting reflected IR light) and / or by comparing the current DAPI image of the sample with the initial DAPI image from the first cycle. During a subsequent image registration step, image registration in the xy plane to subpixel accuracy is then performed, enabling accurate measurement of the same voxels of the fixed biological sample across the final aligned image stack.

[0021] To implement titration in MACSima, the following minor modification to the standard instrument protocol is required. Titration is based on repeated cycles of staining (typically 10 min), washing, and imaging with a single molecular binder; clearing is no longer applied in each cycle. Instead, a series of concentrations is additively applied to the sample. For example, sequential application of 0.625 μg / mL, 1.875 μg / mL, 7.5 μg / mL, and 30 μg / mL of molecular binder corresponds to a four-fold increase in additive staining, with titration steps of 0.625 μg / mL, 2.5 μg / mL, 10 μg / mL, and 40 μg / mL. The concentration range should be carefully selected to ensure sufficient sampling of the complete shape of the unknown saturation curve, where the highest concentration is sufficient to drive the molecular binder to at least slight saturation, similar to the standard requirement for measuring dissociation constants in the context of chemical binding assays.

[0022] Weak nonspecific interactions between molecules and samples should not show saturation over the applied titration range and are expected to increase linearly with additive concentration. However, more complex background models can also be considered (see the mathematical treatment section below).

[0023] Such a background model can further be utilized in the first embodiment of the present invention to obtain the off-rate constant for specific binding and the off-rate constant for background binding from the function.

[0024] In a second embodiment, the on-rate constant for background binding is further obtained from the function.

[0025] Thus, the different profiles expected for saturated signal against a linearly increasing background (or more complex background models) over a series of titration images represent an important aspect of the titration method that allows reliable discrimination of signal from background.

[0026] Specifically, by fitting the integrated signal for each individual image of a titration series (or global fitting based on individual pixel information), the specific on-rate constant of a molecule can be accurately determined at its target epitope.

[0027] Furthermore, at the time of fixation following the final staining / washing step, one or more images can be acquired to separately and more directly determine the off-rate constants for specific and background binding (Figure 1B).

[0028] Therefore, in the third embodiment, before step d, each of the following steps: j. waiting a specific time interval; k. detecting emitted radiation; is executed.

[0029] Step j and step k can be repeated at least once at the same or different time intervals.

[0030] The method further comprises step f: l. Obtaining the on-rate constant and off-rate constant that define the specific binding function from step e. is replaced by

[0031] The method further comprises fitting the function in step e using global analysis.

[0032] Global analysis of the titration image sequence can be used to determine both the optimal global kinetic parameters for specific binding (and, if necessary, kinetic parameters for background binding) and local parameters corresponding to the fractional contribution formed by the ratio of specific binding to background binding at each pixel. The latter allows for the reconstruction of images containing only specific binding or only background binding ("signal" and "background" images in Figure 2). Images of specific binding are importantly free of contamination by background binding up to the noise limit at each pixel, enabling "background-free" immunofluorescence imaging.

[0033] The method further comprises: converting the function in step e into the following two steps: m. In a first step, fitting to the integrated image intensities to determine a specific binding function; n. In a second step, fitting the amount of specific binding and background binding for each concentration to the emission radiation within each aligned pixel across the individual images; The present invention is characterized by fitting the above.

[0034] All embodiments are described in detail below.

[0035] mathematical processing The titration methods, analyses and outputs corresponding to the various embodiments have been described above only generally. In the following, the exact mathematical treatment is carried out. Throughout, the following parameters are assumed: V solution volume A T All applicable antibodies A. Free antibody a T Total applied antibody concentration (A T / V') B-binding antibody E T All epitopes E Free epitope b Percentage of binding epitopes (B / E T ) f Percentage of free epitopes (E / E T ) ε Ratio of total epitopes to total antibodies (E T / A T ) K on On-rate constant [μM -1 s -1 ] K off Off-rate constant [s -1 ] K D Dissociation constant [μM] For standard immunofluorescence staining, fixed biological samples are attached to a cover slide at the bottom of the well, and then a total volume of antibody probe, A T , is immersed in a solution volume V. The total number of epitopes in the sample is E T Storage conditions A T =A+B E T =E+B where B is the bound antibody (1:1 binding to the target epitope), A is the free antibody, and E is the remaining unbound epitope.

[0036] Assumption #1 (fast diffusion, no significant spatial gradient): If diffusion is fast compared to the binding timescale, the exact spatial distribution of epitopes in the chromosome product can be ignored, and the k of the interactionon and k off One can simply examine the increase in total bound epitope with respect to time based on standard chemical kinetics defined by

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[0037] Assumption #2 (Antibodies greatly exceed the target epitopes): In typical immunofluorescence staining, the amount of antibody applied is much greater than the total number of target epitopes in the sample, i.e., E T < T In the limit of ε → 0,

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[0038] specific interaction k on Decision Assumption #3a: If the off-rate constant is negligible (i.e., k off < <k​on a T or equivalently a T >>K D ), Equation 2 becomes b(t)=1-exp(-k on a T t) This becomes:

[0039] Assumption #3b: Alternatively, if the argument in the exponent in Equation 2 is small compared to 1 (far from saturation), a first-order Taylor expansion gives the following linear relationship: b(t)=k on α T t is obtained.

[0040] Under either assumption, the off-rate constant does not affect the evolution of the binding moiety.

[0041] Antibody concentration a at any time period t=t1 T Following immunostaining with =a1, the sample is washed and imaged. The binding sites observed under assumption 3a are b1=1-exp(-k on a1t1) and repeated staining resulted in an exponential decrease (f i =1-b i ) and more easily expressed in terms of f1=f0exp(-k on a1t) In the case of multiple staining (assuming f0=1), this means that

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[0042] specific interaction k on and k off Decision More generally, if the off-rate constant cannot be neglected, the solution is given by the different incubation times t allowed at each step. k and is best expressed in matrix form as follows: According to Equation 1, in terms of the binding moiety at step k-1, (the titer a k (following the application of) the bonded part at step k, i.e.

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[0043] If there is a long waiting time between separate incubations (when the applied antibody concentration is zero), the off-rate constant can play an important role. The intervals here can also be explicitly included in the model. Here, it is assumed that the rebinding of the antibody detached from the epitope can be ignored. This is because the change in the binding fraction due to newly removed antibodies is considered negligible compared to the change in the binding fraction that occurs during the staining step assuming that the applied antibody significantly exceeds the epitope (staining assumption #2, E T <<AT). Therefore, the bound epitope is as follows b k =exp(-k off t k )b k-l decreases by. θ k =exp(-k off t k ) is defined as, which is b k =θ k b k-1 and in matrix form is

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[0044] Above, only the proportion of bound epitopes in the total volume is considered. For an image, the relative intensity from one pixel to the next depends on the local concentration of target epitopes contributing to the staining of pixel p, which we call e p Here, e p Specifically, it refers to the convolution of the true 3D concentration of the epitope with the optical transfer function ("detection volume") of the microscope (e.g., in the case of a confocal microscope, the optical transfer function is σ for each pixel). x ,σ y ,σ z (This is well approximated by a spatially invariant 3D Gaussian with axes k). In this case, the intensity in the immunofluorescence image of a particular signal following titration step k is simply:

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[0045] Specific interactions (k on and / or k off ) and linear background (slope, m) determination If the contribution from the background is significant, the background is expected to increase linearly with the applied titration. As shown above (approximation #3b), the linear approximation is appropriate for binding interactions that are far from saturation, which is a reasonable assumption for the background and is also consistent with our experimental results (e.g., Figure 2). Because nonspecific sites are heterogeneous, they may require different on-rate constants for different classes of nonspecific binding sites j.

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[0046] If the titration is performed in sufficiently rapid succession, the off-rate constant for non-specific binding can be neglected, which means that the incubation time for each step, t s (assuming that the "additive" concentration is equal to

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[0047] In this case, the model-predicted intensity at pixel p at step k is assumed to be specific signal and independent of step k. An additional offset Q (e.g., to account for the incomplete subtraction of the pre-stain image intensity from all subsequent stained images) is added. p and the nonspecific background contribution, i.e.,

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[0048] The percentage of specific binding at step k is calculated as above (matrix form). N p =Ee p and M p =Em p If we define

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[0049] where N is the number of pixels for single pixel fitting across the titer image sequence. p , M p and Q as an optional measure p Up to three local parameters are required. These are k on k as a global value for and an option for specific interactions off Typically, k is fitted over the duration of the titration process. off can be ignored, which results in

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[0050] An error model is required to properly weight and fit the model to the pixel information across the image sequence.

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[0051] Now that we have defined the error model, we can perform an appropriately weighted global fitting of the modeled intensities to the observed intensities. Specifically, this is done by p ,M p ,Q p ) model parameters and global (k on and k off ) minimizing the squared difference between modeled and observed intensities across all pixels p of each titer image k for a given set of model parameters;

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[0052] Global fitting can be performed at the full pixel resolution of the image or for any partitioning of the data into superpixels such as size 2×2, 3×3, etc. In the latter case, it is necessary to simply sum each superpixel using the exponent s instead of p in the above definition of the sum of squares. That is

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[0053] The most extreme partitioning possible corresponds to a single superpixel (S = 1) corresponding to the complete image itself having the total image intensity I over all pixel intensities k In this particular case, the sum of squares is

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[0054] In the case of a global analysis based on fitting either single pixel or superpixel intensities, fewer images are generally required to constrain a model described by both global and local parameters. A global analysis can be performed by fitting one or more global parameters (in the above case, k on) can also provide a better estimate of . For global analysis, Ω corresponds to the sum of all global model parameters G and all local model parameters L needed to completely define the model for each superpixel S. The total model parameters are Ω = L × S + G, and the total data points are Δ = K × S. It is further evident that, as mentioned above, many more data points are needed than the model parameters, Δ ≥ Ω, K×S≧L×S+G Or simply, K≧L+G / S where S is typically much larger than G, so G / S<1, and the minimum number of images required is simply one more than the number of local parameters, or K=L+1. Because the local parameters are typically just normalization coefficients for the distinct model components (e.g., a function describing the signal and a function describing the background), the number of images required is exactly one more than the number of distinct model components and is therefore independent of the number of global parameters required to define the "shape" of the model component functions. For example, global analysis can more easily accommodate models of complex backgrounds than simple linear models. The above assumption is that individual superpixels are sufficiently heterogeneous in the contributions of each model component. The above calculation would not hold if the signal-to-background ratio were always the same, which is highly unlikely when considering a sufficient number of superpixels.

[0055] An example of the power of global analysis is shown in Figure 2, based on a 2x2 recombination of a full-resolution image into superpixels. Global analysis is in excellent agreement with integrated image analysis. onThis returns a value of , demonstrating that there is no practical advantage in this particular example for more accurate determination of the on-rate constant. However, a more pertinent advantage of global analysis is that it allows for optimal estimation of the proportion of the observed intensity at each superpixel contributed by signal versus background. The true signal at each pixel (the "signal" image in Figure 2) can then be determined, at least up to the fundamental limit set by noise, with each pixel's background equally accessible (the "background" image in Figure 2). For global analysis, optimal global and local parameters are determined by minimizing C, where each observed titer image is modeled as a simple scaling sum of trial "signal" and trial "background" images for each step of minimization until a (typically) unique minimum is obtained. The above process assumes that no photobleaching (either of immunofluorescence or sample autofluorescence) occurs during the acquisition of each titer image. If photobleaching due to image acquisition is significant, image-wide photobleaching calibration must be performed, with the predicted model intensities corrected accordingly.

[0056] Example More specifically, Figure 2 shows an example of the titration process applied to several-micron-thick human tonsil tissue slices fixed with paraformaldehyde: (1) row: nuclear staining (DAPI) of tissue slices following incubation with different titrations of dye-labeled molecular binders (additive concentrations indicated on each image); (2) row: immunofluorescence images of dye-labeled molecular binders (equal contrast for all images); (3) row: immunofluorescence images of dye-labeled molecular binders (individual contrast for each image); (4) row: "signal" and "background" images extracted from global analysis of the immunofluorescence image series; (bottom left): fitting of a specific binding model (triangles) to the integrated intensities (circles) of the immunofluorescence images for each additive concentration; (bottom right): fitting of a model (triangles) consisting of the sum of the model for specific binding (diamonds) and a linear background (squares) to the integrated intensities (circles) of the images for each titer. The optimal on-rate constants obtained by global analysis are also displayed for comparison ("single-pixel fitting").

[0057] The tissue shown in Figure 2 was prepared by cryosectioning 8 μm thick sections from a freshly frozen tissue block and placing them on a cover slide fitted with a plastic frame containing well structures. In this case, thin sections were fixed in the wells with paraformaldehyde (4% PFA solution), washed with PBS, stained with DAPI, washed with PBS, and then placed in buffer. The plate was then mounted in the specimen holder of the MACSima Imaging Platform (Kinkhabwala et al., Sci Rep 12, 1911, 2022).

[0058] The titration method was then applied to the MACSima Imaging Platform as follows: Regions of interest were manually selected from a low-magnification overview image of DAPI staining. The instrument then photobleached each selected ROI with high-power LED light for 10 minutes. Image acquisition of each ROI was then performed by moving the stage to a saved lateral position (x,y), determining the optimal focus (z) based on DAPI imaging, acquiring a focused DAPI image, and then acquiring an image in the FITC channel for residual autofluorescence. Next, 0.625 μg / mL of FITC-labeled anti-CKHMW (FabREAL645, Miltenyi Biotec BV & Co. KG) was applied to the sample for 10 minutes. The sample was washed, and then focused images were acquired from all ROIs in the DAPI and FITC channels, with exposure and excitation intensities selected to avoid significant photobleaching. This was repeated for each subsequent titration; separate images are labeled for each additive concentration at the top of Figure 2. The top row of Figure 2 shows DAPI images of one ROI for each titration step. Immunofluorescence images from the FITC channel are displayed in the second row immediately below, where all images have the same contrast. It is clear that the increase in intensity corresponds to incubation of the sample with more antibody. In the third row, separate immunofluorescence images are redisplayed at different contrast levels to reveal the pattern of staining. If no background binding occurs, the pattern of staining should be independent of the exact level of antibody incubation. However, inspection of the image column across the third row shows a clear change in pattern over the progressive increase in titration from left to right.

[0059] The image sequence was then analyzed as follows: k on (1.096×10 4 M -1 s -1A simple model consisting of a specific binding model characterized only by σ = 1.057 × 10 was used. A good fit was obtained, but further analysis showed that the fit was not reliable. A more complex model consisting of an additional linear background term was then used to fit the integrated intensity, which gave a slightly better fit of the intensity, but a σ = 2.457 × 10 4 M -1 s -1 Very different k on It is difficult to determine which fit is actually more effective based solely on the quality of the fit to the integrated intensity of the image.

[0060] However, global analysis was subsequently performed on image sequences demonstrating the superiority of more complex models with additional background contributions. Global analysis considers individual sections of data (in this case, each pixel or superpixel) separately. Global analysis is particularly suitable when different model components contribute unevenly to each data section, allowing for more reliable estimates using global analysis compared to when the data are pooled into a single dataset (integrated intensity as described above) and then fitted. Global analysis has been empirically shown to be more accurate for fitting fluorescence lifetimes across multiple decay curves obtained from a single cuvette than for fitting to a single "pooled" decay curve obtained by directly summing all cuvette data (Knutson et al., Biochem 22, 6054, 1983). Global analysis has subsequently been extended to imaging data for single-pixel fitting of the relative contributions of multiple lifetime components to images obtained by fluorescence lifetime imaging microscopy (Verveer et al., Biophysical Journal 78, 2127, 2004). In global analysis, global parameters (e.g., k on a single global parameter of N) and local parameters associated with each compartment (in this case, the specific binding normalized Np and the background gradient M p The minimization is performed jointly over a set of single-pixel parameters (corresponding to Q in the above mathematical treatment). For the particular image sequence shown in Figure 2, an additional offset parameter (Q p ) was not required. Although a global analysis can often yield more reliable estimates of global parameters, in this case, a global fit based on single pixel fitting resulted in a 2.457 × 10 4 M -1 s -1 Compared with the above integrated intensity value of 2.456×10 4 M -1 s -1 k on The value of σ was obtained. An additional benefit of global analysis is that it allows for the extraction of separate contributions from model components at each aligned pixel in the image sequence. This allows for the extraction of "signal" and "background" images that contain only contributions from specific binding interactions at each pixel. Each individual titration image is then expected to be reconstructed by adding the "signal" and "background" images using the appropriate scaling factor also obtained by global analysis. Note that the staining patterns displayed in the "signal" and "background" images in Figure 2 are quite different. For the tissue slice shown here, for example, it is clear that the brighter stained cells on the left side of the tissue slice arise solely from nonspecific background binding.

Claims

1. 1. A method for determining the on-rate constant for specific binding of a conjugate comprising a fluorescent detection moiety and an antigen-binding moiety applied to a fixed biological sample expressing a corresponding antigen, comprising: a. measuring the emitted radiation of the fixed biological sample as an image formed on a camera before delivering the conjugate; b. Thereafter, providing the conjugate to the fixed biological sample at at least two different concentrations and for a specific time interval; c. detecting the emitted radiation for each concentration as an image formed on a camera; d. registering the images with each other; e. fitting a function that accounts for the amount of specific binding and background binding for each concentration to the emission radiation in each registered pixel across the separate images; f. Obtaining the on-rate constants that define the specific binding function from step e). and A method comprising:

2. 10. The method of claim 1, wherein at each registered pixel of the image of the fixed biological sample, the contributions of the specific binding and the background binding to the emitted radiation are determined.

3. The method comprises: h. creating an image of the specific binding by assigning the emission radiation contributed by the specific binding to each registered pixel; i. creating an image of the background coupling by assigning the emission radiation contributed by the background coupling to each aligned pixel; 3. The method of claim 1 or 2, comprising:

4. Furthermore, before step d), each of the following steps: j. waiting a specific time interval; k. detecting the emitted radiation as an image formed on a camera; 4. The method according to claim 1, wherein the following is performed:

5. Furthermore, in step f), l. From step e), the off-rate constants that define the specific binding function are implemented; 5. The method according to any one of claims 1 to 4.

6. The method of claim 1 , further comprising fitting the function in step e) using a global analysis.

7. The method further comprises: converting the function in step e) into a function of two steps: m. in a first step, performing a fit to the integrated image intensities to determine the specific binding function; n. In a second step, fitting the amount of specific binding and background binding for each concentration to the emission radiation within each aligned pixel across individual images; 6. The method of claim 1, further comprising fitting in

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