Titration method for measuring kinetic binding parameters and for distinguishing specific binding from background

Abstract

A method for determining a kinetic binding parameter of a molecular binding agent coupled to a fluorophore. The repeated staining of the antigen and the detection of emission radiation generate a titration series. Fitting of emission radiation within the titration series allows for determination of kinetic binding parameters. The emitted radiation is detected using a camera, and single pixel fitting using global analysis allows distinguishing between specific binding signals and non-specific background in each pixel.

Description

Technical Field

[0001] The present invention relates to a method for measuring the kinetic binding parameters of a molecular binder to its target epitope and for distinguishing specific binding from background. Background Art

[0002] The state-of-the-art methods for measuring the kinetic binding parameters of a molecular binder to its target epitope are based on the purification of the target epitope to isolate the interaction in vitro. Typically, the binding of a molecule to its target epitope is monitored label-free by immobilizing the target epitope on a glass substrate and measuring the association rate constant and the dissociation rate constant of the molecular binder via changes in surface plasmon resonance (SPR) on the surface of the glass substrate (e.g., Bakhtiar, J Chem Ed 90, 203, 2012). Specifically, an empty buffer is applied to the sample and then rapidly replaced with a buffer containing a specific concentration of the molecular binder to determine the association rate constant k on , which is defined according to the law of mass action as the proportionality constant that relates the rate of change of the concentration B of the epitope bound to the molecular binder to the product of the concentration A of the unbound molecular binder and the concentration E of the unbound target epitope: Then, typically, the sample is allowed to reach equilibrium binding to determine the dissociation constant. Then, the buffer is rapidly replaced with an empty buffer to independently determine the dissociation rate constant, which is defined as the proportionality constant that relates the rate of change of the concentration of the bound epitope to the concentration of the bound epitope:

[0003] Although such in vitro methods are commonly used to determine the association rate constant and the dissociation rate constant of a molecular binder, the purification of the target epitope represents a complex and time-consuming step. For some epitopes, purification may not even be possible. The attachment of the target epitope to the glass represents an additional problematic step because the attachment can lead to misfolding and altered binding. The molecular binder may also additionally and non-specifically bind to the glass substrate, thereby generating background. Ultimately, the kinetic parameters obtained by such in vitro methods may not be transferable to other more relevant contexts such as immunofluorescence, e.g., to accurately predict the binding of a dye-labeled molecular binder to a fixed biological sample.

[0004] It has been reported to determine the kinetic binding constants of fluorescent probes that bind to epitope targets in biological samples in situ, e.g., at the cell population level (Bondza et al., Frontiers in Immunology 8, 455, 2017). In this article, the LigandTracer Green device (Ridgeview Instruments) was used to obtain the kinetic binding curves of immunofluorescent probes applied to cell populations. Specifically, the target cell population was simply stained (30 seconds), washed (5 seconds), and imaged using a microscope (30 seconds) in multiple cycles. Thereby, the kinetic binding curves of this cell population could be sampled at a time scale of approximately 1 min at a fixed concentration of the applied probe. After incubation with the probe at this fixed concentration, a further incubation step at zero probe concentration could be used to determine the dissociation rate constant. The binding curve of control cells that do not express the target epitope was obtained by subtracting this control binding curve from the binding curve of the target cell population to correct for background binding. It has been reported that related methods down to the single cell level (May et al., Molecular Pharmacology 78, 511, 2010) or tissue region level (Dubois et al., BMC Research Notes 6, 542, 2013) also rely on separate measurements of control cells or regions to indirectly estimate the contribution of background binding in the targeted cells or regions. A more precise determination of the actual contribution of specific binding relative to non-specific binding within each region of interest and (ideally) down to the single pixel level has not been achieved.

[0005] Recently, immunofluorescent staining of cells has been extended from classical single imaging to imaging of multiple different targets on the same tissue section, allowing high-content insights into the target epitopes and cell microenvironment of tissues (Kinkhabwala et al., Sci Rep 12, 1911, 2022). The MACSima imaging system (Miltenyi Biotec B.V. & Co. KG) is specifically designed for this technology.

[0006] The state-of-the-art solution for reducing background in immunofluorescence images is to "block" the sample by using specific blockers (e.g., blocking the Fc domain of Fc receptors) or non-specific blockers (e.g., whole serum, bovine serum albumin, or isotype antibody control) before staining. The amount of blocking (concentration of blocker and incubation time) required to improve the signal-to-background ratio for a given antibody stain is difficult to predict. Although blocking can reduce background and thereby improve the contrast of antibody staining, it does not completely remove the background. Blockers can also block targeted epitopes in the sample, thus reducing specific signals.

[0007] The background pattern in the image can be visualized by using isotype antibody control staining, where the control staining uses different fluorescent markers. Subtracting the isotype control staining from the immunofluorescence staining proportionally can be used to remove the background signal. However, the scaling factor to be applied is not clear. Chromaticity shifts or other imaging aberrations resulting from the detection of two different fluorescence channels may also disrupt the final image. Due to the inevitable differences in recognition domains, isotype control staining may not represent the actual non-specific binding of the antibody.

[0008] There is currently no available and sufficiently general method for accurately determining the kinetic binding parameters (specifically, the association rate constant and dissociation rate constant) of the in-situ binding of a molecular binder to a target epitope within a fixed biological sample. The fundamental challenge here is the correct discrimination of specific signals (targeted binding interactions) from multiple potential contaminating backgrounds (mainly due to non-specific binding interactions).

[0009] There is also currently no available and sufficiently general method for credibly extracting specific staining signals from the background in each pixel of an immunofluorescence image of a fixed biological sample, which would allow for the generation of truly background-free immunofluorescence imaging. Summary of the Invention

[0010] We propose a method (“titration method”) based on iterative staining and imaging of a fixed biological sample with a dye-labeled molecular binder using an automated microscope for immunofluorescence imaging, the method: (1) allowing precise discrimination of the specific kinetics of binding of the molecule to its target epitope from non-specific binding interactions, and (2) simultaneously allowing precise discrimination of the specific binding signal from the background in each pixel of the image of the sample. In particular, a model is fitted across an image stack separately corresponding to different titrations of the dye-labeled molecular binder to the sample. Fitting a model that describes both the specific binding interaction and the non-specific binding interaction allows simultaneous extraction of the kinetic binding parameters characterizing the specific interaction as well as the fraction of signal to background in each pixel (which represents a 3D voxel) of the image of the sample. Thus, the main outputs of our method are the kinetic binding parameters of the molecule to its specific target epitope as well as a pure signal image and a pure background image.

[0011] Accordingly, the object of the present invention is a method for determining the binding rate constant of specific binding of a conjugate comprising a fluorescent detection moiety and an antigen-binding moiety (the conjugate being applied to a fixed biological sample expressing the corresponding antigen) and for determining the contribution of specific binding and non-specific binding to the emitted radiation in each pixel of the image of the fixed biological sample, characterized by the following steps: a. Measuring the emitted radiation of the fixed biological sample in the form of an image formed on a camera, before providing the conjugate; b. Subsequently, providing the conjugate to the fixed biological sample at at least two different concentrations and at specified time intervals; c. Detecting the emitted radiation of each concentration in the form of an image formed on a camera; d. Aligning the images with each other; e. Fitting a function that explains the amount of specific binding and non-specific binding for the emitted radiation within each aligned pixel on the individual images; f. Obtaining the binding rate constant that describes the specific binding function from step e.

[0012] Preferably, in addition to obtaining the binding rate constant that describes the specific binding function, determining the contribution of specific binding and non-specific binding to the emitted radiation in each aligned pixel of the image of the fixed biological sample.

[0013] The method may further be characterized in that: g. Creating an image of specific binding by assigning to each aligned pixel the emitted radiation contributed by specific binding; h. Creating an image of background binding by assigning the emission radiation contributed by background binding to each aligned pixel.

[0014] The fixed biological sample can correspond to one of the following: adherent cells, suspended cells, tissue, or smear (e.g., bone marrow). BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 Drawings A and B illustrate the titration method of the present invention.

[0016] Figure 2 An embodiment of the titration method applied to a fixed tissue section is shown.

[0017] A method for measuring the kinetic binding parameters of a molecular binder to its target epitope located in a fixed biological sample is detailed herein. The method is based on applying a series of titrations of the molecular binder to the fixed biological sample and measuring the emission radiation from the sample after each step. If the emission radiation is detected as a microscopic image for each titration step, a global analysis of the aligned images (corresponding to different titrations) can be used. In this case, the global analysis allows the discrimination of the signal (specific binding of the molecular binder) from the background (non-specific binding of the molecular binder) in each pixel of the series of aligned images. Thus, a new image containing only the signal in each pixel, which is proportional to the concentration of the target epitope, can be constructed.

[0018] In the drawings, the following features are denoted by the following reference numerals. Similar reference numerals are used in the various figures to denote components that perform similar or identical functions. 001 Fixed biological sample 002 Coverslip glass 003 Microscope objective 004 Image of nuclear DAPI staining 005 Image of dye-labeled molecular binder (same contrast as other images in this row) 006 Image of dye-labeled molecular binder (arbitrary contrast) 007 Image of extracted specific binding ("signal") 008 Image of extracted non-specific binding ("background") DETAILED DESCRIPTION OF THE INVENTION

[0019] In Figure 1The titration method is depicted in A. The titration method is characterized by a series of staining and washing of single molecule binders that target specific antigens within a fixed biological sample, which is typically a fixed tissue section a few microns thick. For the image series A generated for different titration steps m m can be used, for example, to determine the binding rate constant of specific binding of the molecular binder. The image series can also be used to distinguish the contribution of signal binding from background binding. In Figure 1 B, after the titration process depicted in Figure 1 A, an additional delayed image series including at least one image B1 can be immediately performed to better determine and distinguish the dissociation rate constants of specific binding and background binding.

[0020] Using a modified standard instrument protocol, the titration method of the present invention can be performed with a MACSima imaging system (Miltenyi Biotec B.V. & Co. KG), which allows for automated, continuous immunofluorescent staining of fixed biological samples.

[0021] The standard instrument protocol of MACSima consists of continuous staining and immunofluorescent imaging of a fixed biological sample using a set of molecular binders. The standard protocol is generally characterized by an iterative cycle of staining, washing, imaging, and erasing. Erasure of the fluorescent signal from a specific molecular binder is accomplished by photodestruction (photobleaching) of the fluorophore or by enzymatic cleavage of the molecular binder, with an additional washing step applied to remove the dissolved fluorophore. For continuous staining of a given field of view, return to the same z-position in the sample is ensured by detecting and adjusting the distance of the objective lens to the glass coverslip (the position of the glass is determined by detection of reflected IR light) and / or by comparing the current DAPI image of the sample with the initial DAPI image from the first cycle. Then, during subsequent image registration steps, alignment of the images in the xy plane is performed to sub-pixel accuracy, allowing for precise measurement of the same voxels of the fixed biological sample across the finally aligned image stack.

[0022] To implement this titration method on MACSima, the following minor changes to the standard instrument protocol are required. The titration method is based on an iterative cycle of repeated staining (usually for 10 min), washing, and imaging of a single-molecule binder, without erasing in each cycle. Instead, a series of concentrations are applied to the sample in an additive manner. For example, molecular binders at 0.625 μg / mL, 1.875 μg / mL, 7.5 μg / mL, and 30 μg / mL are applied successively, corresponding to a four-fold additive increase in staining at each titration step of 0.625 μg / mL, 2.5 μg / mL, 10 μg / mL, and 40 μg / mL. The concentration range should be carefully chosen to ensure sufficient sampling of the complete shape of the yet-unknown saturation curve. Here, it is very important that the highest concentration at least slightly saturates the molecular binder, which is similar to the standard requirement for measuring the dissociation constant in the context of a chemical binding assay.

[0023] The weak non-specific interaction of the molecule with the sample should not exhibit saturation over the entire titration range applied, and it is expected to increase linearly with the additive concentration. However, more complex background models can also be considered (see the mathematical treatment section below).

[0024] In a first embodiment of the present invention, such a background model can be used to further obtain the dissociation rate constant of specific binding and the dissociation rate constant of background binding from the function.

[0025] In a second embodiment, the binding rate constant of background binding is further obtained from the function.

[0026] Therefore, the different profiles expected for the saturated signal and the linearly increasing background (or more complex background model) in the titration image series represent a key aspect of this titration method, which allows a reliable distinction between signal and background.

[0027] Specifically, fitting the integrated signal (or global fitting based on individual pixel information) of each individual image in the titration series allows for the precise determination of the specific binding rate constant of the molecule to its target epitope.

[0028] Furthermore, after the final staining / washing step, one or more images can be acquired at a fixed time point to allow for the separate and more direct determination of the dissociation rate constant of specific binding and the dissociation rate constant of background binding ( Figure 1 of B).

[0029] Therefore, in a third embodiment, before step d, the following steps are performed j. Wait for a specific time interval; k. Detect the emitted radiation.

[0030] Steps j and k can be repeated at least once with the same or different time intervals.

[0031] The method can further be characterized in that step f is replaced by the following steps l. Obtain the association rate constant and the dissociation rate constant that describe the specific binding function from step e.

[0032] The method can further be characterized in that global analysis is used to fit the function in step e.

[0033] The global analysis of the series of titration images can be used to determine both the optimal global kinetic parameters of specific binding (and, if necessary, the kinetic parameters of background binding) and the local parameters corresponding to the fractional contributions made by specific binding and background binding in each pixel. The latter allows the reconstruction of an image containing only specific binding or an image containing only background binding (the "signal" and "background" images in Figure 2 . Importantly, the image of specific binding is not contaminated by background binding in each pixel at the noise limit, thus allowing "background-free" immunofluorescence imaging.

[0034] The method can further be characterized in that the function is fitted in two steps in step e: m. In the first step, fit the integrated image intensity to determine the specific binding function; n. In the second step, fit the emitted radiation within each aligned pixel on the individual images for the amounts of specific binding and background binding at each concentration.

[0035] All embodiments are described in detail below. Mathematical processing

[0036] The titration methods, analyses, and outputs corresponding to the respective embodiments were only schematically described above. The exact mathematical processing is given below. Throughout, we assume the following parameters: V Solution volume A T Total antibody applied A Free antibody a T Total antibody concentration applied (A T / V) B Bound antibody E T Total epitope E Free epitope b Fraction of bound epitope (B / E T ) f fraction of free epitopes (E / E T ) ε ratio of total epitopes to total antibodies (E T / A T ) k on association rate constant [μM -1 s -1 k off dissociation rate constant [s -1 K D dissociation constant [μM] For the case of standard immunofluorescence staining, the fixed biological sample is attached to a glass slide at the bottom of the well and then immersed in a solution volume V with the total amount A of the antibody probe. The total number of epitopes in the sample is E T . The conservation conditions dictate that: T . A T = A + B E T = E + B where B is the bound antibody (binding 1:1 to the target epitope), A is the free antibody, and E is the remaining unbound antibody.

[0037] Assumption #1 (fast diffusion, no significant spatial gradients): If diffusion is fast compared to the binding time scale, the exact spatial distribution of epitopes in the stained volume can be neglected, and we can simply monitor the increase in the total bound epitopes over time based on the standard chemical kinetics defined by the k on and k off of this interaction: Define the fraction bound as b = B / E T to obtain: The total antibody concentration a T = A T / V, and the total epitope-to-antibody ratio ε = E T / A T . Although the above equations can, in theory, solve for the time evolution of the fraction bound, further assumptions related to standard immunofluorescence staining are detailed below, which lead to an even simpler analytical result.

[0038] Assumption #2 (antibody greatly exceeds target epitopes): For typical immunofluorescence staining, the amount of antibody applied is much greater than the total number of target epitopes in the sample: E T << A T . In the limit where ε → 0, we obtain:​​ The general solution of the above differential equation is (Equation 1): Taking b0 = 0 gives (Equation 2): Determine the specific interaction k on

[0039] Assumption #3a: If the dissociation rate constant is negligible (i.e., k off << k on a T Or, equivalently, a T >> K D ), then Equation 2 becomes: b(t) = 1 - exp(-k on a T t)

[0040] Assumption #3b: Alternatively, if the argument in the exponent in Equation 2 is less than 1 (far from saturated), then the first-order Taylor expansion gives the following linear relationship: b(t) = k on a T t

[0041] Under either assumption, the dissociation rate constant plays no role in the evolution of the binding fraction.

[0042] After immunostaining with antibody concentration a T = a1 for a certain time t = t1, the sample is washed and imaged. Under Assumption 3a, the observed binding fraction is: b1 = 1 - exp(-k on a1t1) Iterative staining is more easily expressed in terms of the exponential decrease of free epitopes (f i = 1 - b i ): f1 = f0exp(-k on a1t) For multiple stainings (assuming f0 = 1), this can be written as: If the immunostaining incubation time is kept constant (t = t s ) at each step, then: Therefore, iterative immunostaining at each step k is equivalent to "accumulating" the concentration (for the final staining, k = n) for a duration t = t sSingle staining. The binding fraction at each step k is simply given by: Determine the specific interaction k on and k off

[0043] More generally, if the dissociation rate constant cannot be neglected, the solution is best represented in matrix form as follows, allowing for different incubation times t at each step k . According to Equation 1, based on the binding fraction at step k–1, the binding fraction at step k (after applying the titration a k ) is: Introduce and γ k = exp(–k on a k β k t k ), these expressions become: The above can be rewritten in the following convenient matrix form: Here, it is assumed that the initial binding fraction is zero (b0 = 0). Note that each S k matrix depends on four parameters: S k ≡ S k (k on , k off , a k , t k ).

[0044] If there is a long waiting time between incubations (for which the applied antibody concentration is zero), the dissociation rate constant may play a significant role. These intervals can also be explicitly included in the model. Here, we assume that the rebinding of antibodies that have dissociated from the epitope is negligible, since it is assumed that the applied antibody is in far excess relative to the epitope (Assumption #2, stained E T << A T ), and any change in the binding fraction due to newly freed antibodies is considered negligible compared to the change in the binding fraction that occurs during the staining step. Thus, the bound epitope decreases: b k = exp(–k off t k )b k-1 Define θ k = exp(–k off t k), then: b k = θ k b k-1 Its matrix form is: In the case of a sequence where four iterative staining steps (S1, S3, S5, S7) alternate with three waiting steps (W2, W4, W6), the final binding fraction can be determined by the following formula: Although the final binding fraction b7 is algebraically complex, it depends only on at most two fitting parameters (k on and optionally k off ) and the overall normalization factor.

[0045] Above, we only considered the fraction of epitopes bound within the total volume. In the case of an image, the relative intensity from one pixel to the next will depend on the local concentration of the target epitope contributing to the staining of pixel p, which we will call e p . Here, e p Specifically refers to the convolution of the true 3D concentration of the epitope with the optical transfer function of the microscope ("detection volume") (e.g., for a confocal microscope, by a spatially invariant 3D Gaussian with axes σ x = σ y , σ z ) that well approximates the optical transfer function. The intensity of the specific signal in the immunofluorescence image after titration step k is then simplified to: where E is the global normalization factor, which will depend on the excitation intensity, exposure time, pixel quantum efficiency, etc. Determine the specific interaction (k on and / or k off ) and the linear background (slope m)

[0046] In the case of a significant contribution from the background, the background is expected to increase linearly with the applied titration. Above (approximate #3b) it has been shown that the linear approximation is suitable for far-from-unsaturated binding interactions, which is a reasonable assumption for the background and is also consistent with our empirical results (e.g., Figure 2 ). Since the non-specific sites are heterogeneous, it is expected that they will differ in interaction strength, and the binding rate constants required for each different class of non-specific binding site j are different. Of course, a mixture of different non-specific sites may also be within a single pixel of the immunofluorescence image. Incubated with the applied concentration a T for incubation time ts Afterwards, the binding fraction for the type j binding site will be (according to approximation #3b): If is the concentration of non-specific binding sites of type j contributing to the intensity of pixel p, then the pixel intensity observed after the first incubation step (duration t s ) due to the total non-specific background will be: Or simply, where N is the same normalization constant as for specific binding above, and m p is the linear slope of the background specific to pixel p and is defined as the sum of the products of the non-specific binding site concentration and the binding rate constant and the product with the incubation time t s . Note that in the linear approximation, it is not necessary to specify the underlying concentrations or binding rate constants of non-specific binding sites across different classes contributing to the single-pixel parameter m p .

[0047] If titration is performed with a fast enough turnover, the dissociation rate constant of non-specific binding can be neglected, meaning a linear increase in the background after each titration step, which depends only on the "accumulated" concentration (assuming equal incubation time t s for each step):

[0048] The intensity predicted by the model in pixel p at step k is then the sum of the specific signal and the non-specific background contribution, including an additional offset Q p (e.g., to account for the imperfect subtraction of the intensity of the pre-staining image from all subsequent stained images):

[0049] The specific binding fraction at step k is calculated as explained above (in matrix form). Defining N p = Ee p and M p = Em p , for the above equation we obtain:

[0050] Here, single-pixel fitting across the series of titration images requires at most three local parameters: N p , M p and optionally Q p . These parameters are independent of the k of the specific interactionon and optional k off are fit together with the global value. During the duration of the titration process, we can usually neglect k off , obtaining: More complex background models than the simple linear model above can also be considered (e.g., similar in form to the specific staining model component but with different k on illustrated).

[0051] To correctly weight and fit the model to the pixel information across an image series, an error model is required. The Gaussian model provides a very good approximation for the uncertainty in the intensity observed in each pixel of each image, fully accounting for the Poisson shot noise due to photon counting statistics and also for the typical Gaussian camera readout noise (importantly at low intensities). Another significant contribution to the uncertainty can come from the binding site occupancy statistics, which is derived from the underlying binomial distribution but can also be approximated as Gaussian uncertainty. In the absence of an available noise model, a simple Gaussian approximation can be made to the Poisson shot noise distribution (or the binomial distribution of binding site occupancy): The scale factor (partially determined by the camera gain) is assumed to be the same across all pixels of the camera. In this case, the exact value of the scale factor is not required for performing this fit.

[0052] Now that the error model is defined, we can now perform a globally weighted fit of the modeled intensity to the observed intensity. Specifically, this requires minimizing the squared difference between the modeled intensity and the observed intensity for all pixels p across each titration image k for a given set of local (N p , M p , Q p ) and global (k on and k off ) model parameters: Here, we assume that the images have been acquired in the same axial plane and have been laterally registered with each other after acquisition. Return to the same axial plane is achieved by precisely measuring the distance from the objective to the cover glass or by referring to control images obtained in different channels (e.g., using transmitted images or nuclear staining with DAPI). Return to approximately the same lateral position can be achieved using a precision stage to ensure return to the same region of interest at each imaging step. Alternatively, the sample can be kept in a stationary position throughout the titration. The lateral precision of instrument positioning does not need to be as precise as the axial precision because different titration images can be laterally aligned to sub-pixel accuracy using standard image registration algorithms after their acquisition. Proper registration in all three spatial dimensions ensures that for a given pixel, exactly the same voxel is addressed in each aligned image of the titration series.

[0053] Global fitting can be performed at the full pixel resolution of the image or for any partitioning of the data (e.g., partitioning into superpixels of size 2×2, 3×3, etc.). For the latter, we now only need to sum over each superpixel with index s instead of p in the definition of the least squares sum above: The maximum number of independent data points in a series of a total of K images (each having P pixels) is Δ = K × P. If the images are rearranged into a total of S < P superpixels, then Δ = K × S.

[0054] The most extreme possible partitioning will total to a single superpixel corresponding to the full image itself (S = 1), with the total pixel intensity I k corresponding to a simple sum over all pixel intensities. In this special case, the least squares sum becomes: The Gaussian uncertainty of the integrated image intensity is calculated in the standard way as The model prediction for the integrated intensity of the image at titration step k will then simply be: The least squares sum is now explicitly defined as: Minimization of C allows determination of the optimal parameters corresponding to k on 、N、M, and optionally Q. Since each image has only S = 1 superpixel, the total number of data points is simply equal to the number of images, Δ = K × S = K. To uniquely determine the optimal parameters of the model, the number of data points Δ must be equal to or greater than the number of model parameters Ω, i.e., Δ ≥ Ω. In the absence of significant background or bias, there are only Ω = 2 model parameters k onFor M and N, Δ = K ≥ Ω = 2 images are required, or simply K ≥ 2 images. If a significant linear background (slope M) may also be present, then Ω = 3, so K ≥ 3 images are required. If both a linear background and a bias are present, then Ω = 4, so K ≥ 4 images are required.

[0055] In the case of global analysis based on fitting single - pixel or super - pixel intensities, usually fewer images are required to constrain the model now described by both global and local parameters. Global analysis can also provide a better estimate of the global parameter (k on ) in the above case. For global analysis, Ω corresponds to the sum of the total global model parameters G and the total local model parameters L required to fully define the model for each super - pixel S. The total model parameters are then: Ω = L×S + G, and the total data points Δ = K×S. The requirement that the number of data points be more than the model parameters Δ ≥ Ω then becomes more explicit: K×S ≥ L×S + G Or simply: K ≥ L + G / S Since S is usually much larger than G, so G / S < 1, and the minimum number of images required is only one more than the number of local parameters, or K = L + 1. Local parameters are usually just the normalization factors of individual model components (e.g., functions describing the signal and functions describing the background), so the number of images required is only one more than the number of individual model components and is thus independent of the number of global parameters required to define the "shape" of the model component functions. For example, for global analysis, a background model more complex than a simple linear model can be easily considered. The above assumes that individual super - pixels are heterogeneous enough in terms of the contribution of each model component. If the signal - to - background ratio is always the same, the above calculations will not hold, but this possibility is extremely low when considering a sufficient number of super - pixels.

[0056] Based on rearranging the full - resolution image 2×2 into super - pixels, Figure 2 an example of the ability of global analysis is given. Global analysis returns k on values that are very consistent with integrated image analysis and do not show a real advantage in more precisely determining the binding rate constant in this particular example. However, the more relevant advantage of global analysis is its ability to optimally infer the fraction of the intensity observed in each super - pixel contributed by the signal and the background. This allows the true signal in each pixel to be determined, at least up to the fundamental limit set by the noise ( Figure 2 in the "signal" image), and the background in each pixel is similarly obtainable ( Figure 2the "background" image in). For global analysis, the optimal global and local parameters are determined by minimizing C, in which each observed titration image is modeled as a simple scaled sum of the "signal" and "background" images of each step of the experiment until (usually) a unique minimum is obtained. In the above treatment, we assume that no photobleaching (of immunofluorescence or sample autofluorescence) occurs during the acquisition of each titration image. If photobleaching by image acquisition is significant, photobleaching calibration across the images should be performed with the predicted model intensities corrected accordingly. Example

[0057] More specifically, Figure 2 An example of a titration method applied to a few-micron-thick section of paraformaldehyde-fixed human tonsil tissue is shown. First row: Nuclear staining (DAPI) of tissue sections after incubation with different titrations of a dye-labeled molecular binder (the cumulative concentration is indicated above each image). Second row: Immunofluorescence images of the dye-labeled molecular binder (all images have the same contrast). Third row: Immunofluorescence images of the dye-labeled molecular binder (each image has independent contrast). Fourth row: "Signal" and "background" images extracted from the global analysis of this series of immunofluorescence images. Lower left: Integrated intensity (circles) of immunofluorescence images for each cumulative concentration fitted to a specific binding model (triangles). Lower right: Integrated intensity (circles) of images for each titration fitted to a model (triangles) consisting of the sum of a specific binding model (diamonds) and a linear background (squares). The optimal binding rate constant obtained by global analysis is also shown for comparison ("single-pixel fitting").

[0058] The tissue shown in was prepared from a freshly frozen tissue block by cryosectioning to a thickness of 8 μm and placing it on a glass slide on which a plastic frame containing a pore structure was mounted. Figure 2 The thin section was then fixed in the pores with paraformaldehyde (4% PFA solution), washed with PBS, stained with DAPI, washed with PBS, and then left in buffer. The section was then mounted in the sample holder of a MACSima imaging platform (Kinkhabwala et al., SciRep 12, 1911, 2022).

[0059] Then, the titration method was applied to the MACSima imaging platform as follows. First, regions of interest were manually selected from the overview images obtained from DAPI staining at low magnification. The instrument first photobleached each selected ROI with high-power LED light for 10 min. Then, by moving the stage to the saved lateral position (x,y), the optimal focal distance (z) was determined based on DAPI imaging to obtain a clear DAPI image. Then, an image of the residual autofluorescence was obtained in the FITC channel, thereby obtaining an image of each ROI. Next, 0.625 μg / mL of FITC-labeled anti-CKHMW (FabREAL 645, Miltenyi Biotec B.V. & Co. KG) was applied to the sample for 10 min. The sample was washed, and then clear images of all ROIs were obtained in the DAPI and FITC channels, and the exposure and excitation intensities were selected to avoid significant photobleaching. This step was repeated for each subsequent titration, and the cumulative concentration was labeled on Figure 2 the top of each image. In Figure 2 the top row, DAPI images of a single ROI for each titration step are shown. Immediately below in the second row, immunofluorescence images from the FITC channel are shown, and all images have the same contrast. As the sample was incubated with increasing amounts of antibody, the increase in intensity was clear. In the third row, the individual immunofluorescence images are redisplayed at different contrast levels to show the staining pattern. If no background binding occurred, the staining pattern should be independent of the exact level of incubation with the antibody. However, a careful study of the image series in the third row showed a clear change in the pattern with increasing titration from left to right.

[0060] Then, the image series was analyzed as follows. A simple model including a specific binding model characterized only by k on (1.096×10 4 M -1 s -1 ) was used to fit the integrated intensity of the images in the series. Although a good fit was obtained, further analysis showed that this fit should not be trusted. Then, a more complex model including an additional linear background term was used to fit the integrated intensity, for which we obtained a slightly better intensity fit but a very different k on value of 2.457×10 4 M - 1 s -1 . It was difficult to decide which fit was actually more effective based only on the quality of the fit of the integrated intensity of the images.

[0061] However, subsequent global analysis of the image series demonstrated the superiority of a more complex model with an additional background contribution. In global analysis, each individual partition of the data (in this case, each pixel or superpixel) is considered separately. Global analysis is particularly suitable when the contributions of different model components to each data partition are heterogeneous, and more reliable estimates can be achieved compared to pooling the data into a single dataset (the integrated intensity above) and then fitting. Global analysis was first empirically shown to be more accurate for fitting the fluorescence lifetimes of multiple decay curves obtained from a single cuvette compared to fitting a single "pooled" decay curve obtained by directly summing all cuvette data (Knutson et al., Biochem 22, 6054, 1983). Global analysis was subsequently extended to imaging data for single-pixel fitting of the relative contributions of multiple lifetime components in an image obtained using fluorescence lifetime imaging microscopy (Verveer et al., Biophysical Journal 78, 2127, 2004). In global analysis, a set of global parameters (e.g., a single global parameter k on ) and local parameters associated with each partition (in our case, single-pixel parameters N p and M p ) corresponding to specific binding normalization and background slope are minimized jointly. No additional bias parameter (Q p ) as in the above mathematical treatment is required to fit the specific image series shown in Figure 2 . Global analysis generally can produce even more reliable estimates of global parameters; however, in this case, the global fit based on single-pixel fitting yielded a k 4 value of 2.456×10 -1 M -1 s on very similar to the value of 2.457×10 4 M -1 s -1 of the integrated intensity value above. However, an additional advantage of global analysis is the ability to extract the individual contributions from model components in each aligned pixel of the image series. In this case, global analysis allows the extraction of a "signal" image (which contains only the contribution from specific binding interactions in each pixel) and a "background" image. The accumulated "signal" and "background" images, using appropriate scaling factors also obtained by global analysis, are expected to reproduce each individual titration image. Note the very different staining patterns shown in the "signal" and "background" images in Figure 2 . Clearly, for example, for this tissue section, the brighter stained cells on the left side of the tissue section are produced only by non-specific background binding.

Claims

1. A method for determining the binding rate constant of specific binding of a conjugate comprising a fluorescence detection part and an antigen-binding part, wherein the conjugate is applied to a fixed biological sample expressing the corresponding antigen, It is characterized by the following steps: a. Before providing the conjugate, measure the emission radiation of the fixed biological sample in the form of an image formed on a camera; b. Subsequently, provide the conjugate to the fixed biological sample at at least two different concentrations and at specified time intervals; c. Detect the emission radiation of each concentration in the form of an image formed on a camera; d. Align the images with each other; e. Fit a function that explains the amount of specific binding and background binding for the emission radiation within each aligned pixel on the individual images; f. Obtain the binding rate constant that describes the specific binding function from step e; 2. The method according to claim 1, wherein, Determine the contribution of specific binding and background binding to the emission radiation in each aligned pixel of the image of the fixed biological sample; 3. The method according to claim 1 or 2, wherein: h. Create an image of specific binding by assigning the emission radiation contributed by specific binding to each aligned pixel; i. Create an image of background binding by assigning the emission radiation contributed by background binding to each aligned pixel; 4. The method according to any one of claims 1 to 3, further characterized in that, Before step d, perform the following steps: j. Wait for a specific time interval; k. Detect the emission radiation in the form of an image formed on a camera; 5. The method according to any one of claims 1 to 4, further characterized in that, In step f: l. Obtain the dissociation rate constant that describes the specific binding function from step e; 6. The method according to any one of claims 1 to 4, further characterized in that, Use global analysis to fit the function in step e; 7. The method according to any one of claims 1 to 5, further characterized in that, Fit the function in step e in the following two steps: m. In the first step, fit the integrated image intensity to determine the specific binding function; n. In the second step, fit the emission radiation within each aligned pixel on the individual images for the amount of specific binding and background binding of each concentration.

Images