WO2023059832A1 - Estimating kinetic parameters associated with interactions between t cell receptors and peptide-associated major histocompatibility complexes - Google Patents

Abstract

Embodiments described herein provide methods and systems for estimating a set of rate constants. The methods and systems may generally operate by fitting one or more sets of signal intensities to a model of interactions between a ligand, a receptor, and a ligand-receptor complex. In some embodiments, the receptor comprises a T cell receptor (TCR). In some embodiments, the ligand comprises a target monomeric peptide-associated major histocompatibility complex (pMHC). In some embodiments, the one or more sets of signal intensities comprise a set of time points corresponding to an incubation period between the ligand and the receptor. In some embodiments, the one or more sets of signal intensities comprise a set of time points corresponding to a dissociation period of the ligand-receptor complex. In some embodiments, the model comprises a four-state model. In some embodiments, the model comprises a three-state model.

Description

ESTIMATING KINETIC PARAMETERS ASSOCIATED WITH INTERACTIONS BETWEEN T CELL RECEPTORS AND PEPTIDE-ASSOCIATED MAJOR HISTOCOMPATIBILITY COMPLEXES

PRIORITY

[0001] This application claims the benefit of and the priority to U.S. Provisional Application Number 63/254,018, entitled “ESTIMATING KINETIC PARAMETERS ASSOCIATED WITH INTERACTIONS BETWEEN T CELL RECEPTORS AND PEPTIDE- ASSOCIATED MAJOR HISTOCOMPATIBILITY COMPLEXES” and filed on October 8, 2021, which is hereby incorporated by reference in its entirety for all purposes.

TECHNICAL FIELD

[0002] This present disclosure generally relates to immunology, particularly methods of assaybased measurements of immune response activity.

BACKGROUND

[0003] An understanding of the interactions and kinetics between T cell receptors (TCRs) and protein-associated major histocompatibility complexes (pMHCs) may be useful in building models for predicting adaptive immune responses. However, current models are limited by a lack of understanding of such interactions and kinetics. As such, there is a need for models that extract kinetics from high-throughput cell-based assays that probe TCR-pMHC interactions. The present disclosure addresses these and other needs.

SUMMARY

[0004] In an aspect, the present disclosure provides a method for estimating a set of rate constants. In various embodiments, the method comprises: (a) receiving: (i) a first set of signal intensities measured at a first set of time points, each time point of the first set of time points corresponding to an incubation period between a ligand and a receptor and (ii) a second set of signal intensities measured at a second set of time points, each time point of the second set of time points corresponding to a dissociation period of a ligand-receptor complex between the ligand and the receptor; (b) fitting the first set of signal intensities and/or the second set of signal intensities to a four-state model of interactions between the ligand, the receptor, and the ligand-receptor complex; and (c) determining the set of rate constants based on the model. In various embodiments, the first and/or second sets of signal intensities comprise fluorescence signal intensities. In various embodiments, the fluorescence signal intensities comprise flow cytometry fluorescence signal intensities. In various embodiments, the receptor comprises a T cell receptor (TCR). In various embodiments, the ligand comprises a target monomeric peptide-associated major histocompatibility complex (pMHC). In various embodiments, the target monomeric pMHC is associated with a fluorescent label. In various embodiments, the four-state model comprises: (i) a first state in which the ligand and the receptor are not bound and in which the receptor is in an active conformation, (ii) a second state in which the ligand and the receptor are bound in the ligand-receptor complex and in which the receptor is in the active conformation, (iii) a third state in which the ligand and the receptor are bound in the ligand-receptor complex and in which the receptor is in a non-active conformation, and (iv) a fourth state in which the ligand and the receptor are not bound and the receptor is in the non-active conformation. In various embodiments, the set of rate constants comprises any 6, 7, or 8 of: (i) an association rate constant between the first state and the second state, (ii) a dissociation rate constant between the first state and the second state, (iii) an association rate constant between the second state and the third state, (iv) a dissociation rate constant between the second state and the third state, (v) an association rate constant between the third state and the fourth state, (vi) a dissociation rate constant between the third state and the fourth state, (vii) an association rate constant between the receptor in the active conformation, and (viii) a dissociation rate constant between the receptor in the non-active conformation. In various embodiments, the first and/or second sets of signal intensities are associated with a temperature between 0 degrees Celsius (°C) and 10 °C.

[0005] In another aspect, the present disclosure provides a system for estimating a set of rate constants. In various embodiments, the system comprises: a non-transitory memory; and one or more processors coupled to the non-transitory memory and configured to read instructions from the non-transitory memory to cause the system to perform operations comprising: (a) receiving: (i) a first set of signal intensities measured at a first set of time points, each time point of the first set of time points corresponding to an incubation period between a ligand and a receptor and (ii) a second set of signal intensities measured at a second set of time points, each time point of the second set of time points corresponding to a dissociation period of a ligand-receptor complex between the ligand and the receptor; (b) fitting the first set of signal intensities and/or the second set of signal intensities to a four-state model of interactions between the ligand, the receptor, and the ligandreceptor complex; and (c) determining the set of rate constants based on the model. In various embodiments, the first and/or second sets of signal intensities comprise fluorescence signal intensities. In various embodiments, the fluorescence signal intensities comprise flow cytometry fluorescence signal intensities. In various embodiments, the receptor comprises a T cell receptor (TCR). In various embodiments, the ligand comprises a target monomeric peptide-associated major histocompatibility complex (pMHC). In various embodiments, the target monomeric pMHC is associated with a fluorescent label. In various embodiments, the four-state model comprises: (i) a first state in which the ligand and the receptor are not bound and in which the receptor is in an active conformation, (ii) a second state in which the ligand and the receptor are bound in the ligandreceptor complex and in which the receptor is in the active conformation, (iii) a third state in which the ligand and the receptor are bound in the ligand-receptor complex and in which the receptor is in a non-active conformation, and (iv) a fourth state in which the ligand and the receptor are not bound and the receptor is in the non-active conformation. In various embodiments, the set of rate constants comprises any 6, 7, or 8 of: (i) an association rate constant between the first state and the second state, (ii) a dissociation rate constant between the first state and the second state, (iii) an association rate constant between the second state and the third state, (iv) a dissociation rate constant between the second state and the third state, (v) an association rate constant between the third state and the fourth state, (vi) a dissociation rate constant between the third state and the fourth state, (vii) an association rate constant between the receptor in the active conformation, and (viii) a dissociation rate constant between the receptor in the non-active conformation. In various embodiments, the first and/or second sets of signal intensities are associated with a temperature between 0 degrees Celsius (°C) and 10 °C.

[0006] In another aspect, the present disclosure provides a non-transitory, machine-readable medium for estimating a set of rate constants. In various embodiments, the non-transitory, machine- readable medium has stored thereon machine-readable instructions executable to cause a system to perform operations comprising: (a) receiving: (i) a first set of signal intensities measured at a first set of time points, each time point of the first set of time points corresponding to an incubation period between a ligand and a receptor and (ii) a second set of signal intensities measured at a second set of time points, each time point of the second set of time points corresponding to a dissociation period of a ligand-receptor complex between the ligand and the receptor; (b) fitting the first set of signal intensities and/or the second set of signal intensities to a four-state model of interactions between the ligand, the receptor, and the ligand-receptor complex; and (c) determining the set of rate constants based on the model. In various embodiments, the first and/or second sets of signal intensities comprise fluorescence signal intensities. In various embodiments, the fluorescence signal intensities comprise flow cytometry fluorescence signal intensities. In various embodiments, the receptor comprises a T cell receptor (TCR). In various embodiments, the ligand comprises a target monomeric peptide-associated major histocompatibility complex (pMHC). In various embodiments, the target monomeric pMHC is associated with a fluorescent label. In various embodiments, the four-state model comprises: (i) a first state in which the ligand and the receptor are not bound and in which the receptor is in an active conformation, (ii) a second state in which the ligand and the receptor are bound in the ligand-receptor complex and in which the receptor is in the active conformation, (iii) a third state in which the ligand and the receptor are bound in the ligand-receptor complex and in which the receptor is in a non-active conformation, and (iv) a fourth state in which the ligand and the receptor are not bound and the receptor is in the non-active conformation. In various embodiments, the set of rate constants comprises any 6, 7, or 8 of: (i) an association rate constant between the first state and the second state, (ii) a dissociation rate constant between the first state and the second state, (iii) an association rate constant between the second state and the third state, (iv) a dissociation rate constant between the second state and the third state, (v) an association rate constant between the third state and the fourth state, (vi) a dissociation rate constant between the third state and the fourth state, (vii) an association rate constant between the receptor in the active conformation, and (viii) a dissociation rate constant between the receptor in the non-active conformation. In various embodiments, the first and/or second sets of signal intensities are associated with a temperature between 0 degrees Celsius (°C) and 10 °C.

[0007] In another aspect, the present disclosure provides a method for estimating a set of rate constants. In various embodiments, the method comprises: (a) receiving: (i) a first set of signal intensities associated with a first set of time points, each time point of the first set of time points corresponding to an incubation period between a ligand and a receptor and (ii) a second set of signal intensities associated with a second set of time points, each time point of the second set of time points corresponding to a dissociation period of a ligand-receptor complex between the ligand and the receptor; (b) fitting the first set of signal intensities and/or the second set of signal intensities to a three-state model of interactions between the ligand, the receptor, and the ligandreceptor complex; and (c) determining the set of rate constants based on the model. In various embodiments, the first and/or second sets of signal intensities comprise fluorescence signal intensities. In various embodiments, the fluorescence signal intensities comprise flow cytometry fluorescence signal intensities. In various embodiments, the receptor comprises a T cell receptor (TCR). In various embodiments, the ligand comprises a target monomeric peptide-associated major histocompatibility complex (pMHC). In various embodiments, the target monomeric pMHC is associated with a fluorescent label. In various embodiments, the three-state model comprises: i) a first state in which the ligand and the receptor are not bound, (ii) a second state in which the ligand and the receptor are bound in the ligand-receptor complex, and (iii) a third state in which the ligand and the receptor are not bound in the ligand-receptor complex and in which the ligand-receptor complex is internalized by a cell with which the ligand is associated. In various embodiments, the set of rate constants comprises: (i) an association rate constant between the first state and the second state, (ii) a dissociation rate constant between the first state and the second state, and (iii) a rate constant associated with internalization of the ligand-receptor complex by the cell. In various embodiments, the first and/or second sets of signal intensities are associated with a temperature between 15 °C and 40 °C.

[0008] In another aspect, the present disclosure provides a system for estimating a set of rate constants. In various embodiments, the system comprises: a non-transitory memory; and one or more processors coupled to the non-transitory memory and configured to read instructions from the non-transitory memory to cause the system to perform operations comprising: (a) receiving: (i) a first set of signal intensities associated with a first set of time points, each time point of the first set of time points corresponding to an incubation period between a ligand and a receptor and (ii) a second set of signal intensities associated with a second set of time points, each time point of the second set of time points corresponding to a dissociation period of a ligand-receptor complex between the ligand and the receptor; (b) fitting the first set of signal intensities and/or the second set of signal intensities to a three-state model of interactions between the ligand, the receptor, and the ligand-receptor complex; and (c) determining the set of rate constants based on the model. In various embodiments, the first and/or second sets of signal intensities comprise fluorescence signal intensities. In various embodiments, the fluorescence signal intensities comprise flow cytometry fluorescence signal intensities. In various embodiments, the receptor comprises a T cell receptor (TCR). In various embodiments, the ligand comprises a target monomeric peptide-associated major histocompatibility complex (pMHC). In various embodiments, the target monomeric pMHC is associated with a fluorescent label. In various embodiments, the three-state model comprises: (i) a first state in which the ligand and the receptor are not bound, (ii) a second state in which the ligand and the receptor are bound in the ligand-receptor complex, and (iii) a third state in which the ligand and the receptor are not bound in the ligand-receptor complex and in which the ligand-receptor complex is internalized by a cell with which the ligand is associated. In various embodiments, the set of rate constants comprises: (i) an association rate constant between the first state and the second state, (ii) a dissociation rate constant between the first state and the second state, and (iii) a rate constant associated with internalization of the ligand-receptor complex by the cell. In various embodiments, the first and/or second sets of signal intensities are associated with a temperature between 15 °C and 40 °C.

[0009] In another aspect, the present disclosure provides a non-transitory, machine-readable medium for estimating a set of rate constants. In various embodiments, the non-transitory, machine- readable medium has stored thereon machine-readable instructions executable to cause a system to perform operations comprising: (a) receiving: (i) a first set of signal intensities associated with a first set of time points, each time point of the first set of time points corresponding to an incubation period between a ligand and a receptor and (ii) a second set of signal intensities associated with a second set of time points, each time point of the second set of time points corresponding to a dissociation period of a ligand-receptor complex between the ligand and the receptor; (b) fitting the first set of signal intensities and/or the second set of signal intensities to a three-state model of interactions between the ligand, the receptor, and the ligand-receptor complex; and (c) determining the set of rate constants based on the model. In various embodiments, the first and/or second sets of signal intensities comprise fluorescence signal intensities. In various embodiments, the fluorescence signal intensities comprise flow cytometry fluorescence signal intensities. In various embodiments, the receptor comprises a T cell receptor (TCR). In various embodiments, the ligand comprises a target monomeric peptide-associated major histocompatibility complex (pMHC). In various embodiments, the target monomeric pMHC is associated with a fluorescent label. In various embodiments, the three-state model comprises: (i) a first state in which the ligand and the receptor are not bound, (ii) a second state in which the ligand and the receptor are bound in the ligand-receptor complex, and (iii) a third state in which the ligand and the receptor are not bound in the ligand-receptor complex and in which the ligand-receptor complex is internalized by a cell with which the ligand is associated. In various embodiments, the set of rate constants comprises: (i) an association rate constant between the first state and the second state, (ii) a dissociation rate constant between the first state and the second state, and (iii) a rate constant associated with internalization of the ligand-receptor complex by the cell. In various embodiments, the first and/or second sets of signal intensities are associated with a temperature between 15 °C and 40 °C.

BRIEF DESCRIPTION OF THE DRAWINGS

[0010] FIG. 1 is a simplified diagram of a first method for estimating a set of rate constants, in accordance with various embodiments. [0011] FIG. 2 is a simplified diagram of a second method for estimating a set of rate constants, in accordance with various embodiments.

[0012] FIG. 3 is a block diagram of a computer-based system for determining a kinetic parameter, in accordance with various embodiments.

[0013] FIG. 4 is a block diagram of a computer system, in accordance with various embodiments.

[0014] FIG. 5A shows a set of mean fluorescence intensity (MFI) signal intensities corresponding to varying incubation periods between a T cell receptor (TCR) and the peptide OVA-N4 at a concentration of 50 micrograms per milliliter (pg/mL) fitted to a four-state model, in accordance with various embodiments.

[0015] FIG. 5B shows a set of MFI signal intensities corresponding to varying incubation periods between a TCR and the peptide OVA-N4 at a concentration of 30 pg/mL fitted to a four- state model, in accordance with various embodiments.

[0016] FIG. 5C shows a set of MFI signal intensities corresponding to varying incubation periods between a TCR and the peptide OVA-N4 at a concentration of 10 pg/mL fitted to a four- state model, in accordance with various embodiments.

[0017] FIG. 5D shows a set of MFI signal intensities corresponding to varying incubation periods between a TCR lacking CD8 and the peptide OVA-N4 at a concentration of 50 pg/mL fitted to a four-state model, in accordance with various embodiments.

[0018] FIG. 6A shows a set of MFI signal intensities corresponding to varying incubation periods between a TCR and the peptide OVA-N4 at varying concentrations fitted to a three-state model, in accordance with various embodiments.

[0019] FIG. 6B shows a set of MFI signal intensities corresponding to varying incubation periods between a TCR and the peptide OVA-T4 at varying concentrations fitted to a three-state model, in accordance with various embodiments.

[0020] FIG. 6C shows a set of MFI signal intensities corresponding to varying incubation periods between a TCR and the peptide OVA-V4 at varying concentrations fitted to a three-state model, in accordance with various embodiments. [0021] FIG. 7 A shows a set of MFI signal intensities corresponding to varying dissociation periods between a TCR and the peptide OVA-N4 at varying concentrations fitted to a three-state model, in accordance with various embodiments.

[0022] FIG. 7B shows a set of MFI signal intensities corresponding to varying dissociation periods between a TCR and the peptide OVA-T4 at varying concentrations fitted to a three-state model, in accordance with various embodiments.

[0023] FIG. 7C shows a set of MFI signal intensities corresponding to varying dissociation periods between a TCR and the peptide OVA-V4 at varying concentrations fitted to a three-state model, in accordance with various embodiments.

[0024] In various embodiments, not all of the depicted components in each figure may be required, and various embodiments may include additional components not shown in a figure. Variations in the arrangement and type of the components may be made without departing from the scope of the subject disclosure. Additional components, different components, or fewer components may be utilized within the scope of the subject disclosure. In the figures, like numbers denote like elements.

DETAILED DESCRIPTION

[0025] This specification describes exemplary methods and systems for estimating a set of rate constants. The methods and systems may generally operate by fitting one or more sets of signal intensities to a model of interactions between a ligand, a receptor, and a ligand-receptor complex. In some embodiments, the receptor comprises a T cell receptor (TCR). In some embodiments, the ligand comprises a target monomeric peptide-associated major histocompatibility complex (pMHC). In some embodiments, the one or more sets of signal intensities comprise a set of time points corresponding to an incubation period between the ligand and the receptor. In some embodiments, the one or more sets of signal intensities comprise a set of time points corresponding to a dissociation period of the ligand-receptor complex. In some embodiments, the model comprises a four-state model. In some embodiments, the model comprises a three-state model.

[0026] The term “target” is used herein in the most general sense and may be any pMHC capable of forming a pMHC-TCR complex with any TCR. The term “target” should not be interpreted as being confined to meaning a species that is being targeted for therapeutic intervention. [0027] The methods and systems may have particular utility in measuring sets of rate constants associated with pMHC-TCR interactions (including but not limited to interactions with coreceptors such as CD8, etc.) that provoke an immune system response.

[0028] As used herein, the term “or” shall be interpreted as conveying both exclusive and inclusive meaning. For instance, reference to elements A or B shall be interpreted as disclosing element A alone, element B alone, or the combination of elements A and B.

Estimating a set of rate constants using a four-state model

[0029] FIG. 1 is a simplified diagram of a first method 100 for estimating a set of rate constants. In various embodiments, the method 100 comprises a first step 110 of receiving: (i) a first set of signal intensities measured at a first set of time points and (ii) a second set of signal intensities measured at a second set of time points. Each time point of the first set of time points may correspond to an incubation period between a ligand and a receptor. Each time point of the second set of time points may correspond to a dissociation period of a ligand-receptor complex between the ligand and the receptor. The first and/or second sets of signal intensities may comprise fluorescence signal intensities. The fluorescence signal intensities may comprise flow cytometry fluorescence signal intensities. The receptor may comprise a TCR. The ligand may comprise a target pMHC. The ligand may comprise a target monomeric pMHC. The ligand may be associated with a fluorescent label.

[0030] Prior to step 110, the first set of signal intensities may be measured at a set of time points. Each time point may correspond to a particular incubation period between the ligand and the receptor. As the incubation period increases, the signal intensity may increase substantially monotonically, eventually approaching a saturation value. Alternatively, the signal intensity may increase, hit a maximum, then decrease, eventually approaching a steady-state value. Exemplary first sets of signal intensities are discussed in more detail in Example 1.

[0031] Prior to step 110, the second set of signal intensities may be measured at a set of time points. Each time point may correspond to a particular dissociation period of the ligand-receptor complex. As the dissociation period increases, the signal intensity may decrease substantially monotonically. Alternatively, as the dissociation period increases, the signal intensity may decrease, hit a minimum, then increase, eventually approaching a steady-state value. Exemplary first sets of signal intensities are discussed in more detail in Example 1. [0032] In various embodiments, the method 100 comprises a second step 120 of fitting the first set of signal intensities and/or the second set of signal intensities to a four-state model of interactions between the ligand, the receptor, and the ligand-receptor complex. The four-state model may comprise a first state, a second state, a third state, and a fourth state. The first state may represent a state in which the ligand (denoted L herein) and the receptor are not bound and in which the receptor is in an active conformation (denoted R_a herein). The second state may represent a state in which the ligand and the receptor are bound in the ligand-receptor complex and in which the receptor is in the active conformation (denoted X_a herein). The third state may represent a state in which the ligand and the receptor are bound in the ligand-receptor complex and in which the receptor is in a non-active conformation (denoted X_n herein). The fourth state may represent a state in which the ligand and the receptor are not bound, and the receptor is in the non-active conformation (denoted R_n herein).

[0033] As used herein, the term “conformation” indicates any physical change in the receptor that causes the receptor to interact in a particular manner with the ligand. Thus, a conformational change in the receptor indicates any physical change in the receptor that alters the behavior of the ligand-receptor complex.

[0034] In various embodiments, the set of rate constants comprises any 6, 7, or 8 of: (i) an association rate constant between the first state and the second state (denoted k_± herein), (ii) a dissociation rate constant between the first state and the second state (denoted k_t herein), (iii) an association rate constant between the second state and the third state (denoted k₂ herein), (iv) a dissociation rate constant between the second state and the third state (denoted fc_₂ herein), (v) an association rate constant between the third state and the fourth state (denoted k₃ herein), (vi) a dissociation rate constant between the third state and the fourth state (denoted fc_₃ herein), (vii) an association rate constant between the receptor in the active conformation (denoted fc₄ herein), and (viii) a dissociation rate constant between the receptor in the non-active conformation (denoted fc_₄ herein).

[0035] Thus, the reaction scheme for the four-state model may be represented as:

[0036] In this model, the interaction with a co-receptor C (e.g., CD8, etc.) is considered within the reactions described by Equations (2) and (3) as follows:

[0037] The details of Equations (2)-(4) need not be included in the general four-state model, as they do not affect the kinetics curves. Rather, the details of Equations (2)-(4) lead to the following details: k₂ = k₂C and k₄ = k₄C. Here, k₂ and k₄ refer to the detailed rate constants, which are related to a co-receptor C. The four-state model may or may not include the details of Equations (2)-(4).

[0038] The kinetics of the reaction scheme in Equation (1) may be given by Equation (5):

where Ro and Lo are the total concentrations of receptors and ligands, respectively, which are constant during the reaction. Equation (5) has an analytical solution in each of two common cases: L_o » R_o and R_o » L_o . For example, if L_o » R_o (e.g., the ligand concentration greatly exceeds the receptor concentration) then L = L_o and Equation (5) is reduced to the following:

where X corresponds to the total number of fluorescent-labeled complexes on the cell, which is measured in the experiment. Equation (6) can be rewritten as:

[0039] Equation (7) is a system of linear differential equations, which can be rewritten in matrix form and solved by the linear algebra method:

[0040] The general solution to inhomogeneous Equation (8) is the sum of the general solution (X X_a R_a)g of the homogenous equation and the particular solution (X X_a R_a)p of the inhomogeneous equation:

[0041] The general solution of the homogeneous Equation (11) may be determined by finding the eigenvalues A of the 3x3 matrix in Equation (11): (12)

[0042] Equation (12) can be presented in the third-order polynomial equation: (13)

[0043] Here, the intermediate variables a_Q, a_±, and a₂ are defined by:

cx₂ = k_₃L + k₃ + k₂ + k_₃ + k_₂ + k₄ + k_₄ + k₃L

[0044] In order to find the eigenvalues, the cubic equation of Equation (13) may be solved by defining the following intermediate variables:

[0045] Then, the general solution to Equation (7) is given by:

[0046] Here, the eigenvalues

are given by:

[0047] The coefficients Ci are given by:

Cu = «i (23)

[0048] The three constants a_t are found from the initial conditions (i.e., the three initial values of X, X_a, and R_a in Equation (20)).

[0049] Thus, the four-state model yields the following fitting fimction for the first and/or second sets of signal intensities (referred to generically as X(t)):

[0050] In various embodiments, the method 100 comprises a third step 130 of determining the set of rate constants based on the four-state model. The set of rate constants may be determined in accordance with Equations (l)-(25). Equation (25) contains seven fitting parameters (C₁₀, C₁₁₅ C₁₂, C₁₃, A₁₅ A₂, and A₃). The seven fitting parameters may be used to determine seven of the eight rate constants k_1, k__1, k₂, k_₂, k₃, k_₃, k₄, and fc_₄ through Equations (l)-(25).

[0051] In some embodiments, the method 100 is especially usefiil for first and/or second sets of signal intensities that are associated with or obtained at temperatures below room temperature.

Such low temperatures may suppress unwanted fluorescence signals that may result from internalization of the ligand-receptor complex by a cell with which the ligand is associated. For example, the first and/or second sets of signal intensities may be associated with or obtained at a temperature of at least about 0 degrees Celsius (°C), 1 °C, 2 °C, 3 °C, 4 °C, 5 °C, 6 °C, 7 °C, 8 °C, 9 °C, 10 °C, 11 °C, 12 °C, 13 °C, 14 °C, 15 °C, 16 °C, 17 °C, 18 °C, 19 °C, 20 °C, 21 °C, 22 °C, 23 °C, 24 °C, 25 °C, or more. The first and/or second sets of signal intensities may be associated with or obtained at a temperature of at most about 25 °C, 24 °C, 23 °C, 22 °C, 21 °C, 20 °C, 19 °C, 18 °C, 17 °C, 16 °C, 15 °C, 14 °C, 13 °C, 12 °C, 11 °C, 10 °C, 9 °C, 8 °C, 7 °C, 6 °C, 5 °C, 4 °C, 3 °C, 2 °C, 1 °C, 0 °C, or less. The first and/or second sets of signal intensities may be associated with or obtained at a temperature that is within a range defined by any two of the preceding values. For example, the first and/or second sets of signal intensities may be associated with or obtained at a temperature between about 0 °C and 25 °C, 5 °C and 25 °C, 10 °C and 25 °C, 15 °C and 25 °C, 20 °C and 25 °C, 0 °C and 20 °C, 5 °C and 20 °C, 10 °C and 20 °C, 15 °C and 20 °C, 0 °C and 15 °C, 5 °C and 15 °C, 10 °C and 15 °C, 0 °C and 10 °C, 5 °C and 10 °C, or 0 °C and 5 °C.

[0052] A person having ordinary skill in the art will recognize that the four-state model described herein represents one interpretation of the underlying physics of the interaction between the ligand and the receptor, but that this is not the only possible interpretation of the physics that is possible within the confines of the four-state model. Similarly, a person having ordinary skill in the art will recognize that the states and variables described herein with respect to the four-state model may be named differently, but that the four-state model would still function as described herein.

Estimating a set of rate constants using a three-state model

[0053] FIG. 2 is a simplified diagram of a method 200 for estimating a set of rate constants. In various embodiments, the method 200 comprises a first step 210 of receiving: (i) a first set of signal intensities measured at a first set of time points and (ii) a second set of signal intensities measured at a second set of time points. The first step 210 of method 200 may be similar to the first step 110 of method 100 described herein with respect to FIG. 1. Each time point of the first and/or second sets of time points may be similar to each time point described herein with respect to FIG. 1. The first and/or second sets of signal intensities may be similar to the first and/or second sets of time points described herein with respect to FIG. 1. The receptor and/or ligand may be similar to the receptor and/or ligand described herein with respect to FIG. 1. The first and/or second sets of signal intensities may be obtained prior to step 210 in a manner similar to that described herein with respect to FIG. 1.

[0054] In various embodiments, the method 200 comprises a second step 220 of fitting the first set of signal intensities and/or the second set of signal intensities to a three-state model of interactions between the ligand, the receptor, and the ligand-receptor complex. The three-state model may comprise a first state, a second state, and a third state. The first state may represent a state in which the ligand (denoted S herein) and in which the receptor (denoted E herein) are not bound. The second state may represent a state in which the ligand and in which the receptor are bound in the ligand-receptor complex (denoted X herein). The third state may represent a state in which the ligand and the receptor are not bound in the ligand receptor complex and in which the ligand-receptor complex is internalized by a cell with which the ligand is associated. [0055] In various embodiments, the set of rate constants comprises: (i) an association rate constant between the first state and the second state (denoted k_± herein), (ii) a dissociation rate constant between the first state and the second state (denoted k_t herein), and (iii) a rate constant associated with internalization of the ligand-receptor complex by the cell (denoted k₂ herein).

[0056] Thus, the reaction scheme for the three-state model may be represented as: fci - > k₂

E + S < X - > E + P (26) fc-i

[0057] The kinetics of the reaction scheme in Equation (26) may be given by Equations (27) and (28):

[0058] Equations (27) and (28) lead to the solution:

[0059] If k-i + k_±S » k₂, then the signal intensity I(t) is given by:

[0060] Thus, the signal intensity may be fit to the fitting function Y (t; S; A; k_₁; k^, k₂) :

[0061] In Equation (31), t and S are variables representing the times associated with the first and/or second sets of signal intensities and the ligand concentration, respectively, and k_₁₅ k_lf and k₂ are fitting parameters. [0062] In various embodiments, the method 200 comprises a third step 230 of determining the set of rate constants based on the three-state model. The set of rate constants may be determined in accordance with Equations (26)-(31).

[0063] In some embodiments, the method 200 is especially useful for first and/or second sets of signal intensities that are associated with or obtained at temperatures substantially near room temperature. Such temperatures may better model the ligand-receptor interaction under physiological conditions by modeling internalization of the ligand-receptor complex by a cell with which the ligand is associated. For example, the first and/or second sets of signal intensities may be associated with or obtained at a temperature of at least about 15 °C, 16 °C, 17 °C, 18 °C, 19 °C, 20 °C, 21 °C, 22 °C, 23 °C, 24 °C, 25 °C, 26 °C, 27 °C, 28 °C, 29 °C, 30 °C, 31 °C, 32 °C, 33 °C, 34

°C, 35 °C, 36 °C, 37 °C, 38 °C, 39 °C, 40 °C, or more. The first and/or second sets of signal intensities may be associated with or obtained at a temperature of at most about 40 °C, 39 °C, 38 °C, 37 °C, 36 °C, 35 °C, 34 °C, 33 °C, 32 °C, 31 °C, 30 °C, 29 °C, 28 °C, 27 °C, 26 °C, 25 °C, 24

°C, 23 °C, 22 °C, 21 °C, 20 °C, 19 °C, 18 °C, 17 °C, 16 °C, 15 °C, or less. The first and/or second sets of signal intensities may be associated with or obtained at a temperature that is within a range defined by any two of the preceding values. For example, the first and/or second sets of signal intensities may be associated with or obtained at a temperature between about 15 °C and 40 °C, 20 °C and 40 °C, 25 °C and 40 °C, 30 °C and 40 °C, 35 °C and 40 °C, 15 °C and 35 °C, 20 °C and 35 °C, 25 °C and 35 °C, 30 °C and 35 °C, 15 °C and 30 °C, 20 °C and 30 °C, 25 °C and 30 °C, 15 °C and 25 °C, 20 °C and 25 °C, or 15 °C and 20 °C.

[0064] A person having ordinary skill in the art will recognize that the three-state model described herein represents one interpretation of the underlying physics of the interaction between the ligand and the receptor, but that this is not the only possible interpretation of the physics that is possible within the confines of the three-state model. Similarly, a person having ordinary skill in the art will recognize that the states and variables described herein with respect to the three-state model may be named differently, but that the three-state model would still function as described herein.

Estimating a set of rate constants using alternative models

[0065] Although the methods 100 and 200 described herein with respect to FIGs. 1 and 2 refer to four-state and three-state models, respectively, alternative models may be usefiil. For example, the models may utilize 2, 3, 4, 5, 6, or more states. The models may or may not include states that represent conformational changes or internalization of the ligand-receptor complex by a cell with whichtheligandisassociated.Moreover,apersonhavingordinaryskillintheartwillrecognizethatthemodelsdescribedhereinrepresentstwopossibleinterpretationsoftheunderlyingphysicsoftheinteractionbetweentheligandandthereceptor,butthatthesearenottheonlypossibleinterpretationofthephysicsthatarepossiblewithintheconfinesofthedisclosure.Similarly,apersonhavingordinaryskillintheartwillrecognizethatthestatesandvariablesdescribedhereinwithrespecttothemodelsdescribedhereinmaybenameddifferently,butthatthemodelswouldstillfimctionasdescribedherein. Computer-implementedsystemsfordeterminingakineticparameter [0066] Invariousembodiments,atleastaportionofthemethods 100and/or200forestimatingasetofrateconstantscanbeimplementedviasoftware,hardware,firmware,oracombinationthereof. [0067] Thatis,asdepictedinFIG.3,themethodsandsystemsdisclosedherein(suchasmethods100and/or200describedhereinwithrespecttoFIGs.1and2,respectively)canbeimplementedonacomputer-basedsystem300forestimatingasetofrateconstants.Thesystem300maycompriseacomputersystemsuchascomputersystem302(e.g.,acomputingdevice/analyticsserver).Invariousembodiments,thecomputersystem302canbecommunicativelyconnectedtoadatastorage305andadisplaysystem306viaadirectconnectionorthroughanetworkconnection(e.g.,LAN,WAN,Internet,etc.).Thecomputersystem302canbeconfiguredtoreceivedata,suchasimagefeaturedatadescribedherein.Itshouldbeappreciatedthatthecomputersystem302depictedinFIG.3cancompriseadditionalenginesorcomponentsasneededbytheparticularapplicationorsystemarchitecture. [0068] FIG.4isablockdiagramofacomputersysteminaccordancewithvariousembodiments.Computersystem400maybeanexampleofoneimplementationforcomputersystem302describedhereinwithrespecttoFIG.3.Inoneormoreexamples,computersystem400canincludeabus402orothercommunicationmechanismforcommunicatinginformation,andaprocessor404coupledwithbus402forprocessinginformation.Invariousembodiments,computersystem400canalsoincludeamemory,whichcanbearandom-accessmemory(RAM)406orotherdynamicstoragedevice,coupledtobus402fordetermininginstructionstobeexecutedbyprocessor404.Memoryalsocanbeusedforstoringtemporaryvariablesorotherintermediateinformationduringexecutionofinstructionstobeexecutedbyprocessor404.Invariousembodiments,computersystem400canfurtherincludeareadonlymemory(ROM)408orotherstaticstoragedevicecoupledtobus402forstoringstaticinformationandinstructionsforprocessor 404. A storage device 410, such as a magnetic disk or optical disk, can be provided and coupled to bus 402 for storing information and instructions.

[0069] In various embodiments, computer system 400 can be coupled via bus 402 to a display 412, such as a cathode ray tube (CRT) or liquid crystal display (LCD), for displaying information to a computer user. An input device 414, including alphanumeric and other keys, can be coupled to bus 402 for communicating information and command selections to processor 404. Another type of user input device is a cursor control 416, such as a mouse, a joystick, a trackball, a gesture input device, a gaze-based input device, or cursor direction keys for communicating direction information and command selections to processor 404 and for controlling cursor movement on display 412. This input device 414 typically has two degrees of freedom in two axes, a first axis (e.g., x) and a second axis (e.g., y), that allows the device to specify positions in a plane. However, it should be understood that input devices 412 allowing for three-dimensional (e.g., x, y and z) cursor movement are also contemplated herein.

[0070] Consistent with certain implementations of the present teachings, results can be provided by computer system 400 in response to processor 404 executing one or more sequences of one or more instructions contained in RAM 406. Such instructions can be read into RAM 406 from another computer-readable medium or computer-readable storage medium, such as storage device 410. Execution of the sequences of instructions contained in RAM 406 can cause processor 404 to perform the processes described herein. Alternatively, hard-wired circuitry can be used in place of or in combination with software instructions to implement the present teachings. Thus, implementations of the present teachings are not limited to any specific combination of hardware circuitry and software.

[0071] The term "computer-readable medium" (e.g., data store, data storage, storage device, data storage device, etc.) or "computer-readable storage medium" as used herein refers to any media that participates in providing instructions to processor 404 for execution. Such a medium can take many forms, including but not limited to, non-volatile media, volatile media, and transmission media. Examples of non-volatile media can include, but are not limited to, optical, solid state, magnetic disks, such as storage device 410. Examples of volatile media can include, but are not limited to, dynamic memory, such as RAM 406. Examples of transmission media can include, but are not limited to, coaxial cables, copper wire, and fiber optics, including the wires that comprise bus 402. [0072] Common forms of computer-readable media include, for example, a floppy disk, a flexible disk, hard disk, magnetic tape, or any other magnetic medium, a CD-ROM, any other optical medium, punch cards, paper tape, any other physical medium with patterns of holes, a RAM, PROM, and EPROM, a FLASH-EPROM, any other memory chip or cartridge, or any other tangible medium from which a computer can read.

[0073] In addition to computer readable medium, instructions or data can be provided as signals on transmission media included in a communications apparatus or system to provide sequences of one or more instructions to processor 404 of computer system 400 for execution. For example, a communication apparatus may include a transceiver having signals indicative of instructions and data. The instructions and data are configured to cause one or more processors to implement the functions outlined in the disclosure herein. Representative examples of data communications transmission connections can include, but are not limited to, telephone modem connections, wide area networks (WAN), local area networks (LAN), infrared data connections, NFC connections, optical communications connections, etc.

[0074] It should be appreciated that the methodologies described herein, flow charts, diagrams, and accompanying disclosure can be implemented using computer system 400 as a standalone device or on a distributed network of shared computer processing resources such as a cloud computing network.

[0075] The methodologies described herein may be implemented by various means depending upon the application. For example, these methodologies may be implemented in hardware, firmware, software, or any combination thereof. For a hardware implementation, the processing unit may be implemented within one or more application specific integrated circuits (ASICs), digital signal processors (DSPs), digital signal processing devices (DSPDs), programmable logic devices (PLDs), field programmable gate arrays (FPGAs), processors, controllers, microcontrollers, microprocessors, electronic devices, other electronic units designed to perform the functions described herein, or a combination thereof.

[0076] In various embodiments, the methods of the present teachings may be implemented as firmware and/or a software program and applications written in conventional programming languages such as C, C++, Python, etc. If implemented as firmware and/or software, the embodiments described herein can be implemented on a non-transitory computer-readable medium in which a program is stored for causing a computer to perform the methods described above. It should be understood that the various engines described herein can be provided on a computer system, such as computer system 400, whereby processor 404 would execute the analyses and determinations provided by these engines, subject to instructions provided by any one of, or a combination of, the memory components RAM 406, ROM 408, or storage device 410 and user input provided via input device 414.

EXAMPLES

Example 1: Estimation of rate constants using a four-state model

[0077] FIG. 5 A shows a set of mean fluorescence intensity (MFI) signal intensities corresponding to varying incubation periods between a TCR and the peptide OVA-N4 at a concentration of 50 micrograms per milliliter (pg/mL) fitted to a four-state model. The fitted parameters are shown in FIG. 5 A.

[0078] FIG. 5B shows a set of MFI signal intensities corresponding to varying incubation periods between a TCR and the peptide OVA-N4 at a concentration of 30 pg/mL fitted to a four- state model. The fitted parameters are shown in FIG. 5B.

[0079] FIG. 5C shows a set of MFI signal intensities corresponding to varying incubation periods between a TCR and the peptide OVA-N4 at a concentration of 10 pg/mL fitted to a four- state model. The fitted parameters are shown in FIG. 5C.

[0080] FIG. 5D shows a set of MFI signal intensities corresponding to varying incubation periods between a TCR lacking CD8 and the peptide OVA-N4 at a concentration of 50 pg/mL fitted to a four-state model. The fitted parameters are shown in FIG. 5D.

Example 2: Estimation of rate constants using a three-state model

[0081] FIG. 6A shows a set of MFI signal intensities corresponding to varying incubation periods between a TCR and the peptide OVA-N4 at varying concentrations fitted to a three-state model. The fitted parameters are shown in FIG. 6A.

[0082] FIG. 6B shows a set of MFI signal intensities corresponding to varying incubation periods between a TCR and the peptide OVA-T4 at varying concentrations fitted to a three-state model. The fitted parameters are shown in FIG. 6B.

[0083] FIG. 6C shows a set of MFI signal intensities corresponding to varying incubation periods between a TCR and the peptide OVA-V4 at varying concentrations fitted to a three-state model. The fitted parameters are shown in FIG. 6C. [0084] FIG. 7A shows a set of MFI signal intensities corresponding to varying dissociation periods between a TCR and the peptide OVA-N4 at varying concentrations fitted to a three-state model. The fitted parameters are shown in FIG. 7A.

[0085] FIG. 7B shows a set of MFI signal intensities corresponding to varying dissociation periods between a TCR and the peptide OVA-T4 at varying concentrations fitted to a three-state model. The fitted parameters are shown in FIG. 7B.

[0086] FIG. 7C shows a set of MFI signal intensities corresponding to varying dissociation periods between a TCR and the peptide OVA-V4 at varying concentrations fitted to a three-state model. The fitted parameters are shown in FIG. 7C.

[0087] In describing the various embodiments, the specification may have presented a method or process as a particular sequence of steps. However, to the extent that the method or process does not rely on the particular order of steps set forth herein, the method or process should not be limited to the particular sequence of steps described. As one of ordinary skill in the art would appreciate, other sequences of steps may be possible. Therefore, the particular order of the steps set forth in the specification should not be construed as limitations on the claims. In addition, the claims directed to the method and/or process should not be limited to the performance of their steps in the order written, and one skilled in the art can readily appreciate that the sequences may be varied and still remain within the spirit and scope of the various embodiments. Similarly, any of the various system embodiments may have been presented as a group of particular components. However, these systems should not be limited to the particular set of components, now their specific configuration, communication and physical orientation with respect to each other. One skilled in the art should readily appreciate that these components can have various configurations and physical orientations (e.g., wholly separate components, units and subunits of groups of components, different communication regimes between components).

[0088] Although specific embodiments and applications of the disclosure have been described in this specification, these embodiments and applications are exemplary only, and many variations are possible. Various Embodiments

[0089] A method for estimating a set of rate constants, comprising: a. receiving: i) a first set of signal intensities measured at a first set of time points, each time point of the first set of time points corresponding to an incubation period between a ligand and a receptor and ii) a second set of signal intensities measured at a second set of time points, each time point of the second set of time points corresponding to a dissociation period of a ligand-receptor complex between the ligand and the receptor; b. fitting the first set of signal intensities and/or the second set of signal intensities to a four-state model of interactions between the ligand, the receptor, and the ligandreceptor complex; and c. determining the set of rate constants based on the model.

[0090] The method of claim 1, wherein the first and/or second sets of signal intensities comprise fluorescence signal intensities.

[0091] The method of claim 2, wherein the fluorescence signal intensities comprise flow cytometry fluorescence signal intensities.

[0092] The method of any one of claims 1-4, wherein the receptor comprises a T cell receptor (TCR).

[0093] The method of any one of claims 1-5, wherein the ligand comprises a target monomeric peptide- associated major histocompatibility complex (pMHC).

[0094] The method of claim 6, wherein the target monomeric pMHC is associated with a fluorescent label.

[0095] The method of any one of claims 1-7, wherein the four-state model comprises:

(i) a first state in which the ligand and the receptor are not bound and in which the receptor is in an active conformation,

(ii) a second state in which the ligand and the receptor are bound in the ligandreceptor complex and in which the receptor is in the active conformation,

(iii) a third state in which the ligand and the receptor are bound in the ligandreceptor complex and in which the receptor is in a non-active conformation, and

(iv) a fourth state in which the ligand and the receptor are not bound, and the receptor is in the non-active conformation. [0096] The method of claim 8, wherein the set of rate constants comprises any 6, 7, or 8 of:

(i) an association rate constant between the first state and the second state,

(ii) a dissociation rate constant between the first state and the second state,

(iii) an association rate constant between the second state and the third state,

(iv) a dissociation rate constant between the second state and the third state,

(v) an association rate constant between the third state and the fourth state,

(vi) a dissociation rate constant between the third state and the fourth state,

(vii) an association rate constant between the receptor in the active conformation, and

(viii) a dissociation rate constant between the receptor in the non-active conformation.

[0097] The method of any one of claims 1-9, wherein the first and/or second sets of signal intensities are associated with a temperature between 0 degrees Celsius (°C) and 10 °C.

[0098] A system for estimating a set of rate constants, comprising: a non-transitory memory; and one or more processors coupled to the non-transitory memory and configured to read instructions from the non-transitory memory to cause the system to perform operations comprising: a. receiving: i. a first set of signal intensities measured at a first set of time points, each time point of the first set of time points corresponding to an incubation period between a ligand and a receptor and ii. a second set of signal intensities measured at a second set of time points, each time point of the second set of time points corresponding to a dissociation period of a ligand-receptor complex between the ligand and the receptor; b. fitting the first set of signal intensities and/or the second set of signal intensities to a four-state model of interactions between the ligand, the receptor, and the ligandreceptor complex; and c. determining the set of rate constants based on the model.

[0099] The system of claim 11, wherein the first and/or second sets of signal intensities comprise fluorescence signal intensities. [0100] The system of claim 12, wherein the fluorescence signal intensities comprise flow cytometry fluorescence signal intensities.

[0101] The system of any one of claims 11-14, wherein the receptor comprises a T cell receptor (TCR).

[0102] The system of any one of claims 11-15, wherein the ligand comprises a target monomeric peptide-associated major histocompatibility complex (pMHC).

[0103] The system of claim 16, wherein the target monomeric pMHC is associated with a fluorescent label.

[0104] The system of any one of claims 11-17, wherein the four-state model comprises:

(i) a first state in which the ligand and the receptor are not bound and in which the receptor is in an active conformation,

(ii) a second state in which the ligand and the receptor are bound in the ligandreceptor complex and in which the receptor is in the active conformation,

(iii) a third state in which the ligand and the receptor are bound in the ligandreceptor complex and in which the receptor is in a non-active conformation, and

(iv) a fourth state in which the ligand and the receptor are not bound, and the receptor is in the non-active conformation.

[0105] The system of claim 18, wherein the set of rate constants comprises any 6, 7, or 8 of:

(i) an association rate constant between the first state and the second state,

(ii) a dissociation rate constant between the first state and the second state,

(iii) an association rate constant between the second state and the third state,

(iv) a dissociation rate constant between the second state and the third state,

(v) an association rate constant between the third state and the fourth state,

(vi) a dissociation rate constant between the third state and the fourth state,

(vii) an association rate constant between the receptor in the active conformation, and

(viii) a dissociation rate constant between the receptor in the non-active conformation.

[0106] The system of any one of claims 11-19, wherein the first and/or second sets of signal intensities are associated with a temperature between 0 degrees Celsius (°C) and 10 °C.

[0107] A non-transitory, machine-readable medium having stored thereon machine-readable instructions executable to cause a system to perform operations comprising: a. receiving: i. a first set of signal intensities measured at a first set of time points, each time point of the first set of time points corresponding to an incubation period between a ligand and a receptor and ii. a second set of signal intensities measured at a second set of time points, each time point of the second set of time points corresponding to a dissociation period of a ligand-receptor complex between the ligand and the receptor; b. fitting the first set of signal intensities and/or the second set of signal intensities to a four-state model of interactions between the ligand, the receptor, and the ligandreceptor complex; and c. determining the set of rate constants based on the model.

[0108] The non-transitory, machine-readable medium of claim 21, wherein the first and/or second sets of signal intensities comprise fluorescence signal intensities.

[0109] The non-transitory, machine-readable medium of claim 22, wherein the fluorescence signal intensities comprise flow cytometry fluorescence signal intensities.

[0110] The non-transitory, machine-readable medium of any one of claims 21-24, wherein the receptor comprises a T cell receptor (TCR).

[0111] The non-transitory, machine-readable medium of any one of claims 21-25, wherein the ligand comprises a target monomeric peptide-associated major histocompatibility complex (pMHC).

[0112] The non-transitory, machine-readable medium of claim 26, wherein the target monomeric pMHC is associated with a fluorescent label.

[0113] The non-transitory, machine-readable medium of any one of claims 21-27, wherein the four-state model comprises:

(i) a first state in which the ligand and the receptor are not bound and in which the receptor is in an active conformation,

(ii) a second state in which the ligand and the receptor are bound in the ligandreceptor complex and in which the receptor is in the active conformation,

(iii) a third state in which the ligand and the receptor are bound in the ligandreceptor complex and in which the receptor is in a non-active conformation, and

(iv) a fourth state in which the ligand and the receptor are not bound, and the receptor is in the non-active conformation. [0114] The non-transitory, machine-readable medium of claim 28, wherein the set of rate constants comprises any 6, 7, or 8 of:

(i) an association rate constant between the first state and the second state,

(ii) a dissociation rate constant between the first state and the second state,

(iii) an association rate constant between the second state and the third state,

(iv) a dissociation rate constant between the second state and the third state,

(v) an association rate constant between the third state and the fourth state,

(vi) a dissociation rate constant between the third state and the fourth state,

(vii) an association rate constant between the receptor in the active conformation, and

(viii) a dissociation rate constant between the receptor in the non-active conformation.

[0115] The non-transitory, machine-readable medium of any one of claims 21-29, wherein the first and/or second sets of signal intensities are associated with a temperature between 0 degrees Celsius (°C) and 10 °C.

[0116] A method for estimating a set of rate constants, comprising: a. receiving: i. a first set of signal intensities associated with a first set of time points, each time point of the first set of time points corresponding to an incubation period between a ligand and a receptor and ii. a second set of signal intensities associated with a second set of time points, each time point of the second set of time points corresponding to a dissociation period of a ligand-receptor complex between the ligand and the receptor; b. fitting the first set of signal intensities and/or the second set of signal intensities to a three-state model of interactions between the ligand, the receptor, and the ligandreceptor complex; and c. determining the set of rate constants based on the model.

[0117] The method of claim 31, wherein the first and/or second sets of signal intensities comprise fluorescence signal intensities.

[0118] The method of claim 32, wherein the fluorescence signal intensities comprise flow cytometry fluorescence signal intensities. [0119] The method of any one of claims 31-34, wherein the receptor comprises a T cell receptor (TCR).

[0120] The method of any one of claims 31-35, wherein the ligand comprises a target monomeric peptide-associated major histocompatibility complex (pMHC).

[0121] The method of claim 36, wherein the target monomeric pMHC is associated with a fluorescent label.

[0122] The method of any one of claims 31-37, wherein the three-state model comprises:

(i) a first state in which the ligand and the receptor are not bound,

(ii) a second state in which the ligand and the receptor are bound in the ligandreceptor complex, and

(iii) a third state in which the ligand and the receptor are not bound in the ligandreceptor complex and in which the ligand-receptor complex is internalized by a cell with which the ligand is associated.

[0123] The method of claim 38, wherein the set of rate constants comprises:

(i) an association rate constant between the first state and the second state,

(ii) a dissociation rate constant between the first state and the second state, and

(iii) a rate constant associated with internalization of the ligand-receptor complex by the cell.

[0124] The method of any one of claims 31-39, wherein the first and/or second sets of signal intensities are associated with a temperature between 15 °C and 40 °C.

[0125] A system for estimating a set of rate constants, comprising: a non-transitory memory; and one or more processors coupled to the non-transitory memory and configured to read instructions from the non-transitory memory to cause the system to perform operations comprising: a. receiving: i. a first set of signal intensities associated with a first set of time points, each time point of the first set of time points corresponding to an incubation period between a ligand and a receptor and ii. a second set of signal intensities associated with a second set of time points, each time point of the second set of time points corresponding to a dissociation period of a ligand-receptor complex between the ligand and the receptor; b. fitting the first set of signal intensities and/or the second set of signal intensities to a three-state model of interactions between the ligand, the receptor, and the ligandreceptor complex; and c. determining the set of rate constants based on the model.

[0126] The system of claim 41, wherein the first and/or second sets of signal intensities comprise fluorescence signal intensities.

[0127] The system of claim 42, wherein the fluorescence signal intensities comprise flow cytometry fluorescence signal intensities.

[0128] The system of any one of claims 41-44, wherein the receptor comprises a T cell receptor (TCR).

[0129] The system of any one of claims 41-45, wherein the ligand comprises a target monomeric peptide-associated major histocompatibility complex (pMHC).

[0130] The system of claim 46, wherein the target monomeric pMHC is associated with a fluorescent label.

[0131] The system of any one of claims 41-47, wherein the three-state model comprises:

(i) a first state in which the ligand and the receptor are not bound,

(ii) a second state in which the ligand and the receptor are bound in the ligandreceptor complex, and

(iii) a third state in which the ligand and the receptor are not bound in the ligandreceptor complex and in which the ligand-receptor complex is internalized by a cell with which the ligand is associated.

[0132] The system of claim 48, wherein the set of rate constants comprises:

(i) an association rate constant between the first state and the second state,

(ii) a dissociation rate constant between the first state and the second state, and

(iii) a rate constant associated with internalization of the ligand-receptor complex by the cell.

[0133] The system of any one of claims 41-49, wherein the first and/or second sets of signal intensities are associated with a temperature between 15 °C and 40 °C. [0134] A non-transitory, machine-readable medium having stored thereon machine-readable instructions executable to cause a system to perform operations comprising: a. receiving: i. a first set of signal intensities associated with a first set of time points, each time point of the first set of time points corresponding to an incubation period between a ligand and a receptor and ii. a second set of signal intensities associated with a second set of time points, each time point of the second set of time points corresponding to a dissociation period of a ligand-receptor complex between the ligand and the receptor; b. fitting the first set of signal intensities and/or the second set of signal intensities to a three-state model of interactions between the ligand, the receptor, and the ligandreceptor complex; and c. determining the set of rate constants based on the model.

[0135] The non-transitory, machine-readable medium of claim 51, wherein the first and/or second sets of signal intensities comprise fluorescence signal intensities.

[0136] The non-transitory, machine-readable medium of claim 52, wherein the fluorescence signal intensities comprise flow cytometry fluorescence signal intensities.

[0137] The non-transitory, machine-readable medium of any one of claims 51-54, wherein the receptor comprises a T cell receptor (TCR).

[0138] The non-transitory, machine-readable medium of any one of claims 51-55, wherein the ligand comprises a target monomeric peptide-associated major histocompatibility complex (pMHC).

[0139] The non-transitory, machine-readable medium of claim 56, wherein the target monomeric pMHC is associated with a fluorescent label.

[0140] The non-transitory, machine-readable medium of any one of claims 51-57, wherein the three- state model comprises:

(i) a first state in which the ligand and the receptor are not bound,

(ii) a second state in which the ligand and the receptor are bound in the ligandreceptor complex, and

(iii) a third state in which the ligand and the receptor are not bound in the ligandreceptor complex and in which the ligand-receptor complex is internalized by a cell with which the ligand is associated. [0141] The non-transitory, machine-readable medium of claim 58, wherein the set of rate constants comprises:

(i) an association rate constant between the first state and the second state,

(ii) a dissociation rate constant between the first state and the second state, and

(iii) a rate constant associated with internalization of the ligand-receptor complex by the cell.

[0142] The non-transitory, machine-readable medium of any one of claims 51-59, wherein the first and/or second sets of signal intensities are associated with a temperature between 15 °C and 40 °C.

Claims

What is claimed is:

1. A method for estimating a set of rate constants, comprising: a) receiving: i) a first set of signal intensities measured at a first set of time points, each time point of the first set of time points corresponding to an incubation period between a ligand and a receptor and ii) a second set of signal intensities measured at a second set of time points, each time point of the second set of time points corresponding to a dissociation period of a ligand-receptor complex between the ligand and the receptor; b) fitting the first set of signal intensities and/or the second set of signal intensities to a model of interactions between the ligand, the receptor, and the ligandreceptor complex; and c) determining the set of rate constants based on the model.

2. The method of claim 1, wherein the first and/or second sets of signal intensities comprise fluorescence signal intensities.

3. The method of claim 2, wherein the fluorescence signal intensities comprise flow cytometry fluorescence signal intensities.

4. The method of claim 1, wherein the receptor comprises a T cell receptor (TCR).

5. The method of claim 1, wherein the ligand comprises a target monomeric peptide- associated major histocompatibility complex (pMHC).

6. The method of claim 5, wherein the target monomeric pMHC is associated with a fluorescent label.

7. The method of claim 1, wherein the model comprises:

(i) a first state in which the ligand and the receptor are not bound,

(ii) a second state in which the ligand and the receptor are bound in the ligandreceptor complex, and

(iii) a third state in which the ligand and the receptor are not bound in the ligandreceptor complex and in which the ligand-receptor complex is internalized by a cell with which the ligand is associated.

8. The method of claim 7, wherein the set of rate constants comprises:

(i) an association rate constant between the first state and the second state,

(ii) a dissociation rate constant between the first state and the second state, and

32 (iii) a rate constant associated with internalization of the ligand-receptor complex by the cell. The method of claim 7, wherein the first and/or second sets of signal intensities are associated with a temperature between 15 °C and 40 °C. The method of claim 1, wherein the model comprises:

(i) a first state in which the ligand and the receptor are not bound and in which the receptor is in an active conformation,

(ii) a second state in which the ligand and the receptor are bound in the ligandreceptor complex and in which the receptor is in the active conformation,

(iii) a third state in which the ligand and the receptor are bound in the ligandreceptor complex and in which the receptor is in a non-active conformation, and

(iv) a fourth state in which the ligand and the receptor are not bound, and the receptor is in the non-active conformation. The method of claim 10, wherein the set of rate constants comprises any 6, 7, or 8 of:

(i) an association rate constant between the first state and the second state,

(ii) a dissociation rate constant between the first state and the second state,

(iii) an association rate constant between the second state and the third state,

(iv) a dissociation rate constant between the second state and the third state,

(v) an association rate constant between the third state and the fourth state,

(vi) a dissociation rate constant between the third state and the fourth state,

(vii) an association rate constant between the receptor in the active conformation, and

(viii) a dissociation rate constant between the receptor in the non-active conformation. The method of claim 10, wherein the first and/or second sets of signal intensities are associated with a temperature between 0 degrees Celsius (°C) and 10 °C. A system for estimating a set of rate constants, comprising: a non-transitory memory; and one or more processors coupled to the non-transitory memory and configured to read instructions from the non-transitory memory to cause the system to perform operations comprising: a) receiving:

33 i) a first set of signal intensities measured at a first set of time points, each time point of the first set of time points corresponding to an incubation period between a ligand and a receptor and ii) a second set of signal intensities measured at a second set of time points, each time point of the second set of time points corresponding to a dissociation period of a ligand-receptor complex between the ligand and the receptor; b) fitting the first set of signal intensities and/or the second set of signal intensities to a model of interactions between the ligand, the receptor, and the ligandreceptor complex; and c) determining the set of rate constants based on the model. The system of claim 13, wherein the first and/or second sets of signal intensities comprise fluorescence signal intensities. The system of claim 14, wherein the fluorescence signal intensities comprise flow cytometry fluorescence signal intensities. The system of claim 13, wherein the receptor comprises a T cell receptor (TCR). The system of claim 13, wherein the ligand comprises a target monomeric peptide- associated major histocompatibility complex (pMHC). The system of claim 13, wherein the target monomeric pMHC is associated with a fluorescent label. A non-transitory, machine-readable medium having stored thereon machine-readable instructions executable to cause a system to perform operations comprising: a) receiving: i) a first set of signal intensities measured at a first set of time points, each time point of the first set of time points corresponding to an incubation period between a ligand and a receptor and ii) a second set of signal intensities measured at a second set of time points, each time point of the second set of time points corresponding to a dissociation period of a ligand-receptor complex between the ligand and the receptor; b) fitting the first set of signal intensities and/or the second set of signal intensities to a model of interactions between the ligand, the receptor, and the ligandreceptor complex; and c) determining the set of rate constants based on the model.

20. The non-transitory, machine-readable medium of claim 19, wherein the first and/or second sets of signal intensities comprise fluorescence signal intensities.