Daniel Coombs

Dependence of T Cell Antigen Recognition on T Cell Receptor-Peptide MHC Confinement Time

Summary T cell receptor (TCR) binding to diverse peptide-major histocompatibility complex (pMHC) ligands results in various degrees of T cell activation. Here we analyze which binding properties of the TCR-pMHC interaction are responsible for this variation in pMHC activation potency. We have analyzed activation of the 1G4 cytotoxic T lymphocyte clone by cognate pMHC variants and performed thorough correlation analysis of T cell activation with 1G4 TCR-pMHC binding properties measured in solution. We found that both the on rate (kon) and off rate (koff) contribute to activation potency. Based on our results, we propose a model in which rapid TCR rebinding to the same pMHC after chemical dissociation increases the effective half-life or “confinement time” of a TCR-pMHC interaction. This confinement time model clarifies the role of kon in T cell activation and reconciles apparently contradictory reports on the role of TCR-pMHC binding kinetics and affinity in T cell activation.

Activated TCRs remain marked for internalization after dissociation from pMHC

To assess the roles of serial engagement and kinetic proofreading in T cell receptor (TCR) internalization, we have developed a mathematical model of this process. Our determination of TCR down-regulation for an array of TCR mutants, interpreted in the context of the model, has provided new information about peptide-induced TCR internalization. The amount of TCR down-regulation increases to a maximum value and then declines as a function of the half-life of the bond between the TCR and peptide–major histocompatibility complex (pMHC). The model shows that this behavior, which reflects competition between serial engagement and kinetic proofreading, arises only if it is postulated that activated TCRs remain marked for internalization after dissociation from pMHC. The model also predicts that because of kinetic proofreading, the range of TCR-pMHC–binding half-lives required for T cell activation depends on the concentrations and localization of intracellular signaling molecules. We show here that kinetic proofreading provides an explanation for the different requirements for activation observed in naïve and memory T cells.

The influence of transport on the kinetics of binding to surface receptors: application to cells and BIAcore

Accurate estimation of biomolecular reaction rates from binding data, when ligands in solution bind to receptors on the surfaces of cells or biosensors, requires an understanding of the contributions of both molecular transport and reaction. Efficient estimation of parameters requires relatively simple models. In this review, we give conditions under which various transport effects are negligible and identify simple binding models that incorporate the effects of transport, when transport cannot be neglected. We consider effects of diffusion of ligands to cell or biosensor surfaces, flow in a BIAcore biosensor, and distribution of receptors in a dextran layer above the sensor surface. We also give conditions under which soluble receptors can be expected to compete effectively with surface‐bound receptors. Copyright

Equilibrium Thermodynamics of Cell-Cell Adhesion Mediated by Multiple Ligand-Receptor Pairs

In many situations, cell-cell adhesion is mediated by multiple ligand-receptor pairs. For example, the interaction between T cells and antigen-presenting cells of the immune system is mediated not only by T cell receptors and their ligands (peptide-major histocompatibility complex) but also by binding of intracellular adhesion molecules. Interestingly, these binding pairs have different resting lengths. Fluorescent labeling reveals segregation of the longer adhesion molecules from the shorter T cell receptors in this case. Here, we explore the thermal equilibrium of a general cell-cell interaction mediated by two ligand-receptor pairs to examine competition between the elasticity of the cell wall, nonspecific intercellular repulsion, and bond formation, leading to segregation of bonds of different lengths at equilibrium. We make detailed predictions concerning the relationship between physical properties of the membrane and ligand-receptor pairs and equilibrium pattern formation, and suggest experiments to refine our understanding of the system. We demonstrate our model by application to the T cell/antigen-presenting-cell system and outline applications to natural killer cell adhesion.

Calculations show substantial serial engagement of T cell receptors.

The serial engagement model provides an attractive and plausible explanation for how a typical antigen presenting cell, exhibiting a low density of peptides recognized by a T cell, can initiate T cell responses. If a single peptide displayed by a major histocompatibility complex (MHC) can bind, sequentially, to different T cell receptors (TCR), then a few peptides can activate many receptors. To date, arguments supporting and questioning the prevalence of serial engagement have centered on the down-regulation of TCR after contact of T cells with antigen presenting cells. Recently, the existence of serial engagement has been challenged by the demonstration that engagement of TCR can down-regulate nonengaged bystander TCR. Here we show that for binding and dissociation rates that characterize interactions between T cell receptors and peptide-MHC, substantial serial engagement occurs. The result is independent of mechanisms and measurements of receptor down-regulation. The conclusion that single peptide-MHC engage many TCR, before diffusing out of the contact region between the antigen-presenting cell and the T cell, is based on a general first passage time calculation for a particle alternating between states in which different diffusion coefficients govern its transport.

A Hidden Markov Model for Single Particle Tracks Quantifies Dynamic Interactions between LFA-1 and the Actin Cytoskeleton

The extraction of hidden information from complex trajectories is a continuing problem in single-particle and single-molecule experiments. Particle trajectories are the result of multiple phenomena, and new methods for revealing changes in molecular processes are needed. We have developed a practical technique that is capable of identifying multiple states of diffusion within experimental trajectories. We model single particle tracks for a membrane-associated protein interacting with a homogeneously distributed binding partner and show that, with certain simplifying assumptions, particle trajectories can be regarded as the outcome of a two-state hidden Markov model. Using simulated trajectories, we demonstrate that this model can be used to identify the key biophysical parameters for such a system, namely the diffusion coefficients of the underlying states, and the rates of transition between them. We use a stochastic optimization scheme to compute maximum likelihood estimates of these parameters. We have applied this analysis to single-particle trajectories of the integrin receptor lymphocyte function-associated antigen-1 (LFA-1) on live T cells. Our analysis reveals that the diffusion of LFA-1 is indeed approximately two-state, and is characterized by large changes in cytoskeletal interactions upon cellular activation.

A Role for Rebinding in Rapid and Reliable T Cell Responses to Antigen

Experimental work has shown that T cells of the immune system rapidly and specifically respond to antigenic molecules presented on the surface of antigen-presenting-cells and are able to discriminate between potential stimuli based on the kinetic parameters of the T cell receptor-antigen bond. These antigenic molecules are presented among thousands of chemically similar endogenous peptides, raising the question of how T cells can reliably make a decision to respond to certain antigens but not others within minutes of encountering an antigen presenting cell. In this theoretical study, we investigate the role of localized rebinding between a T cell receptor and an antigen. We show that by allowing the signaling state of individual receptors to persist during brief unbinding events, T cells are able to discriminate antigens based on both their unbinding and rebinding rates. We demonstrate that T cell receptor coreceptors, but not receptor clustering, are important in promoting localized rebinding, and show that requiring rebinding for productive signaling reduces signals from a high concentration of endogenous pMHC. In developing our main results, we use a relatively simple model based on kinetic proofreading. However, we additionally show that all our results are recapitulated when we use a detailed T cell receptor signaling model. We discuss our results in the context of existing models and recent experimental work and propose new experiments to test our findings.

A Stochastic Model of Latently Infected Cell Reactivation and Viral Blip Generation in Treated HIV Patients

Motivated by viral persistence in HIV+ patients on long-term anti-retroviral treatment (ART), we present a stochastic model of HIV viral dynamics in the blood stream. We consider the hypothesis that the residual viremia in patients on ART can be explained principally by the activation of cells latently infected by HIV before the initiation of ART and that viral blips (clinically-observed short periods of detectable viral load) represent large deviations from the mean. We model the system as a continuous-time, multi-type branching process. Deriving equations for the probability generating function we use a novel numerical approach to extract the probability distributions for latent reservoir sizes and viral loads. We find that latent reservoir extinction-time distributions underscore the importance of considering reservoir dynamics beyond simply the half-life. We calculate blip amplitudes and frequencies by computing complete viral load probability distributions, and study the duration of viral blips via direct numerical simulation. We find that our model qualitatively reproduces short small-amplitude blips detected in clinical studies of treated HIV infection. Stochastic models of this type provide insight into treatment-outcome variability that cannot be found from deterministic models.

Antigen Potency and Maximal Efficacy Reveal a Mechanism of Efficient T Cell Activation

Efficient T cell activation depends on the rate with which T cell receptors and antigens bind and unbind, rather than simply their equilibrium affinity. Modeling T Cell Activation The efficiency of T cell activation depends on the binding parameters of the interaction between T cell receptors (TCRs) and peptide-bound major histocompatibility complexes (pMHCs). Two models propose different explanations for the relationship between TCR-pMHC binding and T cell functionality. The “affinity model” suggests that the number of TCR-pMHC complexes at equilibrium, which is governed by the dissociation constant KD, is the main determinant, whereas the “productive hit rate model” suggests that T cell responses depend on productive TCR-pMHC interaction times, which depend on the off-rate, koff. Dushek et al. performed mathematical modeling to show that both models predicted a correlation between KD and antigen potency (as measured by the EC50), but that only the productive hit rate model predicted a correlation between the maximal efficiency of antigen-induced responses and koff. Predictions from the productive hit rate model were validated in experiments with T cell clones and a panel of pMHC variants. Improved understanding of TCR-pMHC binding has implications to enhance responsiveness in various immunotherapies. T cell activation, a critical event in adaptive immune responses, depends on productive interactions between T cell receptors (TCRs) and antigens presented as peptide-bound major histocompatibility complexes (pMHCs). Activated T cells lyse infected cells, secrete cytokines, and perform other effector functions with various efficiencies, which depend on the binding parameters of the TCR-pMHC complex. The mechanism through which binding parameters are translated to the efficiency of T cell activation, however, remains controversial. The “affinity model” suggests that the dissociation constant (KD) of the TCR-pMHC complex determines the response, whereas the “productive hit rate model” suggests that the off-rate (koff) is critical. Here, we used mathematical modeling to show that antigen potency, as determined by the EC50 (half-maximal effective concentration), which is used to support KD-based models, could not discriminate between the affinity and the productive hit rate models. Both models predicted a correlation between EC50 and KD, but only the productive hit rate model predicted a correlation between maximal efficacy (Emax), the maximal T cell response induced by pMHC, and koff. We confirmed the predictions made by the productive hit rate model in experiments with cytotoxic T cell clones and a panel of pMHC variants. Thus, we propose that the activity of an antigen is determined by both its potency (EC50) and maximal efficacy (Emax).

Diffusion on a Sphere with Localized Traps : Mean First Passage Time, Eigenvalue Asymptotics, and Fekete Points

A common scenario in cellular signal transduction is that a diffusing surface-bound molecule must arrive at a localized signaling region on the cell membrane before the signaling cascade can be completed. The question then arises of how quickly such signaling molecules can arrive at newly formed signaling regions. Here, we attack this problem by calculating asymptotic results for the mean first passage time for a diffusing particle confined to the surface of a sphere, in the presence of N partially absorbing traps of small radii. The rate at which the small diffusing molecule becomes captured by one of the traps is determined by asymptotically calculating the principal eigenvalue for the Laplace operator on the sphere with small localized traps. The asymptotic analysis relies on the method of matched asymptotic expansions, together with detailed properties of the Greens function for the Laplacian and the Helmholtz operators on the surface of the unit sphere. The asymptotic results compare favorably with ...