Is TCR/pMHC Affinity a Good Estimate of the T-cell Response? An Answer Based on Predictions From 12 Phenotypic Models.

On the T-cell surface the TCR is the only molecule that senses antigen, and the engagement of TCR with its specific antigenic peptide (agonist)/MHC complex (pMHC) is determined by the biochemical parameters of the TCR-pMHC interaction. This interaction is the keystone of the adaptive immune response by triggering intracellular signaling pathways that induce the expression of genes required for T cell-mediated effector functions, such as T cell proliferation, cytokine secretion and cytotoxicity. To study the TCR-pMHC interaction one of its properties most extensively analyzed has been TCR-pMHC affinity. However, and despite of intensive experimental research, the results obtained are far from conclusive. Here, to determine if TCR-pMHC affinity is a reliable parameter to characterize T-cell responses, a systematic study has been performed based on the predictions of 12 phenotypic models. This approach has the advantage that allow us to study the response of a given system as a function of only those parameters in which we are interested while other system parameters remain constant. A little surprising, only the simple occupancy model predicts a direct relationship between affinity and response so that an increase in affinity always leads to larger responses. Conversely, in the others more elaborate models this clear situation does not occur, i.e., that a general positive correlation between affinity and immune response does not exist. This is mainly because affinity values are given by the quotient kon/koff where kon and koff are the rate constants of the binding process (i.e., affinity is in fact the quotient of two parameters), so that different sets of these rate constants can give the same value of affinity. However, except in the occupancy model, the predicted T-cell responses depend on the individual values of kon and koff rather than on their quotient kon/koff. This allows: a) that systems with the same affinity can show quite different responses; and b) that systems with low affinity may exhibit larger responses than systems with higher affinities. This would make affinity a poor estimate of T-cell responses and, as a result, data correlations between affinity and immune response should be interpreted and used with caution.

TCR/pMHC Interaction: Phenotypic Model for an Unsolved Enigma.

TCR-pMHC interaction is the keystone of the adaptive immune response. This process exhibits an impressive capacity of speed, sensitivity, and discrimination that allows detecting foreign pMHCs at very low concentration among much more abundant self-pMHC ligands. However, and despite over three decades of intensive research, the mechanisms by which this remarkable discrimination and sensitivity is attained remain controversial. In kinetic proofreading mechanisms (KPR), an increase of specificity occurs by reducing the sensitivity. To overcome this difficulty, more elaborate models including feedback processes or induced rebinding have been incorporated into the KPR scheme. Here a new approach based on the assumption that the proofreading chain behaves differently for foreign- and self-pMHC complexes has been integrated into a phenotypic model in which the complexes responsible for T cell activation stabilize (for foreign peptides) or weaken (for foreign peptides), resulting in a dramatic increase in sensitivity and specificity. Stabilization and destabilization of complexes may be caused by conformational changes, rebinding, or any other process leading to variations in the dissociation rate constants of the complexes transmitting the activation. The numerical solution and the analytical expression for the steady-state response as a function of koff(i) (i = 0, 1, …, N, where C0, C1, …, CN are the complexes in the proofreading chain) are provided. The activation chain speeds up, and larger increases in sensitivity and discrimination are obtained if the rate of activation along the proofreading chain increases for foreign pMHCs and decreases for self-ligands. Experimental implications and comparison with current models are discussed.

Mathematical modelling and computational study of two-dimensional and three-dimensional dynamics of receptor-ligand interactions in signalling response mechanisms.

Cell signalling processes involve receptor trafficking through highly connected networks of interacting components. The binding of surface receptors to their specific ligands is a key factor for the control and triggering of signalling pathways. But the binding process still presents many enigmas and, by analogy with surface catalytic reactions, two different mechanisms can be conceived: the first mechanism is related to the Eley-Rideal (ER) mechanism, i.e. the bulk-dissolved ligand interacts directly by pure three-dimensional (3D) diffusion with the specific surface receptor; the second mechanism is similar to the Langmuir-Hinshelwood (LH) process, i.e. 3D diffusion of the ligand to the cell surface followed by reversible ligand adsorption and subsequent two-dimensional (2D) surface diffusion to the receptor. A situation where both mechanisms simultaneously contribute to the signalling process could also occur. The aim of this paper is to perform a computational study of the behavior of the signalling response when these different mechanisms for ligand-receptor interactions are integrated into a model for signal transduction and ligand transport. To this end, partial differential equations have been used to develop spatio-temporal models that show trafficking dynamics of ligands, cell surface components, and intracellular signalling molecules through the different domains of the system. The mathematical modeling developed for these mechanisms has been applied to the study of two situations frequently found in cell systems: (a) dependence of the signal response on cell density; and (b) enhancement of the signalling response in a synaptic environment.

Spatio-temporal dependence of the signaling response in immune-receptor trafficking networks regulated by cell density: a theoretical model.

Cell signaling processes involve receptor trafficking through highly connected networks of interacting components. The binding of surface receptors to their specific ligands is a key factor for the control and triggering of signaling pathways. In most experimental systems, ligand concentration and cell density vary within a wide range of values. Dependence of the signal response on cell density is related with the extracellular volume available per cell. This dependence has previously been studied using non-spatial models which assume that signaling components are well mixed and uniformly distributed in a single compartment. In this paper, a mathematical model that shows the influence exerted by cell density on the spatio-temporal evolution of ligands, cell surface receptors, and intracellular signaling molecules is developed. To this end, partial differential equations were used to model ligand and receptor trafficking dynamics through the different domains of the whole system. This enabled us to analyze several interesting features involved with these systems, namely: a) how the perturbation caused by the signaling response propagates through the system; b) receptor internalization dynamics and how cell density affects the robustness of dose-response curves upon variation of the binding affinity; and c) that enhanced correlations between ligand input and system response are obtained under conditions that result in larger perturbations of the equilibrium ligand + surface receptor [Please see text] ligand - receptor complex. Finally, the results are compared with those obtained by considering that the above components are well mixed in a single compartment.