Resolving Early Signaling Events in T-Cell Activation Leading to IL-2 and FOXP3 Transcription

The influence of circadian rhythms on CD8+ T cell activation upon vaccination: A mathematical modeling perspective

Circadian rhythms have been implicated in the modulation of many physiological processes, including those associated with the immune system. For example, these rhythms influence CD8+ T cell responses within the adaptive immune system. The mechanism underlying this immune-circadian interaction, however, remains unclear, particularly in the context of vaccination. Here, we devise a molecularly-explicit gene regulatory network model of early signaling in the naïve CD8+ T cell activation pathway, comprised of three axes (or subsystems) labeled ZAP70, LAT and CD28, to elucidate the molecular details of this immune-circadian mechanism and its relation to vaccination. This is done by coupling the model to a periodic forcing function to identify the molecular players targeted by circadian rhythms, and analyzing how these rhythms subsequently affect CD8+ T cell activation under differing levels of T cell receptor (TCR) phosphorylation, which we designate as vaccine load. By performing both bifurcation and parameter sensitivity analyses on the model at the single cell and ensemble levels, we find that applying periodic forcing on molecular targets within the ZAP70 axis is sufficient to create a day-night discrepancy in CD8+ T cell activation in a manner that is dependent on the bistable switch inherent in CD8+ T cell early signaling. We also demonstrate that the resulting CD8+ T cell activation is dependent on the strength of the periodic coupling as well as on the level of TCR phosphorylation. Our results show that this day-night discrepancy is not transmitted to certain downstream molecules within the LAT subsystem, such as mTORC1, suggesting a secondary, independent circadian regulation on that protein complex. We also corroborate experimental results by showing that the circadian regulation of CD8+ T cell primarily acts at a baseline, pre-vaccination state, playing a facilitating role in priming CD8+ T cells to vaccine inputs according to the time of day. By applying an ensemble level analysis using bifurcation theory and by including several hypothesized molecular targets of this circadian rhythm, we further demonstrate an increased variability between CD8+ T cells (due to heterogeneity) induced by its circadian regulation, which may allow an ensemble of CD8+ T cells to activate at a lower vaccine load, improving its sensitivity. This modeling study thus provides insights into the immune targets of the circadian clock, and proposes an interaction between vaccine load and the influence of circadian rhythms on CD8+ T cell activation.

Theoretical quantification of the polyvalent binding of nanoparticles coated with peptide-major histocompatibility complex to T cell receptor-nanoclusters

Nanoparticles (NPs) coated with peptide-major histocompatibility complexes (pMHCs) can be used as a therapy to treat autoimmune diseases. They do so by inducing the differentiation and expansion of disease-suppressing T regulatory type 1 (Tr1) cells by binding to their T cell receptors (TCRs) expressed as TCR-nanoclusters (TCR_nc). Their efficacy can be controlled by adjusting NP size and number of pMHCs coated on them (referred to as valence). The binding of these NPs to TCR_nc on T cells is thus polyvalent and occurs at three levels: the TCR-pMHC, NP-TCR_nc and T cell levels. In this study, we explore how this polyvalent interaction is manifested and examine if it can facilitate T cell activation downstream. This is done by developing a multiscale biophysical model that takes into account the three levels of interactions and the geometrical complexity of the binding. Using the model, we quantify several key parameters associated with this interaction analytically and numerically, including the insertion probability that specifies the number of remaining pMHC binding sites in the contact area between T cells and NPs, the dwell time of interaction between NPs and TCR_nc, carrying capacity of TCR_nc, the distribution of covered and bound TCRs, and cooperativity in the binding of pMHCs within the contact area. The model was fit to previously published dose-response curves of interferon-γ obtained experimentally by stimulating a population of T cells with increasing concentrations of NPs at various valences and NP sizes. Exploring the parameter space of the model revealed that for an appropriate choice of the contact area angle, the model can produce moderate jumps between dose-response curves at low valences. This suggests that the geometry and kinetics of NP binding to TCR_nc can act in synergy to facilitate T cell activation.

Computational Verification of Large Logical Models-Application to the Prediction of T Cell Response to Checkpoint Inhibitors

At the crossroad between biology and mathematical modeling, computational systems biology can contribute to a mechanistic understanding of high-level biological phenomenon. But as knowledge accumulates, the size and complexity of mathematical models increase, calling for the development of efficient dynamical analysis methods. Here, we propose the use of two approaches for the development and analysis of complex cellular network models. A first approach, called "model verification" and inspired by unitary testing in software development, enables the formalization and automated verification of validation criteria for whole models or selected sub-parts. When combined with efficient analysis methods, this approach is suitable for continuous testing, thereby greatly facilitating model development. A second approach, called "value propagation," enables efficient analytical computation of the impact of specific environmental or genetic conditions on the dynamical behavior of some models. We apply these two approaches to the delineation and the analysis of a comprehensive model for T cell activation, taking into account CTLA4 and PD-1 checkpoint inhibitory pathways. While model verification greatly eases the delineation of logical rules complying with a set of dynamical specifications, propagation provides interesting insights into the different potential of CTLA4 and PD-1 immunotherapies. Both methods are implemented and made available in the all-inclusive CoLoMoTo Docker image, while the different steps of the model analysis are fully reported in two companion interactive jupyter notebooks, thereby ensuring the reproduction of our results.

Understanding the Dynamics of T-Cell Activation in Health and Disease Through the Lens of Computational Modeling

T cells in the immune system are activated by binding to foreign peptides (from an external pathogen) or mutant peptide (derived from endogenous proteins) displayed on the surface of a diseased cell. This triggers a series of intracellular signaling pathways, which ultimately dictate the response of the T cell. The insights from computational models have greatly improved our understanding of the mechanisms that control T-cell activation. In this review, we focus on the use of ordinary differential equation–based mechanistic models to study T-cell activation. We highlight several examples that demonstrate the models’ utility in answering specific questions related to T-cell activation signaling, from antigen discrimination to the feedback mechanisms that initiate transcription factor activation. In addition, we describe other modeling approaches that can be combined with mechanistic models to bridge time scales and better understand how intracellular signaling events, which occur on the order of seconds to minutes, influence phenotypic responses of T-cell activation, which occur on the order of hours to days. Overall, through concrete examples, we emphasize how computational modeling can be used to enable the rational design and optimization of immunotherapies.

Mathematical Models for Immunology: Current State of the Art and Future Research Directions

The advances in genetics and biochemistry that have taken place over the last 10 years led to significant advances in experimental and clinical immunology. In turn, this has led to the development of new mathematical models to investigate qualitatively and quantitatively various open questions in immunology. In this study we present a review of some research areas in mathematical immunology that evolved over the last 10 years. To this end, we take a step-by-step approach in discussing a range of models derived to study the dynamics of both the innate and immune responses at the molecular, cellular and tissue scales. To emphasise the use of mathematics in modelling in this area, we also review some of the mathematical tools used to investigate these models. Finally, we discuss some future trends in both experimental immunology and mathematical immunology for the upcoming years.

A Computational Study of the Effects of Syk Activity on B Cell Receptor Signaling Dynamics

The kinase Syk is intricately involved in early signaling events in B cells and is required for proper response when antigens bind to B cell receptors (BCRs). Experiments using an analog-sensitive version of Syk (Syk-AQL) have better elucidated its role, but have not completely characterized its behavior. We present a computational model for BCR signaling, using dynamical systems, which incorporates both wild-type Syk and Syk-AQL. Following the use of sensitivity analysis to identify significant reaction parameters, we screen for parameter vectors that produced graded responses to BCR stimulation as is observed experimentally. We demonstrate qualitative agreement between the model and dose response data for both mutant and wild-type kinases. Analysis of our model suggests that the level of NF-κB activation, which is reduced in Syk-AQL cells relative to wild-type, is more sensitive to small reductions in kinase activity than Erkp activation, which is essentially unchanged. Since this profile of high Erkp and reduced NF-κB is consistent with anergy, this implies that anergy is particularly sensitive to small changes in catalytic activity. Also, under a range of forward and reverse ligand binding rates, our model of Erkp and NF-κB activation displays a dependence on a power law affinity: the ratio of the forward rate to a non-unit power of the reverse rate. This dependence implies that B cells may respond to certain details of binding and unbinding rates for ligands rather than simple affinity alone.