Stochasticity and spatial heterogeneity in T-cell activation

Modelling the interplay between the CD4[Formula: see text]/CD8[Formula: see text] T-cell ratio and the expression of MHC-I in tumours

Describing the anti-tumour immune response as a series of cellular kinetic reactions from known immunological mechanisms, we create a mathematical model that shows the CD4[Formula: see text]/CD8[Formula: see text] T-cell ratio, T-cell infiltration and the expression of MHC-I to be interacting factors in tumour elimination. Methods from dynamical systems theory and non-equilibrium statistical mechanics are used to model the T-cell dependent anti-tumour immune response. Our model predicts a critical level of MHC-I expression which determines whether or not the tumour escapes the immune response. This critical level of MHC-I depends on the helper/cytotoxic T-cell ratio. However, our model also suggests that the immune system is robust against small changes in this ratio. We also find that T-cell infiltration and the specificity of the intra-tumour TCR repertoire will affect the critical MHC-I expression. Our work suggests that the functional form of the time evolution of MHC-I expression may explain the qualitative behaviour of tumour growth seen in patients.

CD45 in human physiology and clinical medicine

CD45 is an evolutionary highly conserved receptor protein tyrosine phosphatase exclusively expressed on all nucleated cells of the hematopoietic system. It is characterized by the expression of several isoforms, specific to a certain cell type and the developmental or activation status of the cell. CD45 is one of the key players in the initiation of T cell receptor signaling by controlling the activation of the Src family protein-tyrosine kinases Lck and Fyn. CD45 deficiency results in T- and B-lymphocyte dysfunction in the form of severe combined immune deficiency. It also plays a significant role in autoimmune diseases and cancer as well as in infectious diseases including fungal infections. The knowledge collected on CD45 biology is rather vast, but it remains unclear whether all findings in rodent immune cells also apply to human CD45. This review focuses on human CD45 expression and function and provides an overview on its ligands and role in human pathology.

Robust control of the adaptive immune system

The adaptive immune system continually faces unpredictable circumstances yet reproducibly counteracts invading pathogens while limiting damage to self. However, the system is dynamic in nature: many of its internal components are not fixed, but rather, fluctuate over time. This concept is exemplified by αβ T lymphocytes, which vary significantly from cell-to-cell in their spatiotemporal dynamics, antigen-binding receptors, and subcellular protein concentrations. How are reproducible immune functions achieved in the face of such variability? This design principle is known as robustness and requires the system to employ layered control schemes that both buffer and exploit different facets of cellular variation. In this article, we discuss these schemes and their applications to individual αβ T cell responses as well as integrated population level behaviours.

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.

Elastohydrodynamics and Kinetics of Protein Patterning in the Immunological Synapse

We propose a minimal mathematical model for the physical basis of membrane protein patterning in the immunological synapse (IS), which encompass membrane mechanics, protein binding kinetics and motion, and fluid flow in the synaptic cleft. Our theory leads to simple predictions for the spatial and temporal scales of protein cluster formation, growth and arrest as a function of membrane stiffness, rigidity and kinetics of the adhesive proteins, and the fluid flow in the synaptic cleft. Numerical simulations complement these scaling laws by quantifying the nucleation, growth and stabilization of proteins domains on the size of the cell. Direct comparison with experiment shows that passive elastohydrodynamics and kinetics of protein binding in the synaptic cleft can describe the short-time formation and organization of protein clusters, without evoking any active processes in the cytoskeleton. Despite the apparent complexity of the process, our analysis shows that just two dimensionless parameters characterize the spatial and temporal evolution of the protein pattern: a ratio of membrane elasticity to protein stiffness, and the ratio of a hydrodynamic time scale for fluid flow relative to the protein binding rate. A simple phase diagram encompasses the variety of patterns that can arise.

Peripheral residence of naïve CD4 T cells induces MHC class II-dependent alterations in phenotype and function

BACKGROUND

As individual naïve CD4 T lymphocytes circulate in the body after emerging from the thymus, they are likely to have individually varying microenvironmental interactions even in the absence of stimulation via specific target recognition. It is not clear if these interactions result in alterations in their activation, survival and effector programming. Naïve CD4 T cells show unimodal distribution for many phenotypic properties, suggesting that the variation is caused by intrinsic stochasticity, although underlying variation due to subsets created by different histories of microenvironmental interactions remains possible. To explore this possibility, we began examining the phenotype and functionality of naïve CD4 T cells differing in a basic unimodally distributed property, the CD4 levels, as well as the causal origin of these differences.

RESULTS

We examined separated CD4hi and CD4lo subsets of mouse naïve CD4 cells. CD4lo cells were smaller with higher CD5 levels and lower levels of the dual-specific phosphatase (DUSP)6-suppressing micro-RNA miR181a, and responded poorly with more Th2-skewed outcomes. Human naïve CD4lo and CD4hi cells showed similar differences. Naïve CD4lo and CD4hi subsets of thymic single-positive CD4 T cells did not show differences whereas peripheral naïve CD4lo and CD4hi subsets of T cell receptor (TCR)-transgenic T cells did. Adoptive transfer-mediated parking of naïve CD4 cells in vivo lowered CD4 levels, increased CD5 and reactive oxygen species (ROS) levels and induced hyporesponsiveness in them, dependent, at least in part, on availability of major histocompatibility complex class II (MHCII) molecules. ROS scavenging or DUSP inhibition ameliorated hyporesponsiveness. Naïve CD4 cells from aged mice showed lower CD4 levels and cell sizes, higher CD5 levels, and hyporesponsiveness and Th2-skewing reversed by DUSP inhibition.

CONCLUSIONS

Our data show that, underlying a unimodally distributed property, the CD4 level, there are subsets of naïve CD4 cells that vary in the time spent in the periphery receiving MHCII-mediated signals and show resultant alteration of phenotype and functionality via ROS and DUSP activity. Our findings also suggest the feasibility of potential pharmacological interventions for improved CD4 T cell responses during vaccination of older people via either anti-oxidant or DUSP inhibitor small molecules.

A novel statistical analysis and interpretation of flow cytometry data

A recently developed class of models incorporating the cyton model of population generation structure into a conservation-based model of intracellular label dynamics is reviewed. Statistical aspects of the data collection process are quantified and incorporated into a parameter estimation scheme. This scheme is then applied to experimental data for PHA-stimulated CD4+T and CD8+T cells collected from two healthy donors. This novel mathematical and statistical framework is shown to form the basis for accurate, meaningful analysis of cellular behaviour for a population of cells labelled with the dye carboxyfluorescein succinimidyl ester and stimulated to divide.

A division-dependent compartmental model for computing cell numbers in CFSE-based lymphocyte proliferation assays

Some key features of a mathematical description of an immune response are an estimate of the number of responding cells and the manner in which those cells divide, differentiate, and die. The intracellular dye CFSE is a powerful experimental tool for the analysis of a population of dividing cells, and numerous mathematical treatments have been aimed at using CFSE data to describe an immune response [30,31,32,37,38,42,48,49]. Recently, partial differential equation structured population models, with measured CFSE fluorescence intensity as the structure variable, have been shown to accurately fit histogram data obtained from CFSE flow cytometry experiments [18,19,52,54]. In this report, the population of cells is mathematically organized into compartments, with all cells in a single compartment having undergone the same number of divisions. A system of structured partial differential equations is derived which can be fit directly to CFSE histogram data. From such a model, cell counts (in terms of the number of divisions undergone) can be directly computed and thus key biological parameters such as population doubling time and precursor viability can be determined. Mathematical aspects of this compartmental model are discussed, and the model is fit to a data set. As in [18,19], we find temporal and division dependence in the rates of proliferation and death to be essential features of a structured population model for CFSE data. Variability in cellular autofluorescence is found to play a significant role in the data, as well. Finally, the compartmental model is compared to previous work, and statistical aspects of the experimental data are discussed.

Tunable kinetic proofreading in a model with molecular frustration

In complex systems, feedback loops can build intricate emergent phenomena, so that a description of the whole system cannot be easily derived from the properties of the individual parts. Here, we propose that inter-molecular frustration mechanisms can provide non-trivial feedback loops which can develop non-trivial specificity amplification. We show that this mechanism can be seen as a more general form of a kinetic proofreading (KP) mechanism, with an interesting new property, namely the ability to tune the specificity amplification by changing the reactants concentrations. This contrasts with the classical KP mechanism in which specificity is a function of only the reaction rate constants involved in a chemical pathway. These results are also interesting because they show that a wide class of frustration models exists that share the same underlining KP mechanisms, with even richer properties. These models can find applications in different areas such as evolutionary biology, immunology, and biochemistry.

Lck and the nature of the T cell receptor trigger

Exactly how ligand binding 'triggers' T cell receptor (TCR) phosphorylation is unclear. It has been proposed that ligand engagement by the TCR somehow activates the Src kinase Lck, which in turn phosphorylates the receptor. Recent data, however, suggest instead that a significant fraction of the Lck in resting T cells is already activated and that the proportion of active Lck does not change during the early stages of T cell activation. We argue that, caveats notwithstanding, these new observations offer support for the 'kinetic-segregation' model of TCR triggering, which involves spatial reorganization of signalling proteins upon ligand binding and requires a fraction of Lck to be active in resting T cells.

Perspectives for computer modeling in the study of T cell activation

The T cell receptor (TCR) is responsible for discriminating between self- and foreign-derived peptides, translating minute differences in amino-acid sequence into large differences in response. Because of the great variability in the TCR and its ligands, activation of T cells by foreign peptides is a quantitative process, dependent on a mix of upstream signals and downstream integration. Accordingly, quantitative data and computational models have shed light on many important aspects of this process: molecular noise in ligand recognition, spatial dynamics in T cell-APC (antigen presenting cell) interactions, graded versus all-or-none decision making by the TCR apparatus, mechanisms of peptide antagonism and synergism, and the tunability and robustness of activation thresholds. Though diverse in their formalism, these studies together paint a picture of how modeling has shaped and will continue to shape understanding of T cell immunobiology.

Dependence of T cell antigen recognition on T cell receptor-peptide MHC confinement time

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 (k_on) and off rate (k_off) 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 k_on in T cell activation and reconciles apparently contradictory reports on the role of TCR-pMHC binding kinetics and affinity in T cell activation.

Early T-cell activation biophysics

The T-cell is one of the main players in the mammalian immune response. It ensures antigen recognition at the surface of antigen-presenting cells in a complex and highly sensitive and specific process, in which the encounter of the T-cell receptor with the agonist peptide associated with the major histocompatibility complex triggers T-cell activation. While signaling pathways have been elucidated in increasing detail, the mechanism of TCR triggering remains highly controversial despite active research published in the past 10 years. In this paper, we present a short overview of pending questions on critical initial events associated with T-cell triggering. In particular, we examine biophysical approaches already in use, as well as future directions. We suggest that the most recent advances in fluorescence super-resolution imaging, coupled with the new classes of genetic fluorescent probes, will play an important role in elucidation of the T-cell triggering mechanism. Beyond this aspect, we predict that exploration of mechanical cues in the triggering process will provide new clues leading to clarification of the entire mechanism.

Stochastic effects and bistability in T cell receptor signaling

The stochastic dynamics of T cell receptor (TCR) signaling are studied using a mathematical model intended to capture kinetic proofreading (sensitivity to ligand-receptor binding kinetics) and negative and positive feedback regulation mediated, respectively, by the phosphatase SHP1 and the MAP kinase ERK. The model incorporates protein-protein interactions involved in initiating TCR-mediated cellular responses and reproduces several experimental observations about the behavior of TCR signaling, including robust responses to as few as a handful of ligands (agonist peptide-MHC complexes on an antigen-presenting cell), distinct responses to ligands that bind TCR with different lifetimes, and antagonism. Analysis of the model indicates that TCR signaling dynamics are marked by significant stochastic fluctuations and bistability, which is caused by the competition between the positive and negative feedbacks. Stochastic fluctuations are such that single-cell trajectories differ qualitatively from the trajectory predicted in the deterministic approximation of the dynamics. Because of bistability, the average of single-cell trajectories differs markedly from the deterministic trajectory. Bistability combined with stochastic fluctuations allows for switch-like responses to signals, which may aid T cells in making committed cell-fate decisions.

A novel ZAP-70 dependent FRET based biosensor reveals kinase activity at both the immunological synapse and the antisynapse

Many hypotheses attempting to explain the speed and sensitivity with which a T-cell discriminates the antigens it encounters include a notion of relative spatial and temporal control of particular biochemical steps involved in the process. An essential step in T-cell receptor (TCR) mediated signalling is the activation of the protein tyrosine kinase ZAP-70. ZAP-70 is recruited to the TCR upon receptor engagement and, once activated, is responsible for the phosphorylation of the protein adaptor, Linker for Activation of T-cells, or LAT. LAT phosphorylation results in the recruitment of a signalosome including PLCgamma1, Grb2/SOS, GADS and SLP-76. In order to examine the real time spatial and temporal evolution of ZAP-70 activity following TCR engagement in the immune synapse, we have developed ROZA, a novel FRET-based biosensor whose function is dependent upon ZAP-70 activity. This new probe not only provides a measurement of the kinetics of ZAP-70 activity, but also reveals the subcellular localization of the activity as well. Unexpectedly, ZAP-70 dependent FRET was observed not only at the T-cell -APC interface, but also at the opposite pole of the cell or "antisynapse".