Designing lymphocyte functional structure for optimal signal detection: voilà, T cells

Stochastic Effects in Autoimmune Dynamics

Among various possible causes of autoimmune disease, an important role is played by infections that can result in a breakdown of immune tolerance, primarily through the mechanism of “molecular mimicry”. In this paper we propose and analyse a stochastic model of immune response to a viral infection and subsequent autoimmunity, with account for the populations of T cells with different activation thresholds, regulatory T cells, and cytokines. We show analytically and numerically how stochasticity can result in sustained oscillations around deterministically stable steady states, and we also investigate stochastic dynamics in the regime of bi-stability. These results provide a possible explanation for experimentally observed variations in the progression of autoimmune disease. Computations of the variance of stochastic fluctuations provide practically important insights into how the size of these fluctuations depends on various biological parameters, and this also gives a headway for comparison with experimental data on variation in the observed numbers of T cells and organ cells affected by infection.

Understanding the roles of activation threshold and infections in the dynamics of autoimmune disease

Onset and development of autoimmunity have been attributed to a number of factors, including genetic predisposition, age and different environmental factors. In this paper we discuss mathematical models of autoimmunity with an emphasis on two particular aspects of immune dynamics: breakdown of immune tolerance in response to an infection with a pathogen, and interactions between T cells with different activation thresholds. We illustrate how the explicit account of T cells with different activation thresholds provides a viable model of immune dynamics able to reproduce several types of immune behaviour, including normal clearance of infection, emergence of a chronic state, and development of a recurrent infection with autoimmunity. We discuss a number of open research problems that can be addressed within the same modelling framework.

Stochastic responses may allow genetically diverse cell populations to optimize performance with simpler signaling networks

Two theories have emerged for the role that stochasticity plays in biological responses: first, that it degrades biological responses, so the performance of biological signaling machinery could be improved by increasing molecular copy numbers of key proteins; second, that it enhances biological performance, by enabling diversification of population-level responses. Using T cell biology as an example, we demonstrate that these roles for stochastic responses are not sufficient to understand experimental observations of stochastic response in complex biological systems that utilize environmental and genetic diversity to make cooperative responses. We propose a new role for stochastic responses in biology: they enable populations to make complex responses with simpler biochemical signaling machinery than would be required in the absence of stochasticity. Thus, the evolution of stochastic responses may be linked to the evolvability of different signaling machineries.

Specific T-cell activation in an unspecific T-cell repertoire

T-cells are a vital type of white blood cell that circulate around our bodies, scanning for cellular abnormalities and infections. They recognise disease-associated antigens via a surface receptor called the T-cell antigen receptor (TCR). If there were a specific TCR for every single antigen, no mammal could possibly contain all the T-cells it needs. This is clearly absurd and suggests that T-cell recognition must, to the contrary, be highly degenerate. Yet highly promiscuous TCRs would appear to be equally impossible: they are bound to recognise self as well as non-self antigens. We review how contributions from mathematical analysis have helped to resolve the paradox of the promiscuous TCR. Combined experimental and theoretical work shows that TCR degeneracy is essentially dynamical in nature, and that the T-cell can differentially adjust its functional sensitivity to the salient epitope, "tuning up" sensitivity to the antigen associated with disease and "tuning down" sensitivity to antigens associated with healthy conditions. This paradigm of continual modulation affords the TCR repertoire, despite its limited numerical diversity, the flexibility to respond to almost any antigenic challenge while avoiding autoimmunity.

Stochasticity and spatial heterogeneity in T-cell activation

Stochastic and spatial aspects are becoming increasingly recognized as an important factor in T-cell activation. Activation occurs in an intrinsically noisy environment, requiring only a handful of agonist peptide-major histocompatibility complex molecules, thus making consideration of signal to noise of prime importance in understanding sensitivity and specificity. Furthermore, it is widely established that surface-bound ligands are more effective at activation than soluble forms, while surface patternation has highlighted the role of spatial relocation in activation. Here we consider the results of a number of models of T-cell activation, from a realistic model of kinetic segregation-induced T-cell receptor (TCR) triggering through to simple queuing theory models. These studies highlight the constraints on cell activation by a surface receptor that recruits kinases. Our analysis shows that TCR triggering based on trapping of bound TCRs in regions of close proximity that exclude large ectodomain-containing molecules, such as the phosphatases CD45 and CD148, can effectively reproduce known signaling characteristics and is a viable 'signal transduction' mechanism distinct from oligomerization and conformation-based mechanisms. A queuing theory analysis shows the interrelation between sensitivity and specificity, emphasizing that these are properties of individual cell functions and need not be, nor are likely to be, uniform across different functions. In fact, threshold-based mechanisms of detection are shown to be poor at ligand discrimination because, although they can be highly specific, that specificity is limited to a small range of peptide densities. Time integration mechanisms however are able to control noise effectively, while kinetic proofreading mechanisms endow them with good specificity properties. Thus, threshold mechanisms are likely to be important for rapidly detecting minimal signaling requirements, thus achieving efficient scanning of antigen-presenting cells. However, for good specificity, time integration on a scale of hours is required.

Quantitative theories of T-cell responsiveness

We review recent advances toward a comprehensive mathematical theory of T-cell immunity. A key insight is that the efficacy of the T-cell response is best analyzed in terms of T-cell receptor (TCR) avidity and the distribution of this avidity across the TCR repertoire (the 'avidity spectrum'). Modification of this avidity spectrum by a wide range of tuning and tolerance mechanisms allows the system to adapt cross-reactivity and specificity to the challenge at hand while avoiding inappropriate responses against non-pathogenic cells and tissues. Theoretical models relate molecular kinetic parameters and cellular properties to systemic level statistics such as avidity spectra. Such bridge equations are crucial for rational clinical manipulation of T cells at the molecular level.

T-cell activation: A queuing theory analysis at low agonist density

We analyze a simple linear triggering model of the T-cell receptor (TCR) within the framework of queuing theory, in which TCRs enter the queue upon full activation and exit by downregulation. We fit our model to four experimentally characterized threshold activation criteria and analyze their specificity and sensitivity: the initial calcium spike, cytotoxicity, immunological synapse formation, and cytokine secretion. Specificity characteristics improve as the time window for detection increases, saturating for time periods on the timescale of downregulation; thus, the calcium spike (30 s) has low specificity but a sensitivity to single-peptide MHC ligands, while the cytokine threshold (1 h) can distinguish ligands with a 30% variation in the complex lifetime. However, a robustness analysis shows that these properties are degraded when the queue parameters are subject to variation-for example, under stochasticity in the ligand number in the cell-cell interface and population variation in the cellular threshold. A time integration of the queue over a period of hours is shown to be able to control parameter noise efficiently for realistic parameter values when integrated over sufficiently long time periods (hours), the discrimination characteristics being determined by the TCR signal cascade kinetics (a kinetic proofreading scheme). Therefore, through a combination of thresholds and signal integration, a T cell can be responsive to low ligand density and specific to agonist quality. We suggest that multiple threshold mechanisms are employed to establish the conditions for efficient signal integration, i.e., coordinate the formation of a stable contact interface.

Activation-threshold tuning in an affinity model for the T-cell repertoire

Naive T cells respond to peptides from foreign proteins and remain tolerant to self peptides from endogenous proteins. It has been suggested that self tolerance comes about by a 'tuning' mechanism, i.e. by increasing the T-cell activation threshold upon interaction with self peptides. Here, we explore how such an adaptive mechanism of T-cell tolerance would influence the reactivity of the T-cell repertoire to foreign peptides. We develop a computer simulation model in which T cells are tolerized by increasing their activation-threshold dependent on the affinity with which they see self peptides presented in the thymus. Thus, different T cells acquire different activation thresholds (i.e. different cross-reactivities). In previous mathematical models, T-cell tolerance was deletional and based on a fixed cross-reactivity parameter, which was assumed to have evolved to an optimal value. Comparing these two different tolerance-induction mechanisms, we found that the tuning model performs somewhat better than an optimized deletion model in terms of the reactivity to foreign antigens. Thus, evolutionary optimization of clonal cross-reactivity is not required. A straightforward extension of the tuning model is to delete T-cell clones that obtain a too high activation threshold, and to replace these by new clones. The reactivity of the immune repertoires of such a replacement model is enchanced compared with the basic tuning model. These results demonstrate that activation-threshold tuning is a functional mechanism for self tolerance induction.

Antigen presentation on MHC molecules as a diversity filter that enhances immune efficacy

We consider the way in which antigen is presented to T cells on MHC molecules and ask how MHC peptide presentation could be optimized so as to obtain an effective and safe immune response. By analysing this problem with a mathematical model of T-cell activation, we deduce the need for both MHC restriction and high presentation selectivity. We find that the optimal selectivity is such that about one pathogen-derived peptide is presented per MHC isoform, on the average. We also indicate upper and lower bounds to the number of MHC isoforms per individual based on detectability requirements. Thus we deduce that an important role of MHC presentation is to act as a filter that limits the diversity of antigen presentation.

Simplicity belies a complex system: a response to the minimal model of immunity of Langman and Cohn

Langman and Cohn have written a paper entitled "If the immune repertoire evolved to be large, random, and somatically generated, then em leader " This paper uses reductionist logic to prove that the minimal model of immunity proposed by Langman and Cohn is the only reasonable description of the workings of the immune system. Here we analyze the logic behind this model and show that the complexity of the real immune system contradicts the teachings of Langman and Cohn.

A reliable and safe T cell repertoire based on low-affinity T cell receptors

Antigens are presented to T cells as short peptides bound to MHC molecules on the surface of body cells. The binding between MHC/peptides and T cell receptors (TCRs) has a low affinity and is highly degenerate. Nevertheless, TCR-MHC/peptide recognition results in T cell activation of high specificity. Moreover, the immune system is able to mount a cellular response when only a small fraction of the MHC molecules on an antigen-presenting cell is occupied by foreign peptides, while autoimmunity remains relatively rare. We consider how to reconcile these seemingly contradictory facts using a quantitative model of TCR signalling and T cell activation. Taking into account the statistics of TCR recognition and antigen presentation, we show that thymic selection can produce a working T cell repertoire which will produce safe and effective responses, that is, recognizes foreign antigen presented at physiological levels while tolerating self. We introduce "activation curves" as a useful tool to study the repertoire's statistical activation properties.