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

Is there a role played by HLA-E, if any, in HPV immune evasion?

Cervical cancer incidence worldwide exceeds half a million new cases per year. The human papillomavirus (HPV) being the major causative agent of CC uses a variety of strategies to evade immune surveillance, where the immune status varies amongst individuals. This immune evasion altered by HPV is reflected in persistent infections, causing the evolution of cervical neoplasia. The role of the immune system in viral recognition and elimination is of extreme relevance in the development of CC. The interactions of the HLA-E ligand in the target cell along with CD94/NKG2 receptors, which are expressed predominantly, but not exclusively, on NK cells' surface, are responsible for activating or inhibiting cytotoxic activity according to their function. The engagement between HLA-E and CD94/NKG2 molecules is one of the fundamental surveillance mechanisms in patients with CIN I, II and III, where HLA-E expression increases significantly, especially in HPV 16 and 18 infections. Higher HLA-E expression was observed in most histopathological types of CC, and at the same time was correlated to best survival of the patient. This review aims to summarize and discuss the immunological role of HLA-E in the context of HPV infection and immune system evasion, and the oncogenic process of cervical cancer.

Influence of correlated antigen presentation on T-cell negative selection in the thymus

The thymus is the primary organ for the generation of naive T cells, a key component of the immune system. Tolerance of T cells to self is achieved primarily in the thymic medulla, where immature T cells (thymocytes) sample self-peptides presented by medullary thymic epithelial cells (mTECs). A sufficiently strong interaction activates the thymocytes leading to negative selection. A key question of current interest is whether there is any structure in the manner in which mTECs present peptides: can any mTEC present any peptide at any time, or are there particular patterns of correlated peptide presentation? We investigate this question using a mathematical model of negative selection. We find that correlated patterns of peptide presentation may be advantageous in negatively selecting low-degeneracy thymocytes (that is, those thymocytes which respond to relatively few peptides). We also quantify the probability that an auto-reactive thymocyte exits the thymus before it encounters a cognate antigen. The results suggest that heterogeneity of gene co-expression in mTECs has an effect on the probability of escape of autoreactive thymocytes.

COMPARISON OF A DUAL STRATEGY FOR T-CELL ACTIVATION UNDER INHIBITION OF THE CD4 RECEPTOR

We consider a stochastic model for T-cell activation proposed in Refs. [1] and [2] to compare the specificity and sensitivity of two different strategies for T-cell activation that utilize the history of phosphorylation of T-cell receptor (TCR). We compare these two strategies when the temporal signals/events that are essential for progressive T-cell activation are suppressed by blockade of CD4 receptor that may have caused by disease or therapeutic effects.3–6 We show that under these conditions, a threshold-strategy which is capable of maintaining a threshold (for total number of phosphorylated TCRs by time [Formula: see text]) for a further duration [Formula: see text] performs better in discriminating agonist peptides than a single-threshold strategy (reached by time [Formula: see text]) leading to T-cell activation using the Wentzell-Friedlin theory for large deviations for stochastic processes.7,8

How many TCR clonotypes does a body maintain?

We consider the lifetime of a T cell clonotype, the set of T cells with the same T cell receptor, from its thymic origin to its extinction in a multiclonal repertoire. Using published estimates of total cell numbers and thymic production rates, we calculate the mean number of cells per TCR clonotype, and the total number of clonotypes, in mice and humans. When there is little peripheral division, as in a mouse, the number of cells per clonotype is small and governed by the number of cells with identical TCR that exit the thymus. In humans, peripheral division is important and a clonotype may survive for decades, during which it expands to comprise many cells. We therefore devise and analyse a computational model of homeostasis of a multiclonal population. Each T cell in the model competes for self pMHC stimuli, cells of any one clonotype only recognising a small fraction of the many subsets of stimuli. A constant mean total number of cells is maintained by a balance between cell division and death, and a stable number of clonotypes by a balance between thymic production of new clonotypes and extinction of existing ones. The number of distinct clonotypes in a human body may be smaller than the total number of naive T cells by only one order of magnitude.

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The number of T cells of one clonotype is an integer.

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The history of a clonotype starts with release from the thymus, and ends with extinction.

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Competition and cross-reactivity are included in a natural way.

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The average number of cells per clonotype, in a human body, is only of order 10.

Modulation of T-cell receptor functional sensitivity via the opposing actions of protein tyrosine kinases and phosphatases: a mathematical model

Combining receptor kinetics and stochastic modelling of receptor activation, we show that a T-cell can specifically augment its functional sensitivity to one particular peptide ligand while simultaneously decreasing its sensitivity to other ligands, by coordinating the expression levels of the co-receptor CD8 and the relative activities of kinases and phosphatases in the vicinity of the T-cell receptor (TCR). We propose that this focusable degeneracy of epitope recognition allows a TCR to have a wide range of potential ligands but be specifically sensitive to only one or a few of these at any one time, which resolves the paradox of how a relatively small number of clones (∼10(6)) can maintain the potential to respond to a vast space of ligands (∼20(9)) whilst avoiding auto-immunity. We validate the model against experimental data and predict shifts in functional sensitivity following a shift in the kinase/phosphatase balance (which could in principle be induced by experimental means). Moreover, we propose that in vivo, the T-cell gauges ligand quality by monitoring changes in TCR triggering rate concomitant with shifts in this balance, for instance as the immunological synapse matures.

Modeling the T cell immune response: a fascinating challenge

The immune system is designed to protect the organism from infection and to repair damaged tissue. An effective response requires recognition of the threat, the appropriate effector mechanism to clear the pathogen and a return to homeostasis with minimal damage to self-tissues. T cells play a central role in orchestrating the immune response at all stages of the response and have been the subject of intense study by both experimental immunologists and modelers. This review examines some of the more critical questions in T cell biology and describes the latest attempts to address those questions using approaches that combine mathematical modeling and experiments.

Molecular mimicry and clonal deletion: A fresh look

In this article, I trace the historic background of clonal deletion and molecular mimicry, two major pillars underlying our present understanding of autoimmunity and autoimmune disease. Clonal deletion originated as a critical element of the clonal selection theory of antibody formation in order to explain tolerance of self. If we did have complete clonal deletion, there would be major voids, the infamous "black holes", in our immune repertoire. For comprehensive, protective adaptive immunity, full deletion is necessarily a rare event. Molecular mimicry, the sharing of epitopes among self and non-self antigens, is extraordinary common and provides the evidence that complete deletion of self-reactive clones is rare. If molecular mimicry were not common, protective adaptive immunity could not be all-encompassing. By taking a fresh look at these two processes together we can envision their evolutionary basis and understand the need for regulatory devices to prevent molecular mimicry from progressing to autoimmune disease.

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 modelling of T-cell activation

We investigate a specific part of the human immune system, namely the activation of T-cells, using stochastic tools, especially sharp large deviation results. T-cells have to distinguish reliably between foreign and self peptides which are both presented to them by antigen presenting cells. Our work is based on a model studied by Zint et al. (J Math Bio 57(6):841-861, 2008). We are able to dispense with some restrictive distribution assumptions that were used previously, i.e., we establish a higher robustness of the model. A central issue is the analysis of two new perspectives to the scenario (two different quenched systems) in detail. This means that we do not only analyse the total probability of a T-cell activation (the annealed case) but also consider the probability of an activation of one certain clonotype and the probability of a T-cell activation by a certain antigen presentation profile (the quenched cases). Finally, we see analytically that the probability of T-cell activation increases with the number of presented foreign peptides in all three cases.

Theories and quantification of thymic selection

The peripheral T cell repertoire is sculpted from prototypic T cells in the thymus bearing randomly generated T cell receptors (TCR) and by a series of developmental and selection steps that remove cells that are unresponsive or overly reactive to self-peptide–MHC complexes. The challenge of understanding how the kinetics of T cell development and the statistics of the selection processes combine to provide a diverse but self-tolerant T cell repertoire has invited quantitative modeling approaches, which are reviewed here.

Co-Receptor CD8-Mediated Modulation of T-Cell Receptor Functional Sensitivity and Epitope Recognition Degeneracy

The interaction between T-cell receptors (TCRs) and peptide epitopes is highly degenerate: a TCR is capable of interacting productively with a wide range of different peptide ligands, involving not only cross-reactivity proper (similar epitopes elicit strong responses), but also polyspecificity (ligands with distinct physicochemical properties are capable of interacting with the TCR). Degeneracy does not gainsay the fact that TCR recognition is fundamentally specific: for the vast majority of ligands, the functional sensitivity of a given TCR is virtually null whereas this TCR has an appreciable functional sensitivity only for a minute fraction of all possible ligands. Degeneracy can be described mathematically as the probability that the functional sensitivity, of a given TCR to a randomly selected ligand, exceeds a set value. Variation of this value generates a statistical distribution that characterizes TCR degeneracy. This distribution can be modeled on the basis of a Gaussian distribution for the TCR/ligand dissociation energy. The kinetics of the TCR and the MHCI molecule can be used to transform this underlying Gaussian distribution into the observed distribution of functional sensitivity values. In the present paper, the model is extended by accounting explicitly for the kinetics of the interaction between the co-receptor and the MHCI molecule. We show that T-cells can modulate the level of degeneracy by varying the density of co-receptors on the cell surface. This could allow for an analog of avidity maturation during incipient T-cell responses.

Cellular-level versus receptor-level response threshold hierarchies in T-cell activation

Peptide-MHC (pMHC) ligand engagement by T-cell receptors (TCRs) elicits a variety of cellular responses, some of which require substantially more TCR-mediated stimulation than others. This threshold hierarchy could reside at the receptor level, where different response pathways branch off at different stages of the TCR/CD3 triggering cascade, or at the cellular level, where the cumulative TCR signal registered by the T-cell is compared to different threshold values. Alternatively, dual-level thresholds could exist. In this study, we show that the cellular hypothesis provides the most parsimonious explanation consistent with data obtained from an in-depth analysis of distinct functional responses elicited in a clonal T-cell system by a spectrum of biophysically defined altered peptide ligands across a range of concentrations. Further, we derive a mathematical model that describes how ligand density, affinity, and off-rate all affect signaling in distinct ways. However, under the kinetic regime prevailing in the experiments reported here, the TCR/pMHC class I (pMHCI) dissociation rate was found to be the main governing factor. The CD8 coreceptor modulated the TCR/pMHCI interaction and altered peptide ligand potency. Collectively, these findings elucidate the relationship between TCR/pMHCI kinetics and cellular function, thereby providing an integrated mechanistic understanding of T-cell response profiles.

Nonparametric simulation of signal transduction networks with semi-synchronized update

Simulating signal transduction in cellular signaling networks provides predictions of network dynamics by quantifying the changes in concentration and activity-level of the individual proteins. Since numerical values of kinetic parameters might be difficult to obtain, it is imperative to develop non-parametric approaches that combine the connectivity of a network with the response of individual proteins to signals which travel through the network. The activity levels of signaling proteins computed through existing non-parametric modeling tools do not show significant correlations with the observed values in experimental results. In this work we developed a non-parametric computational framework to describe the profile of the evolving process and the time course of the proportion of active form of molecules in the signal transduction networks. The model is also capable of incorporating perturbations. The model was validated on four signaling networks showing that it can effectively uncover the activity levels and trends of response during signal transduction process.

A single autoimmune T cell receptor recognizes more than a million different peptides

The T cell receptor (TCR) orchestrates immune responses by binding to foreign peptides presented at the cell surface in the context of major histocompatibility complex (MHC) molecules. Effective immunity requires that all possible foreign peptide-MHC molecules are recognized or risks leaving holes in immune coverage that pathogens could quickly evolve to exploit. It is unclear how a limited pool of <10(8) human TCRs can successfully provide immunity to the vast array of possible different peptides that could be produced from 20 proteogenic amino acids and presented by self-MHC molecules (>10(15) distinct peptide-MHCs). One possibility is that T cell immunity incorporates an extremely high level of receptor degeneracy, enabling each TCR to recognize multiple peptides. However, the extent of such TCR degeneracy has never been fully quantified. Here, we perform a comprehensive experimental and mathematical analysis to reveal that a single patient-derived autoimmune CD8(+) T cell clone of pathogenic relevance in human type I diabetes recognizes >one million distinct decamer peptides in the context of a single MHC class I molecule. A large number of peptides that acted as substantially better agonists than the wild-type "index" preproinsulin-derived peptide (ALWGPDPAAA) were identified. The RQFGPDFPTI peptide (sampled from >10(8) peptides) was >100-fold more potent than the index peptide despite differing from this sequence at 7 of 10 positions. Quantification of this previously unappreciated high level of CD8(+) T cell cross-reactivity represents an important step toward understanding the system requirements for adaptive immunity and highlights the enormous potential of TCR degeneracy to be the causative factor in autoimmune disease.

Stochastic competitive exclusion in the maintenance of the naïve T cell repertoire

Recognition of antigens by the adaptive immune system relies on a highly diverse T cell receptor repertoire. The mechanism that maintains this diversity is based on competition for survival stimuli; these stimuli depend upon weak recognition of self-antigens by the T cell antigen receptor. We study the dynamics of diversity maintenance as a stochastic competition process between a pair of T cell clonotypes that are similar in terms of the self-antigens they recognise. We formulate a bivariate continuous-time Markov process for the numbers of T cells belonging to the two clonotypes. We prove that the ultimate fate of both clonotypes is extinction and provide a bound on mean extinction times. We focus on the case where the two clonotypes exhibit negligible competition with other T cell clonotypes in the repertoire, since this case provides an upper bound on the mean extinction times. As the two clonotypes become more similar in terms of the self-antigens they recognise, one clonotype quickly becomes extinct in a process resembling classical competitive exclusion. We study the limiting probability distribution for the bivariate process, conditioned on non-extinction of both clonotypes. Finally, we derive deterministic equations for the number of cells belonging to each clonotype as well as a linear Fokker-Planck equation for the fluctuations about the deterministic stable steady state.

The limiting conditional probability distribution in a stochastic model of T cell repertoire maintenance

The limiting conditional probability distribution (LCD) has been much studied in the field of mathematical biology, particularly in the context of epidemiology and the persistence of epidemics. However, it has not yet been applied to the immune system. One of the characteristic features of the T cell repertoire is its diversity. This diversity declines in old age, whence the concepts of extinction and persistence are also relevant to the immune system. In this paper we model T cell repertoire maintenance by means of a continuous-time birth and death process on the positive integers, where the origin is an absorbing state. We show that eventual extinction is guaranteed. The late-time behaviour of the process before extinction takes place is modelled by the LCD, which we prove always exists for the process studied here. In most cases, analytic expressions for the LCD cannot be computed but the probability distribution may be approximated by means of the stationary probability distributions of two related processes. We show how these approximations are related to the LCD of the original process and use them to study the LCD in two special cases. We also make use of the large N expansion to derive a further approximation to the LCD. The accuracy of the various approximations is then analysed.

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.

Kinetic proofreading model

Kinetic proofreading is an intrinsic property of the cell signaling process. It arises as a consequence of the multiple interactions that occur after a ligand triggers a receptor to initiate a ignaling cascade and it ensures that false signals do not propagate to completion. In order for an active signaling complex to form after a ligand binds to a cell surface receptor, a sequence of binding and phosphorylation events must occur that are rapidly reversed if the ligand dissociates from the receptor. This gives rise to a mechanism by which cells can discriminate among ligands that bind to the same receptor but form ligand-receptor complexes with different lifetimes. We review experiments designed to test for kinetic proofreading and models that exhibit kinetic proofreading.

Why do adaptive immune responses cross-react?

Antigen specificity of adaptive immune responses is often in the host's best interests, but with important and as yet unpredictable exceptions. For example, antibodies that bind to multiple flaviviral or malarial species can provide hosts with simultaneous protection against many parasite genotypes. Vaccinology often aims to harness such imprecision, because cross-reactive antibodies might provide broad-spectrum protection in the face of antigenic variation by parasites. However, the causes of cross-reactivity among immune responses are not always known, and here, we explore potential proximate and evolutionary explanations for cross-reactivity. We particularly consider whether cross-reactivity is the result of constraints on the ability of the immune system to process information about the world of antigens, or whether an intermediate level of cross-reactivity may instead represent an evolutionary optimum. We conclude with a series of open questions for future interdisciplinary research, including the suggestion that the evolutionary ecology of information processing might benefit from close examination of immunological data.

Stochastic niche structure and diversity maintenance in the T cell repertoire

The reliability of the immune response to pathogenic challenge depends critically on the size and diversity of the T cell repertoire. We study naïve T cell repertoire diversity maintenance by a stochastic model that incorporates the concept of competition between T cells for survival stimuli emanating from self-antigen presenting cells (APCs). In the mean field approximation we show that clonotype extinction is certain and compute mean extinction times. We introduce the concept of mean niche overlap and show that clones with a mean niche overlap greater than one have a short repertoire lifespan. This selection differential induces minimal recognition commonality between T cell receptors (TCRs) resulting in a diverse T cell repertoire.

Coreceptor CD8-driven modulation of T cell antigen receptor specificity

The CD8 coreceptor modulates the interaction between the T cell antigen receptor (TCR) and peptide-major histocompatibility class I (pMHCI). We present evidence that CD8 not only modifies the affinity of cognate TCR/pMHCI binding by altering both the association rate and the dissociation rate of the TCR/pMHCI interaction, but modulates the sensitivity (triggering threshold) of the TCR as well, by recruiting TCR/pMHCI complexes to membrane microdomains at a rate which depends on the affinity of MHCI/CD8 binding. Mathematical analysis of these modulatory effects indicates that a T cell can alter its functional avidity for its agonists by regulating CD8 expression, and can rearrange the relative potencies of each of its potential agonists. Thus we propose that a T cell can specifically increase its functional avidity for one agonist, while decreasing its functional avidity for other potential ligands. This focussing mechanism means that TCR degeneracy is inherently dynamic, allowing each TCR clonotype to have a wide range of agonists while avoiding autorecognition. The functional diversity of the TCR repertoire would therefore be greatly augmented by coreceptor-mediated ligand focussing.

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.

Agent-based modeling of the context dependency in T cell recognition

Antigen recognition by T cells is a key event in the adaptive immune response. T cells scan the surface of antigen-presenting cells (APCs) or target cells for specific peptides bound to MHC molecules. In the physiological setting, a typical APC presents tens of thousands of diverse endogenous self-derived peptides complexed to MHC (pMHC complexes). When 'foreign' peptides are presented, they constitute a small fraction of the total surface peptide repertoire. As T cells seem to be capable of discerning minute amounts of 'foreign' peptides among a complex background of self-peptides, endogenous peptides are generally assumed to play no role in recognition. However, recent results suggest that these background peptides may alter the sensitivity of T cells to foreign peptides. Current experimental limitations preclude analysis of peptide mixtures approaching physiological complexity, making it difficult to further address the role of complex background peptides. In this paper, we present a computational model to test how complex, varied peptide populations on an APC could potentially modulate a T cell's ability to detect the presence of small numbers of agonist peptides among a diverse population. We use the model to investigate the notion that under physiological conditions, T cell recognition of foreign peptides is context dependent, that is, T cells process signals gathered from all pMHC interactions, not just from a few agonist peptides while ignoring all others.

Foreignness as a matter of degree: the relative immunogenicity of peptide/MHC ligands

The ability of T lymphocytes (T cells) to recognize and attack foreign invaders while leaving healthy cells unharmed is often analysed as a discrete self/non-self dichotomy, with each peptide/MHC ligand classified as either self or non-self. We argue that the ligand immunogenicity is more naturally treated as a continuous quantity, and show how to define and quantitate relative ligand immunogenicity. In our theory, self-tolerance is acquired through reduction of the relative immunogenicity of autoantigens, whereas xenoantigens, typically not presented during induction of deletional tolerance, retain a high degree of relative immunogenicity. Autoantigens that are not prominently presented in deletional tolerance likewise retain a high relative immunogenicity and remain essentially foreign. According to our analysis, any given autoantigen can attain a high level of relative immunogenicity, provided it is presented at sufficiently high levels. Our theory provides a quantitative tool to analyse the immunogenicity of tumour-associated neoantigens and the aetiology of autoimmune disease.

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.

Dynamics of T cell activation threshold tuning

T lymphocytes are believed to alter their sensitivity to TCR stimulation by means of a tunable cellular activation threshold. We present two modelling examples which show that the concept of a tunable threshold can be made mechanistically plausible. The tunable threshold is treated as an emergent property of the dynamics of the T cell's signalling machinery. In addition, we discuss how the dynamic properties of activation threshold tuning can be determined experimentally with the aid of these two models. We propose a novel 'avidity selection' mechanism for the initial stages of the immune response, based on the properties of the T cell activation threshold tuning mechanism we propose for the commitment to differentiation. Our main finding is that activation threshold tuning allows T cells to respond to relevant ligands with a detection threshold that is (i) uniform across both the T cell repertoire and the secondary lymphoid tissues, while (ii) retaining tolerance to autostimulation. Our analysis indicates that central tolerance enhances the efficiency of peripheral tolerance, casting new light on the role of negative selection in the thymus.

The impact of thymic antigen diversity on the size of the selected T cell repertoire

The TCR repertoire of a normal animal is shaped in the thymus by ligand-specific positive- and negative-selection events. These processes are believed to be determined at the single-cell level primarily by the affinity of the TCR-ligand interactions. The relationships among all the variables involved are still unknown due to the complexity of the interactions and the lack of quantitative analysis of those parameters. In this study, we developed a quantitative model of thymic selection that provides estimates of the fractions of positively and negatively selected thymocytes in the cortex and in the medulla, as well as upper-bound ranges for the number of selecting ligands required for the generation of a normal diverse TCR repertoire. Fitting the model to current estimates of positive- and negative-selected thymocytes leads to specific predictions. The results indicate the following: 1) the bulk of thymocyte death takes place in the cortex, and it is due to neglect; 2) the probability of a thymocyte to be negatively selected in the cortex is at least 10-fold lower than in the medulla; 3) <60 ligands are involved in cortical positive selection; and 4) negative selection in the medulla is constrained by a large diversity of selecting ligands on medullary APCs.

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.

Quantitative constraints on the scope of negative selection

Maturing T cells with a high affinity for self-antigens presented in the thymus are deleted in the process of negative selection. Although the expression of various "tissue-specific" antigens has been described in the thymus, it is still controversial what fraction of all self-antigens induces tolerance by this mechanism. We demonstrate that the limited duration of the negative selection phase imposes a constraint on the number of self-peptides that can be reliably selected against. The analysis supports the theory that negative selection is confined to the subset of peptides produced by dendritic cells.

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.

Structural and thermodynamic correlates of T cell signaling

The first crystal structures of intact T cell receptors (TCRs) bound to class I peptide-MHC (pMHCs) antigens were determined in 1996. Since then, further structures of class I TCR/pMHC complexes have explored the degree of structural variability in the TCR-pMHC system and the structural basis for positive and negative selection. The recent determination of class II and allogeneic class I TCR/pMHC structures, as well as those of accessory molecules (e.g., CD3), has pushed our knowledge of TCR/pMHC interactions into new realms, shedding light on clinical pathologies, such as graft rejection and graft-versus-host disease. Furthermore, the determination of coreceptor structures lays the foundation for a more comprehensive structural description of the supramolecular TCR signaling events and those assemblies that arise in the immunological synapse. While these telling photodocumentaries of the TCR/pMHC interaction are composed mainly from static crystal structures, a full description of the biological snapshots in T cell signaling requires additional analytical methods that record the dynamics of the process. To this end, surface plasmon resonance (SPR), isothermal titration calorimetry (ITC), and ultracentrifugation (UC) have furnished both affinities and kinetics of the TCR/pMHC association. In the past year, structural, biochemical, and molecular biological data describing TCR/pMHC interactions have sublimely coalesced into a burgeoning well of understanding that promises to deliver further insights into T cell recognition. The coming years will, through a more intimate union of structural and kinetic data, allow many pressing questions to be addressed, such as how TCR/pMHC ligation is affected by coreceptor binding and what is the mechanism of TCR signaling in both early and late stages of T cell engagement with antigen-presenting cells.