Deriving quantitative constraints on T cell selection from data on the mature T cell repertoire

Quantitative approaches for decoding the specificity of the human T cell repertoire

T cell receptor (TCR)-peptide-major histocompatibility complex (pMHC) interactions play a vital role in initiating immune responses against pathogens, and the specificity of TCRpMHC interactions is crucial for developing optimized therapeutic strategies. The advent of high-throughput immunological and structural evaluation of TCR and pMHC has provided an abundance of data for computational approaches that aim to predict favorable TCR-pMHC interactions. Current models are constructed using information on protein sequence, structures, or a combination of both, and utilize a variety of statistical learning-based approaches for identifying the rules governing specificity. This review examines the current theoretical, computational, and deep learning approaches for identifying TCR-pMHC recognition pairs, placing emphasis on each method's mathematical approach, predictive performance, and limitations.

What's self got to do with it: Sources of heterogeneity among naive T cells

There is a long-standing assumption that naive CD4⁺ and CD8⁺ T cells are largely homogeneous populations despite the extraordinary diversity of their T cell receptors (TCR). The self-immunopeptidome plays a key role in the selection of the naive T cell repertoire in the thymus, and self-peptides are also an important driver of differences between individual naive T cells with regard to their subsequent functional contributions to an immune response. Accumulating evidence suggests that as early as the β-selection stage of T cell development, when only one of the recombined chains of the mature TCR is expressed, signaling thresholds may be established for positive selection of immature thymocytes. Stochastic encounters subsequently made with self-ligands during positive selection in the thymus imprint functional biases that a T cell will carry with it throughout its lifetime, although ongoing interactions with self in the periphery ensure a level of plasticity in the gene expression wiring of naive T cells. Identifying the sources of heterogeneity in the naive T cell population and which functional attributes of T cells can be modulated through post-thymic interventions versus those that are fixed during T cell development, could enable us to better select or generate T cells with particular traits to improve the efficacy of T cell therapies.

Is T Cell Negative Selection a Learning Algorithm?

Our immune system can destroy most cells in our body, an ability that needs to be tightly controlled. To prevent autoimmunity, the thymic medulla exposes developing T cells to normal “self” peptides and prevents any responders from entering the bloodstream. However, a substantial number of self-reactive T cells nevertheless reaches the periphery, implying that T cells do not encounter all self peptides during this negative selection process. It is unclear if T cells can still discriminate foreign peptides from self peptides they haven’t encountered during negative selection. We use an “artificial immune system”—a machine learning model of the T cell repertoire—to investigate how negative selection could alter the recognition of self peptides that are absent from the thymus. Our model reveals a surprising new role for T cell cross-reactivity in this context: moderate T cell cross-reactivity should skew the post-selection repertoire towards peptides that differ systematically from self. Moreover, even some self-like foreign peptides can be distinguished provided that the peptides presented in the thymus are not too similar to each other. Thus, our model predicts that negative selection on a well-chosen subset of self peptides would generate a repertoire that tolerates even “unseen” self peptides better than foreign peptides. This effect would resemble a “generalization” process as it is found in learning systems. We discuss potential experimental approaches to test our theory.

Broad cross-reactivity of the T-cell repertoire achieves specific and sufficiently rapid target searching

The molecular recognition of T-cell receptors is the hallmark of the adaptive immunity. Given the finiteness of the T-cell repertoire, individual T-cell receptors are necessary to be cross-reactive to multiple antigenic peptides. In this study, we quantify the variability of the cross-reactivity by using a string model that estimates the binding affinity between two sequences of amino acids. We examine sequences of 10,000 human T-cell receptors and 10,000 antigenic peptides, and obtain a full spectrum of cross-reactivity of the receptor-peptide binding. Then, we find that the cross-reactivity spectrum is broad. Some T-cells are reactive to 1000 peptides, but some T-cells are reactive to only one or two peptides. Since the degree of cross-reactivity has a correlation with the (un)binding affinity of receptors, we further investigate how the broad cross-reactivity affects the target searching of T-cells. High cross-reactive T-cells may not require many trials for searching correct targets, but they may spend long time to unbind from incorrect targets. In contrast, low cross-reactive T-cells may not spend long time to ignore incorrect targets, but they require many trials for screening correct targets. We evaluate this hypothesis, and show that the broad cross-reactivity of the natural T-cell repertoire can balance the trade-off between the rapid screening and unbinding penalty.

Effects of thymic selection on T cell recognition of foreign and tumor antigenic peptides

The advent of cancer immunotherapy has generated renewed hope for the treatment of many malignancies by introducing a number of novel strategies that exploit various properties of the immune system. These therapies are based on the idea that cytotoxic T lymphocytes (CTLs) directly recognize and respond to tumor-associated neoantigens (TANs) in much the same way as they would to foreign peptides presented on cell surfaces. To date, however, nearly all attempts to optimize immunotherapeutic strategies have been empirical. Here, we develop a model of T cell selection based on the assumption of random interaction strengths between a self-peptide and the various T cell receptors. The model enables the analytical study of the effects of selection on the CTL recognition of TANs and completely foreign peptides and can estimate the number of CTLs that can detect donor-matched transplants. We show that negative selection thresholds chosen to reflect experimentally observed thymic survival rates result in near-optimal production of T cells that are capable of surviving selection and recognizing foreign antigen. These analytical results are confirmed by simulation.

The dual role of autoimmune regulator in maintaining normal expression level of tissue-restricted autoantigen in the thymus: A modeling investigation

The expression level of tissue-restricted autoantigens (TSA) in the thymus is crucial for the negative selection of autoreactive T cells during central tolerance. The autoimmune regulator factor (AIRE) plays an important role in the positive regulation of these TSA in medullary thymic epithelial cells and, consequently, in the negative selection of high-avidity autoreactive T cells. Recent studies, however, revealed that thymic islet cell autoantigen (ICA69) expression level in non-obese diabetic (NOD) mice, prone to developing type 1 diabetes (T1D), is reduced due to an increase in the binding affinity of AIRE to the Ica1-promoter region, which regulates ICA69 protein synthesis. This seemed to suggest that AIRE acts as a transcriptional repressor of Ica1 gene in the thymus, causing down regulation in the expression level of ICA69. To investigate this hypothesis and the apparent dual role of AIRE in negative selection, we develop a series of mathematical models of increasing complexity describing the temporal dynamics of self-reactive T cells, AIRE-mRNA and AIRE-(in)dependent thymic TSA-associated genes. The goal is to understand how changing the binding affinity of AIRE to Ica1-promoter affects both T-cell tolerance and the dual role of the transcription factor. Using stability analysis and numerical computations, we show that the model possesses a bistable switch, consisting of healthy and autoimmune states, in the expression level of Ica1 gene with respect to AIRE binding affinity, and that it can capture the experimentally observed dual role of AIRE. We also show that the model must contain a positive feedback loop exerted by T cells on AIRE expression (e.g., via lymphotoxin released by T cells) to produce bistability. Our results suggest that the expression-level of AIRE-mRNA in the healthy state is lower than that of the autoimmune state, and that negative selection is very sensitive to parameter perturbations in T-cell avidity.

Indoctrinating T cells to attack pathogens through homeschooling

Adaptive immunity is predicated on the ability of the T cell repertoire to have pre-existing specificity for the universe of potential pathogens. Recent findings suggest that T cell receptor (TCR)-self-major histocompatibility protein (pMHC) interactions limit autoimmune responses while enhancing T cell response to foreign antigens. We review these findings here, placing them in context of the current understanding of how TCR-self-pMHC interactions regulate T cell activation thresholds, and suggest that TCR-self-pMHC interactions increase the efficiency of the T cell repertoire by giving a competitive advantage to peptide cross-reactive T cells. We propose that self-reactivity and peptide cross-reactivity are controlled by particular CDR3 sequence motifs, which would allow thymic selection to contribute to solving the feat of broad pathogen specificity by exporting T cells that are pre-screened by positive and negative selection for the ability to be 'moderately' peptide cross-reactive.

Revisiting thymic positive selection and the mature T cell repertoire for antigen

To support effective host defense, the T cell repertoire must balance breadth of recognition with sensitivity for antigen. The concept that T lymphocytes are positively selected in the thymus is well established, but how this selection achieves such a repertoire has not been resolved. Here we suggest that it is direct linkage between self and foreign antigen recognition that produces the necessary blend of TCR diversity and specificity in the mature peripheral repertoire, enabling responses to a broad universe of unpredictable antigens while maintaining an adequate number of highly sensitive T cells in a population of limited size. Our analysis also helps to explain how diversity and frequency of antigen-reactive cells in a T cell repertoire are adjusted in animals of vastly different size scale to enable effective antipathogen responses and suggests a possible binary architecture in the TCR repertoire that is divided between germline-related optimal binding and diverse recognition.

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.

Mechanisms Underlying CD4+ Treg Immune Regulation in the Adult: From Experiments to Models

To maintain immunological balance the organism has to be tolerant to self while remaining competent to mount an effective immune response against third-party antigens. An important mechanism of this immune regulation involves the action of regulatory T-cell (Tregs). In this mini-review, we discuss some of the known and proposed mechanisms by which Tregs exert their influence in the context of immune regulation, and the contribution of mathematical modeling for these mechanistic studies. These models explore the mechanisms of action of regulatory T cells, and include hypotheses of multiple signals, delivered through simultaneous antigen-presenting cell (APC) conjugation; interaction of feedback loops between APC, Tregs, and effector cells; or production of specific cytokines that act on effector cells. As the field matures, and competing models are winnowed out, it is likely that we will be able to quantify how tolerance-inducing strategies, such as CD4-blockade, affect T-cell dynamics and what mechanisms explain the observed behavior of T-cell based tolerance.

Models of self-peptide sampling by developing T cells identify candidate mechanisms of thymic selection

Conventional and regulatory T cells develop in the thymus where they are exposed to samples of self-peptide MHC (pMHC) ligands. This probabilistic process selects for cells within a range of responsiveness that allows the detection of foreign antigen without excessive responses to self. Regulatory T cells are thought to lie at the higher end of the spectrum of acceptable self-reactivity and play a crucial role in the control of autoimmunity and tolerance to innocuous antigens. While many studies have elucidated key elements influencing lineage commitment, we still lack a full understanding of how thymocytes integrate signals obtained by sampling self-peptides to make fate decisions. To address this problem, we apply stochastic models of signal integration by T cells to data from a study quantifying the development of the two lineages using controllable levels of agonist peptide in the thymus. We find two models are able to explain the observations; one in which T cells continually re-assess fate decisions on the basis of multiple summed proximal signals from TCR-pMHC interactions; and another in which TCR sensitivity is modulated over time, such that contact with the same pMHC ligand may lead to divergent outcomes at different stages of development. Neither model requires that T(conv) and T(reg) are differentially susceptible to deletion or that the two lineages need qualitatively different signals for development, as have been proposed. We find additional support for the variable-sensitivity model, which is able to explain apparently paradoxical observations regarding the effect of partial and strong agonists on T(conv) and T(reg) development.

Positive and negative selection, self-nonself discrimination and the roles of costimulation and anergy

It is still unclear whether the adaptive immune system can perform accurate self-nonself discrimination and what could influence its performance. Starting from simple cellular interaction rules we show that it is possible to achieve perfect self-nonself discrimination in a consistent framework provided positive and negative selection operate during repertoire education, and costimulation and anergy are also considered during T cell activation. In this theory T cell receptors diversity is required for cells to sense differently different peptides; positive selection is needed to guarantee maximal lymphocyte's interactivity and to allow negative selection to reduce conjugation lifetimes maximally; costimulation is necessary to signal that an antigen presenting cell established an uncommon rate of long lived conjugations when presenting foreign peptides; anergy is required to guarantee that these stable contacts involved different T cells and not always the same. These results suggest that accurate self-nonself discrimination can have shaped the adaptive immune system.

The effects of age, thymectomy, and HIV Infection on alpha and beta TCR excision circles in naive T cells

Due to homeostasis total naive T cell numbers remain fairly constant over life despite a gradual involution of the thymus. The contribution of the thymus to maintaining naive T cell pools is typically measured with TCR excision circles (TRECs) that are formed in thymocytes. The mechanisms underlying thymic involution are poorly understood. Some data suggest that thymocytes undergo fewer divisions in old (small) than young (large) thymi, and other data suggest that the number of TRECs per thymocyte is independent of age. If thymic involution were associated with a decreased number of divisions of the thymocytes, this would markedly complicate the interpretation of TREC data. To study this we develop a mathematical model in which the division rate of thymocytes decreases with increasing age. We describe the dilution of TRECs formed during the arrangement of both chains of the TCR by division of thymocytes, recent thymic emigrants, and mature naive T cells. The model behavior is complicated as TREC contents in naive T cells can increase with age due to decreased dilution in the thymus. Because our model is consistent with current data on the effects of age and thymectomy on TRECs in peripheral T cells, we conclude that aging may well affect thymocyte division, which markedly complicates the interpretation of TREC data. It is possible, but more difficult, to let the model be consistent with the rapid changes in alpha and beta TRECs observed shortly after HIV infection.

Feedback Loops, Reversals and Nonlinearities in Lymphocyte Development

Systems of differentiating cells are often regarded by experimental biologists as unidirectional processes, in which cells spend a fixed time at each successive developmental stage. However, mathematical modeling has in several cases revealed that differentiating cell systems are more complex than previously believed. For example, non-linear transitions, feedback effects, and even apparent reversals have been suggested by our studies on models for the development of lymphocytes and their receptor repertoires, and are reviewed in this paper. These studies have shown that cell population growth in developing lymphocyte subsets is usually nonlinear, as it depends on the density of cells in each compartment. Additionally, T cell development has been shown to be subject to feedback regulation by mature T cell subsets, and B cell development has been shown to include a phenotypic reflux from an advanced to an earlier developmental stage. The challenges we face in our efforts to understand how the repertoires of these cells are generated and regulated are also discussed here.

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.

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.

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.

Test of a statistical model for molecular recognition in biological repertoires

A chance encounter between members of a random repertoire and a molecular target is characteristic of different biological systems, including the immune and olfactory pathways as well as combinatorial libraries. In such systems, the affinity between the target and members of the repertoire is distributed with a probability function describing the propensity of obtaining a particular affinity value. We have previously proposed a phenomenological receptor affinity distribution (RAD) formalism, which describes this probability function based on simple statistical considerations. In the present analysis, we use published data from diverse experimental systems, including phage display libraries, immunoglobulins and enzymes, to test the RAD model and to compare it to other affinity distribution formalisms. The RAD model is found to provide the best description for binding data for over eight orders of magnitude on the affinity scale, and to account for a relationship between repertoire size and the maximal obtainable affinity within different repertoires. This approach points to a potential universality of the rules that govern affinity distributions in biology.

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 quantitative theory of affinity-driven T cell repertoire selection

Binding of the T cell antigen receptor (TCR) to peptides presented on molecules encoded by major histocompatibility complex (MHC) genes is the key event driving T cell development and activation. Selection of the T cell repertoire in the thymus involves two steps. First, positive selection promotes the survival of cells binding thymic self-MHC-peptide complexes with sufficient affinity. The resulting repertoire is self-MHC restricted: it recognizes foreign peptides presented on self, but not foreign MHC. Second, negative selection deletes cells which may be potentially harmful because their receptors interact with self-MHC-peptide complexes with too high an affinity. The mature repertoire is also highly alloreactive: a large fraction of T cells respond to tissues harboring foreign MHC. We derive mathematical expressions giving the frequency of alloreactivity, the level of self-MHC restriction, and the fraction of the repertoire activated by a foreign peptide, as a function of the parameters driving the generation and selection of the repertoire: self-MHC and self-peptide diversity, the stringencies of positive and negative selection, and the number of peptide and MHC polymorphic residues that contribute to T cell receptor binding. Although the model is based on a simplified digit string representation of receptors, all the parameters but one relate directly to experimentally determined quantities. The only parameter without a biological counterpart has no effect on the model's behavior besides a trivial and easily preventable discretization effect. We further analyse the role of the MHC and peptide contribution to TCR binding, and find that their relative, rather than absolute value, is important in shaping the mature repertoire. This result makes it possible to adopt different physical interpretations for the digit string formalism. We also find that the alloreactivity level can be inferred directly from data on the stringency of selection, and that, in agreement with recent experiments, it is not affected by thymic selection.