How persistent infection overcomes peripheral tolerance mechanisms to cause T cell–mediated autoimmune disease

Significance

Autoimmune diseases afflict millions of people. Persistent or severe infections are associated with triggering T cell–mediated autoimmune diseases, such as multiple sclerosis linked to Epstein–Barr virus infections and type 1 diabetes with enteroviruses. Explanations for these associations do not describe observations like the delay between infection and autoimmunity, the increased risk of autoimmunity upon persistent infections, and why only some individuals with persistent infection acquire autoimmune disease. Here, we integrate a model for T cell development in the thymus and response to infection to provide a unified framework that describes why peripheral tolerance mechanisms are more likely to fail during persistent infection to result in autoimmune diseases. Specific murine experiments to test predictions emerging from these insights are also suggested.

Abstract

T cells help orchestrate immune responses to pathogens, and their aberrant regulation can trigger autoimmunity. Recent studies highlight that a threshold number of T cells (a quorum) must be activated in a tissue to mount a functional immune response. These collective effects allow the T cell repertoire to respond to pathogens while suppressing autoimmunity due to circulating autoreactive T cells. Our computational studies show that increasing numbers of pathogenic peptides targeted by T cells during persistent or severe viral infections increase the probability of activating T cells that are weakly reactive to self-antigens (molecular mimicry). These T cells are easily re-activated by the self-antigens and contribute to exceeding the quorum threshold required to mount autoimmune responses. Rare peptides that activate many T cells are sampled more readily during severe/persistent infections than in acute infections, which amplifies these effects. Experiments in mice to test predictions from these mechanistic insights are suggested.

The key cell types that enable the adaptive immune system to mount pathogen-specific responses to a diverse and evolving world of microbes are T and B lymphocytes (T cells and B cells). Humans have billions of T cells and B cells, each of which expresses a T cell receptor (TCR) or B cell receptor (BCR) on its surface. T and B cell repertoires are characterized by an enormous diversity of TCRs and BCRs generated by VDJ recombination (1–3). Upon infection with a pathogen, some receptors from this pool are likely to bind sufficiently strongly to molecular components of a specific pathogen resulting in T or B cell activation, which can potentially result in an adaptive immune response. For example, TCRs bind to peptides (p) derived from a pathogenic protein bound to protein products of the major histocompatibility (MHC) genes. T cell activation is triggered if the TCR–pMHC bond has a sufficiently long half-life (4–6). Different TCRs tend to bind to different pMHC molecules with sufficiently long half-lives, thus enabling the T cell repertoire to respond specifically to diverse pathogens. At the same time, the T cell repertoire is largely tolerant to pMHC molecules where the peptide is derived from host proteins. Such self-pMHC molecules are expressed ubiquitously on host cells. Tolerance to self is due to processes that occur during T cell development in the thymus and mechanisms that suppress autoimmune responses in peripheral tissues (7–10).

Cells in the thymus (especially those in the medulla) express the AIRE gene which enables promiscuous gene expression and results in these cells displaying pMHC molecules with peptides derived from diverse regions of the host proteome (11). During development, immature T cells (thymocytes) interact with these self-pMHC molecules. To successfully develop into a mature T cell, a thymocyte must bind to at least one self-pMHC molecule it encounters in the thymus with a binding free energy (or half-life) exceeding a threshold in order to receive a survival signal (positive selection) (12). However, if a thymocyte’s TCR binds to any encountered host pMHC molecule with a binding free energy exceeding a higher threshold, it is deleted (negative selection). In this way, positive selection aims to ensure that the mature T cell repertoire expresses TCRs with the ability to bind to pMHC complexes, while negative selection aims to delete self-reactive T cells (13–16). Theoretical and experimental studies have shown that negative selection also plays an important role in mediating the peptide-specificity of TCRs; i.e., most point mutations to a TCR’s cognate peptide abrogate recognition (17–22). Some theoretical and experimental studies also showed that the peptide contact residues on TCRs of mature T cells that undergo normal negative selection are statistically enriched in amino acids that are moderately hydrophobic. We note also that thymocytes that successfully mature but express TCRs that bind more strongly to self-pMHC molecules are more likely to differentiate into regulatory T cells (Tregs) that can suppress responses from conventional mature T cells in tissues (22). On average, a randomly picked conventional T cell from the mature repertoire has a lower probability of being activated by a randomly picked self-pMHC molecule compared to a pathogen-derived pMHC molecule. This is because the activation threshold for mature T cells is slightly higher, but similar, to that for negative selection of thymocytes (23–25), and every mature T cell interacted with some fraction of the self-pMHC molecules displayed in the thymus and was not deleted by negative selection.

However, the difference in probabilities of activation by self and pathogen-derived pMHC molecules is likely to be small. Furthermore, a given thymocyte does not encounter every self-peptide from its host’s proteome during thymic selection. If a mature T cell encounters a self-pMHC molecule that it did not encounter in the thymus, the difference in the probability that it will be activated by this self-pMHC molecule compared to a randomly picked pathogen-derived pMHC molecule is likely to be non-existent. Thus, imperfect thymic selection and stochastic effects associated with T cell activation should prevent robust discrimination between self and foreign antigens at the level of an individual T cell. Indeed, the mature T cell repertoire is known to include T cells that can be activated by some host-derived peptides (9, 26–30). Full blown autoimmune responses to these self-peptides is thought to be suppressed by peripheral tolerance mechanisms such as Tregs (31, 32) and more recent reports of ${\text{CD8}}^{+}$ suppressor T cells (8), yet it remains unclear how self-activated T cells are suppressed while allowing effective responses to pathogens.

In order to mount a functional immune response, T cells must not only be activated but also proliferate and differentiate to acquire effector functions, which requires cytokines (33, 34). For example, IL2 is necessary to promote proliferation (35, 36). Tregs can compete with activated cells for these resources necessary for growth and differentiation to inhibit activated T cells from mounting a functional immune response (10, 37, 38). A theoretical analysis (39) proposed a quorum model of T cell activation wherein if a sufficient number of T cells were activated in the same tissue, they could produce enough of the factors necessary for proliferation and differentiation and share these resources with each other to overcome the competition from suppressive regulatory mechanisms such as those mediated by Tregs. The requirement that a threshold number of T cells must be activated within a tissue before an immune response is mounted makes the probability of successfully discriminating between self and non-self much higher than the ratio of the probabilities of an individual T cell being activated by self or pathogen-derived pMHC, as illustrated by the following example. Let the average probability of a T cell being activated by a pathogen-derived and host-derived pMHC molecule be 0.5 and 0.4, respectively (1.25-fold difference); the difference is due to thymic selection. If the number of T cells that need to be activated for an effective response is 10, the probability of a functional immune response to a pathogenic pMHC molecule is over 9 times higher than to a self pMHC molecule ($0.5^{10}$/$0.4^{10}$). Due to stochastic effects, a 1.25-fold difference in the probability of T cell activation by self and pathogenic pMHC molecules is unlikely to robustly differentiate between self and non-self, but a ninefold difference can be sufficient. Thus, collective effects embodied in the quorum model can provide a robust, non-linear mechanism enabling the T cell repertoire to mount effective responses against pathogens while suppressing T cells activated by self in spite of imperfect thymic selection and stochastic effects. This mechanism is akin to quorum sensing by bacteria (39, 40). The quorum number of activated T cells required for a functional response must, with high probability, be exceeded by pathogen-derived pMHC molecules but not host pMHC (Fig. 1).

Fig. 1.

Schematic depiction of how quorum sensing by T cells can result in functional immune responses to pathogen-derived pMHC molecules and not host-derived ones in spite of the existence of autoreactive T cells in the mature repertoire. For the case depicted, the quorum number is taken to be four.

Several experimental observations provide evidence for the importance of collective effects and the quorum model. Following observations of T cells forming clusters by interacting with the same APC (41) and suggestions of potential cooperativity between T cells (42–45), Gerard et al. used two-photon microscopy in mice to discover the formation of adhesion molecule-mediated junctions between ${\text{CD8}}^{+}$ T cells, and that these interactions increased T cell sensitivity to cytokines like IFN-$\gamma$, important for ${\text{CD8}}^{+}$ T cell differentiation and memory cell development (46). Related results were reported in vitro (47). ${\text{CD8}}^{+}$ T cell clustering around DCs expressing a stimulatory ligand was mediated by adhesion molecules on T cells. CD80 expression also increased on activated T cells, enabling binding to CD28 on neighboring T cells, resulting in signaling that mediates secretion of several cytokines, including IL2 (48–51).

Another elegant study combined experiments in mouse models and computation (10). Tregs require IL2 for mediating their suppressive functions but they do not secrete IL2 (38, 52). The IL2 receptor (IL2R$\alpha$) on Tregs can bind to IL2 produced by vicinal activated T cells to sequester IL2 and trigger Treg proliferation and effector functions. Wong et al. showed that this feedback regulation of Treg’s suppressive effects could be inhibited by preventing the expression of molecules like IL2R$\alpha$ in Tregs. Inhibiting Treg activity led to IL2-mediated signaling and production in activated T cells, which then outcompete Tregs’ ability to bind to IL2. The range of IL2 diffusion is also thus increased, allowing other activated T cells in the vicinity to access IL2. This study also showed that Treg density controls the balance between Treg-mediated suppression and IL2 signaling by activating T cells in a non-linear way. This is consistent with the quorum model, as Treg density should control the number of activated T cells (quorum number) required to outcompete the effects of Tregs non-linearly. Related observations were made in mice and in vitro regarding differentiation of activated ${\text{CD4}}^{+}$ T cells to memory cells (53). Differentiation into memory T cells in mice was dependent on the precursor frequency of antigen-specific ${\text{CD4}}^{+}$ T cells. In vitro, differentiation into memory cells in microwells was density dependent. Evidence for quorum sensing is also suggested by comparing the statistical properties of the sequences of the CDR3 regions of mouse T cell repertoires at different stages of thymic development (54). This study found that post and pre-selection repertoires could be distinguished based on the statistical properties of the ensemble of sequences rather than individual sequences, thus arguing for collective effects in self-nonself discrimination.

A T cell–mediated autoimmune condition results when the central and peripheral tolerance mechanisms described above fail. In several contexts, it has been observed that persistent pathogen infections often trigger T cell–mediated autoimmunity. Examples include type I diabetes (T1D) (55–57) and multiple sclerosis (MS) (58, 59). In the case of MS, longitudinal studies have shown that infection with Epstein–Barr virus (EBV) is a necessary condition for MS (60) (SI Appendix, Fig. S1A). Recent studies suggest that T1D may be triggered by long-term infections by human enteroviruses (EV) or long COVID (61–63) (SI Appendix, Fig. S1B). Even though EV has typically been seen as an acute infection, it seems that EV can persistently infect human pancreatic islet cells (64) that are the targets of autoimmune responses in T1D.

Infection-induced onset of autoimmunity has been attributed to diverse factors including specific MHC genetics, Treg dysfunction, epitope spreading, and molecular mimicry (65, 66). The “molecular mimicry” concept suggests that T cells primed by the foreign antigen are cross-reactive to similar self-peptides, thus resulting in an autoimmune response. ${\text{CD4}}^{+}$ T cells have been shown to be cross-reactive to both EBV-derived peptides and self-antigens like myelin basic protein (MBP), anoctamin 2, alpha-crystallin B, and glial cell adhesion (67–72). For MBP, a self-antigen present in myelin sheaths, there is evidence that MS patients have autoreactive T cells that can be activated by APCs presenting EBV peptides (68). Compared to healthy people, MS patients exhibit higher levels of ${\text{CD4}}^{+}$ T cells that are cross-reactive to EBV peptides and MBP (67, 73). There is also an increase in the presence of MBP-specific ${\text{CD8}}^{+}$ T cells in MS patients (74), and EBV-specific ${\text{CD8}}^{+}$ T cells isolated from these patients were cytotoxic against cells that were pulsed with MBP and cells transfected to endogenously express MBP (75). In another example, human leukocyte antigen (HLA)-B27 is a human MHC allele that is associated with autoimmune diseases like ankylosing spondylitis (AS) and acute anterior uveitis (AAU). Recent studies have identified peptides derived from microbes and self-peptides presented by HLA B27 that activate T cells isolated from AS and AAU patients (73). The “epitope spreading” mechanism proposes that an antiviral immune response leads to tissue damage and the release of otherwise “hidden” self-antigens into the local region, which are then presented by nearby APCs to activate autoreactive T cells (58, 76). In the case of T1D, persistent EV infection leads to inflammation and destruction of islet cells by T cells (77) and an increase in inflammatory cytokines (IFN) (78). ${\text{CD4}}^{+}$ and ${\text{CD8}}^{+}$ T cells progressively destroy islet beta cells in the pancreas (79–82), thus potentially generating higher levels of tissue antigens. Higher levels of inflammation in infected tissues can also result in higher levels of self-antigen presentation on antigen-presenting cells (83–85), including increased cross-priming of MHC class I responses (86). In MS, EBV has been suggested to induce an antiviral immune response against infected cells in the CNS which leads to the release of sequestered self-antigens (87). Despite these proposed mechanisms, clear explanations for several features of the association of autoimmune diseases with persistent viral infections are not available. Why do the mechanisms that normally suppress autoimmunity fail for persistent or severe viral infections? Why does EBV infection only increase the probability of developing MS and not always lead to disease? A sufficient explanation for why individuals with persistent viral infection do not immediately develop autoimmunity (pathogenesis latency) is also unavailable.

Persistent infection due to quickly mutating viruses, such as HIV, are known to lead to the increase of pathogen-derived peptides within a host over time (88, 89), and different peptides are sequentially targeted (90). Even though longitudinal studies on antigen presentation in EBV/EV are sparse, it is known that these infections lead to the targeting of multiple immunogenic epitopes, as EBV and EV have hundreds of potential T cell epitopes (91, 92). In addition, there are several studies that suggest that there is increased antigen presentation during infection and inflammation (60, 93–96). For example, one study showed that inflammation can change the MHC II processing and presentation by increasing antigen-presenting capacity and presentation of pMHC to T cells (84). Another study observed increased MHC expression and a correlation between MHC I antigen presentation and amount of SARS-CoV-2 RNA present in the tissue (97). These studies suggest that increasing numbers of peptides would be targeted upon persistent or severe infections, and we study the consequences of this for triggering autoimmunity.

We first develop a computational model of T cell selection in the thymus and show that appropriately chosen values of positive and negative selection thresholds result in mature repertoires that contain autoreactive T cells while maintaining tolerance to self-antigens with high probability because the quorum threshold is not exceeded by T cells in response to self-antigens alone. We then study the response of our computationally generated T cell repertoires to infection. Our computational results show that the probability of triggering autoimmunity increases monotonically with increasing numbers of pathogen-derived pMHC molecules that are targeted by T cells. Further analyses of our computational results show that rare pathogen-derived peptides that could trigger activation of many T cells may play a significant role in mediating autoimmunity upon persistent viral infection. Based on computational studies, we propose a mechanism for why certain autoimmune conditions are triggered by particular persistent viral infections. This mechanism is compatible with the concepts of molecular mimicry and epitope spreading, but relies critically on understanding why the collective non-linear effects embodied in the quorum model that usually suppress autoimmunity fail upon persistent or severe infections, and provides an explanation for latency of autoimmune pathogenesis. Importantly, we propose experiments in mouse models that could test how collective effects and molecular mimicry are intertwined to break tolerance upon persistent viral infections.

Development of a Simple Computational Model of Thymic Selection and Immune Responses of the Mature T Cell Repertoire

In this section, we first describe our computational model for development of the mature T cell repertoire in the thymus. We then utilize our model to characterize the response of the thus generated mature repertoire to infection (i.e., pathogen-derived pMHC molecules), and the impact of infection on the potential emergence of autoimmunity.

Model for Development of the T Cell Repertoire.

During development, a thymocyte encounters a number of self-pMHC complexes displayed on cells in the thymus and undergoes positive and negative selection. Below, we summarize our model for thymic development and infection; further details are provided in SI Appendix. Our model for the development of a mature T cell repertoire involves generating a panel of self-pMHC molecules and thymocytes (each expressing a TCR) and calculating the binding free energies of every TCR with each encountered self-pMHC molecule. We use a convention in which lower binding free energy corresponds to higher affinity. To successfully mature, the binding free energy of a thymocyte’s TCR and at least one self-pMHC must be lower than ${\text{E}}_{\text{p}}$ (positive selection), and none of the binding free energies must exceed ${\text{E}}_{\text{n}}$ (negative selection). As such, only thymocytes with a minimum binding free energy between ${\text{E}}_{\text{p}}$ and ${\text{E}}_{\text{n}}$ exit the thymus and become part of the mature T cell repertoire. To carry out this procedure, we define a model for TCRs expressed on thymocytes and self-pMHC molecules, and their binding free energies. This model will also be used to study the response of the mature repertoire to pathogen-derived pMHC molecules upon infection.

Our model for TCRs and pMHC molecules and their binding free energies follows the framework of Kosmrlj et al. (19), in which TCR and pMHC molecules are represented as strings of amino acids. TCRs interact with the peptide and the MHC. Past work using a similar model has argued that TCR interaction free energies with the MHC are drawn from a relatively narrow distribution and including these interactions does not change qualitative results (19, 20). Therefore, we only represent the peptides and the peptide contact residues of TCRs as strings of amino acids (Fig. 2 and SI Appendix, String Model Details). We assume that each peptide contact residue on a TCR interacts only with a corresponding site on a peptide. Previous work with a similar model showed that most qualitative results are not altered by considering more complex interaction patterns (98). For a given TCR–pMHC pair, the interaction free energy is calculated as the dot product of the interaction energies between each amino acid pair, with the pairwise interaction energy taken from the Miyazawa–Jernigan (MJ) matrix (99). It is important to note here that the MJ matrix is merely an approximation for TCR–peptide interactions and does not accurately recapitulate them (100). Instead, we chose to use the MJ matrix for simplicity, as it does not alter the final results of the model.

Fig. 2.

Model for TCR–pMHC binding free energy. The variable residues of the TCR that interact with the peptide in the pMHC complex are represented by strings of amino acids. Dot product of pairwise interactions for the two strings provides the total binding free energy.

In Eq. 1, $\ell$ is the length of the variable regions of the TCRs and pMHCs as seen in Fig. 2, and $J(l_i,j_i)$ is the interaction free energy between the amino acid at the i-th peptide contact residue of the TCR ($l_i$) and the peptide ($j_i$).

$$\begin{array}{c}\hfill {\text{E}}_{\text{i}}={\mathrm{\Sigma }}_{i=1}^{\ell }J(l_i,j_i).\end{array}$$ [1]

This simple model of TCR–pMHC interactions has been used previously to study thymic development. One prediction that emerged is that positive and negative selection tune the peptide contact residues of the TCRs on mature T cells to be statistically enriched in amino acids that interact moderately with other amino acids (19–21). Attesting to the utility of the model, this prediction was tested positively in mouse models (22). Amino acids with moderate hydrophobicity, a natural measure of the strength of interactions at an interface like TCR–pMHC binding, were found to be statistically enriched in the key peptide contact residues of TCRs in mature T cells, and this property was dependent on normal negative selection.

Although statistical models for VDJ recombination are available (3, 101, 102), for simplicity, the sequences of peptide contact residues of the TCRs of thymocytes were generated using just the amino acid frequencies of the human proteome (SI Appendix, Table S1); ${10}^6$ unique immature thymocytes were generated. As we will note later, because T cell clonality is not considered in our analyses, our results represent a conservative estimate of the probability of triggering autoimmunity upon persistent viral infection. To generate sequences of self-peptides, we screened the human proteome from UniProt to generate peptides and then used NetMHCPan to find those that bind to HLA-A*01:01, HLA-A*02:01, HLA-B*08:01, and HLA-B*07:02, some of the most commonly found HLAs in the human population (103–105) (SI Appendix, TCR and pMHC Selection). Thus, we generated 10,000 self-peptides (N) with equal numbers of peptides that bind to each HLA type.

To generate the mature T cell repertoire as described above, we expose each thymocyte’s TCR generated as described above to 8,000 self-peptides chosen randomly from our set of 10,000 self-peptides. We generate several mature T cell repertoires using the procedure described above to obtain our results (see latter); each time a different random set of 8,000 self-peptides is chosen. We pick appropriate values for ${\text{E}}_{\text{p}}$ and ${\text{E}}_{\text{n}}$ by finding the values that yield 4% survival rate of thymocytes (106) (SI Appendix, Thymic Selection Gap Selection).

Modeling Infection and Its Impact on Autoimmunity.

During an acute infection, only a few pathogen-derived peptides are immunodominantly targeted by T cells (107). During persistent or severe infection, either as time ensues or at the same time, many more peptides can be targeted by T cells. We thus consider infection with different numbers of pathogen-derived peptides (${\text{N}}_{\text{f}}$) and ask whether the T cell response to these peptides can also trigger a functional autoimmune response. The chosen values of ${\text{N}}_{\text{f}}$ range from 0 to 10, with higher values of ${\text{N}}_{\text{f}}$ representing a persistent or severe infection. Taking Listeria monocytogenes as a model pathogen and its proteome from UniProt (104), we used NetMHCpan to generate 40,000 peptides that can be presented by the same human HLA alleles used in thymic selection of the mature T cell repertoire (103).

Fig. 3 outlines the steps in our method for modeling infection. We first generate a particular realization of a mature naive T cell repertoire using the method in the preceding section. Then, we randomly pick one of the 40,000 Listeria peptides, as well as ${\text{N}}_{\text{T}}$ self-peptides from our panel of 10,000, assuming that both sets can be presented by HLAs in the infected tissue. Next, we calculate the binding free energies of the mature T cells in the repertoire with the pathogen-derived peptide. If this free energy is lower than the activation threshold (${\text{E}}_{\text{a}}$), taken to be ${\text{E}}_{\text{n}}$, we count the T cell as being activated. We chose a sharp threshold of activation because in individual T cells the membrane-proximal signaling network exhibits a digital, all-or-nothing response (108–110). Studies by Yagi and Janeway measured levels of pathogenic peptides required for clonal deletion and activation (24, 25). These studies showed that the negative selection threshold is lower and more sensitive than the activation threshold required for naive peripheral T cell activation and close to the activation threshold required by memory T cells. By setting ${\text{E}}_{\text{a}}$ to ${\text{E}}_{\text{n}}$ in our model, the probabilities of T cell activation by self and pathogen-derived pMHC, and thus the probability of autoimmunity, will be higher than reality. However, our purpose is to reveal mechanisms rather than calculate quantitatively accurate numbers, and so our conservative estimate of the probability of triggering autoimmunity should suffice.

Fig. 3.

Steps in modeling infection: we follow the steps shown and described in the text for increasing numbers of pathogen-derived peptides (or epitopes), ${\text{N}}_{\text{f}}$, and the same number, ${\text{N}}_{\text{T}}$, of self-peptides to calculate the probability of a functional autoimmune response.

We determine how many T cells are activated by the chosen pathogen-derived peptide. If the number of T cells activated by the pathogen-derived peptide is below the quorum number $\text{Q}$, then this event is counted as non-infectious and also does not trigger autoimmunity. If the number of T cells activated by the pathogen-derived peptide exceeds $\text{Q}$, we study the impact of this functional immune response on triggering autoimmunity. Following indications from experiment (47, 53), we choose the quorum number to be $\text{Q}=10$. Note that this value is likely the average value of Q, a point that we will elaborate upon later.

When there is a functional response to the infection, we take each T cell activated by the pathogen-derived peptide and calculate its binding free energy with the ${\text{N}}_{\text{T}}$ self-peptides presented in the tissue. The goal is to determine whether these activated T cells are cross-reactive to the self-peptides in the tissue, which is consistent with the concept of molecular mimicry. We account for the fact that activated T cells have a lower threshold for re-activation by using a binding free energy threshold for reactivation that is higher than ${\text{E}}_{\text{n}}$ upon exposure to self-pMHC molecules. The value of this lower binding free energy, ${\text{E}}_{\text{weak}}$, is chosen based on our experimental data (Fig. 4). We measured the amount of TNF$\alpha$ secreted, a measure of T cell response, of naive and activated B3K508 TCR Tg T cells after exposure to different concentrations of 3K, the antigen that they are specific toward (Fig. 4). Results with B3K506 TCR Tg T cells, which have a different TCR but are also specific to 3K, are shown in SI Appendix, Fig. S4 and yield similar results. We then estimated the higher value of ${\text{E}}_{\text{n}}$ based on the extent to which the curves for naive and activated T cells are shifted. We thus estimate ${\text{E}}_{\text{weak}}-{\text{E}}_{\text{n}}\approx 3{\text{k}}_{\text{B T}}$, and using ${\text{E}}_{\text{n}}=-38{\text{k}}_{\text{B T}}$, we obtain ${\text{E}}_{\text{weak}}=-35{\text{k}}_{\text{B T}}$. We assume that the lower threshold is maintained for reactivation for the time scale of interest to us in this work for reasons noted in SI Appendix (111–119) (SI Appendix, Activation Threshold Shift).

Fig. 4.

Antigen concentration versus % of B3K508 TCR Tg T cells population that are TNF$\alpha$ producers when exposed to 3K. The blue and orange curves are the responses of naive and activated cells, respectively.

There have been several proposed mechanisms for the shift in activation threshold for previously activated T cells (111). Memory cells have greater TCR–pMHC avidity, with one study showing that the TCRs of effector cells have an avidity to pMHC 20 to 50 times higher than that of naive cells, and another showed that memory/effector cells had larger TCR oligomers than their naive counterparts (112, 113). The shift in threshold could also be caused by increased co-stimulatory receptor expression. The co-stimulatory receptor CD47, which is enriched in memory cells, has been shown to activate T cells that otherwise would not have been under low antigen concentration (114). Finally, memory cells do not depend on all of the same co-stimulatory pathways that naive cells do. For instance, memory cells are independent of CD28 co-stimulation, unlike naive cells, which has been shown to be important for activation (115–119).

Using this lower activation threshold, we tested whether any of the pathogen-activated T cells are also activated by the panel of ${\text{N}}_{\text{T}}$ self-peptides presented in the tissue. Let us denote the total number of cross-reactive T cells activated by all ${\text{N}}_{\text{T}}$ self-peptides by ${\text{N}}_{\text{self}}^{\prime }$. If the sum of T cells activated by ${\text{N}}_{\text{T}}$ self-peptides before infection and ${\text{N}}_{\text{self}}^{\prime }$ exceeds the quorum threshold, this event is counted as one that triggers autoimmunity upon infection. This procedure is repeated if additional pathogenic peptides are targeted by T cells during infection until a desired value of ${\text{N}}_{\text{f}}$ is reached (SI Appendix, Modeling Infection).

To obtain statistically meaningful results for the probability of triggering autoimmunity for each value of ${\text{N}}_{\text{f}}$, we repeat the above calculations 10,000 times. Each trial is carried out with new choices of the ${\text{N}}_{\text{f}}$ pathogen-derived peptides and the ${\text{N}}_{\text{T}}$ self-peptides displayed in the tissue, but with the same mature T cell repertoire. The probabilities thus obtained represent the average chance that autoimmunity will be triggered in a particular individual with a specific T cell repertoire for each value of ${\text{N}}_{\text{f}}$. Finally, all the calculations described above are carried out for 30 different realizations of the mature T cell repertoire (or individuals), and the average value for triggering autoimmunity is reported for each value of ${\text{N}}_{\text{f}}$. SI Appendix, Table S2 summarizes the parameter values used in our simulations.

Results

As noted earlier, consistent with data (60, 96), we assume that a persistent or severe infection results in the presentation of multiple pathogen-derived peptides either sequentially or at the same time. Thus, the variation of the probability of triggering autoimmunity as a function of the number of pathogen-derived peptides targeted in a tissue (${\text{N}}_{\text{f}}$) should shed light on differences in the chance of triggering autoimmunity upon persistent infection or severe infections and more usual infections, with severe or persistent infections corresponding to larger values of ${\text{N}}_{\text{f}}$. In the subsections to follow, we will first describe the results of our simulations and then elaborate the mechanistic reasons that underlie our results.

The Probability of Triggering Autoimmunity Grows with the Number of Pathogen-Derived Peptides Targeted by T Cells during Infection.

As depicted in Fig. 5A, simulations show that increasing the number of pathogen-derived peptides targeted by T cells also increases the probability of triggering autoimmunity. The increased chance of autoimmunity with ${\text{N}}_{\text{f}}$ provides an explanation for why persistent or severe infections can increase the chance of developing autoimmune conditions. As the probability of developing autoimmunity is not large, not everyone with a persistent infection develops autoimmunity. Our results also explain why there is a lag time between the establishment of persistent infection and the onset of autoimmunity. As time ensues, increasing numbers of pathogen-derived peptides are presented and targeted by T cells, and the chance of triggering autoimmunity grows as per the results reported in Fig. 5.

Fig. 5.

(A) Probability of triggering autoimmunity, P(auto$\mid {\text{N}}_{\text{f}}$), as a function of the number of pathogen-derived peptides targeted for two different values of Q, $\text{Q}=1$ (no collective effects) and $\text{Q}=10$ (collective effects as per quorum model). (B) Probability of triggering autoimmunity, P(auto$\mid {\text{N}}_{\text{f}}$), normalized by the probability of triggering autoimmunity in the case of no infection, P(auto$\mid {\text{N}}_{\text{f}}$=0). Parameters used are as shown in SI Appendix, Table S2.

Our results also explain why only certain viral infections trigger particular autoimmune conditions. A key component of our model is that T cells activated by pathogen-derived peptides are weakly cross-reactive to self-peptides presented in the same tissue. Such cross-reactivity or molecular mimicry is only possible for certain self-antigens and pathogen-derived peptides, such as the observed cross-reactivity between EBV and myelin-derived peptides in the case of MS (67, 69, 73) and microbial and self-peptides in the case of AS (73). However, such cross-reactivity exists regardless of the collective effects inherent in the quorum model. Fig. 5 shows the influence of collective effects as we compare what happens when $\text{Q}=1$ (no collective effects) and $\text{Q}=10$. Increasing the quorum number, $\text{Q}$, not only has the desired effect of reducing the intrinsic probability of autoimmunity due to circulating autoreactive T cells in the absence of infection (${\text{N}}_{\text{f}}=0$), but also decreases the relative chance of triggering autoimmunity upon viral infections (Fig. 5A). This is because two conditions that depend on collective effects must be satisfied to trigger autoimmunity. First, the number of T cells activated by a pathogen-derived peptide must exceed the quorum threshold and then the ones among these T cells that are cross-reactive to self-antigens in the same tissue must contribute to exceeding the quorum threshold with the self-antigens. In some instances, it is possible that a pathogen-derived peptide can trigger a sufficiently large number of T cells that the ones that are proliferating and cross-reactive to a self-antigen are the major contributors to exceeding the quorum threshold with the self-antigen and triggering autoimmunity. We will discuss this point more fully in the next section. As noted earlier, we do not consider multiple clones of the same T cell. Including clonal T cell populations while still using exactly our model would make the probability of triggering autoimmunity higher compared to that reported in Fig. 5.

The number of self-peptides that T cells encounter in the thymus can vary from person to person and is different for different T cells. Also, experimental results indicate that a HLA allele associated with diabetes binds self-peptides in a less stable way (120), suggesting that T cells restricted by this HLA allele are likely to encounter fewer self-peptides during development. We investigated whether the collective effects embodied in the quorum model can make the immune system more robust by inhibiting autoimmune responses upon persistent or severe infections even in the face of such variations. To address this question, we carried out simulations with different values for the average number of self-peptides T cells encounter in the thymus (M) and calculated the change in probability of triggering autoimmunity upon persistent viral infection (${\text{N}}_{\text{f}}=10$) for different values of Q. Fig. 6A shows the results of simulations for $\text{M}=$8,000 (as in Fig. 5) and a lower value, $\text{M}=$6,500. The increase in the probability of autoimmunity being triggered if $\text{M}=$6,500 is shown for various values of the quorum threshold, Q. As the value of the quorum threshold increases, the increase in the probability of autoimmunity decreases. Thus, the collective effects embodied in the quorum model make the immune system more robust to inter-person variations in thymic development by lowering the change in the probability of triggering autoimmunity upon persistent infections due to such variations.

Fig. 6.

Collective effects in the quorum model confer robustness against autoimmunity. All simulations unless otherwise denoted were performed with the same parameters as in SI Appendix, Table S2. (A) Simulations were performed with $\text{M}=$8,000 and $\text{M}=$6,500 at increasing values of $\text{Q}$ at ${\text{N}}_{\text{f}}=10$. The calculated change in the probability of triggering autoimmunity, P(auto), is graphed as a function of Q. (B) Simulations were performed with ${\text{N}}_{\text{T}}=10$ and ${\text{N}}_{\text{T}}=20$ for increasing values of $\text{Q}$ at ${\text{N}}_{\text{f}}=10$. The calculated change in P(auto) is graphed as a function of Q.

The effector functions of activated T cells that target infected cells can lead to damage to healthy tissue and the release of otherwise sequestered self-antigens into the local tissue, thus increasing the presentation of self-antigens (121, 122). We wondered whether the collective effects inherent to the quorum model might also inhibit the increased chance of autoimmunity being triggered due to enhanced presentation of self-antigens. Fig. 6B shows results of our simulations for the increase in probability of triggering autoimmunity as a function of $\text{Q}$ when the number of self-antigens presented in the tissue (${\text{N}}_{\text{T}}$) increases from ${\text{N}}_{\text{T}}=10$ to ${\text{N}}_{\text{T}}=20$. We find that increasing values of $\text{Q}$ leads to a smaller increase in the risk of autoimmunity given an increase in self-antigen presentation. These results suggest that autoimmunity being triggered by epitope spreading and bystander activation (58) is reduced due to collective effects.

Again, the influence of collective effects in suppressing autoimmunity upon strong perturbations diminishes once the quorum threshold is sufficiently high (Fig. 6). It is important to note, however, that increasing ${\text{N}}_{\text{T}}$ leads to a monotonically increasing risk of autoimmunity in spite of the collective effects embodied in the quorum model (SI Appendix, Fig. S5). This result shows that, in spite of the robustness conferred by the quorum model, substantial changes in the number of self-peptides presented in a tissue enhance the probability of triggering autoimmunity. So, if increased inflammation and tissue damage result in presentation of new self-antigens, autoimmunity would be more likely to be triggered upon infection. While our calculations in Fig. 6 are not meant to be quantitatively accurate, it is interesting to note that this value is consistent with experimental observations that the number of proximal activated T cells required for proliferation and differentiation is of the same order (47, 53).

The results described in this section suggest that collective effects embodied in the quorum model not only confer robustness to the immune system from the standpoint of discriminating between self and pathogen-derived antigens, but also serve to inhibit autoimmunity in spite of inter-person variations in thymic development and when strongly challenged such as upon severe or persistent infection.

The Importance of Rare, Highly Reactive Pathogen-Derived Peptides for Triggering Autoimmunity.

In order to obtain additional mechanistic insights, we first attempted to analyze the simulation results reported above in terms of a simple probabilistic model. The model is framed in terms of the following probabilities:

• $q$, the probability that a pathogen-derived peptide activates a T cell. Thymic selection against $M$ peptides leads to $q\sim 1/M$ (39).

• $q_s$, the probability that a self-peptide activates a T cell. If $M$ out of $N$ possible self-peptides are seen in the thymus, $q_s=q(1-M/N)$.

• $q_w=\alpha q_s$, the probability that a pathogen-activated T cell can be reactivated by a weakly cross-reactive self-peptide. Cross-reactivity is thus encoded in the parameter $\alpha >1$ that can be deduced from Fig. 4.

An important consideration is how many of the T cells patrolling a tissue are on average activated when a self or pathogen-derived peptide is presented. These numbers are estimated using the parameters of SI Appendix, Table S2, as $\overline{n}=Tq\approx {10}^6\times 0.04\times$(8,000)⁻¹ ≈ 5 for pathogen-derived peptides, and ${\overline{n}}_s\approx \overline{n}$(1–8,000/10,000)$\approx 1$ for self-peptides. Assuming that T cell activation events are independent leads to a Poisson distribution for the probability of activating $m$ T cells, and a probability of exceeding the quorum number $\text{Q}$ of

$$\begin{array}{c}\hfill P_Q(\overline{n})={\displaystyle \sum _{m\ge Q}}{e}^{-\overline{n}}\frac{{\overline{n}}^m}{m!}\approx e^{-\overline{n}}\frac{{\overline{n}}^Q}{Q!}.\end{array}$$ [2]

The last approximation is correct as long as quorum number $\text{Q}>\overline{n}$ which holds for the choice of $\text{Q}=10$. This leads to an estimate of a roughly 2% probability for the quorum threshold being exceeded by a pathogen-derived peptide (on average), and a probability of ${10}^{-7}$ for a self-peptide [obtained as $P_Q({\overline{n}}_s$)].

However, the base value of autoimmunity in the absence of infection (${\text{N}}_{\text{f}}=0$) in Fig. 5A is orders of magnitude higher than the ${10}^{-7}$ predicted by Eq. 2 for $P_Q({\overline{n}}_s)$. This discrepancy can be traced back to the Poisson distribution not capturing the characteristics of the T cell repertoire. Fig. 7 shows results of our simulations for the distribution of the number of T cells in the mature repertoire that are activated upon being challenged by our set of 40,000 pathogen-derived peptides and 10,000 self-peptides. These simulations were carried out with many mature T cell repertoires and choices of the self and pathogen-derived peptides. For both self and pathogen-derived antigens, the distribution of the number of activated T cells is very different from a Poisson distribution and is characterized by a long tail. That is, rare peptides can activate a large number of T cells. For example, a peptide composed of highly hydrophobic amino acids would be able to activate many T cells with TCRs containing similar moderately or poorly hydrophobic peptide contact residues. Thus, the activation of these T cells would be correlated and not independent, and the assumption of a Poisson distribution in Eq. 2 would be incorrect. This characteristic of rare peptides being able to activate many T cells can be illustrated with a much simpler model of TCR–peptide interactions than the string model.

Fig. 7.

Distribution of the number of T cells activated by pathogen-derived and self-peptides as obtained from the simpler coarse-grained model described in the text. A total of 9,995 self-peptides activated 0 T cells, 1 self-peptide activated between 1 and 10, and 4 self-peptides activated 10 or more. A total of 39,983 pathogen-derived peptides activated 0 T cells, 4 activated between 1 and 10, and 13 activated 10 or more.

For a given peptide sequence $j$, in the string model, we can construct a reactivity parameter ${\beta }_j$ as the mean of the strength of its interactions with all possible TCR sequences. The ensemble of possible peptides can be characterized by the probability distribution $p(\beta )$ of reactivity. We can construct a similar distribution $p(\alpha )$ describing the mean strength of interactions of pre-selection thymocyte sequences (each sequence, i corresponds to ${\alpha }_i$). To illustrate the role of reactivity, we consider a simplified model in which thymocyte sequences ${\alpha }_i$ and ${\beta }_j$ are taken from the same Gaussian distribution, and their binding free energy is computed simply as

$$\begin{array}{c}\hfill {\text{E}}_{\text{ij}}={\alpha }_i+{\beta }_j.\end{array}$$ [3]

Positive and negative selection prunes the initial TCR ensemble to create a post-selection set of TCRs characterized by a probability distribution, $p(\overline{{\alpha }_i})$, which is concentrated in the range ${\alpha }_{\text{min}}<\overline{{\alpha }_i}<{\alpha }_{\text{max}}<0$ (SI Appendix, Hydrophobicity and Rare Peptides). Possible values of ${\beta }_j$, however, are not similarly restricted, and it is possible (within the model) to encounter rare self-peptides ${\beta }_j$ such that ${\beta }_j+{\alpha }_{\text{min}}<{\text{E}}_{\text{n}}$; such peptides would then activate many T cells. We carried out calculations with this “coarse-grained” model with parameters close to that used in simulations with the “string” model (SI Appendix, Hydrophobicity and Rare Peptides). The resulting distributions for the number of activated T cells are presented in Fig. 7. The distribution of T cell reactivity to peptides is similar to that obtained using the string model (SI Appendix, Fig. S6), including a tail of rare highly reactive peptides that activate many T cells that can overcome the quorum threshold. The chance of sampling such rare peptides from this tail of the distribution grows with the number of pathogen-derived peptides that are targeted as is the case during persistent or severe infections, but not usual acute infections. Such a tail of highly immunogenic antigens has also been observed in the context of SARS-CoV-2 infection. Out of a panel of HLA-I SARS-CoV-2 epitopes, 122 were considered immunogenic (123). This is approximately 0.4% of total possible HLA-I restricted epitopes, which is comparable to the percentage of pathogen-derived peptides above the quorum number in our simulations (roughly 0.14%).

The main insight from the results presented in this section is that rare cross-reactive self and pathogen-derived peptides may work together to trigger autoimmunity by exceeding the pertinent quorum thresholds. Persistent or severe infection makes the chance of sampling these peptides more likely.

Fig. 7 suggests that rare self-peptides would trigger autoimmunity by overcoming the quorum threshold, and so over long times, they should cause autoimmunity in everyone. But, this result is due to limitations of our simple model. In our model, the quorum threshold, Q, is fixed. T cells that bind to self-peptides in the thymus with long half-lives are likely to differentiate into Tregs (124). Therefore, many more conventional effector T cells would have to be activated to beat the suppressive effects of more numerous Tregs that are activated by the same rare self-peptides; i.e., $\text{Q}$ depends upon the T cell reactivity of the self-peptides. Also, the Miyazawa–Jernigan model (99) overemphasizes the strength of hydrophobic interactions and so overestimates the strength of TCR–pMHC interactions.

Experimentally Testable Predictions of the Model

It has been proposed that pathogen-derived peptides with homologs in the host proteome should be associated with higher likelihoods of triggering autoimmunity (125). But, this notion does not account for collective effects embodied in the quorum model and the results we have described above. We propose immunizing mice with increasing numbers of pathogen-derived peptides that are homologous to peptides derived from the mouse proteome. The prediction of our model is that, as the number of such pathogen-derived peptide immunogens introduced into the animals increases, the chance of triggering autoimmunity should also increase. We propose that the mice injected with only one unique pathogenic peptide are used as the control, as this most closely reflects the baseline probability of autoimmunity from acute infection.

We propose immunizing C57BL/6 (B6) mice that express the I-Ab MHC molecule on their APCs with increasing numbers of Mycobacterium tuberculosis peptides. We used NetMHCIIPan to find 15-mer I-Ab binding tuberculosis peptides and peptides from the mouse proteome, respectively (103, 104). Then, following past work (125), we identified mouse homologs for each of the tuberculosis peptides by identifying the mouse peptides with 9-mer cores that shared the same amino acids in the 2, 3, 5, 7, and 8 positions with the tuberculosis peptide’s 9-mer core. The number of mouse homologs per tuberculosis peptide ranged from 0 to 3,000 (SI Appendix, Fig. S8). The pathogen-derived peptides should also be chosen to be different enough from self-peptides such that thymic selection would not have negatively selected against T cells that recognize them. We thus selected tuberculosis peptides that have 17 mouse homologs, which lie approximately at the mean, rather than the tails, of the similarity distribution shown in SI Appendix, Fig. S8. These 122 peptides are listed in SI Appendix, Table S3. Because we expect the rare peptides that activate many T cells to have more hydrophobic amino acids (22), we have also indicated the peptides in our list of homologs that have the most hydrophobic amino acids, which was determined as described in SI Appendix, Tuberculosis Peptides. Immunization with these peptides should be more likely to trigger autoimmunity.

Discussion

Based on theoretical modeling, experiments in mice and in vitro, and analyses of sequences of T cell repertoires, evidence for the importance of collective effects in mediating T cell proliferation, differentiation, and a functional response has accumulated (10, 39, 46, 47, 54). These data suggest that a threshold number (or density) of T cells must be activated in a tissue in order for activated T cells to proliferate and mount an immune response. A threshold number, or quorum, of activated T cells can beat out the suppressive effects of peripheral tolerance mechanisms mediated by Tregs and likely suppressor ${\text{CD8}}^{+}$ T cells (10, 39). The quorum threshold was postulated as a mechanism that prevents autoimmunity due to circulating autoreactive T cells without preventing effective T cell responses to pathogens (39). There is significant empirical evidence that some T cell–mediated autoimmune diseases such as MS and T1D are triggered by persistent viral infections. Here, we studied how persistent or severe infections might overcome the quorum mechanism of suppressing autoimmunity.

We studied a computational model for T cell development in the thymus, and the response of the resulting T cell repertoire to infection. Upon infection, pathogen-derived peptides are targeted by T cells, and an effective functional response results because the quorum threshold is exceeded to some of these pathogen-derived peptides because they were not encountered by the T cell repertoire during development in the thymus. Our results show that some of the activated T cells that normally exhibit weak cross-reactivity to host-derived pMHC molecules can now be efficiently reactivated by these host antigens in the same tissue because previously activated T cells have a lower activation threshold. But, our results show that such molecular mimicry leads to autoimmunity with low probability for typical infections when just a few pathogen-derived peptides are targeted by the T cell repertoire. For autoimmunity to develop, the T cells activated by the pathogen-derived peptides that are cross-reactive to a self-antigen must be sufficiently large in number such that, when added to other T cells that are activated by the same self-antigen, the quorum threshold is exceeded. When just a few pathogen-derived pMHC molecules are targeted, the probability of this happening is small; i.e., peripheral tolerance mechanisms that determine the quorum threshold are able to suppress autoimmunity upon typical infections. This concept is related to observations that ${\text{CD8}}^{+}$ suppressor T cells expand upon infection to kill activated autoreactive T cells (8), and that if the balance is tilted toward Tregs, they expand and effector cells do not (10).

Our results also describe how this mechanism goes awry upon persistent or severe infection. In this case, larger numbers of pathogen-derived pMHC molecules are targeted by the T cell repertoire (65, 66, 84, 88–95, 97). The T cells that target each of these pMHC molecules has a chance of being weakly cross-reactive to host pMHC molecules expressed in the same tissue. So, as the number of targeted pathogen-derived pMHC molecules increases, the total probability of activating T cells cross-reactive to the pathogen-derived pMHC and a self-antigen grows. Our results show that this, in turn, results in increasing the chance that the quorum threshold is exceeded by autoreactive T cells and T cells activated by pathogen-derived pMHC molecules that are weakly cross-reactive to a self-antigen. Thus, we find that the probability of autoimmunity being triggered grows with the number of pathogen-derived pMHC molecules targeted during persistent infection (Fig. 5).

Our model brings together the concepts of molecular mimicry and collective effects to provide a consistent explanation for why viral infections such as EBV do not always result in autoimmunity, why certain viral infections trigger certain autoimmune diseases, why there is a lag time between establishment of a persistent viral infection and onset of the corresponding autoimmune condition, and why this lag time exhibits large variations. Only certain viruses will result in APCs displaying immunogenic pMHC molecules that activate T cells that are cross-reactive to particular self-antigens. This is why certain viral infections are more likely to induce certain autoimmune conditions (e.g., EBV and MS). Our results show that these cross-reactive T cells will contribute to exceeding the quorum threshold for a self-antigen to result in autoimmunity only with a finite probability; therefore, a persistent viral infection will lead to a corresponding autoimmune disease only with some probability (Fig. 5). One of our findings is the importance of rare peptides that can activate many T cells. If a pathogen-derived peptide triggers many T cells, the chance that T cells cross-reactive to a self-antigen are activated and contribute to exceeding the quorum threshold with respect to self-antigens also increases. Such events are rare (Fig. 5 and SI Appendix, Fig. S7) and so autoimmunity may not occur for a very long time, if ever. However, the chance that such an event occurs increases with time during a persistent infection as the chance of T cells targeting more pathogen-derived peptides increases, thus providing an explanation for the lag time. As the lag time is dependent on a stochastic event occurring, it exhibits large variations across individuals.

Our results also show that collective effects embodied in the requirement that the quorum threshold must be exceeded for a functional response lower the probability of triggering autoimmunity because of variations in thymic selection across individuals and when infection leads to strong perturbations (Fig. 6). For example, we found that collective effects embodied in the quorum model make the immune system more robust to autoimmunity when the number of self-antigens T cells are exposed to in the thymus is lower. This situation can be realized either stochastically or because certain HLA alleles, such as one associated with T1D, binds self-peptides less stably (120). The increase in the probability of triggering autoimmunity upon T cells encountering fewer host-derived peptides in the thymus is reduced by the existence of collective effects or the quorum threshold (Fig. 6A). However, the influence of collective effects in suppressing autoimmunity does not matter much beyond a threshold value of the quorum number, $\text{Q}$. $\text{Q}$ is set by the number (or density) of Tregs and other suppressor cells. Thus, our model suggests that beyond a point, having more Tregs will not make the immune system more robust against triggering autoimmunity.

Inflammation and T cell–mediated cell killing can lead to epitope spreading, where tissue damage promotes the presentation of self-epitopes that would otherwise not be presented. In our model, the increased presentation of self-peptides is reflected as an increase in ${\text{N}}_{\text{T}}$. Our results show that increasing ${\text{N}}_{\text{T}}$ increases the number of T cells activated by self-antigens (SI Appendix, Fig. S5), thus contributing to exceeding the quorum threshold. However, we find that the requirement that the quorum threshold be exceeded for a functional immune or autoimmune response suppresses the effects of epitope spreading on triggering autoimmunity (Fig. 6B); another example of collective effects making the immune system more robust against autoimmunity. Inflammation and more cell death also has a higher chance of resulting in expression of rare self-pMHC molecules that can activate many T cells (Fig. 7), thus exceeding the quorum threshold.

The results we have described provide a unifying framework to understand various phenomena, but the model requires further testing. We make a specific prediction to test the veracity of our model. We carried out calculations to identify peptides derived from the proteome of M. tuberculosis that are homologs of peptides from the proteome of C57BL/6 (B6) mice; both sets of peptides bind to the I-Ab MHC molecule expressed by these mice (SI Appendix, Table S3). We predict that immunizing these mice with increasing numbers of the identified M. tuberculosis peptides should result in a higher chance of inducing autoimmune disease. We also expect that the homologous M. tuberculosis peptides that have more hydrophobic amino acids at the sites that contact the TCR could serve as proxies for rare peptides that trigger more T cells, and so we also identify these peptides. Immunizing with a larger number of homolog M. tuberculosis peptides that include these more hydrophobic ones is predicted to increase the probability of triggering autoimmunity. We hope that these experiments will be done as they will likely shed new light on the aberrant regulation of peripheral tolerance mechanisms.

We emphasize again that the purpose of our model is not quantitative recapitulation of a specific experimental result. Rather, our goal was to develop a model that could explore the significant consequences of collective effects that are important for a functional T cell response on mitigating the danger of autoimmunity, and how these tolerance mechanisms can be mis-regulated upon persistent or severe infections. Our model has several limitations. In this manuscript, we have focused on the initial stages of T cell activation and proliferation. It is recognized that the affinity of self-reactive T cell responses also determines whether activated clones up-regulate tissue homing integrins and induce MHC-I cross-priming of self-antigens (22, 126). As details of these processes are further quantified, second-generation computational models will incorporate these attributes to better understand when overt autoimmunity ensues, or a given proliferative burst simply expands self-reactive clones. We do not explicitly treat the effects of innate immunity and inflammation, and implicitly treat their effects on increasing self-antigen presentation by increasing the parameter in our model (${\text{N}}_{\text{T}}$) that represents the number of self-antigens presented in the infected tissue. We do not treat Tregs and suppressor ${\text{CD8}}^{+}$ T cells explicitly either, as their effects are embodied in the quorum threshold number, Q. As we have noted earlier, the value of $\text{Q}$ is not going to be a constant as we have assumed, but rather it will be larger for self-peptides that bind more avidly to T cells as interactions with these self-peptides in the thymus are more likely to result in the development of Tregs (124). Accounting for Tregs and suppressor ${\text{CD8}}^{+}$ T cells and concomitant differences in the values of $\text{Q}$ for different peptides is an important next step for developing a better understanding of the dynamic instability that results in initiating autoimmunity. The development of a dynamical version of our model is an important next step.

Materials and Methods

Link to GitHub with source code for model and tuberculosis peptide files is as follows: https://www.github.com/pinkzephyr/autoimmune_model.

Supplementary Material

Appendix 01 (PDF)

Data, Materials, and Software Availability

All other data are included in the manuscript and/or SI Appendix.