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Without therapy, most persons infected with the human immunodeficiency virus (HIV) ultimately progress to AIDS. Rare individuals (“elite controllers”) maintain very low levels of HIV RNA without therapy, thereby making disease progression and transmission unlikely. Certain HLA Class I alleles are markedly enriched in elite controllers, with the highest association observed for HLA-B571. Since HLA molecules present viral peptides that activate CD8+ T cells, an immune mediated mechanism is likely responsible for superior control of HIV. We report that the peptide binding characteristics of HLA-B57 molecules impact thymic development such that, compared to other HLA-restricted T cells, a larger fraction of the naïve repertoire of B57-restricted clones recognizes a viral epitope and these T cells are more cross-reactive to mutants of targeted epitopes. Our calculations predict that such a T cell repertoire imposes strong immune pressure on immunodominant HIV epitopes and emergent mutants, thereby promoting efficient control of virus. Supporting these predictions, in a large cohort of HLA-typed individuals, our experiments show that the relative ability of HLA-B alleles to control HIV correlates with their peptide binding characteristics that impact thymic development. Our results provide a conceptual framework that unifies diverse empirical observations, with implications for vaccination strategies.
HIV infection leads to acute high level viremia, which is subsequently reduced to a set-point viral load. Without therapy, most patients experience a subsequent increase in viral load, and ultimately the development of AIDS. Viremia levels and time to disease vary widely, and the differences correlate strongly with expression of different HLA class I molecules (reviewed in 2). Effector CD8+ T cells (CTLs) are implicated in viral control because T cell receptors (TCRs) on CD8+ T cells recognize complexes of viral peptides and class I HLA molecules presented on the surface of infected cells, and depletion of CD8+ T cells leads to increased viremia in animal models of HIV infection3. We describe a feature of the B57-restricted CD8+ T cell repertoire that contributes to enhanced control of viremia.
Algorithms4 based on experimental data predict whether a particular peptide will bind to a given HLA molecule5. We tested the veracity of four predictive algorithms against available experimental data on peptide binding to diverse HLA alleles, and found that, in most cases, they are highly accurate (Fig. S1, Table S1). For example, predictions using the best algorithm for HLA-B*5701 were 97 % accurate. Using these algorithms, we computed the fraction of peptides derived from the human proteome6 that bind to various HLA molecules. Of the ~107 unique peptide sequences, only 70,000 are predicted to bind to HLA-B*5701, and 180,000 bind to HLA-B*0701 (an allele that is not protective against HIV). Essentially identical results were obtained for randomly generated peptides (data not shown). The protective allele in Macaques, Mamu-B*17, also binds fewer self peptides than other Mamu molecules for which data are available (Mamu-B*17 binds 4, 6, and 13 times fewer self peptides than Mamu-A*11, Mamu-A*01 and Mamu-A*02, respectively; Table S1).
The intrinsic differences in self peptide binding among HLA alleles are important during T cell repertoire development. Immature T cells are exposed to diverse host-derived peptide-HLA complexes presented in the thymus. Since fewer self peptides are able to bind to HLA-B*5701 (and Mamu-B*17) molecules, a smaller diversity of self-peptide TCR contact sequences will be encountered by HLA-B*5701/Mamu-B*17-restricted T cells in the thymus (Supplementary Discussion 1).
The diversity of self peptides presented in the thymus shapes the characteristics of the mature T cell repertoire. Experiments7,8 and theoretical studies9,10 show that T cells that develop in mice with only one type of peptide in the thymus are more cross-reactive to point mutants of peptide epitopes that they recognize compared to T cells from mice that express diverse self peptides. Thus, by encountering fewer self peptides during thymic development, HLA-B57-restricted CD8+ T cells should be more cross-reactive to point mutants of targeted viral peptides.
We carried out in silico thymic selection experiments to test this hypothesis. We chose a HLA-dependent number of thymic self peptides, each with amino acids of the TCR contact residues picked according to the frequency with which they appear in the human proteome6,9. A diverse set of immature CD8+ T cells (thymocytes) was generated by choosing the sequences of their peptide contact residues in the same way, and by varying the TCR-HLA interactions. A thymocyte emerges from the thymus as a mature CD8+ T cell if its TCR binds to at least one self pMHC molecule with an affinity that exceeds the positive selection threshold, and does not interact with any self peptide more strongly than the negative selection threshold. Using a computational model9,10 in the class of “string models”11, we assessed the affinity of TCR-self-peptide-HLA pairs (Methods) to determine which T cells survive positive and negative selection, and become a part of the mature repertoire. Our qualitative results are independent of parameters used to determine these interaction strengths (Figs. S2, S3 and9,10).
Mature T cells that emerged from these in silico thymic selection experiments were then computationally challenged by a viral peptide (i.e., not seen in the thymus) bound to the same HLA. T cells that recognize this peptide-HLA complex were obtained by assessing whether the interaction strength exceeded the negative selection threshold (equals the recognition threshold in mouse models12); qualitative results were invariant if the recognition threshold is not much weaker than that corresponding to negative selection (Fig. S3). Cross-reactivity of these T cells was then determined in silico by mutating each TCR contact residue of the peptide to the other 19 possibilities. Sites on the viral peptide were called “important contacts” if half the mutations therein abrogated recognition by T cells that target this epitope. The frequency of the number of important contacts in viral peptides that determine T cell recognition was obtained by repeating this procedure 1000 times with different choices of thymocytes and self and foreign peptides.
Our calculations predict that a T cell repertoire restricted by a HLA molecule like HLA-B*5701 which presents fewer self peptides in the thymus has a higher frequency of occurrence of T cells that recognize viral peptides via smaller numbers of important contacts (Fig. 1a). In contrast, the frequency of occurrence of T cells that recognize viral peptides via many important contacts is larger for repertoires restricted by HLA alleles that present a greater diversity of self peptides in the thymus (data not shown for >4 contacts). Mutations at sites different from the important contacts do not affect binding strength substantially. Therefore, when the interaction between peptide-HLA and TCR is mediated by fewer important contacts a larger number of possible point mutations of the peptide do not affect peptide recognition, thereby making the T cells more cross-reactive to mutants that arise. Thus, the HLA-B57-restricted T cell repertoire is expected to be more cross-reactive to mutants of targeted viral peptides than repertoires restricted by HLA alleles, which present a greater diversity of self peptides.
Our computational models reveal this qualitative mechanistic insight, but do not provide quantitative estimates of the extent of this enhanced cross-reactivity of T cells. Turnbull et al. 13 provide compelling experimental data showing that the effect revealed by our studies is significant. Peripheral blood mononuclear cells from patients expressing HLA-B57 contained CTLs that were more cross-reactive to various HIV epitopes and their point mutants compared to HLA-B8 positive patients. HLA-B8 is associated with rapid progression to disease13, and the most accurate algorithm for peptide binding suggests that the HLA-B8 molecule binds a greater diversity of self peptides than HLA-B57 (Table S1, Fig. S4). Other experimental studies also show that patients expressing HLA-B57 cross-recognize point mutants of the dominant epitope and use more public TCRs14,15.
We next computed interaction strengths between diverse viral peptides and members of T cell repertoires restricted by HLA molecules that present differing numbers of self peptides in the thymus. This allowed us to obtain the probability with which a randomly picked T cell clone and viral peptide will interact sufficiently strongly for recognition to occur. The results (Fig. 1b) suggest that a typical CD8+ T cell restricted by a HLA molecule such as HLA-B*5701 that presents fewer peptides in thymus has a higher probability of recognizing a viral epitope compared to a T cell restricted by other HLA molecules. Thus, more HLA-B*5701-restricted T cell clones are likely to recognize a viral epitope, thereby making effective precursor frequencies larger in a HLA-B*5701-restricted repertoire (a strong predictor of response magnitude16). A greater precursor frequency for viral epitopes in the naïve repertoire restricted by HLA B57 is indicated by experimental results showing that HLA-B*5701 contributes most to acute phase CTL responses of all HLA alleles tested17.
The results in Fig. 1 originate from the constraint that thymocytes must avoid being negatively selected by each self peptide-HLA complex encountered during development in the thymus. T cells expressing TCRs with peptide contact residues composed of amino acids that interact strongly with other amino acids (e.g., charged residues, flexible side chains) have a high probability of binding to a self peptide strongly. The greater the diversity of self peptides presented in the thymus, the higher the chance that a TCR with such peptide contact residues will encounter a self peptide with which strong interactions will result in negative selection. Thus, as diversity of self peptides presented in the thymus increases, the peptide contact residues of TCRs in the mature T cell repertoire are increasingly enriched in weakly interacting amino acids (Fig. S5). T cells bearing TCRs with weakly interacting peptide contact residues recognize viral peptides via a number of moderate interactions, making many contacts important for recognition. In contrast, TCRs with peptide contact residues containing strongly interacting amino acids are more likely to recognize more viral peptides via a few important contacts mediated by these residues, making recognition cross-reactive to mutations at other peptide sites. These mechanistic insights are supported by experimental results7,9 (Supplementary Discussion S2).
We explored the consequences of the HLA-B57-restricted CD8+ T cell repertoire having a higher precursor frequency for viral peptides and being more cross-reactive to point mutants of targeted epitopes on control of HIV by studying a model of host-pathogen dynamics that builds on past models of host-HIV interactions18,19,20. Because of the importance of immune control exerted by CD8+ T cells17,21, we focused on the interplay between a mutating virus quasispecies and epitope-directed, variably cross-reactive, host CTL responses.
The essential features of the model are depicted in Fig. 2a (details in Methods). The virus is modeled as a number of epitopes consisting of multiple amino acids, and new viral strains (point mutations of epitopes), which differ in replicative fitness, arise over the course of infection. For each individual, a HLA-dependent CD8+ T cell repertoire is chosen. To mimic the results obtained from our thymic selection calculations (Fig. 1b), more or less cross-reactive repertoires are chosen (Fig. S6) to represent HLA-B57-restricted T cells and those restricted by other HLAs, respectively. Infection rates were limited by target CD4+ T cells, and CTL contraction and memory were included. Other dynamical models were studied, including one which does not incorporate target cell limitation or CTL contraction. Our qualitative results regarding the effects of cross-reactivity are robust to variations in parameters and model assumptions (Fig. S7-S16).
We find that individuals with a more cross-reactive CTL repertoire control viral loads better during the acute phase of the infection (Fig. 2b). This is in agreement with findings in SIV-infected rhesus macaques22, where the number of cross-reactive TCR clones negatively correlates with viral load. Our simulations show (Fig. 2c) that a larger number of CTL clones in a more cross-reactive T cell repertoire recognize epitopes from the infecting virus strain. This is because the predicted higher precursor frequency for viral epitopes (Fig. 1b) leads to a greater response magnitude (as in mouse models16). This conclusion is supported by data showing that, in persons with a protective HLA allele, the initial T cell response to HIV is dominated by T cells restricted by the protective HLA and not those restricted by other HLAs expressed by these persons17. Our simulations also show that enhanced cross-reactivity of the T cell repertoire leads to greater immune pressure on the emergent viral mutants by individuals expressing HLA-B57 compared to those with T cells restricted by HLA molecules that bind more types of self peptides. The stronger immune pressure on infecting and emerging viral strains results in superior control of viral load. Thus, we predict that HIV-infected individuals with HLA alleles that bind fewer self peptides are more likely to control viral loads to low values.
To test this prediction, we studied two large HLA-typed cohorts: 1110 controllers with less than 2000 HIV particles/ml and 628 progressors (or non-controllers) with viral loads exceeding 104/ml (Methods). From these data, we obtained the odds ratio (OR) for individual HLA alleles. Persons with HLA alleles associated with an OR value greater or less than one are more likely to be progressors or controllers, respectively. We focused on HLA-B alleles because they are associated with control of HIV23. Of 40 HLA-B alleles that were studied, significant results (p value < 0.05) were obtained for five HLA-B alleles (Table S2) and peptide binding data are available for four of them. In support of our predictions, HLA-B alleles associated with higher OR values also bind more self peptides (Fig. 3).
Superior control of viral load due to greater precursor frequency and cross-reactivity of T cell repertoires restricted by HLA molecules that bind to few self peptides (e.g., HLA-B57) should also help confer protection against diseases caused by other fast-mutating viruses. Indeed, HLA-B57 is protective against HCV24, another highly mutable viral disease in which CD8+ T cells are important. Also, HLA-B8, which binds a greater diversity of self peptides, is associated with faster disease progression in HCV25 and HIV13. Thus, the correlation between the diversity of peptides presented in the thymus during T cell development and control or progression of disease may be general.
Undoubtedly, many complex factors influence the relationship between HLA-type and disease outcome. The effect of the new factor we have identified should be most significant for HLA molecules that bind relatively few (e.g., HLA-B57) or many (e.g., HLA-B7, B35, B8) self peptides. The strong association of HLA-B27, which binds an intermediate number of self peptides (twice as many as HLA-B57), with viral control indicates that, in this case, the effects of T cell cross-reactivity are reinforced by this molecule binding HIV epitopes that are subject to very strong structural constraints.
Our results also point to a mechanistic explanation for as yet unexplained associations between HLA alleles that confer protection against HIV and autoimmune diseases. T cells restricted by HLA alleles that bind to few self peptides are subject to less stringent negative selection in the thymus, and should therefore be more prone to recognizing self peptides. Indeed HLA-B57 has been associated with autoimmune psoriasis26 and hypersensitivity reactions27. Enhanced cross-reactivity of HLA-B27-restricted T cells and other unique properties of this molecule (misfolding, homodimers28) likely contribute to the enhanced risk of autoimmunity associated with this allele29.
Our results explain another puzzle. Acutely infected patients with low viral loads (and protective HLAs) tend to target an immunodominant epitope that makes a larger relative contribution to the total CTL response as compared to individuals presenting higher levels of viremia30. This is counterintuitive as the most protective responses appear most focused, rather than broadly distributed over many epitopes. We calculated how viral load correlates with the number of CTLs responding to the immunodominant epitope divided by the total number of CTLs activated by the virus (a quantity analogous to relative contribution30). Mirroring experimental data, HLA alleles that restrict a more cross-reactive repertoire and are more protective also correspond to a larger relative contribution (Fig. S13). This result unifies the ideas of a broad and focused response. The more cross-reactive repertoire targets more epitopes and emergent mutants, but a larger number of clones also recognize the dominant epitope (Fig. 2c).
Cross-reactive T cells are rarer in persons with HLA alleles that present more self peptides in the thymus than the B57 allele, but they exist. Our results suggest that a T cell vaccine for a diverse population must aim to “fish” out and activate these rare cross-reactive T cells that also target epitopes from a conserved region of the HIV genome (like HLA-B57 Gag epitopes). This will enable robust responses to infecting and mutant strains, until a strain with low replicative fitness emerges, enhancing control of viral load.
Prediction algorithm tools for peptide binding to HLA and Mamu molecules were obtained from the Immune Epitope Database (IEDB)4 and were used to predict fraction of bound peptides derived from human and macaque proteome6. Accuracies of these tools were tested on experimental data obtained from IEDB4. To assess the effects of thymic selection on TCRs restricted by different MHC molecules (HLA or Mamu), we used a computational model of thymic selection described in Methods (and previously9,10).
For exploration of host-pathogen dynamics, we constructed a small model of the HIV virus with distinct epitopes and sequence diversity, based in part on past work18,19,20. We carried out numerical simulations of ordinary differential equation models, schematically shown in Fig. 2a and S7. Parameters and their justification are given in Tables S3-S4 and in the Supplementary Methods. To explore cross-reactivity, we varied the distribution of pairwise interaction free energies of TCR-pMHC contacts. Our goal was not to obtain numbers, but to examine the qualitative effects of variation in repertoire cross-reactivity on virus control. Qualitative results are robust to variations in parameters and assumptions (Fig. S8–S16).
HLA typed-cohorts of persons of diverse races were divided into HIV controllers and HIV non-controllers, and analyzed for HLA association with the ability to control HIV. The results (Fig. 3, Table S2) were adjusted for the effects of HLA-B*0702, HLA-B*3501, HLA-B*2705 and HLA-B*5701.
There are at present several HLA peptide binding prediction methods. The performance of these algorithms to identify new epitopes has recently been benchmarked against experimental data31. In general, artificial neural networks (ANN)32 and the stabilized matrix method (SMM)33 were found to be superior to other methods31. We used ANN and SMM (versions 2009-09-01 and 2007-12-27) prediction tools provided by the Immune Epitope Database (IEDB)4. Accuracy of prediction tools was tested against experimental data downloaded from IEDB in September 2009 (Fig. S1, Table S1, Supplementary Notes 1). These experimental data were obtained by two methods (competition assays where purified MHC and radioactive labeling are used and association studies where purified MHC and fluorescence labeling are used). Data obtained from the two methods show significant correlation of measured binding affinities (as measured by IC50 and EC50 values)5. Prediction tools were tested against experimental data for accuracy of classifying peptides into binders (IC50 < 500 nM) and non-binders (IC50≥500 nM); the chosen thresholds are commonly accepted values5. We also tested how well these tools predict absolute measured affinity values, not just classification of binders and non-binders, which is dependent upon the chosen thresholds. The accuracy of the prediction tools thus determined are summarized in Table S1 and Fig. S1. We excluded all HLA and Mamu alleles for which there was not enough experimental data (at least 50 binders and 50 non-binders) or prediction tools that are not sufficiently accurate (Supplementary Notes 1). For each HLA and Mamu allele, the most accurate prediction tool was used to predict the fraction of unique peptides derived from the human and macaque proteome (Homo_sapiens.GRCh37.55.pep.all.fa and Macaca_mulatta.MMUL_1.56.pep.all.fa obtained from Ensembl6) that can bind to that allele. We focused only on the binding abilities of 9-mer peptides to HLA molecules, because there is not enough experimental data available for binding affinities of 8-,10-and 11-mer peptides to HLA-B*5701 and the other relevant HLA-B alleles that emerged from our analyses (HLA-B*2705, HLA-B*0702 and HLA-B*3501).
The TCR contact residues of peptides and the peptide contact residues of TCRs are represented as strings of sites of length N. One million sequences of TCR peptide contact residues were subject to development in a thymus containing M self peptides with TCR contact residues generated according to their frequency of occurrence in the human proteome. A particular TCR with the sequence of peptide contact residues, , successfully matures in the thymus, if it avoids negative selection with all self-peptides (Eint > En) and is positively selected by at least one self-peptide (Eint < Ep). Interaction free energy between sequences of TCR and peptide contacts, and , respectively is:
where Ec represents interaction between TCR and HLA and J encodes an empirically determined statistical potential between interacting amino acids on TCR and peptide. Antigenic peptides are recognized by a mature TCR if binding is stronger than threshold for recognition (Eint < Er). The statistical potentials do not necessarily provide quantitatively accurate values of the interaction free energies. However, theoretical analyses and computational results9,10 show that the following qualitative result is true regardless of the choice of the statistical potentials: the smaller the diversity of self peptides presented in the thymus, the greater the cross-reactivity of the mature T cell repertoire that develops therein. More details of the model and the insensitivity of our results to parameter variations (e.g., qualitative results do not depend upon the choice of J or Ec (as long as Ec is not too small or large) are described in supplementary information (Figs. S2–S4) and elsewhere9,10. Parameters used for results in main text are: N=5, En – Ec =−21 kBT, Ep -En =2.5 kBT, Er =En and Miyazawa-Jernigan statistical potential J 34. Numbers of self-peptides presented in the thymus, M, were varied to represent different HLA alleles.
We construct a small model of HIV with distinct epitopes and sequence diversity, based in part on models developed by Nowak and de Boer and coworkers18,19. The virus is modeled as displaying L epitopes, each consisting of M amino acid residues that may be of N types. Different viral strains arise through point mutations at the amino acid sites, giving (NM)L distinct strains. The number of different pMHC types is L*NM, because peptide sequences at epitope positions 1…L are considered to be distinct. The system of ordinary differential equations corresponding to the model in Figure 2 and based on the work of Wodarz and Thomsen20 is as follows:
Target CD4+ cells, It, are infected by free virus particles, where Vn denotes virions of strain n. In denotes CD4+ T cells infected by virus of strain n, Pn,j is a peptide-MHC (pMHC) complex of peptide j derived from viral strain n, displayed on the surface of the infected cell, is pMHC displayed by antigen presenting cells, and Ti is a naive CD8+ T cell of clonotype i. Activated T cells undergo D rounds of cell division before becoming effector CTLs: is an activated CD8+ cell of type i that has not yet begun dividing and are the dividing cells, where m runs from 0 to D-1. Effector CTLs differentiate into memory CD8+ T cells, Mi, which are activated upon rexposure to pMHC.
If T cell clone i recognizes pMHC j, σi, j is 1, and 0 otherwise. In Equation (2), the sum denotes the sum over viral strains m that are Hamming distance 1 away from strain n. That is, only point mutations are allowed. The third term of Equation (5) ensures that if an infected cell is killed, the pMHC bound on its surface must also disappear: denotes the third term of Equation (4), which describes killing of an dt infected cell by CTLs that recognize pMHC on its surface. Simulations were performed using ode45 and ode15s solvers in MATLAB. An additional dynamic model, which does not incorporate target cell limitation and allows unlimited expansion of activated CTLs was also developed to show robustness of our results to model assumptions. It is discussed in the Supplement (Fig. S7–S12).
Rate constants used in the models are given in Tables S3–S4, and are in keeping with literature values. We assume a concentration of 106 CD4+/ml blood prior to infection, with 1% of these cells activated and thus targets for HIV infection initially35,36. The initial conditions of infection in the simulations are chosen to be one infected CD4+ cell/mL of plasma and a naïve CD8+ repertoire size of one cell/mL of each clonotype. We assume that the number of epitopes, length of each epitope, and number of amino acids (L,M,N) are all 2, giving 8 pMHC types and 16 possible viral strains. We choose the number of CD8+ clonotypes to be 20.
The interplay between antigen and immune receptor diversity is captured in this model through variability in σi, j and viral fitness. Different fitness levels for different strains of the virus are modeled by randomly selecting , the virus proliferation rate, for each strain from a uniform distribution between 0 and 2000 (day−1)18,37, with the assumption that the infecting strain has the maximum fitness. The matrix σi, j encodes the ability of T cells to recognize pMHCs. We generate σi, j in such a way as to mimic the results of the thymic selection model (Fig. 1b), in order to investigate the effects of those predictions on host-pathogen dynamics. That is, we assume that T cell repertoires restricted by different HLAs differ in their interaction free energies of TCR-pMHC contacts, and generate σi, j accordingly using a type of random energy-like model (Fig. S6). The interaction free energy between a T cell and an epitope is given by , where J(i, ja) is the interaction free energy between T cell of clonotype i and residue a on epitope j. Similar to the models used for thymic selection, the total interaction free energy is taken to be the sum of the individual residue interactions and recognition is said to occur when it exceeds a recognition threshold (in the dynamical model, T cell sequences are not specified explicitly). J(i, ja) is a random variable chosen from a uniform distribution, and the width of the distribution determines the probability that the summed interaction energy falls above the threshold, and thus the probability that a peptide is recognized by a given T cell. Repertoires generated in this way approach a Gaussian distribution of interaction energies, and the distribution shifts and thus cross-reactivity increases when the uniform distribution from which J(i, ja) is selected is wider. Generating σi, j in this way allows us to describe variable cross-reactivities of the T cell repertoire (both intra- and inter-epitope), and also accounts for correlated interaction energies and thus recognition probabilities of similar peptide sequences.
SAS 9.1 (SAS Institute) was used for data management and statistical analyses. Odds ratios and 95% confidence intervals were determined using PROC LOGISTIC in a comparison of HIV controllers (those individuals who maintained viral loads of less than 2,000 copies of the virus/ml plasma on three determinations over at least a year of follow-up and, on average, for approximately 15 years38) to HIV non-controllers (those individuals whose viral loads exceeded 10,000 copies of the viurs/ml plasma). In order to eliminate the confounding effects of B*0702, B*3501, B*2705 and B*5701, alleles strongly associated with progression or control, these factors were used as covariates in the logistic regression model for the analysis of all other HLA class I types39. All ethnic groups were included in the analyses shown (European, African American and others) and we adjusted for ethnicity in the logistical regression model. All p values were corrected for multiple tests using Bonferroni correction, a stringent and commonly used approach for multiple comparisons40.
Financial support: Mark and Lisa Schwartz Foundation, NIH Director’s Pioneer award (AKC), Philip T and Susan M Ragon Foundation, Jane Coffin Childs Foundation (ELR), the Bill and Melinda Gates Foundation, and the NIAID (BDW, TA, MA). This project has been funded in whole or in part with federal funds from the National Cancer Institute, National Institutes of Health, under Contract No. HHSN261200800001E. The content of this publication does not necessarily reflect the views or policies of the Department of Health and Human Services, nor does mention of trade names, commercial products, or organizations imply endorsement by the U.S. Government. This Research was supported in part by the Intramural Research Program of the NIH, National Cancer Institute, Center for Cancer Research.
Author contributions: A.K. and E.L.R. contributed equally to this work. A.K.C. and B.D.W. initiated the project. A.K., E.L.R. and A.K.C. developed the computational models. A.K., E.L.R, A.K.C and B.D.W. analyzed computational results. Y.Q., F.P., M.C., S.G.D. and B.D.W. collected and analyzed the data from cohorts of HIV infected persons. A.K., E.L.R., T.M.A., M.A, M.C., B.D.W. and A.K.C. contributed to the writing of the manuscript.