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Repertoire Selection from Data on the Mature T Cell Deriving Quantitative Deriving Quantitative Constraints on T Cell Selection from Data on the Mature T Cell Repertoire This information is current as Vincent Detours, Ramit Mehr and Alan S. Perelson of October 2, 2021. J Immunol 2000; 164:121-128; ; doi: 10.4049/jimmunol.164.1.121 http://www.jimmunol.org/content/164/1/121 Downloaded from References This article cites 75 articles, 24 of which you can access for free at: http://www.jimmunol.org/content/164/1/121.full#ref-list-1 Why The JI? Submit online. http://www.jimmunol.org/ • Rapid Reviews! 30 days* from submission to initial decision • No Triage! Every submission reviewed by practicing scientists • Fast Publication! 4 weeks from acceptance to publication *average by guest on October 2, 2021 Subscription Information about subscribing to The Journal of Immunology is online at: http://jimmunol.org/subscription Permissions Submit copyright permission requests at: http://www.aai.org/About/Publications/JI/copyright.html Email Alerts Receive free email-alerts when new articles cite this article. Sign up at: http://jimmunol.org/alerts The Journal of Immunology is published twice each month by The American Association of Immunologists, Inc., 1451 Rockville Pike, Suite 650, Rockville, MD 20852 Copyright © 2000 by The American Association of Immunologists All rights reserved. Print ISSN: 0022-1767 Online ISSN: 1550-6606. Deriving Quantitative Constraints on T Cell Selection from Data on the Mature T Cell Repertoire1 Vincent Detours,*†‡ Ramit Mehr,§ and Alan S. Perelson2* The T cell repertoire is shaped in the thymus through positive and negative selection. Thus, data about the mature repertoire may be used to infer information on how TCR generation and selection operate. Assuming that T cell selection is affinity driven, we derive the quantitative constraints that the parameters driving these processes must fulfill to account for the experimentally observed levels of alloreactivity, self MHC restriction and the frequency of cells recognizing a given foreign Ag. We find that affinity-driven selection is compatible with experimental estimates of these latter quantities only if 1) TCRs see more peptide residues than MHC polymorphic residues, 2) the majority of positively selected clones are deleted by negative selection, 3) between 1 and 3.6 clonal divisions occur on average in the thymus after completion of TCR rearrangement, and 4) selection is driven by 103–105 self peptides. The Journal of Immunology, 2000, 164: 121–128. Downloaded from he T cell repertoire is shaped in the thymus by three pro- the affinity model. We go one step further in the present paper by cesses. First, TCR V-region coding genes are generated determining what ranges of parameters driving repertoire genera- T by randomly rearranging V(D)J segments and inserting tion are implied by the observed properties of the mature random nucleotides between them. This mechanism creates the repertoire. diverse repertoire of TCRs needed for the immune system to cope The parameters of our model fall into three categories. TCR/ with unpredictable pathogens. Second, positive selection (1, 2) MHC-peptide interaction is quantitatively controlled by the num- http://www.jimmunol.org/ promotes the differentiation to a further developmental stage of bers of peptide and of MHC residues involved in binding to TCR. cells bearing receptors with a sufficiently large affinity for peptides At the level of sets of molecules, peptides and MHCs are charac- presented on molecules of the MHC expressed in the thymus. This terized by their respective diversity. Finally, the stringencies of confers to T cells the property of self MHC restriction: they rec- positive and negative selection are expressed as affinity selection ognize peptides presented in the groove of host MHC molecules, thresholds. The stringency of positive selection can be inferred but ignore them when presented on foreign MHC (3–7). Third, from data on the overall stringency of selection and on the amount negative selection (8, 9) deletes cells whose TCRs bind thymic of thymic clonal expansion following TCR rearrangement (16). MHC-peptide complexes with very high affinity, thus preventing Our analysis consists of calculating the levels of self MHC restric- the emergence of self reactive T cells. Overall, only about 3% of tion, alloreactivity, and foreign Ag response frequencies for all the by guest on October 2, 2021 thymocytes have the intermediate affinity needed to fully mature (10). combinations of parameter values that could be inferred from ex- In addition to self MHC restriction, the mature repertoire is also perimental data. Although a significant portion of the parameter characterized by a high alloreactivity. Typically, 1–24% of T cells space thus defined is consistent with the generation of a repertoire react against the product of a given foreign MHC allele (11, 12). with realistic properties through affinity-based selection, some This high response frequency is hard to reconcile with the fact that measurements reported in the literature are incompatible with it. only one T cell in 104–106 of the naive repertoire recognizes a given pathogen (13, 14). Quantitative Model of T Cell Selection What should the quantitative properties of the processes driving We give a concise verbal description of the concepts underlying TCR generation and selection be to produce the experimentally our model of T cell selection. A rigorous mathematical definition observed levels of self restriction, alloreactivity, and Ag response? of this model can be found in Refs. 15 and 16. A computer im- Previously, we developed a mathematical model relating these lat- plementation is also available (a software package in C language ter quantities to the parameters driving affinity-based selection (15) implementing the model and related simulations can be down- and showed that this model gives a reasonable quantitative account loaded from ftp://ftp-t10.lanl.gov/pub/detours/abs-lab-1.1.tar.gz). of self MHC restriction, alloreactivity, and Ag response frequency (16). In particular, we found that the difference between alloreac- Protein shapes and binding affinities tivity and Ag response frequencies is satisfactorily explained by The features of two proteins that determine their binding can be described with a relatively small number of parameters, such as *Theoretical Biology and Biophysics, and †Center for Nonlinear Studies, Los Alamos their geometric shape, charges, and hydrophobicity. All these pa- ‡ National Laboratory, Los Alamos NM 87545; Santa Fe Institute, Santa Fe NM rameters combine to form the protein’s “generalized shape” as 87501; and §Department of Molecular Biology, Princeton University, Princeton, NJ 08544 defined in Ref. 17. As in previous simulation studies (reviewed in Received for publication May 18, 1999. Accepted for publication October 18, 1999. Ref. (18), we model the generalized shape of a protein as a string 1 Portions of this work were performed under the auspices of the U.S. Department of of digits, from an alphabet of up to 255 digits. (The size of the Energy. This work was supported by National Institutes of Health (NIH) Grants alphabet does not affect the results, as long as it is large enough RR06555 and AI28433 (A.S.P.), NIH Grant GM20964-25 for the study of genetics (15).) The strength of binding of two proteins is then defined as the and regulation of autoimmunity, and NIH Grant AI10227-01 (R.M.). degree of complementarity between the digits representing their 2 Address correspondence and reprint requests to Dr. Alan S. Perelsun, Theoretical Biology and Biophysics, MS K710, Los Alamos National Laboratory, Los Alamos, generalized shapes (Fig. 1). Only the interface between TCRs and NM 87545. E-mail address: [email protected]. MHC-peptide complexes (framed region in upper diagram in Fig. Copyright © 2000 by The American Association of Immunologists 0022-1767/00/$02.00 122 QUANTITATIVE CONSTRAINTS ON T CELL REPERTOIRE SELECTION (6, 26) according to which the TCR senses peptide-induced struc- tural features of the MHC rather that the peptide itself. Positive and negative selection Selection is implemented by introducing two affinity thresholds for , positive and negative selection, KP and KN (KP KN). Clones binding at least one self MHC-peptide complex with affinity K larger than KP survive positive selection. Negative selection de- letes clones binding one or more self MHC-peptide complexes with affinity K larger than KN. The values of KP and KN are derived FIGURE 1. Digit-string representation of MHC-peptide and TCR inter- from experimental data by considering the fractions of clones sur- action. MHC-peptide complexes are constructed by inserting a peptide viving the different stages of selection. Thus, a clone will become string of length lp digits in an MHC string of length lm digits. TCRs are 1 part of the peripheral repertoire if its affinity K falls between KP sequences of lm lp digits chosen randomly. The interaction strength, I, between two facing digits in the two aligned strings, is a measure of their and KN. The fraction f of clones allowed to reach the periphery is: complementarity (see text). Affinity, K, is the sum of interaction strengths 5 z of contacting digits in the two aligned strings. f fP fN (1) where fP is the fraction of clones surviving positive selection (a 1) is represented in the model. We define the affinity, K, between similar parameter is used in Ref. 27), and fN is the fraction of Downloaded from two digit string proteins, as the sum of their individual digit positively selected clones that survive negative selection (27–30). interactions. The values of f and fN can be inferred from recent experimental Our model describes residues at the interface between TCRs and data (see below). MHC-peptide complexes, not the full structure of these molecules. MHC and peptide are random strings, lm and lp digits long, re- T cell activation and self-tolerance spectively. In computing binding interactions the strings are http://www.jimmunol.org/ The activation of selected T cells has to be defined in our model in aligned so that the central digits of a TCR always contact a peptide, order to study alloreactivity and Ag response frequency.
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