How T-cells use large deviations to recognize foreign antigens

A stochastic model for the activation of T-cells is analysed. T-cells are part of the immune system and recognize foreign antigens against a background of the body’s own molecules. The model under consideration is a slight generalization of a model introduced by Van den Berg et al. (J Theor Biol 209:465–486, 2001), and is capable of explaining how this recognition works on the basis of rare stochastic events. With the help of a refined large deviation theorem and numerical evaluation it is shown that, for a wide range of parameters, T-cells can distinguish reliably between foreign antigens and self-antigens.

[1]  S. Hunt,et al.  Immunobiology (5th edn.). The Immune System in Health and Disease (by CA Janeway, P Travers, M Walport and M Shlomchik) , 2002 .

[2]  E. Seidemann,et al.  Probability model for molecular recognition in biological receptor repertoires: significance to the olfactory system. , 1993, Proceedings of the National Academy of Sciences of the United States of America.

[3]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1951 .

[4]  M. Davis,et al.  Kinetics of T-cell receptor binding to peptide/I-Ek complexes: correlation of the dissociation rate with T-cell responsiveness. , 1994, Proceedings of the National Academy of Sciences of the United States of America.

[5]  David A Rand,et al.  Foreignness as a matter of degree: the relative immunogenicity of peptide/MHC ligands. , 2004, Journal of theoretical biology.

[6]  David A Rand,et al.  Dynamics of T cell activation threshold tuning. , 2004, Journal of theoretical biology.

[7]  D. Rand,et al.  Quantifying the strength of ligand antagonism in TCR triggering , 2002, Bulletin of mathematical biology.

[8]  E. Rothenberg,et al.  How T Cells Count , 1996, Science.

[9]  R. Henderson,et al.  Characterization of peptides bound to the class I MHC molecule HLA-A2.1 by mass spectrometry. , 1992, Science.

[10]  Stephen Wolfram,et al.  The Mathematica Book , 1996 .

[11]  A. Casrouge,et al.  A Direct Estimate of the Human αβ T Cell Receptor Diversity , 1999 .

[12]  Frank E. Grubbs,et al.  An Introduction to Probability Theory and Its Applications , 1951 .

[13]  D A Rand,et al.  A reliable and safe T cell repertoire based on low-affinity T cell receptors. , 2001, Journal of theoretical biology.

[14]  H. Berg,et al.  Thymic Presentation of Autoantigens and the Efficiency of Negative Selection , 2003 .

[15]  D. Mason,et al.  A very high level of crossreactivity is an essential feature of the T-cell receptor. , 1998, Immunology today.

[16]  David A Rand,et al.  Antigen presentation on MHC molecules as a diversity filter that enhances immune efficacy. , 2003, Journal of theoretical biology.

[17]  S. Varadhan,et al.  Large deviations , 2019, Graduate Studies in Mathematics.

[18]  A. Lanzavecchia,et al.  Serial triggering of TCRs: a basis for the sensitivity and specificity of antigen recognition. , 1997, Immunology today.

[19]  L. Chess,et al.  Regulation of immune responses by T cells. , 2006, New England Journal of Medicine.

[20]  D. Aldous.  Review: Stewart N. Ethier and Thomas G. Kurtz, Markov processes: Characterization and convergence , 1987 .

[21]  Daniel Coombs,et al.  Supplementary information for Activated TCRs remain marked for internalization after dissociation from pMHC , 2022 .

[22]  S. Ethier,et al.  Markov Processes: Characterization and Convergence , 2005 .

[23]  Antonio Lanzavecchia,et al.  T Cell Activation Determined by T Cell Receptor Number and Tunable Thresholds , 1996, Science.

[24]  W. Feller,et al.  An Introduction to Probability Theory and Its Applications, Vol. II , 1972, The Mathematical Gazette.

[25]  N. R. Chaganty,et al.  Strong Large Deviation and Local Limit Theorems , 1993 .

[26]  Stephen Wolfram,et al.  The Mathematica book, 5th Edition , 2003 .

[27]  A. Lanzavecchia,et al.  Serial triggering of many T-cell receptors by a few peptide–MHC complexes , 1995, Nature.

[28]  Mark M. Davis,et al.  Two-step binding mechanism for T-cell receptor recognition of peptide–MHC , 2002, Nature.

[29]  P. Norman,et al.  Immunobiology: The immune system in health and disease , 1995 .

[30]  Amir Dembo,et al.  Large Deviations Techniques and Applications , 1998 .

[31]  T. McKeithan,et al.  Kinetic proofreading in T-cell receptor signal transduction. , 1995, Proceedings of the National Academy of Sciences of the United States of America.