B and T lymphocytes activate the humoral and cellular arms of the adaptive immune system. The adaptive strategy works because receptors of adaptive immune cells can mount an immune response based on their affinity for antigens. Thus, affinity discrimination is central to adaptive immunity and has important biomedical ramifications. Due to its intricate connection to the affinity maturation process, affinity discrimination has a special significance in B-cell-mediated immune response. The role of affinity-matured high-affinity antibodies is increasingly recognized in vaccine development. In this paper, we discuss the recent progress made in mathematical and computational studies to explore the cellular and molecular mechanisms of B-cell affinity discrimination. Formation of B-cell receptor (BCR) oligomers and BCR-lipid rafts, upon antigenic stimulation, emerge to be key factors in B-cell affinity discrimination (at the level of single cells). It also provides a new way of thinking about kinetic proofreading and serial triggering, concepts that have been widely utilized to understand affinity discrimination in adaptive immune cells. Potential future applications of mathematical and computational modeling of affinity discrimination are discussed in the context of autoimmune disorders and vaccine design. 1. Introduction The adaptive immune system confers an extraordinary protection to higher organisms from invading foreign pathogens. The adaptive feature of the immune system relies on clonal expansion of B and T lymphocytes (upon antigenic stimulation) equipped with high-affinity antigen-specific receptors and generation of memory cells with similar high-affinity receptors (consistent with the clonal selection theory [1]), while a large pool of lower affinity receptors are maintained for efficient sampling of unforeseen antigenic epitopes. Clearly, such a strategy works because receptors of adaptive immune cells can mount an immune response based on recognition of antigenic affinity (affinity discrimination). In B cells, the additional flexibility of generating higher affinity receptors through the genetic process of somatic hypermutation aids selective expansion of high-affinity clones (also known as affinity maturation), making it a powerful strategy to combat foreign pathogens. Thus, in B cells, affinity discrimination and affinity maturation are intricately linked. In addition to its fundamental importance in the mechanism of immune cell activation, the role of affinity-matured antibodies is now increasingly explored in vaccine development [2–6].
References
[1]
T. J. Kindt, B. A. Osborne, and R. A. Goldsby, Kuby Immunology, Macmillan, New York, NY, USA, 2006.
[2]
M. A. Moody, N. L. Yates, J. D. Amos, et al., “HIV-1 gp120 vaccine induces affinity maturation in both new and persistent antibody clonal lineages,” Journal of Virology, vol. 86, no. 14, pp. 7496–7507, 2012.
[3]
D. Lingwood, P. M. McTamney, H. M. Yassine, et al., “Structural and genetic basis for development of broadly neutralizing influenza antibodies,” Nature, vol. 489, no. 7417, pp. 566–570, 2012.
[4]
S. Khurana, D. Frasca, B. Blomberg, and H. Golding, “AID activity in B cells strongly correlates with polyclonal antibody affinity maturation in-vivo following pandemic 2009-H1N1 vaccination in humans,” PLoS Pathog, vol. 8, no. 9, Article ID e1002920, 2012.
[5]
C. A. Siegrist, M. Pihlgren, C. Tougne et al., “Co-administration of CpG oligonucleotides enhances the late affinity maturation process of human anti-hepatitis B vaccine response,” Vaccine, vol. 23, no. 5, pp. 615–622, 2004.
[6]
A. M. Barkoff, K. Grondahl-Yli-Hannuksela, J. Vuononvirta, J. Mertsola, T. Kallonen, and Q. He, “Differences in avidity of IgG antibodies to pertussis toxin after acellular pertussis booster vaccination and natural infection,” Vaccine, vol. 30, no. 48, pp. 6897–6902, 2012.
[7]
F. D. Batista and M. S. Neuberger, “Affinity dependence of the B cell response to antigen: a threshold, a ceiling, and the importance of off-rate,” Immunity, vol. 8, no. 6, pp. 751–759, 1998.
[8]
V. Kouskoff, S. Famiglietti, G. Lacaud et al., “Antigens varying in affinity for the B cell receptor induce differential B lymphocyte responses,” Journal of Experimental Medicine, vol. 188, no. 8, pp. 1453–1464, 1998.
[9]
F. D. Batista and M. S. Neuberger, “B cells extract and present immobilized antigen: Implications for affinity discrimination,” EMBO Journal, vol. 19, no. 4, pp. 513–520, 2000.
[10]
A. M. Kalergis, N. Boucheron, M. A. Doucey et al., “Efficient T cell activation requires an optimal dwell-time of interaction between the TCR and the pMHC complex,” Nature Immunology, vol. 2, no. 3, pp. 229–234, 2001.
[11]
D. Coombs, A. M. Kalergis, S. G. Nathenson, C. Wofsy, and B. Goldstein, “Activated TCRs remain marked for internalization after dissociation from pMHC,” Nature Immunology, vol. 3, no. 10, pp. 926–931, 2002.
[12]
S. J. Fleire, J. P. Goldman, Y. R. Carrasco, M. Weber, D. Bray, and F. D. Batista, “B cell ligand discrimination through a spreading and contraction response,” Science, vol. 312, no. 5774, pp. 738–741, 2006.
[13]
W. Liu, T. Meckel, P. Tolar, H. W. Sohn, and S. K. Pierce, “Antigen affinity discrimination is an intrinsic function of the B cell receptor,” Journal of Experimental Medicine, vol. 207, no. 5, pp. 1095–1111, 2010.
[14]
J. Ye, E. S. Bromage, and S. L. Kaattari, “The strength of B cell interaction with antigen determines the degree of IgM polymerization,” Journal of Immunology, vol. 184, no. 2, pp. 844–850, 2010.
[15]
P. K. Tsourkas, W. Liu, S. C. Das, S. K. Pierce, and S. Raychaudhuri, “Discrimination of membrane antigen affinity by B cells requires dominance of kinetic proofreading over serial engagement,” Cellular & Molecular Immunology, vol. 9, no. 1, pp. 62–74, 2012.
[16]
P. K. Tsourkas, C. D. Somkanya, P. Yu-Yang, W. Liu, S. K. Pierce, and S. Raychaudhuri, “Formation of BCR oligomers provides a mechanism for B cell affinity discrimination,” Journal of Theoretical Biology, vol. 307, pp. 174–182, 2012.
[17]
G. I. Bell, “Cell-cell adhesion in the immune system,” Immunology Today, vol. 4, no. 8, pp. 237–240, 1983.
[18]
B. Goldstein, J. R. Faeder, and W. S. Hlavacek, “Mathematical and computational models of immune-receptor signalling,” Nature Reviews Immunology, vol. 4, no. 6, pp. 445–456, 2004.
[19]
T. A. Y. Shih, E. Meffre, M. Roederer, and M. C. Nussenzweig, “Role of BCR affinity in T cell-dependent antibody responses in vivo,” Nature Immunology, vol. 3, no. 6, pp. 570–575, 2002.
[20]
T. A. Y. Shih, M. Roederer, and M. C. Nussenzweig, “Role of antigen receptor affinity in T cell-independent antibody responses in vivo,” Nature Immunology, vol. 3, no. 4, pp. 399–406, 2002.
[21]
J. Ye, I. M. Kaattari, and S. L. Kaattari, “The differential dynamics of antibody subpopulation expression during affinity maturation in a teleost,” Fish and Shellfish Immunology, vol. 30, no. 1, pp. 372–377, 2011.
[22]
P. K. A. Mongini, C. A. Blessinger, and J. P. Dalton, “Affinity requirements for induction of sequential phases of human B cell activation by membrane IgM-cross-linking ligands,” Journal of Immunology, vol. 146, no. 6, pp. 1791–1800, 1991.
[23]
B. P. O'Connor, L. A. Vogel, W. Zhang, et al., “Imprinting the fate of antigen-reactive B cells through the affinity of the B cell receptor,” The Journal of Immunology, vol. 177, no. 11, pp. 7723–7732, 2006.
[24]
M. J. Benson, L. D. Erickson, M. W. Gleeson, and R. J. Noelle, “Affinity of antigen encounter and other early B-cell signals determine B-cell fate,” Current Opinion in Immunology, vol. 19, no. 3, pp. 275–280, 2007.
[25]
B. M. Kessler, P. Bassanini, J. C. Cerottini, and I. F. Luescher, “Effects of epitope modification on T cell receptor-ligand binding and antigen recognition by seven H-2K(d)-restricted cytotoxic T lymphocyte clones specific for a photoreactive peptide derivative,” Journal of Experimental Medicine, vol. 185, no. 4, pp. 629–640, 1997.
[26]
J. Ye, E. Bromage, I. Kaattari, and S. Kaattari, “Transduction of binding affinity by B lymphocytes: a new dimension in immunological regulation,” Developmental and Comparative Immunology, vol. 35, no. 9, pp. 982–990, 2011.
[27]
G. D. Victora and M. C. Nussenzweig, “Germinal centers,” Annual Review of Immunology, vol. 30, pp. 429–457, 2012.
[28]
D. A. Lauffenburger and J. J. Linderman, Receptors: Models for Binding, Trafficking, and Signaling, Oxford University Press, New York, NY, USA, 1996.
[29]
S. Raychaudhuri, P. K. Tsourkas, and E. Willgohs, “Computational modeling of receptor ligand binding and cellular signaling processes,” in Fundamental Concepts in Biophysics, T. Jue, Ed., Humana Press, New York, NY, USA, 2009.
[30]
S. Raychaudhuri, “Kinetic Monte Carlo simulation in biophysics and systems biology,” in Theory and Applications of Monte Carlo Simulations, W. K. V. Chan, Ed., InTech Open Access Publishing, 2013.
[31]
T. W. McKeithan, “Kinetic proofreading in T-cell receptor signal transduction,” Proceedings of the National Academy of Sciences of the United States of America, vol. 92, no. 11, pp. 5042–5046, 1995.
[32]
S. Valitutti, S. Muller, M. Cella, E. Padovan, and A. Lanzavecchia, “Serial triggering of many T-cell receptors by a few peptide-MHC complexes,” Nature, vol. 375, no. 6527, pp. 148–151, 1995.
[33]
S. Valitutti and A. Lanzavecchia, “Serial triggering of TCRs: a basis for the sensitivity and specificity of antigen recognition,” Immunology Today, vol. 18, no. 6, pp. 299–304, 1997.
[34]
E. San José, A. Borroto, F. Niedergang, A. Alcover, and B. Alarcón, “Triggering the TCR complex causes the downregulation of nonengaged receptors by a signal transduction-dependent mechanism,” Immunity, vol. 12, no. 2, pp. 161–170, 2000.
[35]
C. Wofsy, D. Coombs, and B. Goldstein, “Calculations show substantial serial engagement of T cell receptors,” Biophysical Journal, vol. 80, no. 2, pp. 606–612, 2001.
[36]
M. Krogsgaard, Q. J. Li, C. Sumen, J. B. Huppa, M. Huse, and M. M. Davis, “Agonist/endogenous peptide-MHC heterodimers drive T cell activation and sensitivity,” Nature, vol. 434, no. 7030, pp. 238–243, 2005.
[37]
P. P. Yachi, J. Ampudia, N. R. J. Gascoigne, and T. Zal, “Nonstimulatory peptides contribute to antigen-induced CD8-T cell receptor interaction at the immunological synapse,” Nature Immunology, vol. 6, no. 8, pp. 785–792, 2005.
[38]
N. Anikeeva, D. Gakamsky, J. Scholler, and Y. Sykulev, “Evidence that the density of self peptide-MHC ligands regulates T-cell receptor signaling,” PLoS One, vol. 7, no. 8, Article ID e41466, 2012.
[39]
S. Tian, R. Maile, E. J. Collins, and J. A. Frelinger, “CD8+ T cell activation is governed by TCR-peptide/MHC affinity, not dissociation rate,” Journal of Immunology, vol. 179, no. 5, pp. 2952–2960, 2007.
[40]
J. D. Stone, A. S. Chervin, and D. M. Kranz, “T-cell receptor binding affinities and kinetics: impact on T-cell activity and specificity,” Immunology, vol. 126, no. 2, pp. 165–176, 2009.
[41]
O. Dushek, R. Das, and D. Coombs, “A role for rebinding in rapid and reliable T cell responses to antigen,” PLoS Computational Biology, vol. 5, no. 11, Article ID e1000578, 2009.
[42]
M. Aleksic, O. Dushek, H. Zhang et al., “Dependence of T cell antigen recognition on T cell receptor-peptide MHC confinement time,” Immunity, vol. 32, no. 2, pp. 163–174, 2010.
[43]
W. W. A. Schamel and M. Reth, “Monomeric and oligomeric complexes of the B cell antigen receptor,” Immunity, vol. 13, no. 1, pp. 5–14, 2000.
[44]
J. M. Dal Porto, S. B. Gauld, K. T. Merrell, D. Mills, A. E. Pugh-Bernard, and J. Cambier, “B cell antigen receptor signaling 101,” Molecular Immunology, vol. 41, no. 6-7, pp. 599–613, 2004.
[45]
C. Ulivieri and C. T. Baldari, “The BCR signalosome: where cell fate is decided,” Journal of Biological Regulators and Homeostatic Agents, vol. 19, no. 1-2, pp. 1–16, 2005.
[46]
P. Hou, E. Araujo, T. Zhao et al., “B cell antigen receptor signaling and internalization are mutually exclusive events,” PLoS Biology, vol. 4, no. 7, p. e200, 2006.
[47]
R. L. Geahlen, “Syk and pTyr'd: signaling through the B cell antigen receptor,” Biochimica et Biophysica Acta, vol. 1793, no. 7, pp. 1115–1127, 2009.
[48]
P. Tolar, H. W. Sohn, and S. K. Pierce, “Viewing the antigen-induced initiation of B-cell activation in living cells,” Immunological Reviews, vol. 221, no. 1, pp. 64–76, 2008.
[49]
S. K. Pierce and W. Liu, “The tipping points in the initiation of B cell signalling: how small changes make big differences,” Nature Reviews Immunology, vol. 10, no. 11, pp. 767–777, 2010.
[50]
N. E. Harwood and F. D. Batista, “Early events in B cell activation,” Annual Review of Immunology, vol. 28, pp. 185–210, 2010.
[51]
P. M. Waterman and J. C. Cambier, “The conundrum of inhibitory signaling by ITAM-containing immunoreceptors: potential molecular mechanisms,” FEBS Letters, vol. 584, no. 24, pp. 4878–4882, 2010.
[52]
M. Weber, B. Treanor, D. Depoil, et al., “Phospholipase C-γ2 and Vav cooperate within signaling microclusters to propagate B cell spreading in response to membrane-bound antigen,” Journal of Experimental Medicine, vol. 205, no. 4, pp. 853–868, 2008.
[53]
D. Depoil, S. Fleire, B. L. Treanor et al., “CD19 is essential for B cell activation by promoting B cell receptor-antigen microcluster formation in response to membrane-bound ligand,” Nature Immunology, vol. 9, no. 1, pp. 63–72, 2008.
[54]
B. Treanor, D. Depoil, A. Bruckbauer, and F. D. Batista, “Dynamic cortical actin remodeling by ERM proteins controls BCR microcluster organization and integrity,” Journal of Experimental Medicine, vol. 208, no. 5, pp. 1055–1068, 2011.
[55]
P. Tolar, H. W. Sohn, and S. K. Pierce, “The initiation of antigen-induced B cell antigen receptor signaling viewed in living cells by fluorescence resonance energy transfer,” Nature Immunology, vol. 6, no. 11, pp. 1168–1176, 2005.
[56]
H. W. Sohn, P. Tolar, T. Jin, and S. K. Pierce, “Fluorescence resonance energy transfer in living cells reveals dynamic membrane changes in the initiation of B cell signaling,” Proceedings of the National Academy of Sciences of the United States of America, vol. 103, no. 21, pp. 8143–8148, 2006.
[57]
H. W. Sohn, S. K. Pierce, and S. J. Tzeng, “Live cell imaging reveals that the inhibitory FcγRIIB destabilizes B cell receptor membrane-lipid interactions and blocks immune synapse formation,” Journal of Immunology, vol. 180, no. 2, pp. 793–799, 2008.
[58]
P. Tolar, J. Hanna, P. D. Krueger, and S. K. Pierce, “The constant region of the membrane immunoglobulin mediates B cell-receptor clustering and signaling in response to membrane antigens,” Immunity, vol. 30, no. 1, pp. 44–55, 2009.
[59]
S. P. Persaud, D. L. Donermeyer, K. S. Weber, D. M. Kranz, and P. M. Allen, “High-affinity T cell receptor differentiates cognate peptide-MHC and altered peptide ligands with distinct kinetics and thermodynamics,” Molecular Immunology, vol. 47, no. 9, pp. 1793–1801, 2010.
[60]
P. K. Tsourkas, N. Baumgarth, S. I. Simon, and S. Raychaudhuri, “Mechanisms of B-cell synapse formation predicted by Monte Carlo simulation,” Biophysical Journal, vol. 92, no. 12, pp. 4196–4208, 2007.
[61]
P. K. Tsourkas, M. L. Longo, and S. Raychaudhuri, “Monte Carlo study of single molecule diffusion can elucidate the mechanism of B cell synapse formation,” Biophysical Journal, vol. 95, no. 3, pp. 1118–1125, 2008.
[62]
A. S. Reddy, S. Chilukuri, and S. Raychaudhuri, “The network of receptors characterize B cell receptor micro- and macroclustering in a monte carlo model,” Journal of Physical Chemistry B, vol. 114, no. 1, pp. 487–494, 2010.
[63]
A. Srinivas Reddy, P. K. Tsourkas, and S. Raychaudhuri, “Monte Carlo study of B-cell receptor clustering mediated by antigen crosslinking and directed transport,” Cellular and Molecular Immunology, vol. 8, no. 3, pp. 255–264, 2011.
[64]
P. K. Tsourkas and S. Raychaudhuri, “Modeling of B cell synapse formation by monte carlo simulation shows that directed transport of receptor molecules is a potential formation mechanism,” Cellular and Molecular Bioengineering, vol. 3, no. 3, pp. 256–268, 2010.
[65]
P. K. Tsourkas and S. Raychaudhuri, “Monte carlo investigation of diffusion of receptors and ligands that bind across opposing surfaces,” Annals of Biomedical Engineering, vol. 39, no. 1, pp. 427–442, 2011.
[66]
K. Simons and R. Ehehalt, “Cholesterol, lipid rafts, and disease,” Journal of Clinical Investigation, vol. 110, no. 5, pp. 597–603, 2002.
[67]
K. Simons and D. Toomre, “Lipid rafts and signal transduction,” Nature Reviews Molecular Cell Biology, vol. 1, no. 1, pp. 31–39, 2000.
[68]
M. Triantafilou, K. Miyake, D. T. Golenbock, and K. Triantafilou, “Mediators of innate immune recognition of bacteria concentrate in lipid rafts and facilitate lipopolysaccharide-induced cell activation,” Journal of Cell Science, vol. 115, part 12, pp. 2603–2611, 2002.
[69]
V. Michel and M. Bakovic, “Lipid rafts in health and disease,” Biology of the Cell, vol. 99, no. 3, pp. 129–140, 2007.
[70]
R. Lindner and R. Knorr, “Rafting trips into the cell,” Communitative and Integrative Biology, vol. 2, no. 5, pp. 420–421, 2009.
[71]
S. Manes, G. del Real, and A. C. Martinez, “Pathogens: raft hijackers,” Nature Reviews Immunology, vol. 3, no. 7, pp. 557–568, 2003.
[72]
P. C. Cheng, M. L. Dykstra, R. N. Mitchell, and S. K. Pierce, “A role for lipid rafts in B cell antigen receptor signaling and antigen targeting,” Journal of Experimental Medicine, vol. 190, no. 11, pp. 1549–1560, 1999.
[73]
M. J. Aman and K. S. Ravichandran, “A requirement for lipid rafts in B cell receptor induced Ca2+x flux,” Current Biology, vol. 10, no. 7, pp. 393–396, 2000.
[74]
M. Dykstra, A. Cherukuri, H. W. Sohn, S. J. Tzeng, and S. K. Pierce, “Location is everything: lipid rafts and immune cell signaling,” Annual Review of Immunology, vol. 21, pp. 457–481, 2003.
[75]
S. K. Pierce, “Lipid rafts and B-cell activation,” Nature Reviews Immunology, vol. 2, no. 2, pp. 96–105, 2002.
[76]
R. Xavier, T. Brennan, Q. Li, C. McCormack, and B. Seed, “Membrane compartmentation is required for efficient T cell activation,” Immunity, vol. 8, no. 6, pp. 723–732, 1998.
[77]
K. A. Field, D. Holowka, and B. Baird, “Compartmentalized activation of the high affinity immunoglobulin E receptor within membrane domains,” Journal of Biological Chemistry, vol. 272, no. 7, pp. 4276–4280, 1997.
[78]
K. A. Field, D. Holowka, and B. Baird, “Structural aspects of the association of FcεRI with detergent-resistant membranes,” Journal of Biological Chemistry, vol. 274, no. 3, pp. 1753–1758, 1999.
[79]
A. Viola and N. Gupta, “Tether and trap: regulation of membrane-raft dynamics by actin-binding proteins,” Nature Reviews Immunology, vol. 7, no. 11, pp. 889–896, 2007.
[80]
H. W. Sohn, P. Tolar, and S. K. Pierce, “Membrane heterogeneities in the formation of B cell receptor-Lyn kinase microclusters and the immune synapse,” Journal of Cell Biology, vol. 182, no. 2, pp. 367–379, 2008.
[81]
N. Gupta and A. L. DeFranco, “Visualizing lipid raft dynamics and early signaling events during antigen receptor-mediated B-lymphocyte activation,” Molecular Biology of the Cell, vol. 14, no. 2, pp. 432–444, 2003.
[82]
N. Gupta, B. Wollscheid, J. D. Watts, B. Scheer, R. Aebersold, and A. L. DeFranco, “Quantitative proteomic analysis of B cell lipid rafts reveals that ezrin regulates antigen receptor-mediated lipid raft dynamics,” Nature Immunology, vol. 7, no. 6, pp. 625–633, 2006.
[83]
C. Klammt and B. F. Lillemeier, “How membrane structures control T cell signaling,” Frontiers in Immunology, vol. 3, p. 291, 2012.
[84]
W. W. Schamel and B. Alarcon, “Organization of the resting TCR in nanoscale oligomers,” Immunological Reviews, vol. 251, no. 1, pp. 13–20, 2013.
[85]
V. Horejsí, “Lipid rafts and their roles in T-cell activation,” Microbes and Infection, vol. 7, no. 2, pp. 310–316, 2005.
[86]
D. Filipp, O. Ballek, and J. Manning, “Lck, membrane microdomains, and TCR triggering machinery: defining the new rules of engagement,” Frontiers in Immunology, vol. 3, p. 155, 2012.
[87]
D. A. Zacharias, J. D. Violin, A. C. Newton, and R. Y. Tsien, “Partitioning of lipid-modified monomeric GFPs into membrane microdomains of live cells,” Science, vol. 296, no. 5569, pp. 913–916, 2002.
[88]
R. Varma and S. Mayor, “GPI-anchored proteins are organized in submicron domains at the cell surface,” Nature, vol. 394, no. 6695, pp. 798–801, 1998.
[89]
P. Sharma, R. Varma, R. C. Sarasij et al., “Nanoscale organization of multiple GPI-anchored proteins in living cell membranes,” Cell, vol. 116, no. 4, pp. 577–589, 2004.
[90]
D. E. Shvartsman, M. Kotler, R. D. Tall, M. G. Roth, and Y. I. Henis, “Differently anchored influenza hemagglutinin mutants display distinct interaction dynamics with mutual rafts,” Journal of Cell Biology, vol. 163, no. 4, pp. 879–888, 2003.
[91]
A. Pralle, P. Keller, E. L. Florin, K. Simons, and J. K. H. H？rber, “Sphingolipid-cholesterol rafts diffuse as small entities in the plasma membrane of mammalian cells,” Journal of Cell Biology, vol. 148, no. 5, pp. 997–1008, 2000.
[92]
W. K. Subczynski and A. Kusumi, “Dynamics of raft molecules in the cell and artificial membranes: approaches by pulse EPR spin labeling and single molecule optical microscopy,” Biochimica et Biophysica Acta, vol. 1610, no. 2, pp. 231–243, 2003.
[93]
K. Gaus, E. Gratton, E. P. W. Kable et al., “Visualizing lipid structure and raft domains in living cells with two-photon microscopy,” Proceedings of the National Academy of Sciences of the United States of America, vol. 100, no. 26, pp. 15554–15559, 2003.
[94]
D. M. Owen, D. Williamson, A. Magenau, and K. Gaus, “Optical techniques for imaging membrane domains in live cells (live-cell palm of protein clustering),” Methods in Enzymology, vol. 504, pp. 221–235, 2012.
[95]
T. M. Razzaq, P. Ozegbe, E. C. Jury, P. Sembi, N. M. Blackwell, and P. S. Kabouridis, “Regulation of T-cell receptor signaling by membrane microdomains,” Immunology, vol. 113, no. 4, pp. 413–426, 2004.
[96]
M. Edidin, “The state of lipid rafts: from model membranes to cells,” Annual Review of Biophysics and Biomolecular Structure, vol. 32, pp. 257–283, 2003.
[97]
J. Liu, S. Qi, J. T. Groves, and A. K. Chakraborty, “Phase segregation on different length scales in a model cell membrane system,” Journal of Physical Chemistry B, vol. 109, no. 42, pp. 19960–19969, 2005.
[98]
G. Nudelman and Y. Louzoun, “Cell surface dynamics: the balance between diffusion, aggregation and endocytosis,” IEE Proceedings Systems Biology, vol. 153, no. 1, pp. 34–42, 2006.
[99]
G. Nudelman, M. Weigert, and Y. Louzoun, “In-silico cell surface modeling reveals mechanism for initial steps of B-cell receptor signal transduction,” Molecular Immunology, vol. 46, no. 15, pp. 3141–3150, 2009.
[100]
F. G. Karnell, R. J. Brezski, L. B. King, M. A. Silverman, and J. G. Monroe, “Membrane cholesterol content accounts for developmental differences in surface B cell receptor compartmentalization and signaling,” Journal of Biological Chemistry, vol. 280, no. 27, pp. 25621–25628, 2005.
[101]
M. E. J. Newman and G. T. Barkema, Monte Carlo Methods in Statistical Physics, Oxford University Press, New York, NY, USA, 1999.
[102]
P. P. Yu-Yang, “Development of a Monte Carlo simulation of early events in B cell activation,” in Biomedical Engineering, University of California, Davis, Calif, USA, 2012.
[103]
F. Flores-Borja, P. S. Kabouridis, E. C. Jury, D. A. Isenberg, and R. A. Mageed, “Altered lipid raft-associated proximal signaling and translocation of CD45 tyrosine phosphatase in B lymphocytes from patients with systemic lupus erythematosus,” Arthritis and Rheumatism, vol. 56, no. 1, pp. 291–302, 2007.
[104]
V. R. Moulton and G. C. Tsokos, “Abnormalities of T cell signaling in systemic lupus erythematosus,” Arthritis Research & Therapy, vol. 13, no. 2, p. 207, 2011.
[105]
M. Reth, “Oligomeric antigen receptors: a new view on signaling for the selection of lymphocytes,” Trends in Immunology, vol. 22, no. 7, pp. 356–360, 2001.
[106]
J. Yang and M. Reth, “Oligomeric organization of the B-cell antigen receptor on resting cells,” Nature, vol. 467, no. 7314, pp. 465–469, 2010.
[107]
A. Yethiraj and J. C. Weisshaar, “Why are lipid rafts not observed in vivo?” Biophysical Journal, vol. 93, no. 9, pp. 3113–3119, 2007.
[108]
S. L. Veatch and S. L. Keller, “Miscibility phase diagrams of giant vesicles containing sphingomyelin,” Physical Review Letters, vol. 94, no. 14, Article ID 148101, 2005.
[109]
A. Jansson, “Kinetic proofreading and the search for nonself-peptides,” Self/Nonself, vol. 2, no. 1, pp. 1–3, 2011.
[110]
J. Rossy, D. J. Williamson, C. Benzing, and K. Gaus, “The integration of signaling and the spatial organization of the T cell synapse,” Frontiers in Immunology, vol. 3, p. 352, 2012.
[111]
J. R. James, J. McColl, M. I. Oliveira, P. D. Dunne, E. Huang, A. Jansson, et al., “The T cell receptor triggering apparatus is composed of monovalent or monomeric proteins,” The Journal of Biological Chemistry, vol. 286, no. 37, pp. 31993–32001, 2011.
[112]
R. N. Germain, “Computational analysis of T cell receptor signaling and ligand discrimination—past, present, and future,” FEBS Letters, vol. 584, no. 24, pp. 4814–4822, 2010.
[113]
T. Mamo and G. A. Poland, “Nanovaccinology: the next generation of vaccines meets 21st century materials science and engineering,” Vaccine, vol. 30, no. 47, pp. 6609–6611, 2012.
[114]
S. Y. Qi, J. T. Groves, and A. K. Chakraborty, “Synaptic pattern formation during cellular recognition,” Proceedings of the National Academy of Sciences of the United States of America, vol. 98, no. 12, pp. 6548–6553, 2001.
[115]
N. J. Burroughs and C. Wülfing, “Differential segregation in a cell-cell contact interface: the dynamics of the immunological synapse,” Biophysical Journal, vol. 83, no. 4, pp. 1784–1796, 2002.
[116]
S. Raychaudhuri, A. K. Chakraborty, and M. Kardar, “Effective membrane model of the immunological synapse,” Physical Review Letters, vol. 91, no. 20, Article ID 208101, 4 pages, 2003.
[117]
T. R. Weikl and R. Lipowsky, “Pattern formation during T-cell adhesion,” Biophysical Journal, vol. 87, no. 6, pp. 3665–3678, 2004.
[118]
D. Coombs, M. Dembo, C. Wofsy, and B. Goldstein, “Equilibrium thermodynamics of cell-cell adhesion mediated by multiple ligand-receptor Pairs,” Biophysical Journal, vol. 86, no. 3, pp. 1408–1423, 2004.
[119]
K. I. Lim and J. Yin, “Localization of receptors in lipid rafts can inhibit signal transduction,” Biotechnology and Bioengineering, vol. 90, no. 6, pp. 694–702, 2005.
[120]
K. H. Lee, A. R. Dinner, C. Tu et al., “The immunological synapse balances T cell receptor signaling and degradation,” Science, vol. 302, no. 5648, pp. 1218–1222, 2003.
[121]
C. R. F. Monks, B. A. Freiberg, H. Kupfer, N. Sciaky, and A. Kupfer, “Three-dimensional segregation of supramolecular activation clusters in T cells,” Nature, vol. 395, no. 6697, pp. 82–86, 1998.
[122]
A. Grakoui, S. K. Bromley, C. Sumen et al., “The immunological synapse: a molecular machine controlling T cell activation,” Science, vol. 285, no. 5425, pp. 221–227, 1999.
[123]
F. D. Batista, D. Iber, and M. S. Neuberger, “B cells acquire antigen from target cells after synapse formation,” Nature, vol. 411, no. 6836, pp. 489–494, 2001.
[124]
Y. R. Carrasco, S. J. Fleire, T. Cameron, M. L. Dustin, and F. D. Batista, “LFA-1/ICAM-1 interaction lowers the threshold of B cell activation by facilitating B cell adhesion and synapse formation,” Immunity, vol. 20, no. 5, pp. 589–599, 2004.
[125]
S. ？emerski, J. Das, E. Giurisato et al., “The balance between T cell receptor signaling and degradation at the center of the immunological synapse is determined by antigen quality,” Immunity, vol. 29, no. 3, pp. 414–422, 2008.
[126]
D. H. Busch and E. G. Pamer, “T cell affinity maturation by selective expansion during infection,” Journal of Experimental Medicine, vol. 189, no. 4, pp. 701–709, 1999.
[127]
P. A. Savage, J. J. Boniface, and M. M. Davis, “A kinetic basis for T cell receptor repertoire selection during an immune response,” Immunity, vol. 10, no. 4, pp. 485–492, 1999.
[128]
A. Amranl, J. Verdaguer, P. Serra, S. Tafuro, R. Tan, and P. Santamaria, “Progression of autoimmune diabetes driven by avidity maturation of a T- cell population,” Nature, vol. 406, no. 6797, pp. 739–742, 2000.
[129]
M. K. Slifka and J. L. Whitton, “Functional avidity maturation of CD8+ T cells without selection of higher affinity TCR,” Nature Immunology, vol. 2, no. 8, pp. 711–717, 2001.
[130]
A. S. Perelson, M. Mirmirani, and G. F. Oster, “Optimal strategies in immunology. I. B cell differentiation and proliferation,” Journal of Mathematical Biology, vol. 3, no. 3-4, pp. 325–367, 1976.
[131]
A. S. Perelson, M. Mirmirani, and G. F. Oster, “Optimal strategies in immunology. II. B memory cell production,” Journal of Mathematical Biology, vol. 5, no. 3, pp. 213–256, 1978.
[132]
A. S. Perelson and G. F. Oster, “Theoretical studies of clonal selection: minimal antibody repertoire size and reliability of self-non-self discrimination,” Journal of Theoretical Biology, vol. 81, no. 4, pp. 645–670, 1979.
[133]
Z. Agur, G. Mazor, and I. Meilijson, “Maturation of the humoral immune response as an optimization problem,” Proceedings of the Royal Society, vol. 245, no. 1313, pp. 147–150, 1991.
[134]
T. B. Kepler and A. S. Perelson, “Somatic hypermutation in B cells: an optimal control treatment,” Journal of Theoretical Biology, vol. 164, no. 1, pp. 37–64, 1993.
[135]
H. Qi, J. G. Egen, A. Y. C. Huang, and R. N. Germain, “Extrafollicular activation of lymph node B cells by antigen-bearing dendritic cells,” Science, vol. 312, no. 5780, pp. 1672–1676, 2006.
[136]
C. D. C. Allen, T. Okada, H. L. Tang, and J. G. Cyster, “Imaging of germinal center selection events during affinity maturation,” Science, vol. 315, no. 5811, pp. 528–531, 2007.
[137]
Y. R. Carrasco and F. D. Batista, “B cells acquire particulate antigen ina macrophage-rich area at the boundary between the follicle andthe subcapsular sinus of the lymph node,” Immunity, vol. 27, no. 1, pp. 160–171, 2007.
[138]
T. Junt, E. A. Moseman, M. Iannacone et al., “Subcapsular sinus macrophages in lymph nodes clear lymph-borne viruses and present them to antiviral B cells,” Nature, vol. 450, no. 7166, pp. 110–114, 2007.
[139]
T. G. Phan, I. Grigorova, T. Okada, and J. G. Cyster, “Subcapsular encounter and complement-dependent transport of immune complexes by lymph node B cells,” Nature Immunology, vol. 8, no. 9, pp. 992–1000, 2007.
[140]
F. D. Batista and N. E. Harwood, “The who, how and where of antigen presentation to B cells,” Nature Reviews Immunology, vol. 9, no. 1, pp. 15–27, 2009.
[141]
M. Meyer-Hermann, M. T. Figge, and K. M. Toellner, “Germinal centres seen through the mathematical eye: B-cell models on the catwalk,” Trends in Immunology, vol. 30, no. 4, pp. 157–164, 2009.
[142]
H. P. Mirsky, M. J. Miller, J. J. Linderman, and D. E. Kirschner, “Systems biology approaches for understanding cellular mechanisms of immunity in lymph nodes during infection,” Journal of Theoretical Biology, vol. 287, pp. 160–170, 2011.
[143]
R. M. Vroomans, A. F. Maree, R. J. de Boer, and J. B. Beltman, “Chemotactic migration of T cells towards dendritic cells promotes the detection of rare antigens,” PLOS Computational Biology, vol. 8, no. 11, Article ID e1002763, 2012.
[144]
M. T. Figge, A. Garin, M. Gunzer, M. Kosco-Vilbois, K. M. Toellner, and M. Meyer-Hermann, “Deriving a germinal center lymphocyte migration model from two-photon data,” Journal of Experimental Medicine, vol. 205, no. 13, pp. 3019–3029, 2008.
[145]
Y. Takahashi, D. M. Cerasoli, J. M. Dal Porto et al., “Relaxed negative selection in germinal centers and impaired affinity maturation in bcl-x(L) transgenic mice,” Journal of Experimental Medicine, vol. 190, no. 3, pp. 399–409, 1999.
[146]
S. Raychaudhuri, E. Willgohs, T. N. Nguyen, E. M. Khan, and T. Goldkorn, “Monte Carlo simulation of cell death signaling predicts large cell-to-cell stochastic fluctuations through the type 2 pathway of apoptosis,” Biophysical Journal, vol. 95, no. 8, pp. 3559–3562, 2008.
[147]
J. G. Albeck, J. M. Burke, S. L. Spencer, D. A. Lauffenburger, and P. K. Sorger, “Modeling a snap-action, variable-delay switch controlling extrinsic cell death,” PLoS Biology, vol. 6, no. 12, article e299, pp. 2831–2852, 2008.
[148]
H. Düssmann, M. Rehm, C. G. Concannon et al., “Single-cell quantification of Bax activation and mathematical modelling suggest pore formation on minimal mitochondrial Bax accumulation,” Cell Death and Differentiation, vol. 17, no. 2, pp. 278–290, 2010.
[149]
J. Skommer, T. Brittain, and S. Raychaudhuri, “Bcl-2 inhibits apoptosis by increasing the time-to-death and intrinsic cell-to-cell variations in the mitochondrial pathway of cell death,” Apoptosis, vol. 15, no. 10, pp. 1223–1233, 2010.
[150]
J. Skommer, S. C. Das, A. Nair, T. Brittain, and S. Raychaudhuri, “Nonlinear regulation of commitment to apoptosis by simultaneous inhibition of Bcl-2 and XIAP in leukemia and lymphoma cells,” Apoptosis, vol. 16, no. 6, pp. 619–626, 2011.
[151]
S. Raychaudhuri, “How can we kill cancer cells: insights from the computational models of apoptosis,” World Journal of Clinical Oncology, vol. 1, no. 1, pp. 24–28, 2010.
[152]
P. S. Kabouridis and E. C. Jury, “Lipid rafts and T-lymphocyte function: implications for autoimmunity,” FEBS Letters, vol. 582, no. 27, pp. 3711–3718, 2008.
[153]
J. Surls, C. Nazarov-Stoica, M. Kehl, C. Olsen, S. Casares, and T. D. Brumeanu, “Increased membrane cholesterol in lymphocytes diverts T-cells toward an inflammatory response,” PLoS One, vol. 7, no. 6, Article ID e38733, 2012.
[154]
A. K. Dey and I. K. Srivastava, “Novel adjuvants and delivery systems for enhancing immune responses induced by immunogens,” Expert Review of Vaccines, vol. 10, no. 2, pp. 227–251, 2011.
