Skip to main content
SpringerLink
Log in

Emergent Group Dynamics Governed by Regulatory Cells Produce a Robust Primary T Cell Response

  • Original Article
  • Published:
Bulletin of Mathematical Biology Aims and scope Submit manuscript

Abstract

The currently accepted paradigm for the primary T cell response is that effector T cells commit to autonomous developmental programs. This concept is based on several experiments that have demonstrated that the dynamics of a T cell response is largely determined shortly after antigen exposure and that T cell dynamics do not depend on the level and duration of antigen stimulation. Another experimental study has also shown that T cell responses are robust to variations in antigen-specific precursor frequency.

Various mathematical models have corroborated the first result that programmed T cell responses are insensitive to the level of antigen stimulation. However, this paper proposes that programmed responses do not entirely explain the robustness of T cell dynamics to variations in precursor frequency. This work studies the hypothesis that the dynamics of a T cell response may also be governed by a feedback loop involving adaptive regulatory cells rather than by intrinsic developmental programs.

We formulate two mathematical models based on T cell developmental programs. In one model, effector cells undergo a fixed number of divisions before dying. In the second model, effector cells live for a fixed time during which they may divide. The study of these models suggests that developmental programs are not sufficiently robust as they produce an immune response that directly scales with precursor frequencies. Consequently, we derive a third model based on the principle that adaptive regulatory T cells develop in the course of an immune response and suppress effector cells. Our simulations show that this feedback mechanism responds robustly over a range of at least four orders of magnitude of precursor frequencies.

We conclude that the proliferation program paradigm does not entirely capture the observed robustness of T cell responses to variations in precursor frequency. We propose an alternative mechanism by which the primary T cell response is governed by an emergent group dynamic and not by individual T cell programs.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Allan, M.J., Callard, R., Stark, J., Yates, A., 2004. Comparing antigen-independent mechanisms of T cell regulation. J. Theor. Biol. 228(1), 81–95.

    Article  MathSciNet  Google Scholar 

  • Antia, R., Bergstrom, C.T., Pilyugin, S.S., Kaech, S.M., Ahmed, R., 2003. Models of CD8+ responses: 1. What is the antigen-independent proliferation program. J. Theor. Biol. 221(4), 585–598.

    Article  MathSciNet  Google Scholar 

  • Badovinac, V.P., Haring, J.S., Harty, J.T., 2007. Initial T cell receptor transgenic cell precursor frequency dictates critical aspects of the CD8(+) T cell response to infection. Immunity 26(6), 827–841.

    Article  Google Scholar 

  • Belz, G.T., Zhang, L., Lay, M.D., Kupresanin, F., Davenport, M.P., 2007. Killer T cells regulate antigen presentation for early expansion of memory, but not naïve, CD8+ T cell. Proc. Natl. Acad. Sci. USA 104(15), 6341–6346.

    Article  Google Scholar 

  • Blattman, J.N., Antia, R., Sourdive, D.J., Wang, X., Kaech, S.M., Murali-Krishna, K., Altman, J.D., Ahmed, R., 2002. Estimating the precursor frequency of naive antigen-specific cd8 t cells. J. Exp. Med. 195(5), 657–664.

    Article  Google Scholar 

  • Burroughs, N.J., de Oliveira, B.M.P.M., Pinto, A.A., 2006. Regulatory T cell adjustment of quorum growth thresholds and the control of local immune responses. J. Theor. Biol. 241(1), 134–141.

    Article  Google Scholar 

  • Cantor, H., Shen, F.W., Boyse, E.A., 1976. Separation of helper T cells from suppressor T cells expressing different Ly components. II. Activation by antigen: after immunization, antigen-specific suppressor and helper activities are mediated by distinct T-cell subclasses. J. Exp. Med. 143, 1391–1340.

    Article  Google Scholar 

  • Carneiro, J., Paixão, T., Milutinovic, D., Sousa, J., Leon, K., Gardner, R., Faro, J., 2005. Immunological self-tolerance: Lessons from mathematical modeling. J. Comput. Appl. Math. 184(1), 77–100.

    Article  MathSciNet  MATH  Google Scholar 

  • Catron, D.M., Itano, A.A., Pape, K.A., Mueller, D.L., Jenkins, M.K., 2004. Visualizing the first 50 hr of the primary immune response to a soluble antigen. Immunity 21(3), 341–347.

    Article  Google Scholar 

  • Chang, C.C., Ciubotariu, R., Manavalan, J.S., Yuan, J., Colovai, A.I., Piazza, F., Lederman, S., Colonna, M., Cortesini, R., Dalla-Favera, R., Suciu-Foca, N., 2002. Tolerization of dendritic cells by T(S) cells: the crucial role of inhibitory receptors ILT3 and ILT4. Nat. Immunol. 3(3), 237–243.

    Article  Google Scholar 

  • De Boer, R.J., Oprea, M., Antia, R., Murali-Krishna, K., Ahmed, R., Perelson, A.S., 2001. Recruitment times, proliferation, and apoptosis rates during the CD8(+) T-cell response to lymphocytic choriomeningitis virus. J. Virol. 75(22), 10663–10669.

    Article  Google Scholar 

  • De Boer, R.J., Homann, D., Perelson, A.S., 2003. Different dynamics of CD4+ and CD8+ T cell responses during and after acute lymphocytic choriomeningitis virus infection. J. Immunol. 171(8), 3928–3935.

    Google Scholar 

  • Effros, R.B., Pawelec, G., 1997. Replicative senescence of T cells: does the Hayflick Limit lead to immune exhaustion? Immunol. Today 18(9), 450–454.

    Article  Google Scholar 

  • Fouchet, D., Regoes, R., 2008. A population dynamics analysis of the interaction between adaptive regulatory t cells and antigen presenting cells. PLoS ONE 3(5), e2306.

    Article  Google Scholar 

  • Haribhai, D., Lin, W., Relland, L.M., Truong, N., Williams, C.B., Chatila, T.A., 2007. Regulatory T cells dynamically control the primary immune response to foreign antigen. J. Immunol. 178(5), 2961–2972.

    Google Scholar 

  • Harris, N.L., Watt, V., Ronchese, F., Le Gros, G., 2002. Differential T cell function and fate in lymph node and nonlymphoid tissues. J. Exp. Med. 195(3), 317–326.

    Article  Google Scholar 

  • Janeway, C.A. Jr., Travers, P., Walport, M., Shlomchik, M.J., 2005. Immunobiology: The Immune System in Health and Disease, 6th edn. Garland, New York.

    Google Scholar 

  • Kaech, S.M., Ahmed, R., 2001. Memory CD8+ T cell differentiation: initial antigen encounter triggers a developmental program in naïve cells. Nat. Immunol. 2(5), 415–422.

    Google Scholar 

  • Kim, P.S., Lee, P.P., Levy, D., 2007. Modeling regulation mechanisms of the immune system. J. Theor. Biol. 246(1), 33–69.

    Article  MathSciNet  Google Scholar 

  • León, K., Peréz, R., Lage, A., Carneiro, J., 2000. Modelling T-cell-mediated suppression dependent on interactions in multicellular conjugates. J. Theor. Biol. 207(2), 231–254.

    Article  Google Scholar 

  • León, K., Peréz, R., Lage, A., Carneiro, J., 2001. Three-cell interactions in T cell-mediated suppression? a mathematical analysis of its quantitative implications. J. Immunol. 166(9), 5356–5365.

    Google Scholar 

  • León, K., Lage, A., Carneiro, J., 2003. Tolerance and immunity in a mathematical model of T-cell mediated suppression. J. Theor. Biol. 225(1), 107–126.

    Article  Google Scholar 

  • León, K., Faro, J., Lage, A., Carneiro, J., 2004. Inverse correlation between the incidences of autoimmune disease and infection predicted by a model of T cell mediated tolerance. J Autoimmunity 22(1), 31–42.

    Article  Google Scholar 

  • León, K., Lage, A., Carneiro, J., 2007a. How regulatory CD25+CD4+ T cells impinge on tumor immunobiology? on the existence of two alternative dynamical classes of tumors. J. Theor. Biol. 247(1), 122–137.

    Article  Google Scholar 

  • León, K., Lage, A., Carneiro, J., 2007b. How regulatory CD25+CD4+ T cells impinge on tumor immunobiology: the differential response of tumors to therapies. J. Immunol. 179(9), 5659–5668.

    Google Scholar 

  • Mercado, R., Vijh, S., Allen, S.E., Kerksiek, K., Pilip, I.M., Pamer, E.G., 2000. Early programming of T cell populations responding to bacterial infection. J. Immunol. 165(12), 6833–6839.

    Google Scholar 

  • Mohri, H., Perelson, A.S., Tung, K., Ribeiro, R.M., Ramratnam, B., Markowitz, M., Kost, R., Hurley, A., Weinberger, L., Cesar, D., Hellerstein, M.K., Ho, D.D., 2001. Increased turnover of T lymphocytes in HIV-1 infection and its reduction by antiretroviral therapy. J. Exp. Med. 194(9), 1277–1287.

    Article  Google Scholar 

  • Razvi, E.S., Jiang, Z., Woda, B.A., Welsh, R.M., 1995. Lymphocyte apoptosis during the silencing of the immune response to acute viral infections in normal, lpr, and Bcl-2-transgenic mice. Am. J. Pathol. 147(1), 79–91.

    Google Scholar 

  • Renno, T., Attinger, A., Locatelli, S., Bakker, T., Vacheron, S., MacDonald, H.R., 1999. Cutting edge: apoptosis of superantigen-activated T cells occurs preferentially after a discrete number of cell divisions in vivo. J. Immunol. 162(11), 6312–6315.

    Google Scholar 

  • Sakaguchi, S., Sakaguchi, N., Asano, M., Itoh, M., Toda, M., 1995. Immunologic self-tolerance maintained by activated T cells expressing IL-2 receptor a-chains (CD25). Breakdown of a single mechanism of self-tolerance causes various autoimmune diseases. J. Immunol. 155(3), 1151–1164.

    Google Scholar 

  • Sakaguchi, S., Yamaguchi, T., Nomura, T., Ono, M., 2008. Regulatory t cells and immune tolerance. Cell 133(5), 775–787.

    Article  Google Scholar 

  • Taams, L.S., Vukmanovic-Stejic, M., Smith, J., Dunne, P.J., Fletcher, J.M., Plunkett, F.J., Ebeling, S.B., Lombardi, G., Rustin, M.H., Bijlsma, J.W., Lafeber, F.P., Salmon, M., Akbar, A.N., 2002. Antigen-specific T cell suppression by human CD4+CD25+ regulatory T cells. Eur. J. Immunol. 32(6), 1621–1630.

    Article  Google Scholar 

  • van Stipdonk, M.J., Lemmens, E.E., Schoenberger, S.P., 2001. Naïve CTLs require a single brief period of antigenic stimulation for clonal expansion and differentiation. Nat. Immunol. 2(5), 423–429.

    Google Scholar 

  • van Stipdonk, M.J., Hardenberg, G., Bijker, M.S., Lemmens, E.E., Droin, N.M., Green, D.R., Schoenberger, S.P., 2003. Dynamic programming of CD8+ T lymphocyte responses. Nat. Immunol. 4(4), 361–365.

    Article  Google Scholar 

  • Veiga-Fernandes, H., Walter, U., Bourgeois, C., McLean, A., Rocha, B., 2000. Response of naïve and memory CD8+ T cells to antigen stimulation in vivo. Nat. Immunol. 1(1), 47–53.

    Article  Google Scholar 

  • Walker, M.R., Kasprowicz, D.J., Gersuk, V.H., Benard, A., Van Landeghen, M., Buckner, J.H., Ziegler, S.F., 2003. Induction of FoxP3 and acquisition of T regulatory activity by stimulated human CD4+CD25- T cells. J. Clin. Invest. 112(9), 1437–1443.

    Google Scholar 

  • Walker, M.R., Carson, B.D., Nepom, G.T., Ziegler, S.F., Buckner, J.H., 2005. De novo generation of antigen-specific CD4+CD25+ regulatory T cells from human CD4+CD25-cells. Proc. Natl. Acad. Sci. USA 102(11), 4103–4108.

    Article  Google Scholar 

  • Wodarz, D., Thomsen, A.R., 2005. Effect of the CTL proliferation program on virus dynamics. Int. Immunol. 17(9), 1269–1276.

    Article  Google Scholar 

  • Yang, Y., Kim, D., Fathman, C.G., 1998. Regulation of programmed cell death following T cell activation in vivo. Int. Immunol. 10(2), 175–183.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Utah, Salt Lake City, UT, 84112-0090, USA

    Peter S. Kim

  2. Division of Hematology, Department of Medicine, Stanford University, Stanford, CA, 94305, USA

    Peter P. Lee

  3. Department of Mathematics and Center for Scientific Computation and Mathematical Modeling (CSCAMM), University of Maryland, College Park, MD, 20742, USA

    Doron Levy

Authors
  1. Peter S. Kim
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Peter P. Lee
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Doron Levy
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Doron Levy.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kim, P.S., Lee, P.P. & Levy, D. Emergent Group Dynamics Governed by Regulatory Cells Produce a Robust Primary T Cell Response. Bull. Math. Biol. 72, 611–644 (2010). https://doi.org/10.1007/s11538-009-9463-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11538-009-9463-1

Keywords

Search

Navigation