Immunological self tolerance: Lessons from mathematical modeling

J. Carneiro, T. Paixao, D. Milutinovic, J. Sousa, K. Leon, R. Gardner, J. Faro, Journal of Computational and Applied Mathematics 184 (2005) 77–100.

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Abstract
One of the fundamental properties of the immune system is its capacity to avoid autoimmune diseases. The mechanism underlying this process, known as self-tolerance, is hitherto unresolved but seems to involve the control of clonal expansion of autoreactive lymphocytes. This article reviews mathematical modeling of self-tolerance, addressing two specific hypotheses. The first hypothesis posits that self-tolerance is mediated by tuning of activation thresholds, which makes autoreactive T lymphocytes reversibly "anergic" and unable to proliferate. The second hypothesis posits that the proliferation of autoreactive T lymphocytes is instead controlled by specific regulatory T lymphocytes. Models representing the population dynamics of autoreactive T lymphocytes according to these two hypotheses were derived. For each model we identified how cell density affects tolerance, and predicted the corresponding phase spaces and bifurcations. We show that the simple induction of proliferative anergy, as modeled here, has a density dependence that is only partially compatible with adoptive transfers of tolerance, and that the models of tolerance mediated by specific regulatory T cells are closer to the observations.
Publishing Year
Date Published
2005-12-01
Journal Title
Journal of Computational and Applied Mathematics
Acknowledgement
The work was financially supported by Fundação para a Ciência e Tecnologia: grants P/BIA/10094/1998, POCTI/36413/99, and POCTI/MGI/46477/2002; and fellowships to JF (Praxis/BCC/18972/98), JS (BD/13546/97), KL (SFRH/BPD+/1157/2002), DM (SFRH/BD/2960/2000) and TP (SFRH/BD/10550/2002).
Volume
184
Issue
1
Page
77 - 100
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Carneiro J, Paixao T, Milutinovic D, et al. Immunological self tolerance: Lessons from mathematical modeling. Journal of Computational and Applied Mathematics. 2005;184(1):77-100. doi:10.1016/j.cam.2004.10.025
Carneiro, J., Paixao, T., Milutinovic, D., Sousa, J., Leon, K., Gardner, R., & Faro, J. (2005). Immunological self tolerance: Lessons from mathematical modeling. Journal of Computational and Applied Mathematics, 184(1), 77–100. https://doi.org/10.1016/j.cam.2004.10.025
Carneiro, Jorge, Tiago Paixao, Dejan Milutinovic, João Sousa, Kalet Leon, Rui Gardner, and Jose Faro. “Immunological Self Tolerance: Lessons from Mathematical Modeling.” Journal of Computational and Applied Mathematics 184, no. 1 (2005): 77–100. https://doi.org/10.1016/j.cam.2004.10.025.
J. Carneiro et al., “Immunological self tolerance: Lessons from mathematical modeling,” Journal of Computational and Applied Mathematics, vol. 184, no. 1, pp. 77–100, 2005.
Carneiro J, Paixao T, Milutinovic D, Sousa J, Leon K, Gardner R, Faro J. 2005. Immunological self tolerance: Lessons from mathematical modeling. Journal of Computational and Applied Mathematics. 184(1), 77–100.
Carneiro, Jorge, et al. “Immunological Self Tolerance: Lessons from Mathematical Modeling.” Journal of Computational and Applied Mathematics, vol. 184, no. 1, Elsevier, 2005, pp. 77–100, doi:10.1016/j.cam.2004.10.025.

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