---
OA_type: free access
_id: '2895'
abstract:
- lang: eng
  text: 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.
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).'
article_processing_charge: No
article_type: original
author:
- first_name: Jorge
  full_name: Carneiro, Jorge
  last_name: Carneiro
- first_name: Tiago
  full_name: Paixao, Tiago
  id: 2C5658E6-F248-11E8-B48F-1D18A9856A87
  last_name: Paixao
  orcid: 0000-0003-2361-3953
- first_name: Dejan
  full_name: Milutinovic, Dejan
  last_name: Milutinovic
- first_name: João
  full_name: Sousa, João
  last_name: Sousa
- first_name: Kalet
  full_name: Leon, Kalet
  last_name: Leon
- first_name: Rui
  full_name: Gardner, Rui
  last_name: Gardner
- first_name: Jose
  full_name: Faro, Jose
  last_name: Faro
citation:
  ama: 'Carneiro J, Paixao T, Milutinovic D, et al. Immunological self tolerance:
    Lessons from mathematical modeling. <i>Journal of Computational and Applied Mathematics</i>.
    2005;184(1):77-100. doi:<a href="https://doi.org/10.1016/j.cam.2004.10.025">10.1016/j.cam.2004.10.025</a>'
  apa: 'Carneiro, J., Paixao, T., Milutinovic, D., Sousa, J., Leon, K., Gardner, R.,
    &#38; Faro, J. (2005). Immunological self tolerance: Lessons from mathematical
    modeling. <i>Journal of Computational and Applied Mathematics</i>. Elsevier. <a
    href="https://doi.org/10.1016/j.cam.2004.10.025">https://doi.org/10.1016/j.cam.2004.10.025</a>'
  chicago: 'Carneiro, Jorge, Tiago Paixao, Dejan Milutinovic, João Sousa, Kalet Leon,
    Rui Gardner, and Jose Faro. “Immunological Self Tolerance: Lessons from Mathematical
    Modeling.” <i>Journal of Computational and Applied Mathematics</i>. Elsevier,
    2005. <a href="https://doi.org/10.1016/j.cam.2004.10.025">https://doi.org/10.1016/j.cam.2004.10.025</a>.'
  ieee: 'J. Carneiro <i>et al.</i>, “Immunological self tolerance: Lessons from mathematical
    modeling,” <i>Journal of Computational and Applied Mathematics</i>, vol. 184,
    no. 1. Elsevier, pp. 77–100, 2005.'
  ista: '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.'
  mla: 'Carneiro, Jorge, et al. “Immunological Self Tolerance: Lessons from Mathematical
    Modeling.” <i>Journal of Computational and Applied Mathematics</i>, vol. 184,
    no. 1, Elsevier, 2005, pp. 77–100, doi:<a href="https://doi.org/10.1016/j.cam.2004.10.025">10.1016/j.cam.2004.10.025</a>.'
  short: J. Carneiro, T. Paixao, D. Milutinovic, J. Sousa, K. Leon, R. Gardner, J.
    Faro, Journal of Computational and Applied Mathematics 184 (2005) 77–100.
das_tickbox: '1'
date_created: 2018-12-11T12:00:12Z
date_published: 2005-12-01T00:00:00Z
date_updated: 2026-07-15T13:16:15Z
day: '01'
doi: 10.1016/j.cam.2004.10.025
extern: '1'
intvolume: '       184'
issue: '1'
language:
- iso: eng
month: '12'
oa_version: None
page: 77 - 100
publication: Journal of Computational and Applied Mathematics
publication_identifier:
  eissn:
  - 1879-1778
  issn:
  - 0377-0427
publication_status: published
publisher: Elsevier
publist_id: '3863'
status: public
title: 'Immunological self tolerance: Lessons from mathematical modeling'
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 184
year: '2005'
...