Bulletin of Mathematical Biology

, Volume 72, Issue 3, pp 611–644 | Cite as

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

Original Article


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.


Delay differential equations Age-structured equations Adaptive regulatory T cells T cell response 


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Copyright information

© Society for Mathematical Biology 2009

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of UtahSalt Lake CityUSA
  2. 2.Division of Hematology, Department of MedicineStanford UniversityStanfordUSA
  3. 3.Department of Mathematics and Center for Scientific Computation and Mathematical Modeling (CSCAMM)University of MarylandCollege ParkUSA

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