Bulletin of Mathematical Biology

, Volume 77, Issue 6, pp 1046–1064 | Cite as

A Mathematical Framework for Understanding Four-Dimensional Heterogeneous Differentiation of \(\hbox {CD4}^{+}\) T Cells

  • Tian Hong
  • Cihan Oguz
  • John J. Tyson
Original Article


At least four distinct lineages of \(\hbox {CD4}^{+}\) T cells play diverse roles in the immune system. Both in vivo and in vitro, naïve \(\hbox {CD4}^{+}\) T cells often differentiate into a variety of cellular phenotypes. Previously, we developed a mathematical framework to study heterogeneous differentiation of two lineages governed by a mutual-inhibition motif. To understand heterogeneous differentiation of \(\hbox {CD4}^{+}\) T cells involving more than two lineages, we present here a mathematical framework for the analysis of multiple stable steady states in dynamical systems with multiple state variables interacting through multiple mutual-inhibition loops. A mathematical model for \(\hbox {CD4}^{+}\) T cells based on this framework can reproduce known properties of heterogeneous differentiation involving multiple lineages of this cell differentiation system, such as heterogeneous differentiation of \(\hbox {T}_\mathrm{H}1\)\(\hbox {T}_\mathrm{H}2, \hbox {T}_\mathrm{H}1\)\(\hbox {T}_\mathrm{H}17\) and \(\hbox {iT}_\mathrm{Reg}\)\(\hbox {T}_\mathrm{H}17\) under single or mixed types of differentiation stimuli. The model shows that high concentrations of differentiation stimuli favor the formation of phenotypes with co-expression of lineage-specific master regulators.


\(\hbox {CD4}^{+}\) T cells Cell differentiation Mathematical model 



This work was supported by Grant R01GM078989-07 from the National Institutes of Health to JJT. The authors thank the two anonymous reviewers for their insightful and constructive comments, which helped us to improve the manuscript

Supplementary material

11538_2015_76_MOESM1_ESM.docx (131 kb)
Supplementary material 1 (docx 130 KB)


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Copyright information

© Society for Mathematical Biology 2015

Authors and Affiliations

  1. 1.Department of Biological SciencesVirginia Polytechnic Institute and State UniversityBlacksburgUSA

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