Bulletin of Mathematical Biology

, Volume 77, Issue 6, pp 1046–1064

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

Original Article

DOI: 10.1007/s11538-015-0076-6

Cite this article as:
Hong, T., Oguz, C. & Tyson, J.J. Bull Math Biol (2015) 77: 1046. doi:10.1007/s11538-015-0076-6


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 cellsCell differentiationMathematical model

Supplementary material

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

Copyright information

© Society for Mathematical Biology 2015

Authors and Affiliations

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