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Bull Math Biol. 2015 Jun;77(6):1046-64. doi: 10.1007/s11538-015-0076-6. Epub 2015 Mar 17.

A Mathematical Framework for Understanding Four-Dimensional Heterogeneous Differentiation of CD4+ T Cells.

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Department of Biological Sciences, Virginia Polytechnic Institute and State University, Blacksburg, VA, 24061, USA.


At least four distinct lineages of CD4+ T cells play diverse roles in the immune system. Both in vivo and in vitro, naïve 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 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 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 TH1-TH2, TH1-TH17 and iTReg-TH17 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.

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