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

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.