At least four distinct lineages of CD4+\documentclass[12pt]{minimal}
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\begin{document}$$\hbox {CD4}^{+}$$\end{document} T cells play diverse roles in the immune system. Both in vivo and in vitro, naïve CD4+\documentclass[12pt]{minimal}
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\begin{document}$$\hbox {CD4}^{+}$$\end{document} 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+\documentclass[12pt]{minimal}
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\begin{document}$$\hbox {CD4}^{+}$$\end{document} 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+\documentclass[12pt]{minimal}
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\begin{document}$$\hbox {CD4}^{+}$$\end{document} 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\documentclass[12pt]{minimal}
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\begin{document}$$\hbox {T}_\mathrm{H}1$$\end{document}–TH2,TH1\documentclass[12pt]{minimal}
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\begin{document}$$\hbox {T}_\mathrm{H}2, \hbox {T}_\mathrm{H}1$$\end{document}–TH17\documentclass[12pt]{minimal}
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\begin{document}$$\hbox {T}_\mathrm{H}17$$\end{document} and iTReg\documentclass[12pt]{minimal}
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\begin{document}$$\hbox {iT}_\mathrm{Reg}$$\end{document}–TH17\documentclass[12pt]{minimal}
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\begin{document}$$\hbox {T}_\mathrm{H}17$$\end{document} 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.
