Multistability and predominant double-positive states in a four node mutually repressive network: a case study of Th1/Th2/Th17/T-reg differentiation

Elucidating the emergent dynamics of complex regulatory networks enabling cellular differentiation is crucial to understand embryonic development and suggest strategies for synthetic circuit design. A well-studied network motif often driving cellular decisions is a toggle switch - a set of two mutually inhibitory lineage-specific transcription factors A and B. A toggle switch often enables two possible states mutually exclusive states - (high A, low B) and (low A, high B) - from a common progenitor cell. However, the dynamics of networks enabling differentiation of more than two cell types from a progenitor cell is not well-studied. Here, we investigate the dynamics of four master regulators A, B, C and D inhibiting each other, thus forming a toggle tetrahedron. Our simulations show that a toggle tetrahedron predominantly allows for co-existence of six 'double positive' or hybrid states where two of the nodes are expressed relatively high as compared to the remaining two - (high A, high B, low C, low D), (high A, low B, high C, low D), (high A, low B, low C, high D), (low A, high B, high C, low D), (low A, low B, high C, high D) and (low A, high B, low C, high D). Stochastic simulations showed state-switching among these phenotypes, indicating phenotypic plasticity. Finally, we apply our results to understand the differentiation of naive CD4+ T cells into Th1, Th2, Th17 and Treg subsets, suggesting Th1/Th2/Th17/Treg decision-making to be a two-step process. Our results reveal multistable dynamics and establish the stable co-existence of hybrid cell-states, offering a potential explanation for simultaneous differentiation of multipotent naive CD4+ T cells. ### Competing Interest Statement The authors have declared no competing interest.