Multi-potent stem or progenitor cells undergo a sequential series of binary fate decisions which ultimately generates the diversity of differentiated cell . Efforts to understand cell fate control have focused on simple gene regulatory circuits that predict the presence of multiple stable states, bifurcations and switch-like transition . However, existing gene network models do not explain more complex properties of cell fate dynamics such as the hierarchical branching of developmental paths. Here, we construct a generic minimal model of the genetic regulatory network which naturally exhibits five elementary characteristics of cell differentiation: stability,  branching, exclusivity, directionality, and promiscuous expression. We argue that a modular architecture comprised of repeated network elements in principle reproduces these features of differentiation by repressing irrelevant modules and hence , channeling the dynamics in the high-dimensional phase spacethrough a simpler, lower dimensional subspace . We implement our model both with ordinary differential equations (ODEs)  to explore the role of bifurcations in producing the one-way character of differentiation  and with stochastic differential equations (SDEs)  to demonstrate the effect of noise on the system in simulations . We further argue that binary cell fate decisions are prevalent in cell differentiation due to general features of dynamical systems . This minimal model makes testable predictions about the structural basis for directional, discrete and diversifying cell phenotype development and thus , can guide the evaluation of real gene regulatory networks that govern differentiation.
Multi-potent stem or progenitor cells undergo a sequential series of binary fate decisions , which ultimately generate the diversity of differentiated cells . Efforts to understand cell fate control have focused on simple gene regulatory circuits that predict the presence of multiple stable states, bifurcations and switch-like transitions . However, existing gene network models do not explain more complex properties of cell fate dynamics such as the hierarchical branching of developmental paths. Here, we construct a generic minimal model of the genetic regulatory network controlling cell fate determination, which exhibits five elementary characteristics of cell differentiation: stability, directionality, branching, exclusivity, and promiscuous expression. We argue that a modular architecture comprising repeated network elements reproduces these features of differentiation by sequentially repressing selected modules and hence restricting the dynamics to lower dimensional subspaces of the high-dimensional state space . We implement our model both with ordinary differential equations (ODEs) , to explore the role of bifurcations in producing the one-way character of differentiation , and with stochastic differential equations (SDEs) , to demonstrate the effect of noise on the system . We further argue that binary cell fate decisions are prevalent in cell differentiation due to general features of the underlying dynamical system . This minimal model makes testable predictions about the structural basis for directional, discrete and diversifying cell phenotype development and thus can guide the evaluation of real gene regulatory networks that govern differentiation.
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