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We study the asymptotic behaviors of stochastic cell fate decision betweenproliferation and differentiation. We propose a model of a self-replicatingLangevin system, where cells choose their fate (i.e. proliferation ordifferentiation) depending on local cell density. Based on this model, wepropose a scenario for multi-cellular organisms to maintain the density ofcells (i.e., homeostasis) through finite-ranged cell-cell interactions.Furthermore, we numerically show that the distribution of the number ofdescendant cells changes over time, thus unifying the previously proposed twomodels regarding homeostasis: the critical birth death process and the votermodel. Our results provide a general platform for the study of stochastic cellfate decision in terms of nonequilibrium statistical mechanics.

Dynamical Crossover in a Stochastic Model of Cell Fate Decision