The different cell types in a URLanism are an outcome of the process of cell differentiation in which a progenitor cell state differentiates into two distinct cell types. Experimental evidence and analysis of large-scale microarray data establish the key role of a two-gene motif in the process of cell differentiation . The two genes express transcription factors which repress each other's expression and autoactivate their own production. A number of theoretical models have recently been proposed based on the two-gene motif to provide a physical understanding of how cell differentiation works . In this paper, we study a simple model of cell differentiation which assumes no cooperativity in the regulation of gene expression by the transcription factors. The latter repress each other's activity directly through DNA binding and indirectly through the formation of heterodimers. We specifically investigate how deterministic processes combined with stochasticity contribute in bringing about cell differentiation. The deterministic dynamics of our model give rise to a supercritical pichfork bifurcation from an undifferentiated stable steady state to two differentiated stable steady states. The stochastic dynamics of our model are studied using the approach based on the Langevin equations  . The simulation results are consistent with the recent experimental observations. We further propose experimental measurements of quantities like the variance and the lag-1 autocorrelation function in protein fluctuations as  early signatures of an approaching bifurcation point in the cell differentiation process.
The different cell types in a URLanism acquire their identity through the process of cell differentiation in which the multipotent progenitor cells differentiate into distinct cell types. Experimental evidence and analysis of large-scale microarray data establish the key role played by a two-gene motif in cell differentiation in a number of cell systems . The two genes express transcription factors which repress each other's expression and autoactivate their own production. A number of theoretical models have recently been proposed based on the two-gene motif to provide a physical understanding of how cell differentiation occurs . In this paper, we study a simple model of cell differentiation which assumes no cooperativity in the regulation of gene expression by the transcription factors. The later repress each other's activity directly through DNA binding and indirectly through the formation of heterodimers. We specifically investigate how deterministic processes combined with stochasticity contribute in bringing about cell differentiation. The deterministic dynamics of our model give rise to a supercritical pitchfork bifurcation from an undifferentiated stable steady state to two differentiated stable steady states. The stochastic dynamics of our model are studied using the approaches based on the Langevin equations and the linear noise approximation . The simulation results provide a new physical understanding of recent experimental observations. We further propose experimental measurements of quantities like the variance and the lag-1 autocorrelation function in protein fluctuations as the early signatures of an approaching bifurcation point in the cell differentiation process.
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a progenitor cell state differentiates into two
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