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Understanding the differentiation, a biological process from a multipotentstem or progenitor state to a mature cell is critically important. We develop atheoretical framework to quantify the underlying potential landscape andbiological paths for cell development and differentiation. We propose a newmechanism of differentiation and development through binding/unbinding ofregulatory proteins to the gene promoters. We found indeed the differentiatedstates can emerge from the slow promoter binding/unbinding processes.Furthermore, under slow promoter binding/unbinding, we found multiplemeta-stable differentiated states. This can explain the origin of multiplestates observed in the recent experiments. In addition, the kinetic timequantified by mean first passage transition time for the differentiation andreprogramming strongly depends on the time scale of the promoterbinding/unbinding processes. We discovered an optimal speed for differentiationfor certain binding/unbinding rates of regulatory proteins to promoters. Moreexperiments in the future might be able to tell if cells differentiate at atthat optimal speed. In addition, we quantify kinetic pathways for thedifferentiation and reprogramming. We found that they are irreversible. Thiscaptures the non-equilibrium dynamics in multipotent stem or progenitor cells.Such inherent time-asymmetry as a result of irreversibility of state transitionpathways as shown may provide the origin of time arrow for cell development.

A new mechanism of development and differentiation through slow binding/unbinding of regulatory proteins to the genes