Energy landscape decomposition for cell differentiation with proliferation effect

Complex interactions between genes determine the development and differentiation of cells. We establish a landscape theory for cell differentiation with proliferation effect, in which the developmental process is modeled as a stochastic dynamical system with a birth-death term. We find that two different energy landscapes, denoted U and V, collectively contribute to the establishment of non-equilibrium steady differentiation. The potential U is known as the energy landscape leading to the steady distribution, whose metastable states stand for cell types, while V indicates the differentiation direction from pluripotent to differentiated cells. This interpretation of cell differentiation is different from the previous landscape theory without the proliferation effect. We propose feasible numerical methods and a mean-field approximation for constructing landscapes U and V. Successful applications to typical biological models demonstrate the energy landscape decomposition's validity and reveal biological insights into the considered processes.