Modelling of cell choice between differentiation and apoptosis on the basis of intracellular and extracellular regulations and stochasticity

The work is devoted to the analysis of cell population dynamics where cells make a choice between differentiation and apoptosis. This choice is based on the values of intracellular proteins whose concentrations are described by a system of ordinary differential equations with bistable dynamics. Intracellular regulation and cell fate are controlled by the extracellular regulation through the number of differentiated cells. Initial intracellular protein concentrations are considered for each cell as random variables with a given area of variation. Intracellular regulation, extracellular regulation and random initial conditions work together to produce differentiated cells and to control their number. The role of intracellular regulation is to provide a possible choice between differentiation and apoptosis, extracellular regulation controls the number of differentiated cells, stochastic initial conditions can suppress oscillations and provide stability of the system.