  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.
