Stochastic Models of Cellular Survival and Evolution*

Simple models of growing and dying cell populations could be useful for studying cellular evolution. Using an Ornstein-Uhlenbeck process, we simulate fluctuating protein levels within an initial set of agents capable of division and death, which could represent living cells. We verify that the average, standard deviation, and autocorrelation coefficient correspond to expectations for the Ornstein-Uhlenbeck process. To model cytotoxic stress, we then introduce a Heaviside Step Function as a condition to induce agent replication and agent death and analyze the number of descendants as a function of the death/replication threshold, correlation time, and standard deviation. Furthermore, we utilize this model in simulating the long-term evolution of agent populations.