A Review of Stochastic and Deterministic Modeling of Stem Cell Dynamics

Purpose of ReviewThis paper briefly describes recent mathematical models that use stochastic and deterministic approaches to understand stem cell dynamics and how these models are utilized to study the roles of stem cells' dynamics in cancer and aging.Recent FindingsStochastic compartmental models have been developed to investigate the generalized double-hit mutant production under the influence of different types of stem cell divisions. More specialized examination of the generation, spread, and optimizing structure of 2-hit mutants in the colon crypts has also been conducted. The recent introduction of a hybrid stochastic-deterministic model creates innovative approaches to studying carcinogenesis, while other stochastic models interested in the stem cell renewal process have explored the phenomenon of aging.The results of these studies indicate that asymmetric stem cell divisions increase the probability of mutants production and their fixation probability. Moreover, the hybrid stochastic-deterministic model demonstrates how a low rate of dedifferentiation can significantly accelerate carcinogenesis. Finally, a stochastic model for the stem cell renewal process behind aging shows that the fixation probability of an altered stem cell with a longer cell cycle than the rest is higher than other stem cells.