A mathematical modelling framework for the regulation of intra-cellular OCT4 in human pluripotent stem cells

Human pluripotent stem cells (hPSCs) have promising clinical applications in regenerative medicine, drug-discovery and personalised medicine due to their potential to differentiate into all cell types, a property know as pluripotency. A deeper understanding of how pluripotency is regulated is required to assist in controlling pluripotency and differentiation trajectories experimentally. Mathematical modelling provides a non-invasive tool through which to explore, characterise and replicate the regulation of pluripotency and the consequences on cell fate. Here we use experimental data of the expression of the pluripotency transcription factor OCT4 in a growing hPSC colony to develop and evaluate mathematical models for temporal pluripotency regulation. We consider fractional Brownian motion and the stochastic logistic equation and explore the effects of both additive and multiplicative noise. We illustrate the use of time-dependent carrying capacities and the introduction of Allee effects to the stochastic logistic equation to describe cell differentiation. This mathematical framework for describing intra-cellular OCT4 regulation can be extended to other transcription factors and developed into sophisticated predictive models.