  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.
