An application of fractional Brownian motion and the stochastic logistic equation to describe temporal properties of the pluripotency transcription factor OCT4. 

An analysis of the temporal behaviour of the pluripotency transcription factor OCT4, quantifying its intra-cellular self-regulation and fluctuations. The quantitative framework provides a basis for experimental comparison and developments of mathematical models. 

A spatio-temporal analysis of a hESC colony in terms of cell fates. The time at which patterning first arises is calculated and this cell cooperation of pluripotency is quantified, along with their transition probabilities at cell division.

  • L E Wadkin, S Orozco-Fuentes, I Neganova, M Lako, N G Parker and A Shukurov. An introduction to the mathematical modelling of iPSCs. Submitted book chapter for Elsevier “Induced pluripotent stem cells: novel concepts” (2020).

A chapter conveying the importance and usefulness of mathematical modelling as a tool to achieve a deeper understanding of stem cell biology, introducing key mathematical concepts (random walk theory, differential equations and agent-based modelling) for non-mathematical readers.

A review of the recent developments in the mathematical modelling of the key behaviours of pluripotent stem cells, suitable for both biologists and mathematicians. 

A stochastic exponential growth model for colony formation is developed based on experimental data. The model is a diagnostic tool for biologists to predict the time of clonality loss at varying seeding densities. 

The morphological characteristics of hESC colonies are quantified to develop a colony characteristics database. Self-organisation of colonies is observed and quantified. 

Important parameters of the movement of single and pairs of cells, such as velocities, diffusivity and correlation times are extracted from analysis of experimental data.

The individual motions of single and pairs of cells from experimental data are analysed. The correlated random walks and super-diffusive behaviour of cells is presented.