A mathematical framework for human pluripotent stem cell behaviour

Abstract

Human pluripotent stem cells, hPSCs, have unparalleled potential for developments in regenerative medicine, personalised medicine and drug discovery. For these promising clinical applications to become a reality, a deeper understanding of their complex behaviours across a multi-scale hierarchy is required. The use of techniques from mathematics and physics allows the identification of the systematic and universal behaviours inherent in a biological system, provides a framework for comparisons, tests and predictions, and can ultimately guide experimental decision making. We take a methodical approach to developing coherent models of hPSC behaviours, considering some of their key properties in isolation. The range of models developed includes a descriptive analysis of cell movements that leads to their association into pairs and further into colonies, the growth of clonal cell groups within a colony and the dynamics of intra-cellular pluripotency. We consider the kinematics of single and pairs of hPSCs in two-dimensions using time-lapse microscopy imaging, quantifying their movements within a random walk framework and characterising their inherent correlation properties. This analysis reveals single cells perform an unusual anisotropic random walk along a local axis, with increased migration speeds in the direction of cell elongation. Pairs of cells in close proximity show a preference for moving in the same direction. The addition of a common biological marker (CellTracer) negatively impacts the motility of both single and pairs of cells. Clonal (genetically identical) hPSC colonies are required for many in-vitro applications. We consider the impact of spatial colony growth on undesirable clonality loss. Our experimental data show that colony populations are multi-modal, with a growth rate dependent on the number of founding cells. From this data, we extract the parameters for a stochastic exponential growth model which can be used to predict the time at which clonality is lost due to the merging of neighbouring colonies at different seeding densities. Finally, we examine the internal regulation of cell pluripotency – the defining characteristic of hPSCs which allows for their differentiation into other cell types. Pluripotency is regulated by a complex network of pluripotency transcription factors (PTFs). We use experimental data to quantify the temporal regulation of the PTF OCT4 in a growing stem cell colony using the Hurst exponent, autocorrelation and diffusion analysis. We then present a ‘tool kit’ of temporal models which can be used to capture the fluctuation of PTFs (as a proxy for cell pluripotency) and evaluate the successes and limitations of each model. Throughout this work the mathematics is rigorously underpinned by experimental results. Our global aim is to apply a variety of mathematical tools to deepen our understanding of stem cell behaviours and bridge the gap between experiments and theory.