Novel Single-Cell Mathematical Modelling Approaches and Analysis of Human Stem Cell Populations

The purpose of this thesis is to develop and apply novel modelling and analytical tools for human pluripotent stem cell (hPSC) populations. Two major types of observed heterogeneity across cells in culture are dealt with: (1) in the varied expression levels of several key genetic markers both before and after differentiation, and (2) in specific genetic mutations at the chromosomal level which confer advantages for the cells. The aim of (1) is to enable the novel development of efficient and low-cost differentiation protocols, while (2) seeks to improve quality control in stem cell research as unwanted genetic mutations are challenging to automatically detect.

A novel spatial analysis is developed with the aim of understanding how continuous single-cell Nanog expression levels are linked to the local cellular environment. Nanog expression per cell is thus shown to be inversely proportional to the cell’s neighbour count. These results drive the formulation of a new model for predicting continuous single-cell gene expression, incorporating effects of both diffusive and juxtacrine (contactbased) signalling. It is shown that cells expressing low Nanog levels are less responsive to signalling cues from their environment.

Following this, cell fate selection upon differentiation is modelled through juxtacrine signalling. A novel paradigm for modelling node symmetries of an undirected graph is proposed, which is applied to hPSCs by modelling single cells as nodes, assigning edges between cells that are physically contacting in culture. Importantly, nodes possess internal dynamics. To model cell differentiation, internal dynamics are given by a novel dynamical model for the concentration levels of the differentiating morphogen at each cell. Symmetric cells have symmetrical functions for their internal dynamics, thereby sharing identical equilibria. Model equilibria qualitatively recapitulate experimental fate patterning results, suggesting that geometric symmetries of hPSC cultures may orchestrate fate selection.

Next, a local density analysis is applied to time-lapse images of wildtype and variant hPSC cultures. This helps to uncover that decreasing wildtype cell membrane resilience, thus lowering survival rates at high densities, is a crucial strategy in mechanical cell competition. Lastly, a new ensemble model is developed as an automated tool for quickly and accurately identifying variant cells in culture. Importantly, the model does not rely on cell tagging, meaning that it may be applied to wildtype hPSC cultures without knowing a priori if variant cells are present.