New insights into probabilistic pattern formation of embryonic stem cells using agent-based modelling
Embryonic stem cells (ESCs) hold great potential for developing future therapies for a wide range of diseases. However, the mechanisms of pattern formation during embryonic development remain poorly understood. ESCs in culture self-organise to form spatial patterns of gene expression upon geometrical confinement indicating that patterning is an emergent phenomenon that results from the many interactions between the cells. Here, we applied an agent-based modelling approach to identify biologically plausible rules acting at the mesoscale within stem cell collectives that may explain spontaneous patterning. We tested different models involving differential motile behaviours including exploring effects due to neighbour interactions. We introduced a new metric, the stem cell aggregate pattern distance (SCAPD), to assess the deviation between the probabilistic experimental pattern formation (used as ground truth) and the probabilistic simulated outcome. We demonstrated our models can produce broadly realistic pattern formation (when compared to experimental data) with a quantified level of uncertainty. The best of our models improve fitness, evaluated by SCAPD, by 70% and 77% over the random models for a discoidal or an ellipsoidal stem cell confinement, respectively. Collectively, our findings provide compelling arguments that a parsimonious mechanism that involves differential motility is sufficient to explain the spontaneous patterning of the cells upon confinement. Furthermore, our work also defines a region of the parameter space that is compatible with patterning, which assists future studies in the field of cell engineering. We envisage that the novel approaches explored within this work will be applicable to many biological systems and will contribute towards facilitating progress by reducing the need for extensive and costly experiments.