Spatial-Temporal Modelling and Analysis of Bacterial Colonies with Phase Variable Genes

This article defines a novel spatial-temporal modelling and analysis methodology applied to a systems biology case study, namely phase variation patterning in bacterial colony growth. We employ coloured stochastic Petri nets to construct the model and run stochastic simulations to record the development of the circular colonies over time and space. The simulation output is visualised in 2D, and sector-like patterns are automatically detected and analysed. Space is modelled using 2.5 dimensions considering both a rectangular and circular geometry, and the effects of imposing different geometries on space are measured. We close by outlining an interpretation of the Petri net model in terms of finite difference approximations of partial differential equations (PDEs). One result is the derivation of the “best” nine-point diffusion model. Our multidimensional modelling and analysis approach is a precursor to potential future work on more complex multiscale modelling.