Discrete and Continuum Multiscale Behaviour in Bacterial Communication

The interacting effects operating on subcellular (gene regulatory processes), cellular (interactions between neighbouring cells) and population (signalling molecule transport) scales are exemplified and explored through simple multiscale models. Specific attention is focused on how the upregulation (or downregulation) of small numbers of discrete cells can influence the behaviour of the population as a whole, by investigating toy models for positive autoregulation and by the simulation of a much more detailed model for quorum sensing within a Gram-positive population of bacteria. The implications for delays associated with gene expression are also investigated in a spatio-temporal context through the analysis of blow-up behaviour, as a mathematical symptom of upregulation through positive feedback, in some model reaction-diffusion delay equations.