Modelling collective behaviour and pattern formation in bacterial colonies
Farrell, Fred Desmond Casimir
In this Thesis I present simulation- and theory-based studies of pattern formation and growth in collections of micro-organisms, in particular bacterial colonies. The aim of these studies is to introduce simple models of the 'micro-scale' behaviour of bacterial cells in order to study the emergent behaviour of large collections of them. To do this, computer simulations and theoretical techniques from statistical physics, and in particular non-equilibrium statistical physics, were used, as the systems under study are far from thermodynamic equilibrium, in common with most biological systems. Since the elements making up these sytems - the micro-organisms - are active, constantly transducing energy from their environment in order to move and grow, they can be viewed as `active matter' systems. First, I describe my work on a generalization of an archetypal model of active matter - the Vicsek model of flocking behaviour - in which the speed of motion of active particles depends on the local density of particles. Such an interaction had previously been shown to be responsible for some forms of pattern formation in bacterial colonies grown on agar plates in the laboratory. Simulations and theory demonstrated a variety of pattern formation in this system, and these results may be relevant to explaining behaviour observed in experiments done on collections of molecular motors and actin fibres. I then go on to describe work on modelling pattern formation and growth in bacterial biofilms - dense colonies of cells growing on top of solid surfaces. I introduce a simple simulation model for the growth of non-motile cells on a flat surface, whereby they move only by growing and pushing on each other as they grow. Such colonies have previously been observed experimentally to demonstrate a transition from round to 'branched' colonies, with a pattern similar to diffusion-limited aggregation. From these simulations and analytical modelling, a theory of the growth of such colonies is developed which is quite different from previous theories. For example, I find that the colony cannot grow at a constant speed if the cells are not compressible. Finally, I present some results on genetic drift and evolution in growing bacterial colonies. Genetic drift is greatly enhanced in colonies which are expanding in space, as only a few individuals at the edge of the population are able to pass on their genes onto their progeny. The individual-based simulations of biofilms described above are used to analyse which factors - such as the shape of the colony, the thickness of the growing layer of cells, and the interactions between the cells - affect the rate of genetic drift and the probability of fixation of beneficial mutations. This has implications, for example, for the evolution of antibiotic resistance in such colonies.
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