Collective behaviour of chemotactic microorganisms in a viscous environment

The aim of this DPhil thesis is the investigation of collective effects that can occur in a colony of interacting bacteria. The non-equilibrium dynamics of living organisms can lead to fascinating patterns and behaviours which cannot be found in equilibrium systems. It is our goal to obtain a better understanding of bacterial colonies and to develop a general theoretical description for living systems undergoing chemotaxis. Some types of bacteria are able to release chemical attractants to their environ- ment, which enables them to sense each other and to form biofilms in a coordinated way. E. Coli, for example, secrete aspartate if succinate is present, which diffuses in their environment and enables interactions. In the first part of the thesis we will derive a general model for bacteria or cells that interact with each other via chemo- taxis and also undergo divisions. Using Renormalization Group calculations we will show that division and chemotactic terms are of the same relevance, and that the competition between them can lead to a rich phase diagram and a transition from controlled behaviour to uncontrolled growth. In the second chapter, we will examine microorganism interaction in the limit where the secreted particles are effectively non-diffusive. On a surface, Pseudomonas aeruginosa bacteria leave a trail of polysaccharides behind them, which is followed by other P. aeruginosa bacteria [1,2]. These interactions between individuals can lead to a local accumulation and spatial correlations of bacteria [3, 4], which are important at the early stages of the biofilm formation. Starting with a generic single microorganism, we will derive the underlying equations of motion. As an important qualitative feature, we will obtain trail alignment with the gradient in addition to a trail-dependent velocity in conventional chemotaxis. Using a simplified version of the model, we will analytically investigate the effects of autochemotaxis with a self-deposited trail and show that it can lead to enhanced rotational diffusion and even trapping. However, if a microorganism is following an existing trail, it can also lead to oscillatory behaviour and to perpendicular trail escapes. We will then compare the full model to experimental results and find that it can both explain single-bacteria behaviour and collective microcolony formation of P. aeruginosa. The collective polysaccharide distributions can also be understood within the framework of a simple calculation inspired by network theory, which gives surprisingly good results.