Chemotactic cell motility plays an essential role in cancer metastasis, leukocyte extravasation, angiogenesis, wound healing and embryogenesis. Bacteria like E. coli, for example, have developed an efficient run-and-tumble search strategy for the needed chemicals by coupling sensing of the chemicals to the motility machinery via signalling pathways that have a feedback control on the preferred direction of the rotation of the flagellar motors. On a coarse-grained level, the resulting motion can be phenomenologically modelled as a directed mobility towards (away from) increasing concentrations of molecules that act as chemo-attractant (-repellant).

But one of the characteristic features of the long-time dynamics of living cells is that number conservation does not hold due to cell division and death processes, which has consequences on their collective behaviour. We have studied, using dynamical renormalization group methods, the combined effect of this nonequilibrium property of a colony of living cells and long-range chemotactic interactions among the cells. The combination of the effective long-range chemotactic interaction and lack of number conservation leads to a rich variety of phase behaviour in the system, which includes a sharp transition from a phase that is controlled by a weakly coupled perturbatively accessible fixed point to a phase controlled by a nonaccessible strong coupling fixed point.

Group members involved: A. Gelimson and R. Golestanian

Bacteria from the species Pseudomonas aeruginosa are used by our collaborators from G. C. L. Wong's group (UCLA) to study the early stages of biofilm formation. A number of features of these bacteria have to be taken into account to model their motion. First of all, they attach to the surface by expressing filaments called type IV pili. The bacteria pull themselves forward by retracting these pili before they slingshot new ones at the surface. In addition Pseudomonas express exopolysaccharides (EPS), PSL being the most important. These EPS trails serve two functions: They promote the surface attachement but they also serve as a chemical that other individuals can react to. As a bacterium only has a small number of pili, there is necessarily a degree of randomness to the motion.

We set up a simple model that captures both the crawling motion and the autochemotactic interaction with the PSL. Based on this model and using numerical and analytical approaches, we study the trail-following behaviour of a bacterium on a preexisting trail and the interaction of a bacterium with its own trail. The latter can lead to an observable dynamics that drastically differs from the underlying microscopic model.

Ultimately, we aim to interpret experimental observations in terms of a simple, physically sound model.

Group members involved: A. Gelimson, T. Kranz and R. Golestanian