Summary: Proteus mirabilis colonies display striking symmetry and periodicity. Based on experimental observations of cellular differentiation and group motility, a kinetic model has been developed to describe the swarmer cell differentiation-dedifferentiation cycle and the spatial evolution of swimmer and swarmer cells during Proteus mirabilis swarm colony development. A key element of the model is the age dependence of swarmer cell behaviour, in particular specifying a minimal age for motility and maximum age for septation and dedifferentiation to swimmer cells. Density thresholds for collective motility by mature swarmer cells serve to synchronize the movements of distinct swarmer cell groups and thus help provide temporal coherence to colony expansion cycles.
Numerical computations show that the model fits experimental data by generating a complete swarming plus consolidation cycle period that is robust to changes in parameters which affect other aspects of swarmer cell migration and colony development. The kinetic equations underlying this model provide a different mathematical basis for a temporal oscillator from reaction-diffusion partial differential equations. The modelling shows that Proteus colony geometries arise as a consequence of macroscopic rules governing collective motility. Thus, in this case, pattern formation results from the operation of an adaptive bacterial system for spreading on solid substrates, not as an independent biological function. Kinetic models similar to this one may be applicable to periodic phenomena displayed by other biological systems with differentiated components of defined lifetimes.