A generalized discrete model linking rippling pattern formation and individual cell reversal statistics in colonies of myxobacteria

Self-organization processes in multicellular aggregates of bacteria and amoebae offer fascinating insights into the evolution of cooperation and differentiation of cells. During myxobacterial development a variety of spatio-temporal patterns emerges such as counterpropagating waves of cell density that are known as rippling. Recently, several models have been introduced that qualitatively reproduce these patterns. All models include active motion and a collision-triggered reversal of individual bacteria. Here, we present a systematic study of a generalized discrete model that is based on similar assumptions as the continuous model by Igoshin et al (2001 Proc. Natl Acad. Sci. USA 98 14913). We find counterpropagating as well as unidirectional rippling waves in extended regions of the parameter space. If the interaction strength and the degree of cooperativity are large enough, rippling patterns appear even in the absence of a refractory period. We show for the first time that the experimentally observed double peak in the reversal statistics of bacteria in rippling colonies (Welch and Kaiser 2001 Proc. Natl Acad. Sci. USA 98 14907) can be reproduced in simulations of counterpropagating rippling waves which are dominant in experiments. In addition, the reversal statistics in the pre-rippling phase is correctly reproduced.