Abstract
Swarming bacteria use kin discrimination to preferentially associate with their clonemates for certain cooperative behaviors. Kin discrimination can manifest as an apparent demarcation line (a region lacking cells or with much lower cell density) between antagonist strains swarming toward each other. In contrast, two identical strains merge with no demarcation. Experimental studies suggest contact-dependent killing between different strains as a mechanism of kin discrimination, but it is not clear whether this killing is sufficient to explain the observed patterns. Here, we investigate the formation of demarcation line with a mathematical model. First, using data from competition experiments between kin discriminating strains of Myxococcus xanthus and Proteus mirabilis, we found the rates of killing between the strains to be highly asymmetric, i.e., one strain kills another at a much higher rate. Then, to investigate how such asymmetric interactions can lead to a stable demarcation line, we construct reaction-diffusion models for colony expansion of kin-discriminatory strains. Our results demonstrate that a stable demarcation line can form when both cell movement and cell growth cease at low nutrient levels. Further, our study suggests that, depending on the initial separation between the inoculated colonies, the demarcation line may move transiently before stabilizing. We validated these model predictions by observing dynamics of merger between two M. xanthus strains, where one strain expresses a toxin protein that kills a second strain lacking the corresponding antitoxin. Our study therefore provides a theoretical understanding of demarcation line formation between kin-discriminatory populations, and can be used for analyzing and designing future experiments.