Extinction, coexistence, and localized patterns of a bacterial population with contact-dependent inhibition

Contact-dependent inhibition (CDI) has been recently revealed as an intriguing but ubiquitous mechanism for bacterial competition in which a species injects toxins into its competitors through direct physical contact for growth suppression. Although the molecular and genetic aspects of CDI systems are being increasingly explored, a quantitative and systematic picture of how CDI systems benefit population competition and hence alter corresponding competition outcomes is not well elucidated.

By constructing a mathematical model for a population consisting of CDI+ and CDI- species, we have systematically investigated the dynamics and possible outcomes of population competition. In the well-mixed case, we found that the two species are mutually exclusive: Competition always results in extinction for one of the two species, with the winner determined by the tradeoff between the competitive benefit of the CDI+ species and its growth disadvantage from increased metabolic burden. Initial conditions in certain circumstances can also alter the outcome of competition. In the spatial case, in addition to exclusive extinction, coexistence and localized patterns may emerge from population competition. For spatial coexistence, population diffusion is also important in influencing the outcome. Using a set of illustrative examples, we further showed that our results hold true when the competition of the population is extended from one to two dimensional space.

We have revealed that the competition of a population with CDI can produce diverse patterns, including extinction, coexistence, and localized aggregation. The emergence, relative abundance, and characteristic features of these patterns are collectively determined by the competitive benefit of CDI and its growth disadvantage for a given rate of population diffusion. Thus, this study provides a systematic and statistical view of CDI-based bacterial population competition, expanding the spectrum of our knowledge about CDI systems and possibly facilitating new experimental tests for a deeper understanding of bacterial interactions.