Abstract
Microbes growing in animal host environments face fluctuations that have elements of both randomness and predictability. In the mammalian gut, fluctuations in nutrient levels and other physiological parameters are structured by the host's behavior, diet, health and microbiota composition. Microbial cells that can anticipate environmental fluctuations by exploiting this structure would likely gain a fitness advantage (by adapting their internal state in advance). We propose that the problem of adaptive growth in structured changing environments, such as the gut, can be viewed as probabilistic inference. We analyze environments that are "meta-changing": where there are changes in the way the environment fluctuates, governed by a mechanism unobservable to cells. We develop a dynamic Bayesian model of these environments and show that a real-time inference algorithm (particle filtering) for this model can be used as a microbial growth strategy implementable in molecular circuits. The growth strategy suggested by our model outperforms heuristic strategies, and points to a class of algorithms that could support real-time probabilistic inference in natural or synthetic cellular circuits.