Bacterial diffusion in disordered media, by forgetting the media

Bacterial transport is important for many natural and engineering processes. However, building models of transport in the complex environments that bacteria navigate is challenging. Here, we theoretically study bacterial diffusion in a model of disordered porous media. This problem is complicated by the interactions between the bacterium and surfaces in the media, and made worse by the fact that we rarely know the geometry of the environment. To sidestep these difficulties, we abstract away the environment to cell states, defined by the number of obstacles the cell is in contact with. Then, we derive simplified dynamics in and transitions among these states. This allows an approximate diffusion coefficient to be derived analytically, which shows excellent agreement with simulations. The same approach can be used to make progress on several variations of this problem. These results point towards a relatively small set of microscopic features, depending on the cell’s motion, the environment, and their interactions, that are needed to describe long-term diffusive transport of bacteria.