Anomalous diffusive behaviors and optimal navigation strategy of the run-and-tumble particle swimming in porous media.

Although the behavior of active matter such as run-and-tumble particle (RTP) swimming in homogeneous liquid environments has been well investigated, less is known about how RTP navigates in complex environments such as animal tissues, soil, and viscous liquids, where it has to deal with environmental heterogeneities. In this article, we present a phenomenological random walk model to describe the spreading behavior of RTP swimming in porous media where an additional trap state originating from the mechanical constraints of the environment is incorporated. Based on the derived propagator of the model, the anomalous diffusive behaviors are investigated and discussed. It is found that the sojourn time distribution characterized by the smallest power exponent plays a crucial role in determining the diffusive behaviors. Furthermore, the navigation strategy of RTP swimming in porous media is discussed with respect to the mean first passage time (MFPT). While increasing the mean running time can enhance bacterial navigation, it also elevates the probability of RTP being captured by random mechanical trappings, which has no contribution to the navigation. We find that these conflict effects lead to a non-monotonic relationship between the MFPT and the mean running time. Notably, we demonstrate that there exists an optimal navigation pattern, which represents a classic trade-off strategy.