Optimal chemotactic navigation in disordered landscapes
Active navigation in disordered media depends on a biased random walk interacting with environmental constraints. Using E. coli chemotactic navigation in agar gels as a model system, we reveal a fundamental trade-off between diffusive exploration and chemotactic directional bias that dictates the optimal strategy for population range expansion. Counter-intuitively, evolution selects for shorter mean run times ({\tau}_f) to achieve faster chemotactic migration in denser environments. Controlled experiments reveal a non-monotonic relationship between chemotactic navigation speed and {\tau}_f, with the optimum shifting according to the density of physical traps in the gel. Single-cell analysis demonstrates that escape from these traps occurs independently of the tumbling mechanism, challenging the classical view that reorientation is essential for navigation in obstructed spaces. Based on these insights, we develop a minimal theoretical model showing that the optimal {\tau}_f emerges from an antagonistic scaling: while the diffusion coefficient increases with {\tau}_f, the chemotactic bias coefficient decreases with it. This work establishes a general principle for optimizing active transport through complex, disordered environments.