CHEMOTAXIS ON RUGGED LANDSCAPES

Bacteria are often tasked to navigate dynamically changing, noisy, and spatially complex environments. At very small scales, there exist fundamental limits to sensing and information retrieval, yet bacteria are known to navigate their environments very near those physical limits. Thus, the navigational mechanisms that cells employ need to efficiently operate under stringent limitations. We developed a continuous dynamical system to study the run-tumble dynamics in stochastically changing environments. Runs occur at the stable fixed points of the model, while the location of the interior unstable fixed point is promoted to a dynamical degree of freedom that encodes the history of fluctuations and impacts tumble decisions in the presence of noise. We show that a small amount of memory, encoded through a dynamical lag that can be much shorter than the fluctuation timescale, allows the cells to travel across rugged landscapes. Our mathematical formulation, commensurate with the chemotaxis mechanism employed by E. coli, can also be more generally applied to decision-making processes when sensors are poor and environments noisy.