Interplay between energetics and dynamics in bacterial motility

We study how self-propelled organisms administer their energetic resources in order to optimize space exploration. Noting the existence of two very different time scales, we use a quasistatic approximation to analyze the relation between bacterial dynamics and changes in the energy stored by a bacterium. We then find both steady-state and time-dependent solutions for the bacterial speed and stored energy. The model also predicts the volume of the region that a bacterium may visit in a resource-depleted medium.