Repulsion from slow-diffusing molecules improves chemotactic capture of moving sources

Chemotaxis, or the following of chemical gradients, is essential for microbes to locate resources. In general, a microbe should swim in the direction of increasing nutrient concentrations to reach the source. However, microbes often display paradoxical chemotactic behaviors: for example, E coli is repulsed by several amino acids. We present a new explanation for why microbes may be repulsed by certain nutrients. We consider that nutrient sources are often moving and demonstrate that simply following the gradient of an attractant produces inefficient trajectories for intercepting moving targets. However, when attraction to a fast-diffusing molecule and repulsion from a slow-diffusing molecule are combined, the time to intercept a moving target is significantly reduced. We show that a simple differential strategy is superior to any purely attractive strategy across parameters and initial conditions. When the source is moving faster than the microbe can swim employing a differential strategy can even make the difference as to whether the source is ever intercepted at all. We conclude by showing that E coli is attracted to fast-diffusing amino acids and repulsed by slow-diffusing amino acids, as would be necessary to implement this differential strategy. Our results thus offer an explanation for surprising experimental observations and propose a new strategy by which microbes may accomplish a difficult task.