Enhancement of Bacterial Motility due to Speed-Dependent Absorption

Abstract

Marine bacteria often reach high swimming speeds, either to take advantage of evanescent nutrient patches or to beat Brownian forces. Since this implies that a sizable part of their energetic budget must be allocated to motion, it is reasonable to assume that some bacteria are able to increase their nutrient intake by increasing their speed v. We formulate a model that uses the concept of internal energy depot originally developed by Schweitzer, Ebeling, and Tilch to investigate this hypothesis. We postulate that the nutrient absorption rate is of the form q(v) = q0 +Av, with q0 and A being constants. If the fraction c of energy spent non-mechanically is low, we find that there is a single stable velocity v1*, but if c is large, there is a critical value of A, Ac, below which only the v = 0 solution is stable. Above the bifurcation point Ac a second stable solution appears, whose value v2* increases monotonically with A. The mechanical efficiency of the molecular motors is also shown to increase with A. The description of the motion is further clarified by the use of the Fokker-Planck formalism. Solutions obtained using realistic parameter values indicate that the speed increase due to the enhanced nutrient absorption may be substantial.