Does Speed–Dependent Nutrient Absorption Influence the Motion of Self-Propelled Microorganisms?

M.E. DI SALVO; C.A. CONDAT; G.J. SIBONA

Bariloche

Taller; VI Taller Regional de Física Estad. y Aplic. a la Materia Cond. – TREFEMAC 08; 2008

Medyfinol 08

We generalize the model for the motion of self-propelled Brownian objects put forward by Schweitzer, Ebeling, and Tilch in order to describe the motion of microorganisms when nutrient absorption is a function of the speed v of the microorganism. We postulate that the absorption rate is of the form q(v) = q0 +Av, with q0 and A being constants. If the fraction of energy spent non-mechanically is relatively large (as it is likely to be the case for bacteria), 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 v* increases monotonically with A. The mechanical efficiency of the molecular motors is also shown to increase monotonically with A. The problem is worked out both analytically and with the use of Monte Carlo simulations.