Genetic noise mechanism for power-law switching in bacterial flagellar motors

Abstract

Switching of the direction of flagella rotations is the key control mechanism governing the chemotactic activity of E. coli and many other bacteria. Power-law distributions of switching times are most peculiar because their emergence cannot be deduced from simple thermodynamic arguments. Recently it was suggested that by adding finite-time correlations into Gaussian fluctuations regulating the energy height of barrier between the two rotation states, one can generate a power-law switching statistics. By using a simple model of a regulatory pathway, we demonstrate that the required amount of correlated `noise' can be produced by finite number fluctuations of reacting protein molecules, a condition common to the intracellular chemistry. The corresponding power-law exponent appears as a tunable characteristic controlled by parameters of the regulatory pathway network such as equilibrium number of molecules, sensitivities, and the characteristic relaxation time.