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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 the barrier between the two rotation states, it is possible to generate switching statistics with an intermediate power-law asymptotics. 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 the equilibrium number of molecules, sensitivities, and the characteristic relaxation time.