Restoration of Coherent Population Movement from Noise-Induced Chaos in the Chemotaxis of E. Coli: A Fractal Interpretation

Abstract

Bacteria navigating in a chemically guided manner are under the impact of noise from at least three sources-inside the cells, at the binding sites between chemoattractants in the environment and corresponding receptors of the cells, and in the environment itself. For Escherichia coli as model system, compounded effects of these sources of noise were investigated recently by using the fractal dimensions of the trajectories of the cells as an index of the nature of population motility. It was observed that environmental noise can drive synchronized movement of a population toward a chemoattractant into stochastic chaos. Those results have been used here to explore the effectiveness of different kinds of noise filters in restoring coherent motion of the cells. An auto-associative neural filter was the best, followed by the extended Kalman filter. The performance of either filter depended on the relative rates of motion of the bacteria and the chemoattractant, and on whether the responses of the cells to fluctuations in the external chemoattractant was non-adaptive or adaptive. The results establish: a the validity and usefulness of fractal indexes to characterize noise-affected chemotaxis, b the significance of the effect of environmental noise on chemotactic motility, and c the effectiveness of a neural filter in rescuing coherent population movement from noise-induced chaos.