Indications of Spontaneous Chaos in the Chemotaxis of E. coli under Noise-Induced Parametric Perturbations

Abstract

Bacteria such as Escherichia coli navigating through real environments in response to chemical stimuli are under the continual influence of perturbations or 'noise' from within the cells, at the interface between the cell walls and the chemical ligands, and from the extra-cellular surroundings. These perturbations interact with one another and affect the chemosensory reactions that determine the movements of a population of cells. A recent analysis has shown that the response coefficients of certain key variables describing the chemotaxis of E. coli can vary by several orders of magnitude when the kinetic parameters are disturbed by noise-induced fluctuations, thereby inducing corresponding variations in cellular locomotion. This possibility is explored quantitatively here by using the same mathematical model as in the earlier work. The model considers the cells to be in one of three states: some cells moving toward the chemoattractant, some moving away and others in an intermediate 'tumbling' state. The focus was on the tumbling cells since they are the most sensitive to disturbances. Based on previous work, the fractal dimensions of the cells tracked over a length of time were used as indicators of stable or unstable chemotaxis. Results showed that while noise-induced variations in some parameters had only marginal effects on cell motility, other parameters strongly influenced the population movement. In the latter cases the chemically guided movement of the population toward the chemoattractant could, under sufficiently intense noise, become chaotic in certain intervals of time. Significantly, the time intervals for such spontaneous chaos differed from one parameter to another, being contiguous with one another, rather than overlapping. Thus at any point in time there is the likelihood of chaotic instability caused by one or more of the parameters, thereby destabilizing the population as a whole. These observations underscore a the importance of analyzing the effects of noise on bacterial chemosensory kinetics, b limiting the intensity of noise permeating the cells, and c the usefulness of fractal dimensions in aiding such analysis.