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J R Soc Interface. 2009 Nov 6;6(40):1035-46. doi: 10.1098/rsif.2008.0397. Epub 2009 Feb 25.

Swimming patterns and dynamics of simulated Escherichia coli bacteria.

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Section of Plant Physiology, Swammerdam Institute for Life Sciences, University of Amsterdam, Kruislaan 318, 1098 SM, Amsterdam, The Netherlands.


A spatially and temporally realistic simulation of Escherichia coli chemotaxis was used to investigate the swimming patterns of wild-type and mutant bacteria within a rectangular arena in response to chemoattractant gradients. Swimming dynamics were analysed during long time series with phase-space trajectories, power spectra and estimations of fractal dimensions (FDs). Cell movement displayed complex trajectories in the phase space owing to interaction of multiple attractors that captured runs and tumbles. Deletion of enzymes responsible for adaptation (CheR and CheB) restricted the pattern of bacterial swimming in the absence of a gradient. In the presence of a gradient, there was a strong increase in trajectories arising from runs and attenuation of those arising from tumbles. Similar dynamics were observed for mutants lacking CheY, which are unable to tumble. The deletion of CheR, CheB and CheY also caused significant shifts in chemotaxis spectral frequencies. Rescaled range analysis and estimation of FD suggest that wild-type bacteria display characteristics of fractional Brownian motion with positive correlation between past and future events. These results reveal an underlying order in bacterial swimming dynamics, which enables a chemotactic search strategy conforming to a fractal walk.

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