Cell balance equation for chemotactic bacteria with a biphasic tumbling frequency |
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Authors: | Email author" target="_blank">Kevin C?ChenEmail author Roseanne M?Ford Peter T?Cummings |
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Institution: | (1) Laboratory of Molecular Biology, National Cancer Institute, National Institutes of Health, Bethesda, MD 20892-4264, USA;(2) Department of Chemical Engineering, University of Virginia, Charlottesville, VA 22904-4741, USA;(3) Department of Chemical Engineering, Nanomaterials Theory Institute, Oak Ridge National Laboratory, Vanderbilt University, Nashville, Oak Ridge, TN 37235-1604, 37831-6110, USA |
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Abstract: | Alts three-dimensional cell balance equation characterizing the chemotactic bacteria was analyzed under the presence of one-dimensional spatial chemoattractant gradients. Our work differs from that of others who have developed rather general models for chemotaxis in the use of a non-smooth anisotropic tumbling frequency function that responds biphasically to the combined temporal and spatial chemoattractant gradients. General three-dimensional expressions for the bacterial transport parameters were derived for chemotactic bacteria, followed by a perturbation analysis under the planar geometry. The bacterial random motility and chemotaxis were summarized by a motility tensor and a chemotactic velocity vector, respectively. The consequence of invoking the diffusion-approximation assumption and using intrinsic one-dimensional models with modified cellular swimming speeds was investigated by numerical simulations. Characterizing the bacterial random orientation after tumbles by a turn angle probability distribution function, we found that only the first-order angular moment of this turn angle probability distribution is important in influencing the bacterial long-term transport.
Mathematics Subject Classification (2000):60G05, 60J60, 82A70 |
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Keywords: | Chemotaxis Random motility Series expansion Perturbation theory |
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