Motile bacteria swim in fluid environments propelled by one or more flagella, spiral filaments that are attached to the cell body and a rotary motor. The direction of rotation determines the mode of swimming, and therefore the cell’s trajectory. We test mathematical models for chemotaxis, the directed migration of a bacterial population in the direction of increasing attractants or decreasing repellents. The types of motion patterns that we examine are: the run-and-tumble strategy, used by Escherichia coli and other multi-flagellated bacteria; and the run-reverse-flick strategy, used by Caulobacter crescentus and other uni-flagellated bacteria. The sequence of straight runs followed by tumbles and reorientations to move in a new direction provides a diffusive search pattern for cells, while an extended run in a preferred direction can generate a mean drift velocity. Bacterial chemotaxis has been studied extensively by tracking swimming cells, resulting in mathematical models that describe how the average duration of a forward run varies in response to changes in concentration levels of attractants in recently explored environment. We set up a universal framework for existing cell response models and explore their equivalency. We also evaluate these models for E. coli by two-dimensional random walk simulations and their ability to capture the relatively strong chemotactic responses that have been observed in recent experiments. We also show that these existing reduced models are not sufficient to describe the observed chemotactic response of uni-flagellated cells that execute run-reverse-flick motion. Therefore, we turn to a more detailed approach, based on chemical pathways in the cell cytoplasm that governs the bias for random switching of the flagellum motor. Such models are nonlinear but have features comparable to the reduced models for cell response. Finally, in contrast to mean drift velocity, random motility, another quantity characterizing the collective behavior of a cell population, is harder to measure in experiments and less data is available. Our results show that random motility can increase with chemotaxis and that it is not isotropic, being larger in the direction of attractant gradient. This contradicts the standard assumption that random motility doesn't change with chemotaxis.
Kilikian, Virginia Eirini,
"Chemotactic Response Models for Motile Bacteria"
(2017).
Applied Mathematics Theses and Dissertations.
Brown Digital Repository. Brown University Library.
https://doi.org/10.7301/Z00R9MVQ
