Dynamics of Chemotactic Microorganisms

The chemotactic dynamics of gradient-sensing typical eukaryotic microorganisms are studied by computer simulations, and two situations are examined in details. First, the case of autochemotaxis is considered, when the microbe is coupled to its own diffusing chemical secretion and performs biased random walk. Both cases of chemoattractant and chemorepellent are analyzed for $ d = 1, 2, 3 $ spatial dimensions. For chemoattractant, we find a transient dynamical arrest until the microorganism diffuses for long times. For a chemorepellent, there is a transient ballistic motion in all dimensions and a long-time diffusion. These results are interpreted with the help of a theoretical analysis. Next, the model is extended to study a discrete chemotactic predator-prey system in which the prey secrets a diffusing chemical which is sensed by the predator and vice versa. Two dynamical states corresponding to catching and escaping are identified and it is shown that steady hunting is unstable. For the escape process, the predator-prey distance is diffusive for short times but exhibits a transient subdiffusive behavior which scales as a power law $ t^1/3 $ with time $ t $ and ultimately crosses over to diffusion again. This allows us to classify the motility and dynamics of various predatory microbes and phagocytes. In particular, there is a distinct region in the parameter space where they prove to be infallible predators.