Theory of microbe motion in a poisoned environment

The motility of a microorganism which tries to avoid a poisoned environment by chemotaxis is studied within a simple model which couples its velocity to the concentration field of the poison. The latter is time independent but inhomogeneous in space. The presence of the poison is assumed to irreversibly reduce the propulsion speed. The model is solved analytically for different couplings of the total poison dose experienced by the microbe to the propulsion mechanism. In a stationary poison field resulting from a constant emission of a fixed point source, we find a power law for the distance traveled by the microbe as a function of time with a nonuniversal exponent which depends on the coupling in the model. With an inverted sign in the couplings, the acceleration of microbe motion induced by a food field can also be described.