Phenomenological model of bacterial aerotaxis with a negative feedback

Abstract

A phenomenological model for the suspension of the aerotactic swimming microorganisms placed in a chamber with its upper surface open to air is presented. The model was constructed to embody some complexity of the aerotaxis phenomenon, especially, changes in the average bacteria drift velocity under changing environmental conditions. It was assumed that effective forces applied to the cell (gravitational, drag, and thrust) should be essential for the overall system dynamics; and that bacterial propulsion force, but not their swimming velocity, is proportional to the gradient of the oxygen concentration. Mathematically, the model consists of three coupled equations for the oxygen dynamics; for the cell conservation; and for the balance of forces acting on bacteria. An analytical steady-state solution is given for the shallow and deep layers and numerical results are given for the steady-state and initial value problems which are compared with corresponding ones to the Keller–Segel model.