Modelling of Microscale Patch Encounter by Chemotactic Protozoa

Abstract

A model of protozoan chemotaxis, based on the rate of change of chemoreceptor occupancy, was used to analyse the efficiency of chemotaxis in a variety of situations. Simulated swimming behaviour replicated patterns observed experimentally. These were classified into three forms of chemosensory behaviour; run-tumble, steered turning, and helical klinotaxis. All three could be simulated from a basic model of chemotaxis by modifying memory times and rotational velocities. In order to steer during helical klinotaxis, the cell must have a short term memory for responding to a signal within a fraction of the time period of the helix. Steered turning was identified as a form where cells react to negative changes in concentration by steering around the turn to swim back up the gradient. All 3 forms were quite effective for encountering targets within the response radius. A response to negative changes in concentration, experienced when the cell is moving away from a target, was found to be important in the absence of periodic changes in swimming direction. The frequency of patch encounter at a fixed density was calculated to be roughly proportional to swimming speed. On the basis of the model, cells are only able to sense point sources within a radius of a few mm. However, even a response radius of 1 mm is enough to increase encounter probability of otherwise minute targets by 2 orders of magnitude. The mean time for patch encounter was calculated to be an exponential function of the mean distance between patches. This results in a very sharp threshold at approximately 6 cm, above which they are not encountered by protozoa within time periods of several days.