Chemotaxis and random motility in unsteady chemoattractant fields: a computational study.

We discuss a generic computational model which captures the effects of transient chemoattractant concentration on the chemotactic motility of individual cells. The model solves the appropriate unsteady chemoattractant transport equation using finite differences, while simultaneously executing biased random walks representing individual cells. The simulations were implemented for a 2D homogeneous domain, and two case studies were considered. In the first case study, we consider a single-point source at the origin of the domain which produces chemoattractant, while other cells execute biased random walks toward this point source. We observe that for continuous chemoattractant production, chemoattractant diffusivity has no effect on cell motility, as measured by the mean of time to reach the source. However, in the case of pulsed random production with a specific average duty cycle, the mean time-to-contact is generally minimal with respect to chemoattractant diffusivity over a moderate range of diffusivities. In the second case study, two mobile cells which simultaneously secrete chemoattractant are initially placed a certain distance apart and are then allowed to execute biased random walks. Our model shows that a pulsed random protocol for chemoattractant production facilitates the two cells "finding" one another compared to continuous production. From this case study we also learn that there exists a range of moderate chemoattractant diffusivities for which the mean time-to-contact is minimal when cells both produce/detect chemoattractant and chemotactically migrate. Using these case studies, we discuss how transience in chemoattractant concentration becomes important in characterizing the effectiveness of chemotaxis.