Memoryless Chemotaxis with Discrete Cues

A wide array of biological systems can navigate in shallow gradients of chemoattractant with remarkable precision. Whilst previous approaches model such systems using coarse-grained chemical density profiles, we construct a dynamical model consisting of a chemotactic cell responding to discrete cue particles. For a cell without internal memory, we derive an effective velocity with which the cell approaches a point source of cue particles. We find that the effective velocity becomes negative beyond some homing radius, which represents an upper bound on the distance within which chemotaxis can be reliably performed. This work lays the foundation for the analytical characterisation of more detailed models of chemotaxis.
Comment: 8 pages, 5 figures