From the volcano effect to banding: a minimal model for bacterial behavioral transitions near chemoattractant sources

Sharp chemoattractant (CA) gradient variations near food sources may give rise to dramatic behavioral changes of bacteria neighboring these sources. For instance, marine bacteria exhibiting run-reverse motility are known to form distinct bands around patches (large sources) of chemoattractant such as nutrient-soaked beads while run-and-tumble bacteria have been predicted to exhibit a 'volcano effect' (spherical shell-shaped density) around a small (point) source of food. Here we provide the first minimal model of banding for run-reverse bacteria and show that, while banding and the volcano effect may appear superficially similar, they are different physical effects manifested under different source emission rate (and thus effective source size). More specifically, while the volcano effect is known to arise around point sources from a bacterium's temporal differentiation of signal (and corresponding finite integration time), this effect alone is insufficient to account for banding around larger patches as bacteria would otherwise cluster around the patch without forming bands at some fixed radial distance. In particular, our model demonstrates that banding emerges from the interplay of run-reverse motility and saturation of the bacterium's chemoreceptors to CA molecules and our model furthermore predicts that run-reverse bacteria susceptible to banding behavior should also exhibit a volcano effect around sources with smaller emission rates.