Stigmergy in active furrowers

Stigmergy is the emergence of spatiotemporal coordination between agents through interactions mediated by their environment. Pheromone trail-following in ants is a well-known example. Recently, a mechanical form of stigmergy has been observed in colonies of motile bacteria that create networks of furrows as they advance over soft agar [Gloag et al., PNAS, 2015]. Vanguard rafts of bacteria mechanically deform the substrate to create a physical signal that other cells follow. Under certain conditions, extensive furrow networks emerge with a distinctive morphology that spans a broad range of length scales. It is possible that the formation of such a sparse network of furrows is a strategy to loosely colonize large areas with a small number of cells. We investigate the conditions under which extensive furrow networks emerge using simulations of self-propelled rods that furrow through a passive elastic or plastic medium. The structure of the furrow network appears to critically depend upon the clustering behaviour of active rods at the advancing edge, which, in turn, depends on substrate stiffness and the self-propulsion velocity of the rods. We attempt to explain our observations through a coarse-grained, but general, model of stigmergy.