Emergent probability fluxes in confined microbial navigation

When the motion of a motile cell is observed closely, it appears erratic, and yet the combination of nonequilibrium forces and surfaces can produce striking examples of organization in microbial systems. While our current understanding is based on bulk systems or idealized geometries, it remains elusive how and at which length scale self-organization emerges in complex geometries. Here, using experiments, analytical and numerical calculations we study the motion of motile cells under controlled microfluidic conditions, and demonstrate that a robust topology of probability flux loops organizes active motion even at the level of a single cell exploring an isolated habitat. By accounting for the interplay of activity and interfacial forces, we find that the boundary's curvature determines the nonequilibrium probability fluxes of the motion. We theoretically predict a universal relation between fluxes and global geometric properties that is directly confirmed by experiments. Our results represent the first general description of the structure of nonequilibrium fluxes down at the single cell level opening the possibility to decipher the most probable trajectories of motile cells and may enable the design of active topological materials.