Swimming limited aggregation of Escherichia coli bacteria in liquid crystals

The aggregation of motile organisms is a common example of collective biological behavior. The emergent dynamics are typically governed by the interactions between organisms, as well as by the confinement and rheological properties of their environment. We investigated the collective swimming of fluorescently labelled Escherichia coli bacteria in liquid crystals and observed long-lived chains of swimming bacteria aligned with the nematic director. Remarkably, we found that longer chains swim faster, contrary to the prediction of fundamental force-balance models and the observed trajectories of merging bacterial pairs. To explain this counterintuitive observation and identify the physical mechanism driving bacterial aggregation in liquid crystals, we combined our experimental findings with agent-based simulations and intuitive theoretical models. Taking into account the speed distribution of individual bacteria, our simulations revealed a positive correlation between the emerging chain length and speed, consistent with the experimental results. A minimal aggregation model, based on encounter probabilities between three neighbouring cells, supports our explanation that longer bacterial chains swim faster as they are more likely to contain faster swimming individuals, which require less time to meet and merge with their neighbours.