From microbial communities to cancer cells, many such complex collectives embody emergent and self-organising behaviour. Such behaviour drives cells to develop composite features such as formation of aggregates or expression of specific genes as a result of cell-cell interactions within a cell population. Currently, we lack universal mathematical tools for analysing the collective behaviour of biological swarms. To address this, we propose a multifractal inspired framework to measure the degree of emergence and self-organisation from scarce spatial (geometric) data and apply it to investigate the evolution of the spatial arrangement of Enterobacter cloacae aggregates. In a plate of semi-solid media, Enterobacter cloacae form a spatially extended pattern of high cell density aggregates. These aggregates nucleate from the site of inoculation and radiate outward to fill the entire plate. Multifractal analysis was used to characterise these patterns and calculate dynamics changes in emergence and self-organisation within the bacterial population. In particular, experimental results suggest that the new aggregates align their location with respect to the old ones leading to a decrease in emergence and increase in self-organisation.

Some strains of motile bacteria self-organize to form spatial patterns of high and low cell density over length scales that can be observed by eye. One such collective behavior is the formation in semisolid agar media of a high cell density swarm band. We isolated 7 wild strains of the Enterobacter cloacae complex capable of forming this band and found its propagation speed can vary 2.5 fold across strains. To connect such variability in collective motility to strain properties, each strain’s single-cell motility and exponential growth rates were measured. The band speed did not significantly correlate with any individual strain property; however, a multilinear analysis revealed that the band speed was set by a combination of the run speed and tumbling frequency. Comparison of variability in closely-related wild isolates has the potential to reveal how changes in single-cell properties influence the collective behavior of populations.

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