Abstract
Swarming behaviour is a type of bacterial motility that has been found to be dependent on reaching a local density threshold of cells. With this in mind, the process through which cell-to-cell interactions develop and how an assembly of cells reaches collective motility becomes increasingly important to understand. Additionally, populations of cells and organisms have been modelled through graphs to draw insightful conclusions about population dynamics on a spatial level. In the present study, we make use of analogous random graph structures to model the formation of large chain subgraphs, representing interactions between multiple cells, as a random graph Markov process. Using numerical simulations and analytical results on how quickly paths of certain lengths are reached in a random graph process, metrics for intercellular interaction dynamics at the swarm layer that may be experimentally evaluated are proposed.
Highlights
Swarming behaviour refers to collective movement in a population of organisms and has been found to occur in individual cells, herds of cattle and flocks of birds [1, 2]; it is best described as a group of organisms moving purely through individual directives
Swarming can occur on two or three dimensions; for the purpose of this study, we will focus on populations of single cells, moving through intercellular interactions
We find that akin to descriptions of random graph processes, the giant component, once formed, ‘engulfs’ smaller connected components as time progresses, explaining the sudden increases in size that we see in our numerical simulation
Summary
Swarming behaviour refers to collective movement in a population of organisms and has been found to occur in individual cells, herds of cattle and flocks of birds [1, 2]; it is best described as a group of organisms moving purely through individual directives. A textbook example of this cell–cell interaction is swarming in bacterial colonies [3] This process, in comparison to tissue formation and bird flocking, occurs largely on the two-dimensional plane of the media on which the cells grow, and much data have been collected on swarming and continue to be collected, as bacterial motility and its governing forces are of great interest in the laboratory and clinic. A gram-negative bacterium, displays swarming behaviour and has been demonstrated to form multicellular rafts of elongated and hyperflagellated swarmer cells [4]. This differentiation into the swarmer phenotype has been found to precede the swarming motility of the entire population of cells. Since swarming comprises so many individual cellular and population-level behaviours, these mathematical models differ significantly in how effectively they are able to explain certain beha-
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