Abstract
The growth of bacterial colonies is described in terms of a simple mathematical model that incorporates aspects of nutrient acquisition and quorum sensing signal molecule production. Quorum sensing describes cell communication mechanism that allows bacterial cells to control colony’s behaviour in relation to the population density. The consecutive relation of cell transition and quorum sensing signal molecule production is explored using a continuum representation. This paper demonstrates a simple interaction model for non-motile bacteria based on existing mathematical descriptions. The model considers the population of bacteria as consisting of down-regulated and up-regulated bacteria in which the signal molecules being produced at much faster rate by the up-regulated bacteria. The finding highlights the existence of fold bifurcation phenomenon on the fraction of up-regulated bacteria that behaves as an “on-off” quorum sensing switch in response to the effective diffusion constant.
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