Discrete and Continuum Multiscale Behaviour in Bacterial Communication
The interacting effects operating on subcellular (gene regulatory processes), cellular (interactions between neighbouring cells) and population (signalling molecule transport) scales are exemplified and explored through simple multiscale models. Specific
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Abstract The interacting effects operating on subcellular (gene regulatory processes), cellular (interactions between neighbouring cells) and population (signalling molecule transport) scales are exemplified and explored through simple multiscale models. Specific attention is focused on how the upregulation (or downregulation) of small numbers of discrete cells can influence the behaviour of the population as a whole, by investigating toy models for positive autoregulation and by the simulation of a much more detailed model for quorum sensing within a Gram-positive population of bacteria. The implications for delays associated with gene expression are also investigated in a spatio-temporal context through the analysis of blow-up behaviour, as a mathematical symptom of upregulation through positive feedback, in some model reaction-diffusion delay equations.
1 Bacterial Communication The belief that bacteria within a colony operate independently of one another was abandoned in the 1970s with the discovery of cell-density dependent behaviour in the marine bacterium Vibrio fischeri [16]. It was found that these bacteria emit light only when present at sufficiently high concentrations, most likely either to obtain camouflage from predators (by mimicking moonlight on the water’s surface) or to attract mates; at lower bacterial concentrations, the amount of light S. Jabbari University of Birmingham, Edgbaston, Birmingham B15 2TT, England e-mail: [email protected] J. R. King (&) Centre for Mathematical Medicine and Biology, University of Nottingham, University Park, Nottingham NG7 2RD, UK e-mail: [email protected]
Stud Mechanobiol Tissue Eng Biomater (2013) 14: 299–320 DOI: 10.1007/8415_2012_155 Ó Springer-Verlag Berlin Heidelberg 2012 Published Online: 17 October 2012
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emitted would not merit the energy expended on generating the bioluminescence, meaning that this phenotype should be induced only at high population density. This understanding between the cells is mediated by extracellular signal molecules and the process has been termed ‘quorum sensing’ (the behaviour of the bacteria alters once a quorum has been attained). Cell communication is now known to be prevalent throughout the bacterial kingdom [5, 28]. Though signalling pathways vary between species (most notably between Gram-positive and Gram-negative bacteria) the phenomenon generally consists of the production of diffusible signal molecules and their excretion into the environment, allowing detection by other cells. The level of signal molecules in the environment is a reflection of the population size or density, and the number of signal molecules detected by an individual cell will determine the regulatory gene cascade which is triggered and ultimately the behaviour of the cell. A sufficiently well-mixed population should therefore act in a synchronised manner. Since its discovery in the form of bioluminescence, quorum sensing has been found to regulate a spectrum of bacterial behaviours, many of which, su
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