Mathematical Modeling of Quorum-Sensing Control in Biofilms

Ward, J. P.

doi:10.1007/7142_2007_010

Cited by 13 publications

(19 citation statements)

References 53 publications

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“…The study discussed here makes explicit the assumptions that underpin the biofilm models studied in [34,36,37]. The core of the modelling assumes that bacteria in the biofilm behave on the long timescales of biofilm growth rather like a low Reynolds' number viscous fluid blob (though with volumetric growth) with a small height-to-length ratio.…”

Section: Discussionmentioning

confidence: 99%

“…To make a comparison between this equation and our earlier studies [34,36,37], we consider the cross-sectional total QSM concentration A, defined as A = B H, to get…”

Section: Asymptotic Analysismentioning

confidence: 99%

“…The basis of these models is not unlike that of the current one, in which growth creates, and death removes, material volume, causing local movement that is described by a velocity field. This general approach to modelling has been adapted to investigate the role of QS on growth and development P. aeruginosa biofilms [2,3,9,10,19,34]. There is less published study on biofilm growth in higher dimensions, describing development along a solid substratum as well as perpendicular to it; it includes Cogan and Keener [11], modelling EPS as gel, and a series of articles by Eberl et al [15,16], in which biofilm expansion is described by nonlinear (density-dependent) diffusion.…”

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confidence: 98%

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Thin-film modelling of biofilm growth and quorum sensing

Ward

King

2011

J Eng Math

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Biofilms are slimy films of bacteria that typically grow on solid surfaces with a fluid interface. Two mathematical models for nutrient-dependent, early-stage biofilm growth and quorum sensing (QS) are proposed and studied. The aim of this study is to use thin-film methods to derive a dimensionally reduced model on a stronger theoretical basis to that of Ward et al. (J Math Biol 47:23-55, 2003). The biofilm structure is described as a viscous fluid, and the two models apply different boundary conditions between the biofilm and the solid surface: namely (1) shear-stress-free; and (2) no-slip conditions. The complexity and dimensionality of each of the models are reduced by the application of asymptotic methods in biologically relevant thin-film limits. The first model reduces to a system of first-order PDEs, whilst the second results in a high-order, degenerate Fisher-type equation. We present a hodograph solution for model (1) and analyse model (2) in the travelling-wave limit. A key difference between the models is that the long-time solutions have contrasting properties: for model (1) the large-time solutions are dependent on the initial conditions, whilst in model (2) the long-time attractor is a travelling wave, the speed of which is approximated in a certain limit that depends on conditions at the biofilm edge and substratum interface. The QS aspects of the model derived using the systematic asymptotic approach are shown to be relatively unchanged from those of Ward et al. (2003), and the results therein are thus applicable to the current models.

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Section: Discussionmentioning

confidence: 99%

“…To make a comparison between this equation and our earlier studies [34,36,37], we consider the cross-sectional total QSM concentration A, defined as A = B H, to get…”

Section: Asymptotic Analysismentioning

confidence: 99%

mentioning

confidence: 98%

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Thin-film modelling of biofilm growth and quorum sensing

Ward

King

2011

J Eng Math

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“…Their model is one-dimensional and consists of 10 PDEs and one ODE, with growth occurring perpendicular to the a solid surface. Ward (2008) investigated what happens when the three QSIs are administrated (by drip-feeding or by pretreatment of the growth media) and they compare their potency. For both, batch cultures and biofilms, they found that the time of application of the QSI may be a key parameter for the efficacy of the treatment.…”

Section: Quorum Quenchingmentioning

confidence: 99%

Mathematical Modelling of Bacterial Quorum Sensing: A Review

2016

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Bacterial quorum sensing (QS) refers to the process of cell-to-cell bacterial communication enabled through the production and sensing of the local concentration of small molecules called autoinducers to regulate the production of gene products (e.g. enzymes or virulence factors). Through autoinducers, bacteria interact with individuals of the same species, other bacterial species, and with their host. Among QS-regulated processes mediated through autoinducers are aggregation, biofilm formation, bioluminescence, and sporulation. Autoinducers are therefore "master" regulators of bacterial lifestyles. For over 10 years, mathematical modelling of QS has sought, in parallel to experimental discoveries, to elucidate the mechanisms regulating this process. In this review, we present the progress in mathematical modelling of QS, highlighting the various theoretical approaches that have been used and discussing some of the insights that have emerged. Modelling of QS has benefited almost from the onset of the involvement of experimentalists, with many of the papers which we review, published in non-mathematical journals. This review therefore attempts to give a broad overview of the topic to the mathematical biology community, as well as the current modelling efforts and future challenges.B Judith Pérez-Velázquez

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“…Naturally, modeling of QS is an important part of the general effort in modeling the genetic processes involved in biofilm development. Ward [60] gives a good review of early mathematical modeling of QS.…”

Section: Modeling the Genetic Basis Of Biofilm Developmentmentioning

confidence: 99%

Modeling Biofilms: From Genes to Communities

Zhang

2017

Processes

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Biofilms are spatially-structured communities of different microbes, which have a huge impact on both ecosystems and human life. Mathematical models are powerful tools for understanding the function and evolution of biofilms as diverse communities. In this article, we give a review of some recently-developed models focusing on the interactions of different species within a biofilm, the evolution of biofilm due to genetic and environmental causes and factors that affect the structure of a biofilm.

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Mathematical Modeling of Quorum-Sensing Control in Biofilms

Cited by 13 publications

References 53 publications

Thin-film modelling of biofilm growth and quorum sensing

Thin-film modelling of biofilm growth and quorum sensing

Mathematical Modelling of Bacterial Quorum Sensing: A Review

Modeling Biofilms: From Genes to Communities

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