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Three-Dimensional Numerical Simulations of Biofilm Dynamics with Quorum Sensing in a Flow Cell

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Abstract

We develop a multiphasic hydrodynamic theory for biofilms taking into account interactions among various bacterial phenotypes, extracellular polymeric substance (EPS), quorum sensing (QS) molecules, solvent, and antibiotics. In the model, bacteria are classified into down-regulated QS, up-regulated QS, and non-QS cells based on their QS ability. The model is first benchmarked against an experiment yielding an excellent fit to experimental measurements on the concentration of QS molecules and the cell density during biofilm development. It is then applied to study development of heterogeneous structures in biofilms due to interactions of QS regulation, hydrodynamics, and antimicrobial treatment. Our 3D numerical simulations have confirmed that (i). QS is beneficial for biofilm development in a long run by building a robust EPS population to protect the biofilm; (ii). biofilms located upstream can induce QS downstream when the colonies are close enough spatially; (iii). QS induction may not be fully operational and can even be compromised in strong laminar flows; (v). the hydrodynamic stress alters the biofilm morphology. Through further numerical investigations, our model suggests that (i). QS-regulated EPS production contributes to the structural formation of heterogeneous biofilms; (ii) QS down-regulated cells tend to grow at the surface of the biofilm while QS up-regulated ones tend to grow in the bulk; (iii) when nutrient supply is sufficient, QS induction might be more effective upstream than downstream; (iv) QS may be of little benefit in a short timescale in term of fighting against invading strain/species; (v) the material properties of biomass (bacteria and EPS) have strong impact on the dilution of QS molecules under strong shear flow. In addition, with this modeling framework, hydrodynamic details and rheological quantities associated with biofilm formation under QS regulation can be resolved.

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Acknowledgements

Qi Wang is partially supported by NIH and NSF through awards DMS-1200487, DMS-1517347, R01GM078994-05A1, and NSFC awards 11571032 and 91630207. Jia Zhao is partially supported by an ASPIRE grant from the Office of the Vice President for Research at the University of South Carolina.

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Authors and Affiliations

  1. Department of Mathematics, University of South Carolina, Columbia, SC, 29208, USA

    Jia Zhao & Qi Wang

  2. Department of Mathematics, University of North Carolina at Chapel Hill, Chapel Hill, NC, 27599, USA

    Jia Zhao

  3. Beijing Computational Science Research Center, Beijing, 100193, People’s Republic of China

    Qi Wang

  4. School of Materials Sciences and Engineering, Nankai University, Tianjin, 300071, People’s Republic of China

    Qi Wang

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Correspondence to Qi Wang.

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Zhao, J., Wang, Q. Three-Dimensional Numerical Simulations of Biofilm Dynamics with Quorum Sensing in a Flow Cell. Bull Math Biol 79, 884–919 (2017). https://doi.org/10.1007/s11538-017-0259-4

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