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Three-Dimensional Numerical Simulations of Biofilm Dynamics with Quorum Sensing in a Flow Cell. Bull Math Biol 2017; 79:884-919. [PMID: 28290008 DOI: 10.1007/s11538-017-0259-4] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/14/2016] [Accepted: 02/15/2017] [Indexed: 10/20/2022]
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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Shen Y, Zhao J, de la Fuente-Núñez C, Wang Z, Hancock REW, Roberts CR, Ma J, Li J, Haapasalo M, Wang Q. Experimental and Theoretical Investigation of Multispecies Oral Biofilm Resistance to Chlorhexidine Treatment. Sci Rep 2016; 6:27537. [PMID: 27325010 PMCID: PMC4914838 DOI: 10.1038/srep27537] [Citation(s) in RCA: 42] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/04/2016] [Accepted: 05/11/2016] [Indexed: 01/10/2023] Open
Abstract
We investigate recovery of multispecies oral biofilms following chlorhexidine gluconate (CHX) and CHX with surface modifiers (CHX-Plus) treatment. Specifically, we examine the percentage of viable bacteria in the biofilms following their exposure to CHX and CHX-Plus for 1, 3, and 10 minutes, respectively. Before antimicrobial treatment, the biofilms are allowed to grow for three weeks. We find that (a). CHX-Plus kills bacteria in biofilms more effectively than the regular 2% CHX does, (b). cell continues to be killed for up to one week after exposure to the CHX solutions, (c). the biofilms start to recover after two weeks, the percentage of the viable bacteria recovers in the 1 and 3 minutes treatment groups but not in the 10 minutes treatment group after five weeks, and the biofilms fully return to the pretreatment levels after eight weeks. To understand the mechanism, a mathematical model for multiple bacterial phenotypes is developed, adopting the notion that bacterial persisters exist in the biofilms together with regulatory quorum sensing molecules and growth factor proteins. The model reveals the crucial role played by the persisters, quorum sensing molecules, and growth factors in biofilm recovery, accurately predicting the viable bacterial population after CHX treatment.
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Affiliation(s)
- Ya Shen
- Division of Endodontics, Department of Oral Biological and Medical Sciences, Faculty of Dentistry, University of British Columbia, Vancouver, British Columbia, V6T 1Z3 Canada
| | - Jia Zhao
- Department of Mathematics, University of South Carolina, Columbia, SC 29208, USA
| | - César de la Fuente-Núñez
- Centre for Microbial Diseases and Immunity Research, Department of Microbiology and Immunology, University of British Columbia, Vancouver, V6T 1Z3 Canada.,Synthetic Biology Group, MIT Synthetic Biology Center, Research Laboratory of Electronics, Department of Biological Engineering, Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - Zhejun Wang
- Division of Endodontics, Department of Oral Biological and Medical Sciences, Faculty of Dentistry, University of British Columbia, Vancouver, British Columbia, V6T 1Z3 Canada
| | - Robert E W Hancock
- Centre for Microbial Diseases and Immunity Research, Department of Microbiology and Immunology, University of British Columbia, Vancouver, V6T 1Z3 Canada
| | - Clive R Roberts
- Department of Oral Biological and Medical Sciences, Faculty of Dentistry, University of British Columbia, Vancouver, British Columbia, V6T 1Z3 Canada
| | - Jingzhi Ma
- Department of Stomatology, Tongji Hospital, Tongji Medical College, Huazhong University of Science and Technology, Wuhan, 430030 China
| | - Jun Li
- School of Mathematical Sciences, Nankai University, Tianjin 300071, China
| | - Markus Haapasalo
- Division of Endodontics, Department of Oral Biological and Medical Sciences, Faculty of Dentistry, University of British Columbia, Vancouver, British Columbia, V6T 1Z3 Canada
| | - Qi Wang
- Department of Mathematics, University of South Carolina, Columbia, SC 29208, USA.,Beijing Computational Science Research Center, Beijing 100193, China and School of Materials Science and Engineering, Nankai University, Tianjin 300071, China
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A Mixed-Culture Biofilm Model with Cross-Diffusion. Bull Math Biol 2015; 77:2086-124. [PMID: 26582360 DOI: 10.1007/s11538-015-0117-1] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/29/2014] [Accepted: 10/15/2015] [Indexed: 10/22/2022]
Abstract
We propose a deterministic continuum model for mixed-culture biofilms. A crucial aspect is that movement of one species is affected by the presence of the other. This leads to a degenerate cross-diffusion system that generalizes an earlier single-species biofilm model. Two derivations of this new model are given. One, like cellular automata biofilm models, starts from a discrete in space lattice differential equation where the spatial interaction is described by microscopic rules. The other one starts from the same continuous mass balances that are the basis of other deterministic biofilm models, but it gives up a simplifying assumption of these models that has recently been criticized as being too restrictive in terms of ecological structure. We show that both model derivations lead to the same PDE model, if corresponding closure assumptions are introduced. To investigate the role of cross-diffusion, we conduct numerical simulations of three biofilm systems: competition, allelopathy and a mixed system formed by an aerobic and an anaerobic species. In all cases, we find that accounting for cross-diffusion affects local distribution of biomass, but it does not affect overall lumped quantities such as the total amount of biomass in the system.
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Lindley B, Wang Q, Zhang T. Multicomponent hydrodynamic model for heterogeneous biofilms: two-dimensional numerical simulations of growth and interaction with flows. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:031908. [PMID: 22587124 DOI: 10.1103/physreve.85.031908] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/26/2011] [Revised: 12/06/2011] [Indexed: 05/31/2023]
Abstract
We develop a tricomponent (ternary) hydrodynamic model for multiphase flows of biomass and solvent mixtures, which we employ to simulate biofilm. In this model, the three predominant effective components in biofilms, which are the extracellular polymeric substance (EPS) network, the bacteria, and the effective solvent (consisting of the solvent and nutrient, etc.), are modeled explicitly. The tricomponent fluid mixture is assumed incompressible as a whole, while intercomponent mixing, dissipation, and conversion are allowed among the effective components. Bacterial growth and EPS production due to the growing bacterial population are modeled in the biomass transport equations. Bacterial decay due to starvation and natural causes is accounted for in the bacterial population dynamics to capture the possible bacterial population reduction due to the depletion of the nutrient. In the growth regime for biofilms, the mixture behaves like a multiphase viscous fluid, in which the molecular relaxation is negligible in the corresponding time scale. In this regime, the dynamics of biofilm growth in the solvent (water) are simulated using a two-dimensional finite difference solver that we developed, in which the distribution and evolution of the EPS and bacterial volume fractions are investigated. The hydrodynamic interaction between the biomass and the solvent flow field is also simulated in a shear cell environment, demonstrating the spatially and temporally heterogeneous distribution of the EPS and bacteria under shear. This model together with the numerical codes developed provides a predictive tool for studying biomass-flow interaction and other important biochemical interactions in the biofilm and solvent fluid mixture.
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Affiliation(s)
- Brandon Lindley
- Code 6792, Plasma Physics Division, US Naval Research Laboratory, Washington, District of Columbia 20375, USA.
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Little TS, Mironov V, Nagy Mehesz A, Markwald R, Sugi Y, Lessner SM, Sutton MA, Liu X, Wang Q, Yang X, Blancette JO, Skiles M. Engineering a 3D, biological construct: representative research in the South Carolina Project for Organ Biofabrication. Biofabrication 2011; 3:030202. [DOI: 10.1088/1758-5082/3/3/030202] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023]
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