A Multiscale Model of Biofilm as a Senescence-Structured Fluid

We derive a physiologically structured multiscale model for biofilm development. The model has components on two spatial scales, which induce different time scales into the problem. The macroscopic behavior of the system is modeled using growth‐induced flow in a domain with a moving boundary. Cell‐level processes are incorporated into the model using a so‐called physiologically structured variable to represent cell senescence, which in turn affects cell division and mortality. We present computational results for our models which shed light on modeling the combined role senescence and the biofilm state play in the defense strategy of bacteria.

[1]  K. Lewis,et al.  Riddle of Biofilm Resistance , 2001, Antimicrobial Agents and Chemotherapy.

[2]  Alexander R. A. Anderson,et al.  Computational Methods and Results for Structured Multiscale Models of Tumor Invasion , 2005, Multiscale Model. Simul..

[3]  R. Walmsley,et al.  Replicative ageing in the fission yeast Schizosaccharomyces pombe , 1999, Yeast.

[4]  R. Mortimer,et al.  Life Span of Individual Yeast Cells , 1959, Nature.

[5]  R. LeVeque.  Finite Volume Methods for Hyperbolic Problems: Characteristics and Riemann Problems for Linear Hyperbolic Equations , 2002 .

[6]  Philip S. Stewart,et al.  Modeling Antibiotic Tolerance in Biofilms by Accounting for Nutrient Limitation , 2004, Antimicrobial Agents and Chemotherapy.

[7]  Glenn F. Webb,et al.  α- and β-curves, sister-sister and mother-daughter correlations in cell population dynamics , 1989 .

[8]  P. Stewart,et al.  Modelling protection from antimicrobial agents in biofilms through the formation of persister cells. , 2005, Microbiology.

[9]  G. Webb,et al.  Diffusion epidemic models with incubation and crisscross dynamics. , 1995, Mathematical biosciences.

[10]  J. Costerton,et al.  Biofilms as complex differentiated communities. , 2002, Annual review of microbiology.

[11]  K. Lewis,et al.  Persister cells and tolerance to antimicrobials. , 2004, FEMS microbiology letters.

[12]  P. Stewart,et al.  Senescence can explain microbial persistence. , 2006, Microbiology.

[13]  Isaac Klapper,et al.  Finger Formation in Biofilm Layers , 2002, SIAM J. Appl. Math..

[14]  Bruce P. Ayati,et al.  A Variable Time Step Method for an Age-Dependent Population Model with Nonlinear Diffusion , 1997, SIAM J. Numer. Anal..

[15]  Todd F. Dupont,et al.  Convergence of a step-doubling Galerkin method for parabolic problems , 1999, Mathematics of Computation.

[16]  Philip S. Stewart,et al.  A Three-Dimensional Computer Model of Four Hypothetical Mechanisms Protecting Biofilms from Antimicrobials , 2006, Applied and Environmental Microbiology.

[17]  M. R. Brown,et al.  Influence of growth rate on susceptibility to antimicrobial agents: biofilms, cell cycle, dormancy, and stringent response , 1990, Antimicrobial Agents and Chemotherapy.

[18]  Jelena Pjesivac-Grbovic,et al.  A multiscale model for avascular tumor growth. , 2005, Biophysical journal.

[19]  Bruce P Ayati,et al.  A structured-population model of Proteus mirabilis swarm-colony development , 2004, Journal of mathematical biology.

[20]  I. Klapper,et al.  A Multidimensional Multispecies Continuum Model for Heterogeneous Biofilm Development , 2007 .

[21]  S. Leibler,et al.  Bacterial Persistence as a Phenotypic Switch , 2004, Science.

[22]  James A. Shapiro,et al.  Kinetic model of Proteus mirabilis swarm colony development , 1998 .

[23]  Todd F. Dupont,et al.  Galerkin Methods in Age and Space for a Population Model with Nonlinear Diffusion , 1998, SIAM J. Numer. Anal..

[24]  N G Cogan,et al.  Effects of persister formation on bacterial response to dosing. , 2006, Journal of theoretical biology.

[25]  François Taddei,et al.  In Brief , 2003, Nature Reviews Microbiology.