A Bayesian approach to modelling the impact of hydrodynamic shear stress on biofilm deformation

We investigate the feasibility of using a surrogate-based method to emulate the deformation and detachment behaviour of a biofilm in response to hydrodynamic shear stress. The influence of shear force, growth rate and viscoelastic parameters on the patterns of growth, structure and resulting shape of microbial biofilms was examined. We develop a statistical modelling approach to this problem, using combination of Bayesian Poisson regression and dynamic linear models for the emulation. We observe that the hydrodynamic shear force affects biofilm deformation in line with some literature. Sensitivity results also showed that the expected number of shear events, shear flow, yield coefficient for heterotrophic bacteria and extracellular polymeric substance (EPS) stiffness per unit EPS mass are the four principal mechanisms governing the bacteria detachment in this study. The sensitivity of the model parameters is temporally dynamic, emphasising the significance of conducting the sensitivity analysis across multiple time points. The surrogate models are shown to perform well, and produced ≈ 480 fold increase in computational efficiency. We conclude that a surrogate-based approach is effective, and resulting biofilm structure is determined primarily by a balance between bacteria growth, viscoelastic parameters and applied shear stress.

[1]  P. G. Jayathilake,et al.  A mechanistic Individual-based Model of microbial communities , 2017, PloS one.

[2]  E Morgenroth,et al.  Monitoring biofilm detachment under dynamic changes in shear stress using laser-based particle size analysis and mass fractionation. , 2003, Water science and technology : a journal of the International Association on Water Pollution Research.

[3]  K. Foster,et al.  Adhesion as a weapon in microbial competition , 2014, The ISME Journal.

[4]  D. Head,et al.  Linear surface roughness growth and flow smoothening in a three-dimensional biofilm model. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  P. Gupta,et al.  Gaussian process emulation of an individual-based model simulation of microbial communities , 2017, J. Comput. Sci..

[6]  Hanqing Yu,et al.  Characterization of extracellular polymeric substances produced by mixed microorganisms in activated sludge with gel-permeating chromatography, excitation-emission matrix fluorescence spectroscopy measurement and kinetic modeling. , 2009, Water research.

[7]  A. O'Hagan,et al.  Bayesian calibration of computer models , 2001 .

[8]  Jost Wingender,et al.  What are Bacterial Extracellular Polymeric Substances , 1999 .

[9]  K. Kockelman,et al.  Bayesian Multivariate Poisson Regression for Models of Injury Count, by Severity , 2006 .

[10]  J. Seoane,et al.  Growth dependence of conjugation explains limited plasmid invasion in biofilms: an individual-based modelling study. , 2011, Environmental microbiology.

[11]  J J Heijnen,et al.  Effect of diffusive and convective substrate transport on biofilm structure formation: a two-dimensional modeling study. , 2000, Biotechnology and bioengineering.

[12]  Yilei Zhang,et al.  Individual based modeling of Pseudomonas aeruginosa biofilm with three detachment mechanisms , 2015 .

[13]  Dieter Gerten,et al.  Emulating global climate change impacts on crop yields , 2015 .

[14]  A. O'Hagan,et al.  Probabilistic sensitivity analysis of complex models: a Bayesian approach , 2004 .

[15]  Thomas J. Santner,et al.  Design and analysis of computer experiments , 1998 .

[16]  Joo-Hwa Tay,et al.  The essential role of hydrodynamic shear force in the formation of biofilm and granular sludge. , 2002, Water research.

[17]  J J Heijnen,et al.  Two-dimensional model of biofilm detachment caused by internal stress from liquid flow. , 2001, Biotechnology and bioengineering.

[18]  Peter C. Young,et al.  Statistical Emulation of Large Linear Dynamic Models , 2011, Technometrics.

[19]  Cory J. Rupp,et al.  Biofilm material properties as related to shear-induced deformation and detachment phenomena , 2002, Journal of Industrial Microbiology and Biotechnology.

[20]  C. Picioreanu,et al.  A mass-spring model unveils the morphogenesis of phototrophic Diatoma biofilms , 2014, Scientific Reports.

[21]  Alain Liné,et al.  Effect of shear stress and growth conditions on detachment and physical properties of biofilms. , 2011, Water research.

[22]  GraphicsHani Doss.  Bayesian Poisson Regression using the Gibbs Sampler : Sensitivity Analysis through Dynamic , 2007 .

[23]  Giovanni Petris,et al.  State Space Models in R , 2011 .

[24]  M. V. van Loosdrecht,et al.  Results from the multi-species benchmark problem (BM3) using one-dimensional models. , 2004, Water science and technology : a journal of the International Association on Water Pollution Research.

[25]  S. Chib,et al.  Understanding the Metropolis-Hastings Algorithm , 1995 .

[26]  D. M. Titterington,et al.  Bayesian regression and classification using mixtures of Gaussian processes , 2003 .

[27]  B. Rittmann,et al.  Measurement of the Activity of a Biofilm: Effects of Surface Loading and Detachment on a Three-Phase, Liquid-Fluidized-Bed Reactor , 1992 .

[28]  Nuno Vasconcelos,et al.  Bayesian Poisson regression for crowd counting , 2009, 2009 IEEE 12th International Conference on Computer Vision.

[29]  Giovanni Petris,et al.  Dynamic linear models , 2009 .

[30]  P. G. Jayathilake,et al.  Extracellular Polymeric Substance Production and Aggregated Bacteria Colonization Influence the Competition of Microbes in Biofilms , 2017, Front. Microbiol..

[31]  Mark C M van Loosdrecht,et al.  A general description of detachment for multidimensional modelling of biofilms. , 2005, Biotechnology and bioengineering.

[32]  P Reichert,et al.  Mathematical modeling of mixed‐culture biofilms , 1996, Biotechnology and bioengineering.

[33]  G. Booth,et al.  BacSim, a simulator for individual-based modelling of bacterial colony growth. , 1998, Microbiology.

[34]  G. Casella,et al.  Explaining the Gibbs Sampler , 1992 .

[35]  R. Bakke,et al.  Modeling Pseudomonas aeruginosa biofilm detachment , 2003 .

[36]  A. Saltelli,et al.  Making best use of model evaluations to compute sensitivity indices , 2002 .

[37]  Anders Heyden,et al.  Three‐dimensional biofilm model with individual cells and continuum EPS matrix , 2006, Biotechnology and bioengineering.

[38]  Eoin Casey,et al.  Detachment characteristics of a mixed culture biofilm using particle size analysis , 2013 .

[39]  C. Geyer.  Markov Chain Monte Carlo Maximum Likelihood , 1991 .

[40]  Steve Plimpton,et al.  Fast parallel algorithms for short-range molecular dynamics , 1993 .