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A point process model for generating biofilms with realistic microstructure and rheology

Published online by Cambridge University Press:  16 May 2018

JAY ALEXANDER STOTSKY ,
VANJA DUKIC  and
DAVID M. BORTZ
JAY ALEXANDER STOTSKY
Affiliation:
Department of Applied Mathematics, University of Colorado, Boulder, CO 80309-0526, USA emails: Jay.Stotsky@colorado.edu, Vanja.Dukic@colorado.edu, dmbortz@colorado.edu
VANJA DUKIC
Affiliation:
Department of Applied Mathematics, University of Colorado, Boulder, CO 80309-0526, USA emails: Jay.Stotsky@colorado.edu, Vanja.Dukic@colorado.edu, dmbortz@colorado.edu
DAVID M. BORTZ
Affiliation:
Department of Applied Mathematics, University of Colorado, Boulder, CO 80309-0526, USA emails: Jay.Stotsky@colorado.edu, Vanja.Dukic@colorado.edu, dmbortz@colorado.edu
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Abstract

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Biofilms are communities of bacteria that exhibit a multitude of multiscale biomechanical behaviours. Recent experimental advances have led to characterisations of these behaviours in terms of measurements of the viscoelastic moduli of biofilms grown in bioreactors and the fracture and fragmentation properties of biofilms. These properties are macroscale features of biofilms; however, a previous work by our group has shown that heterogeneous microscale features are critical in predicting biofilm rheology. In this paper, we use tools from statistical physics to develop a generative statistical model of the positions of bacteria in biofilms. Specifically, the model is a type of pairwise interaction model (PIM). We show through simulation that the macroscopic mechanical properties of biofilms depend on the choice of microscale spatial model. A key finding is that uniform and non-uniform sets of points lead to differing mechanical properties. This distinction appears not to have been previously considered in mathematical biofilm literature. We also found that realisations of a biologically informed PIM have realistic in silico mechanical properties, and have statistical properties that closely match experimental data. We also note that a Poisson spatial point process of suitable number density also yields realistic mechanical properties, but that the spatial distribution of points does not reflect those occurring in our experimentally observed biofilm.

Keywords

BiofilmsBiomechanicsNonparametric Density EstimationSpatial Stochastic Processes
Type
Papers
Information
European Journal of Applied Mathematics , Volume 29 , Special Issue 6: Biofilms , December 2018 , pp. 1141 - 1177
Copyright
Copyright © Cambridge University Press 2018 

Footnotes

†This work was supported in part by the National Science Foundation grants PHY-0940991 and DMS-1225878 to DMB, and by the Department of Energy through the Computational Science Graduate Fellowship program, DE-FG02-97ER25308, to JAS.

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