A Stochastic Formulation of Bacterial Attachment in a Spatially Explicit Model of Cellulolytic Biofilm Formation

Abstract

We propose a mathematical framework for introducing random attachments of bacterial cells in continuum models of biofilms. Our approach deploys the formalism of stochastic differential equations to model an auxiliary stochastic process that drives impulses of bacterial cells. We especially apply the proposed framework to a spatially explicit model of cellulolytic biofilm formation, which comprises a coupled PDE-ODE system that governs the bacterial biomass and the carbon substrate. The model equations are discretized in space by a standard finite volume method and temporally integrated by explicit numerical schemes. We explore some computational and programming solutions for improving the speed and efficiency of simulations and preventing instability issues. Our numerical simulations reproduce the specific features of cellulolytic biofilms with cell attachments. Grid refinement studies show convergence for the expected values of spatially integrated biomass density and carbon concentration. We also examine the sensitivity of random attachments to a few model parameters.