MSc Math Defence: A Stochastic formulation of bacterial attachment in a spatially explicit model of cellulolytic biofilm formation

CANDIDATE:  YOUSEF ROHANIZADEGAN

ABSTRACT:

We propose a mathematical framework for introducing the discrete random phenomenon of bacterial cell attachment to underlying structures in continuum models of biofilm formations. Our approach deploys the formalism of stochastic differential equations for generating a non-physical continuous stochastic process which is translated into impulses of bacterial cells whenever certain conditions are satisfied. We especially apply the proposed framework to a spatially explicit model of cellulolytic biofilm formation which comprises a highly nonlinear degenerate coupled PDE-ODE system for describing the growth of cellulose degrading biomass and the consumption of immobilized carbon in the cellulosic substratum. The governing equations are discretized in space by using a standard finite volume method and the temporal integration of the resulting system of SDEs is implemented by explicit numerical schemes to optimally capture the stochastic behavior. We explore some computational and programming solutions for improving the speed and efficiency of the computer simulations and the prevention of possible instability issues associated with the application of explicit methods. Our numerical simulations reproduce the specific features of cellulolytic biofilm formations that undergo random cell attachments as experimental data suggests. Grid refinement studies show convergence for the expected values of spatially integrated biomass density and carbon concentration over many sampled simulations. We also identify the most sensitive model parameters for controlling the spatiotemporal intensity of random attachments and lay out possible simulation scenarios for numerical experimentation by manipulating these parameters and the initial data for state variables.