"Modeling Biofilm Spatio-temporal Organization as a Viscoelastic Gel-mix"
Biofilms are complex heterogeneous substances that can be viewed from the perspective of soft matter physics and continuum mechanics. Biofilm structure can be modeled as a multiphase system where each component has its own rheological characteristics. From the biophysics point of view, the biofilm components create a gel-mix consisting of a polymeric network (polysaccharides) and fluid solvent. The biological and mechanical interactions between these components govern biofilm physics and its spatial variation. We developed a mathematical model to describe the spatiotemporal organization of the biofilm components as a multiphase system where each volume in space is fractionally occupied by the polymeric network and the fluid solvent. The polymeric network is modeled as a viscoelastic fluid that induces viscoelastic stresses due to the rheological behavior of polysaccharides. This viscoelastic stress is a function of the biofilm viscoelastic properties, which are estimated using a Markov Chain Monte Carlo method based on experimental data. The fluid solvent is modeled as a Newtonian fluid, creating viscous stresses within the computational domain. The dynamics of the phases are governed by the conservation of mass and momentum. Each phase moves with its own velocity, introducing a drag force between the phases that is proportional to the velocity difference between the phases. The motion and interaction of the gel-mix components are formulated as a set of equations in an incompressible Navier-Stokes form. These equations are discretized in integral form for infinitesimal control volumes on a two-dimensional staggered grid. This model helps us understand the motion of the biofilm components and can help future researches elucidate the dynamics of polymeric network that forms the backbone of the biofilm.
Additional authors: N. G. Cogan Florida State University