Mathematical Modeling of Spatio-temporal Organization of Biofilm Structure

Biofilms are initiated by individual polymer producing bacteria in aqueous. These polymers form a network combined with the fluid solvent creating a gel-like fluid that exhibits complex, viscoelastic rheological behavior and is involved in biofilm development and integrity. In this work, we developed a mathematical model to describe the spatio-temporal organization of the biofilm components in various settings. The biofilm is modeled as a multi-phase system where each volume in space is fractionally occupied by the polymeric network and the fluid solvent. The polymeric network is modeled as a chemically active, viscoelastic fluid that induces viscoelastic stresses and osmotic pressure due to the chemical reactions of the active polymers. The fluid solvent is modeled as a Newtonian fluid. Each fluid moves with its own velocity and the difference in velocities develop a drag force between the phases, coupling the mechanics. Using numerical methods similar to those used to solve the Navier-Stokes equations, we investigated the dynamics and motion of the biofilm. Our numerical results help characterize the role of polymeric networks and various extracellular polymeric substances in the pattern formation of the biofilm structure.