A multiscale mathematical model for biofilm structure and viscoelasticity

Biofilms are initiated by individual polymer-producing bacteria in aqueous that undergo a phenotypic switch and produce various types of extracellular polymeric substances (EPS). The EPS form a polymeric network combined with the fluid solvent creating a gel-like fluid that exhibits rheological behavior. We developed a mathematical model to study this complex heterogeneous system across different scales. First, we implemented a linear viscoelastic model to describe the biofilm viscoelastic response during a creep-recovery test. Then, using a Bayesian framework, we estimated the viscoelastic parameters and quantified the uncertainty in their estimation for three different Pseudomonas aeruginosa biofilm variants at different stages of formation based on experimental data. Finally, we modeled the spatiotemporal organization of biofilm composition as a multi-phase system where each volume in space is fractionally occupied by the polymeric network and the fluid solvent. Each fluid moves with its own velocity, and the difference in velocities develops a drag force between the phases, coupling the mechanics. We formulated the motion and interaction of these components as a set of equations in an incompressible Navier-Stokes form. This model helps us understand the motion of the biofilm components and can help future research works elucidate the dynamics of polymeric network that forms the backbone of the biofilm.