3-D Numerical Simulations of Biofilm Dynamics with Quorum Sensing in a Flow Cell

We develop a multiphasic hydrodynamic theory for biofilms taking into account interactions among various bacterial phenotypes, extracellular polymeric substances (EPS), quorum sensing (QS) molecules, solvent, and possibly antibiotics. In the model, bacteria are classified into down-regulated QS, upregulated QS, and non QS cells based on their QS ability. We then develop a second-order numerical scheme to solve the governing system of partial differential equations and implement it in 3D space and time on GPUs. The model is first bench-marked against an experiment yielding an excellent fit to experimental measurements on the concentration of QS molecules and the cell density during biofilm development. It is then applied to study development of heterogeneous structures in biofilms due to interactions of QS regulation, hydrodynamics, and possibly antimicrobial treatment. It shows that QS is beneficial for biofilm development in a long run by building a robust EPS population to protect the biofilm, but maybe of little benefit in a short time frame because it can slow down the growth of certain bacteria. 3D numerical simulations show that (i). QS down-regulated cells tend to grow at the surface of the biofilm while QS up-regulated ones tend to grow in the bulk; (ii). QS induction may not be fully operational and can even be compromised in strong laminar flows; (iii). biofilms located upstream can induce QS downstream when the colonies are close enough spatially; (iv). when nutrient supply is sufficient, QS induction is more effective upstream than downstream; (v). the hydrodynamic stress alters morphology of the biofilm. With the model, hydrodynamic details and rheological quantities associated with biofilm formation under QS regulation can be resolved.