Mathematical model of beta-lactam penetration into a biofilm of Pseudomonas aeruginosa while undergoing simultaneous inactivation by released beta-lactamases.

We present a mathematical model that describes penetration of an antibacterial agent into a bacterial biofilm and, in particular, the penetration of a beta-lactam compound into a biofilm of Pseudomonas aeruginosa. As well as dealing with this penetration, and the consequent bacterial lysis, the model considered diffusion of the released beta-lactamases in the extracellular space and the consequent inactivation there of further incoming antibiotic; it also allowed for any chosen fraction of the total beta-lactamase to be permanently accessible to exogenous substrate. The modelling scheme was validated against analytical solutions under appropriately simplified conditions. Using published experimental data we show here that lysis of cells in the surface layers of a film could have an important protective effect on the viability of underlying bacteria, especially in thick biofilms.