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 antib acterial agent into a bacterial biofilm and, in particular, the penetr ation of a beta-lactam compound into a biofilm of Pseudomonas aerugino sa. As well as dealing with this penetration, and the consequent bacte rial lysis, the model considered diffusion of the released beta-lactam ases in the extracellular space and the consequent inactivation there of further incoming antibiotic; it also allowed for any chosen fractio n of the total beta-lactamase to be permanently accessible to exogenou s substrate. The modelling scheme was validated against analytical sol utions under appropriately simplified conditions. Using published expe rimental data we show here that lysis of cells ill the surface layers of a film could have an important protective effect on the viability o f underlying bacteria, especially in thick biofilms.