Pharmacodynamic model of the dynamic response of Pseudomonas aeruginosa biofilms to drug treatments

Chronic infection by gram-negative bacteria such as Pseudomonas aeruginosa is a leading cause of morbidity and mortality in cystic fibrosis patients in whom overabundant mucus and the formation of bacterial biofilms pose barriers to drug delivery and effectiveness. Accurate pharmacokinetic-pharmacodynamic (PK-PD) models of biofilm treatment could be used to guide formulation and administration strategies to better control bacterial lung infections. To this end, we have developed a detailed pharmacodynamic model of P. aeruginosa treatment with the front-line antibiotics, tobramycin and colistin, and validated it on a detailed dataset of killing dynamics. A compartmental model structure was developed in which the key features are diffusion of drug through a boundary layer to the bacteria, concentration dependent interactions with bacteria, and passage of the bacteria through successive transit states before death. The number of transit states employed was greater for tobramycin, which is a ribosomal inhibitor, than for colistin, which disrupts bacterial membranes. For both drugs, the experimentally observed delay in killing of bacteria following drug exposure was replicated and was consistent with the diffusion time, though for tobramycin, there was an additional delay reflected in the model by passage through the transit states. For each drug, the PD model with a single set of parameters described data across a ten-fold range of concentrations and for both continuous and transient exposure protocols. Furthermore, the parameters fit for each drug individually were used to model the response of biofilms to combined treatment with tobramycin and colistin. The ability to predict drug response over a range of administration protocols allows this PD model to be integrated with PK descriptions to describe in vivo antibiotic response dynamics and to predict drug delivery strategies for improved control of bacterial lung infections. Author Summary Biofilms are self-assembling bacterial communities that adhere to a surface and encase themselves in a protective coating. Biofilm infections are notoriously difficult to treat with conventional antibiotic administrations. To understand better the dynamics of bacterial biofilm killing in response to antibiotic treatment, we developed a mathematical model that integrates several features: drug diffusion through a boundary layer that includes the biofilm casing, concentration dependent cell damage, and passage of the cell through damaged states to eventual death. We validated the model by comparison with an extensive published dataset of biofilm response to treatment with the antibiotics, tobramycin and colistin. The model fits to these datasets were able to capture the observed trends for several antibiotic administration protocols, with model parameters reflecting the differences in mechanism of action between the two drugs. This validated model can be integrated with pharmacokinetic descriptions of drug distribution in the body over time to predict dosing and administration protocols for preclinical and clinical studies.