Modeling the response of a biofilm to silver-based antimicrobial

Abstract

Biofilms are found within the lungs of patients with chronic pulmonary infections, in particular patients with cystic fibrosis, and are the major cause of morbidity and mortality for these patients. The work presented here is part of a large interdisciplinary effort to develop an effective drug delivery system and treatment strategy to kill biofilms growing in the lung. The treatment strategy exploits silver-based antimicrobials, in particular, silver carbene complexes (SCC). This manuscript presents a mathematical model describing the growth of a biofilm and predicts the response of a biofilm to several basic treatment strategies. The continuum model is composed of a set of reaction-diffusion equations for the transport of soluble components (nutrient and antimicrobial), coupled to a set of reaction-advection equations for the particulate components (living, inert, and persister bacteria, extracellular polymeric substance, and void). We explore the efficacy of delivering SCC both in an aqueous solution and in biodegradable polymer nanoparticles. Minimum bactericidal concentration (MBC) levels of antimicrobial in both free and nanoparticle-encapsulated forms are estimated. Antimicrobial treatment demonstrates a biphasic killing phenomenon, where the active bacterial population is killed quickly followed by a slower killing rate, which indicates the presence of a persister population. Finally, our results suggest that a biofilm with a ready supply of nutrient throughout its depth has fewer persister bacteria and hence may be easier to treat than one with less nutrient.

Figure 1

Effect of different concentrations of surface antimicrobial (C_source) on the mass of living bacteria.

Figure 2

Effect of different concentrations of surface antimicrobial (C_source) on the height of the biofilm.

Figure 3

The mass of living bacteria as a function of time predicted by simulations for different numbers of nanoparticles/mL.

Figure 4

Effect of different amounts of antimicrobial-loaded nanoparticles/mL on the height of the biofilm.

Figure 5

Concentration of antimicrobial present in biofilm vs time due to antimicrobial release from nanoparticles/mL.

Figure 6

Mass of living bacteria over time for different source values of nutrient in the presence of 5 × 10¹⁰ antimicrobial-loaded nanoparticles/mL.

Figure 7

Effect of changing k_r and k_r on the mass of living bacteria in the presence of 5 × 10¹⁰ nanoparticles/mL.