Theoretical aspects of antibiotic diffusion into microbial biofilms

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Abstract
Antibiotic penetration into microbial biofilm was investigated theoretically by the solution of mathematical equations describing various combinations of the processes of diffusion, sorption, and reaction. Unsteady material balances on the antibiotic and on a reactive or sorptive biomass constituent, along with associated boundary and initial conditions, constitute the mathematical formulations. Five cases were examined: diffusion of a noninteracting solute; diffusion of a reversibly sorbing, nonreacting solute; diffusion of an irreversibly sorbing, nonreacting solute; diffusion of a stoichiometrically reacting solute; and diffusion of a catalytically reacting solute. A noninteracting solute was predicted to penetrate biofilms of up to 1 mm in thickness relatively quickly, within a matter of seconds or minutes. In the case of a solute that does not sorb or react in the biofilm, therefore, the diffusion barrier is not nearly large enough to account for the reduced susceptibility of biofilms to antibiotics. Reversible and irreversible sorption retards antibiotic penetration. On the basis of data available in the literature at this point, the extent of retardation of antibiotic diffusion due to sorption does not appear to be sufficient to account for reduced biofilm susceptibility. A catalytic (e.g., enzymatic) reaction, provided it is sufficiently rapid, can lead to severe antibiotic penetration failure. For example, calculation of beta-lactam penetration indicated that the reaction-diffusion mechanism may be a viable explanation for failure of certain of these agents to control biofilm infections. The theory presented in this study provides a framework for the design and analysis of experiments to test these mechanisms of reduced biofilm susceptibility to antibiotics.