Diffusion of antibiotics through a biofilm in the presence of diffusion and absorption barriers
- We propose a model of antibiotic diffusion through a bacterial biofilm when diffusion and/or absorption barriers develop in the biofilm. The idea of this model is: We deduce details of the diffusion process in a medium in which direct experimental study is difficult, based on probing diffusion in external regions. Since a biofilm has a gel-like consistency, we suppose that subdiffusion of particles in the biofilm may occur. To describe this process we use a fractional subdiffusion-absorption equation with an adjustable anomalous diffusion exponent. The boundary conditions at the boundaries of the biofilm are derived by means of a particle random walk model on a discrete lattice leading to an expression involving a fractional time derivative. We show that the temporal evolution of the total amount of substance that has diffused through the biofilm explicitly depends on whether there is antibiotic absorption in the biofilm. This fact is used to experimentally check for antibiotic absorption in the biofilm and if subdiffusion andWe propose a model of antibiotic diffusion through a bacterial biofilm when diffusion and/or absorption barriers develop in the biofilm. The idea of this model is: We deduce details of the diffusion process in a medium in which direct experimental study is difficult, based on probing diffusion in external regions. Since a biofilm has a gel-like consistency, we suppose that subdiffusion of particles in the biofilm may occur. To describe this process we use a fractional subdiffusion-absorption equation with an adjustable anomalous diffusion exponent. The boundary conditions at the boundaries of the biofilm are derived by means of a particle random walk model on a discrete lattice leading to an expression involving a fractional time derivative. We show that the temporal evolution of the total amount of substance that has diffused through the biofilm explicitly depends on whether there is antibiotic absorption in the biofilm. This fact is used to experimentally check for antibiotic absorption in the biofilm and if subdiffusion and absorption parameters of the biofilm change over time. We propose a four-stage model of antibiotic diffusion in biofilm based on the following physical characteristics: whether there is absorption of the antibiotic in the biofilm and whether all biofilm parameters remain unchanged over time. The biological interpretation of the stages, in particular their relation with the bacterial defense mechanisms, is discussed. Theoretical results are compared with empirical results of ciprofloxacin diffusion through Pseudomonas aeruginosa biofilm, and ciprofloxacin and gentamicin diffusion through Proteus mirabilis biofilm.…
Author details: | Tadeusz KosztolowiczORCiD, Ralf MetzlerORCiDGND |
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DOI: | https://doi.org/10.1103/PhysRevE.102.032408 |
ISSN: | 2470-0045 |
ISSN: | 2470-0053 |
Pubmed ID: | https://pubmed.ncbi.nlm.nih.gov/33075880 |
Title of parent work (English): | Physical review : E, Statistical, nonlinear and soft matter physics |
Publisher: | American Physical Society |
Place of publishing: | Melville, NY |
Publication type: | Article |
Language: | English |
Date of first publication: | 2020/09/16 |
Publication year: | 2020 |
Release date: | 2023/04/19 |
Volume: | 102 |
Issue: | 3 |
Article number: | 032408 |
Number of pages: | 11 |
Funding institution: | Jan Kochanowski University in Kielce [SMGR.RN.20.222.628]; German; Science Foundation (DFG)German Research Foundation (DFG) [ME 1535/7-1]; Foundation for Polish Science (FNP) within an Alexander von Humboldt; Honorary Polish Research Scholarship |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie |
DDC classification: | 5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik |
Peer review: | Referiert |