Diffusion of antibiotics through a biofilm in the presence of diffusion and absorption barriers

Kosztołowicz, Tadeusz; Metzler, Ralf

doi:10.1103/physreve.102.032408

Cited by 26 publications

(22 citation statements)

References 58 publications

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“…It can be assumed that then the bacteria have been inactivated. In order to find the answer to this problem we study experimentally the time evolution of the amount of antibiotic W B that has diffused from region A to B through the biofilm in a system presented schematically in Fig 1. The theoretical description is derived from a model based on the subdiffusion-absorption equation with fractional time derivative which describes antibiotic diffusion in a pure biofilm [21]. The theoretical model shows that the form of W B depends on the presence of antibiotic molecule absorption in the biofilm.…”

Section: Methodsmentioning

confidence: 99%

“…To describe diffusion-absorption in a biofilm, we use the approximation of a homogeneous medium M. The parameters α, D M , and κ are effective parameters describing diffusion and absorption throughout the medium; they represent antibiotic diffusion through the matrix and the interaction with the biofilm plums. The boundary conditions at the border between the media, which were derived in [21], are…”

Section: Theorymentioning

confidence: 99%

“…The boundary conditions mean that the diffusion flux at the biofilm surface is continuous and that the antibiotic molecule that tries to leave the biofilm can do so without any obstacles, but its passage into the biofilm surface in the opposite direction can be made with asymmetric probabilities 1 − q A (for the biofilm surface located at x 1 ) and 1 − q B (at x 2 ) [21,39].…”

Section: Theorymentioning

confidence: 99%

“…In this case, the process is described by the subdiffusion equation in which the reaction term is absent. The foundations of the theoretical model and calculation details are presented in [21], where subdiffusion of an antibiotic through a dense biofilm is described; in a dense biofilm antibiotic molecules can interact with bacteria throughout the biofilm volume.…”

Section: Introductionmentioning

confidence: 99%

“…This function takes different forms depending on whether or not antibiotic molecules are absorbed in the biofilm. To derive this function, the homogeneous biofilm approximation and the quasi-stationary approximation have been used [21]. Four stages in the process of transporting antibiotics through a biofilm have been defined by means of two criteria: (a) whether or not absorption of antibiotic particles in the biofilm occurs, (b) whether or not all biofilm parameters remain constant over time.…”

Section: Introductionmentioning

confidence: 99%

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Modelling experimentally measured of ciprofloxacin antibiotic diffusion in Pseudomonas aeruginosa biofilm formed in artificial sputum medium

et al. 2020

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We study the experimentally measured ciprofloxacin antibiotic diffusion through a gel-like artificial sputum medium (ASM) mimicking physiological conditions typical for a cystic fibrosis layer, in which regions occupied by Pseudomonas aeruginosa bacteria are present. To quantify the antibiotic diffusion dynamics we employ a phenomenological model using a subdiffusion-absorption equation with a fractional time derivative. This effective equation describes molecular diffusion in a medium structured akin Thompson’s plumpudding model; here the ‘pudding’ background represents the ASM and the ‘plums’ represent the bacterial biofilm. The pudding is a subdiffusion barrier for antibiotic molecules that can affect bacteria found in plums. For the experimental study we use an interferometric method to determine the time evolution of the amount of antibiotic that has diffused through the biofilm. The theoretical model shows that this function is qualitatively different depending on whether or not absorption of the antibiotic in the biofilm occurs. We show that the process can be divided into three successive stages: (1) only antibiotic subdiffusion with constant biofilm parameters, (2) subdiffusion and absorption of antibiotic molecules with variable biofilm transport parameters, (3) subdiffusion and absorption in the medium but the biofilm parameters are constant again. Stage 2 is interpreted as the appearance of an intensive defence build–up of bacteria against the action of the antibiotic, and in the stage 3 it is likely that the bacteria have been inactivated. Times at which stages change are determined from the experimentally obtained temporal evolution of the amount of antibiotic that has diffused through the ASM with bacteria. Our analysis shows good agreement between experimental and theoretical results and is consistent with the biologically expected biofilm response. We show that an experimental method to study the temporal evolution of the amount of a substance that has diffused through a biofilm is useful in studying the processes occurring in a biofilm. We also show that the complicated biological process of antibiotic diffusion in a biofilm can be described by a fractional subdiffusion-absorption equation with subdiffusion and absorption parameters that change over time.

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Section: Methodsmentioning

confidence: 99%

Section: Theorymentioning

confidence: 99%

Section: Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Modelling experimentally measured of ciprofloxacin antibiotic diffusion in Pseudomonas aeruginosa biofilm formed in artificial sputum medium

et al. 2020

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Diffusion profiles in L. lactis biofilms under different conditions

Chodorski

Hauth

Strieth

et al. 2020

Engineering in Life Sciences

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Despite being an important topic in biofilm research, we still know little about diffusion in biofilms. Emerging biofilms of Lactococcus lactis growing in custom‐made flow‐cells were monitored and diffusion constants across the height of the biofilms recorded. The biofilms showed different diffusional behavior with regard to flow rate and pH variations, despite growing to similar thickness. At a higher flow rate, the biofilm exhibits slower diffusion compared to the reference cultivation at lower flow rate. By increasing pH, the biofilm exhibited fast growth and little difference in diffusion compared to the reference cultivation. Furthermore, the diffusion inside of the biofilms differed depending on the position in the flow‐cell. The present study reveals new insights in how external factors can affect structure and density of biofilms. The method can be reliably used for L. lactis biofilms with a thickness up to 120 μm.

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Error analysis of a highly efficient and accurate temporal multiscale method for a fractional differential system

Wang,

Lin

2024

Chaos, Solitons & Fractals

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Diffusion of antibiotics through a biofilm in the presence of diffusion and absorption barriers

Cited by 26 publications

References 58 publications

Modelling experimentally measured of ciprofloxacin antibiotic diffusion in Pseudomonas aeruginosa biofilm formed in artificial sputum medium

Modelling experimentally measured of ciprofloxacin antibiotic diffusion in Pseudomonas aeruginosa biofilm formed in artificial sputum medium

Diffusion profiles in L. lactis biofilms under different conditions

Error analysis of a highly efficient and accurate temporal multiscale method for a fractional differential system

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