Model of ciprofloxacin subdiffusion inPseudomonas aeruginosabiofilm formed in artificial sputum medium

Abstract

We study theoretically and empirically ciprooxacin antibiotic diusion through a gel-like articial sputum medium (ASM) mimicking physiological conditions typical for a cystic brosis layer, in which regions occupied by Pseudomonas aeruginosa bacteria are present. Our theoretical model is based on the subdiusionabsorption equation with a fractional time derivative that describes molecules diusion in a medium structured as Thompson's plumpudding model; the pudding`background' represents ASM and the plums represent the bacterial biolm. We show that the process can be divided into three successive stages: (1) only antibiotic subdiusion with constant biolm parameters, (2) subdiusion and absorption of antibiotic molecules with variable biolm parameters, (3) subdiffusion and absorption in the medium but biolm parameters are constant. Stage 2 is interpreted as the appearance of an intensive defence bulidup of bacteria against the action of an antibiotic, 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 substance that has diused through the ASM with bacteria. Our analysis shows good agreement between experimental and our theoretical results.

Experimental and Theoretical Analysis of Metal Complex Diffusion through Cell Monolayer

“…These conditions depend on the probabilities of a particle passing across the thin membrane and the kind of diffusion in the considered system. For example, in the case of subdiffusion (this process occurs in many biological processes, such as antibiotics transport in a bacterial biofilm [ 17 , 25 ]), the mean time that a particle waits to take its next step is infinite, as opposed to the diffusion process in which this time is finite. This means that the frequencies of a particle’s attempts to pass across the membrane for these processes are described by qualitatively different functions; for subdiffusion, this frequency is significantly lower than for normal diffusion.…”

“…In practice, the derivation of for the system considered in this paper is analogous with the derivation of a similar function in the system in which antibiotics diffuse across the bacterial biofilm [ 17 , 25 ].…”

“…Laser interferometry was previously used by us to test various theoretical models of diffusion, to study membrane substance transport, to determine membrane transport parameters under concentration polarization conditions, to analyze anomalous diffusion (subdiffusion) in gel systems, and to probe hydrodynamic instability [ 15 , 16 , 17 , 18 ]. After various modifications, we also employed laser interferometry to test the release and interactions of macromolecules with biologically active substances, such as bacterial liposaccharide (LPS) endotoxin with colistin, chitosan and saponin [ 19 , 20 , 21 ].…”

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

“…Moreover, in some cases the order of the stages may be different than the one presented in Sec. 6 [49].…”