Metzler, R. | bioRxiv Science

bioRxiv2020

Model of ciprofloxacin subdiffusion in Pseudomonas aeruginosa biofilm formed in artificial sputum medium

We study theoretically and empirically ciprofioxacin 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. Our theoretical model is based on the subdiffusion-absorption equation with a fractional time derivative that describes molecules diffusion in a medium structured as Thompsons plumpudding model; the pudding background represents ASM and the plums represent the bacterial biofilm. 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 parameters, (3) subdiffusion and absorption in the medium but biofilm parameters are constant. Stage 2 is interpreted as the appearance of an intensive defence bulid-up 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 diffused through the ASM with bacteria. Our analysis shows good agreement between experimental and our theoretical results.

biophysics↗

bioRxiv2019

Serotonergic Axons as Fractional Brownian Motion Paths: Insights into the Self-organization of Regional Densities

All vertebrate brains contain a dense matrix of thin fibers that release serotonin (5-hydroxytryptamine), a neurotransmitter that modulates a wide range of neural, glial, and vascular processes. Perturbations in the density of this matrix have been associated with a number of mental disorders, including autism and depression, but its self-organization and plasticity remain poorly understood. We introduce a model based on reflected Fractional Brownian Motion (FBM), a rigorously defined stochastic process, and show that it recapitulates some key features of regional serotonergic fiber densities. Specifically, we use supercomputing simulations to model fibers as FBM-paths in two-dimensional brain-like domains and demonstrate that the resultant steady state distributions approximate the fiber distributions in physical brain sections immunostained for the serotonin transporter (a marker for serotonergic axons in the adult brain). We suggest that this framework can support predictive descriptions and manipulations of the serotonergic matrix and that it can be further extended to incorporate the detailed physical properties of the fibers and their environment.

neuroscience↗