Random walk calculations for bacterial migration in porous media

Abstract

Bacterial migration is important in understanding many practical problems ranging from disease pathogenesis to the bioremediation of hazardous waste in the environment. Our laboratory has been successful in quantifying bacterial migration in fluid media through experiment and the use of population balance equations and cellular level simulations that incorporate parameters based on a fundamental description of the microscopic motion of bacteria. The present work is part of an effort to extend these results to bacterial migration in porous media. Random walk algorithms have been used successfully to date in nonbiological contexts to obtain the diffusion coefficient for disordered continuum problems. This approach has been used here to describe bacterial motility. We have generated model porous media using molecular dynamics simulations applied to a fluid with equal sized spheres. The porosity is varied by allowing different degrees of sphere overlap. A random walk algorithm is applied to simulate bacterial migration, and the Einstein relation is used to calculate the effective bacterial diffusion coefficient. The tortuosity as a function of particle size is calculated and compared with available experimental results of migration of Pseudomonas putida in sand columns. Tortuosity increases with decreasing obstacle diameter, which is in agreement with the experimental results.

Turn angle and run time distributions characterize swimming behavior for Pseudomonas putida

“…Why does P. putida not simply use the same distribution as E. coli? To help answer this question cellular dynamic simulations were run as described in Duffy et al (7). Parameter values for the bacterial size (2 m), the swimming speed (44 m/s), and the duration (0.025 s) and frequency (0.5 s…”

Digital Object Identifier (DOI)

“…For example, in section 4.1 an explicit formula (22) is given for converting the local turn angle probability density distribution W (α) to a global distribution K(θ |θ), which is needed for analyzing the chemotactic cell balance equation. This is experimentally relevant because the random turning process of motile bacteria is typically characterized in local coordinates [5,14,16]. The most salient point of this work is the adoption of a non-smooth, biphasic tumbling frequency.…”

“…This biphasic form in (3) has been used previously by Rivero et al [33] and Ford and coworkers [7,9,15,16,21,40] in their simulations. Note that the biphasic β in (3) is non-smooth at the point + e · ξ = 0 due to the discontinuous slope of β with respect to the overall chemical material gradient + e · ξ .…”

Cold SQUIDs and hot samples

“…I formulated one possibility during a foray into the biology literature. While skimming through a biophysics journal, I came across an article by Professor Roseanne Ford's group at the University of Virginia describing calculations of the dynamics of bacterial migration in porous media [61]. One of the key references [62] described her group's experimental measurements of the effective diffusion constant of swimming bacteria in a liquid-saturated sand column in the presence of a chemoattractant gradient.…”