The Effect of Pore Geometry on Upscaled Models of Transport of Motile Bacteria

Abstract:

Accurate models of bacterial motion dynamics are important in several applications, including development of improved predictive tools for bioremediation. While many bioremediation models neglect the motility of the bacteria, others have treated motility using an advection dispersion equation (ADE), which assumes that the motion of the bacteria is Brownian. The assumption of Brownian motion to describe motility has enormous implications on predictive capabilities of bioremediation models, yet experimental evidence of this assumption is mixed^[1][2][3]. We have found that in open domains this is due to scale dependence of the motion dynamics.

Using a single motile bacterial species (Paenibacillus) we identify the effect of pore geometry on the timescale when transition from Brownian motion (diffusive behavior) to sub-diffusive or super-diffusive behavior occurs. We analyze videos of Paenibacillus in four porous domains with different geometries and compare their behavior in these domains to their natural behavior in open domains. Trajectories of individual cells ranging from several seconds to few minutes in duration are extracted in neutral conditions (in the absence of any chemical or redox gradient). The density of the bacteria is kept low so that the interaction between individual cells is minimal. This analysis helps in determining the suitability of ADE based transport models as a function of timescale and environmental conditions, and provides a pathway for development of methodologies to include bacterial motion dynamics in bioremediation implementations. We discuss potential alternatives to ADE based upscaling approaches for timescales when transport cannot be described with Brownian motion.

[1] Ariel, Gil, et al. "Swarming bacteria migrate by Lévy Walk." Nature Communications 6 (2015).

[2] Saragosti, Jonathan, Pascal Silberzan, and Axel Buguin. "Modeling E. coli tumbles by rotational diffusion. Implications for chemotaxis." PloS one 7.4 (2012): e35412.

[3] Wu, Mingming, et al. "Collective bacterial dynamics revealed using a three-dimensional population-scale defocused particle tracking technique." Applied and Environmental Microbiology 72.7 (2006): 4987-4994.