Single File Dynamics Advances with a Focus on Biophysical Relevance

Abstract

In this review (appearing in the Special Issue on single file dynamics in biophysics and related extensions), three recently treated variants in file dynamics are presented: files with density that is not fixed, files with heterogeneous particles, and files with slow particles. The results in these files include:• In files with a density law that is not fixed, but decays as a power law with an exponent a the distance from the origin, the particle in the origin mean square displacement (MSD) scales like MSD ~ t[1+a]/2, with a Gaussian probability density function (PDF). This extends the scaling, MSD ~ t1/2, seen in a constant density file.• When, in addition, the particles' diffusion coefficients are distributed like a power law with an exponent γ (around the origin), the MSD follows MSD ~ t[1-γ]/[2/(1+a) - γ], with a Gaussian PDF.• In anomalous files that are renewal, namely, when all particles attempt a jump together, yet, with jump times taken from a PDF that decays as a power law with an exponent -1 - ε, ψ(t) ~ t-1-ε, the MSD scales like the MSD of the corresponding normal file, in the power ε.• In anomalous files of independent particles, the MSD is very slow and scales like MSD ~ log2(t). Even more exciting, the particles form clusters, defining a dynamical phase transition: depending on the anomaly power ε, the percentage of particles in clusters ξ follows [Formula: see text], yet when ε > 1, fluidity rather than clusters is seen.We talk about utilizing these results while focusing on biophysical processes and applications: dynamics in channels, membranes, biosensors, etc.[Formula: see text] Special Issue Comments: In this article, results about recently suggested variants in single file dynamics appear: heterogeneous files and slow files, yet also, the relevance with biophysical processes. It is related to the Special Issue articles about expansions in files,61files with force,62and the zig zag occurrences in files.63