Molecular theory of anomalous diffusion - Application to Fluorescence Correlation Spectroscopy

TL;DR

This paper develops a nonlinear microscopic theory of anomalous diffusion, providing analytical solutions that explain experimental fluorescence correlation spectroscopy data, especially for sub-diffusive lipid molecules in cell membranes.

Contribution

It introduces an explicit analytical solution to the nonlinear diffusion equation applicable to fluorescence correlation spectroscopy analysis of biological systems.

Findings

The theory accurately reproduces experimental correlation spectra.

It explains sub-diffusive behavior of lipids in cell membranes.

The model captures the effects of particle interactions on diffusion.

Abstract

The nonlinear theory of anomalous diffusion is based on particle interactions giving an explicit microscopic description of diffusive processes leading to sub-, normal, or super-diffusion as a result competitive effects between attractive and repulsive interactions. We present the explicit analytical solution to the nonlinear diffusion equation which we then use to compute the correlation function which is experimentally measured by correlation spectroscopy. The theoretical results are applicable in particular to the analysis of fluorescence correlation spectroscopy of marked molecules in biological systems. More specifically we consider the case of fluorescently labeled lipids and we find that the nonlinear correlation spectrum reproduces very well the experimental data indicating sub-diffusive molecular motion of lipid molecules in the cell membrane.