A Universal Model of Restricted Diffusion for Fluorescence Correlation Spectroscopy

Fluorescence correlation spectroscopy (FCS) is frequently used to study the processes of restricted diffusion. The most important quantity to determine is the size of the structures that hinder the Brownian motion of the molecules. We study three qualitatively different models of restricted diffusion, widely applied in biophysics and material science: Diffusion constrained by elastic force (i), walking confined diffusion (ii), and hop diffusion (iii). They cover the diversity of statistical behaviors, from purely Gaussian (i) to sharply non-Gaussian on intermediate time scales (ii) and, additionally, discrete (iii). We test whether one can use the Gaussian approximation of the FCS autocorrelation function to interpret the non-Gaussian data. We show that (i-iii) have approximately the same mean square displacements. Using simulations, we show that the FCS data suspected of restricted diffusion can be reliably interpreted using one archetypal model (i). Even if the underlying mechanism of the restriction is different or unknown, the accuracy of fitting the confinement size is excellent, and diffusion coefficients are also estimated with a good accuracy. This study gives a physical insight into the statistical behavior of different types of restricted diffusion and into the ability of fluorescence correlation spectroscopy to distinguish between them.