The diffusion of macromolecules in cells and in complex fluids is often found to deviate from simple Fickian diffusion. One explanation offered for this behavior is that molecular crowding renders diffusion anomalous, where the mean-squared displacement of the particles scales as r 2 ∝ t α with α < 1. Unfortunately, methods such as fluorescence correlation spectroscopy (FCS) or fluorescence recovery after photobleaching (FRAP) probe diffusion only over a narrow range of lengthscales and cannot directly test the dependence of the mean-squared displacement (MSD) on time. Here we show that variable-lengthscale FCS (VLS-FCS), where the volume of observation is varied over several orders of magnitude, combined with a numerical inversion procedure of the correlation data, allows retrieving the MSD for up to five decades in time, bridging the gap between diffusion experiments performed at different lengthscales. In addition, we show that VLS-FCS provides a way to assess whether the propagator associated with the diffusion is Gaussian or non-Gaussian. We used VLS-FCS to investigate two systems where anomalous diffusion had been previously reported. In the case of dense cross-linked agarose gels, the measured MSD confirmed that the diffusion of small beads was anomalous at short lengthscales, with a cross-over to simple diffusion around ≈ 1 µm, consistent with a caged diffusion process. On the other hand, for solutions crowded with marginally entangled dextran molecules, we uncovered an apparent discrepancy between the MSD, found to be linear, and the propagators at short lengthscales, found to be non-Gaussian. These contradicting features call to mind the "anomalous, yet Brownian" diffusion observed in several biological systems, and the recently proposed "diffusing diffusivity" model.

The resolution of stimulated emission depletion (STED) microscopes is ultimately limited by the quality of the doughnut-shaped illumination profile of the STED erase beam. We show here that in the focal plane this illumination profile is well approximated by an analytical expression - a difference of Gaussian functions, which tends towards a first order Laguerre-Gaussian profile in the case of a well aligned beam with a true zero-intensity central minimum. We further show that along the optical axis the maximum intensity profile is reasonably approximated by a Gaussian decay away from the focal plane. The result is a fully Gaussian analytical approximation of the three-dimensional point-spread function of STED erase beams. This allows the derivation of an analytical form for the autocorrelation function of the fluorescence generated by fluorophore diffusion through the STED depletion volume. We verified this form to be correct by performing fluorescence correlation spectroscopy (FCS) experiments in solutions of the dye Alexa Fluor 532. Since the quality of the illumination profile is reflected in the shape of the autocorrelation function, we propose that fluctuation analysis can be used as a tool to assess the quality of STED erase beams.