Characterizing anomalous diffusion in crowded polymer solutions and gels over five decades in time with variable-lengthscale fluorescence correlation spectroscopy.

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.

Anomalous diffusion of proteins due to molecular crowding.

We have studied the diffusion of tracer proteins in highly concentrated random-coil polymer and globular protein solutions imitating the crowded conditions encountered in cellular environments. Using fluorescence correlation spectroscopy, we measured the anomalous diffusion exponent alpha characterizing the dependence of the mean-square displacement of the tracer proteins on time, r(2)(t) approximately t(alpha). We observed that the diffusion of proteins in dextran solutions with concentrations up to 400 g/l is subdiffusive (alpha < 1) even at low obstacle concentration. The anomalous diffusion exponent alpha decreases continuously with increasing obstacle concentration and molecular weight, but does not depend on buffer ionic strength, and neither does it depend strongly on solution temperature. At very high random-coil polymer concentrations, alpha reaches a limit value of alpha(l) approximately 3/4, which we take to be the signature of a coupling between the motions of the tracer proteins and the segments of the dextran chains. A similar, although less pronounced, subdiffusive behavior is observed for the diffusion of streptavidin in concentrated globular protein solutions. These observations indicate that protein diffusion in the cell cytoplasm and nucleus should be anomalous as well, with consequences for measurements of solute diffusion coefficients in cells and for the modeling of cellular processes relying on diffusion.