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 ⟨r2⟩∝tα 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 ≈1μm, 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