Protein Diffusion and Stokes-Einstein Deviation in Supercooled Cryoprotectant Solutions

Vitrification during cryopreservation requires a detailed understanding of the dynamic behavior of biological solutions. We investigate ferritin diffusion in glycerol-water mixtures at supercooled temperatures using X-ray Photon Correlation Spectroscopy (XPCS). Diffusion coefficients were measured from ambient conditions to $T = 210$ K and analyzed using the Vogel-Fulcher-Tammann (VFT) relation, yielding an arrest temperature of $T_0 = 85 \pm 11$ K for ferritin ($R_{\rm h} = 7.3$ nm), markedly lower than $T_0 = 122 \pm 4$ K for larger nanoparticles ($R_{\rm h} = 50$ nm). Below $T \approx 230$ K, ferritin diffusion exceeds the Stokes-Einstein prediction by up to a factor of 2.7, revealing nanoscale deviations from bulk viscosity. A fluctuating-friction model quantitatively links this enhancement to local friction heterogeneity, with fluctuations increasing upon cooling and reaching $\sim 80\%$ of the mean friction at $T=210$ K. These results establish a molecular-scale connection between protein diffusion and solvent dynamical heterogeneity in cryoprotected solutions.