Protein Diffusion and Stokes-Einstein Deviation in Supercooled Cryoprotectant Solutions

TL;DR

Understanding protein diffusion in cryoprotected aqueous solutions and its relation to solvent dynamical heterogeneity is addressed by measuring ferritin diffusion in glycerol–water with XPCS and SAXS across 293–193 K. The study finds that ferritin diffusion deviates from Stokes–Einstein predictions below ~230 K and follows a Vogel–Fulcher–Tammann relation with $T_0 = 85 \pm 12$ K for ferritin, contrasted with $T_0 = 122 \pm 4$ K for 50 nm nanoparticles; the diffusion enhancement relative to SE grows with cooling, reaching $D/D_0 \approx 2.7$ at $T=210$ K. A minimal fluctuating–friction model connects the enhancement to local friction fluctuations, with relative amplitude $\delta = \Delta\gamma /\gamma_0$ rising from ~0.57 at 220 K to ~0.79 at 210 K. SAXS confirms ferritin structure remains intact and no crystallization or denaturation occurs, establishing a molecular-scale link between protein diffusion and solvent dynamical heterogeneity in cryoprotected media and highlighting that mobility can persist well below the solvent glass transition.

Abstract

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.

Figures (4)

• Figure 1: Temperature-dependent SAXS intensity $I(q)$ for ferritin solutions in glycerol--water mixtures at $c \approx 70$ mg mL$^{-1}$ (solid lines). The nearly invariant scattering profiles indicate structural stability and the absence of cold denaturation or nanocrystallization upon cooling.
• Figure 2: (a) Intensity autocorrelation functions $g_2(q,t)$ for ferritin solutions at $q = 0.1$ nm$^{-1}$ and various temperatures. Solid lines represent exponential fits. (b) Relaxation rate $\Gamma(q)$ as a function of $q^2$ for the same temperatures. Linear fits with $\Gamma(q)=Dq^2$ yield the diffusion coefficients $D(T)$. Error bars reflect fitting uncertainties propagated from the exponential model.
• Figure 3: (a) Diffusion coefficient of ferritin solutions (red triangles) compared to nanoparticle solutions (blue circles) obtained from XPCS measurements between $T = 250$ K and $T = 210$ K. Solid lines are fits using the Vogel-Fulcher-Tammann (VFT) relation. (b) The diffusion coefficients normalized by the hydrodynamics radius $R_{\rm h}$ (for ferritin $R_{\rm h}=7.3$ nm and for nanoparticles $R_{\rm h}=50$ nm). Here is also shown the nanoparticle data obtained from DLS (blue squares). Solid lines are the VFT fits, where the arrest temperature $T_0$ is indicated.
• Figure 4: Ratio of the measured ferritin diffusion coefficient $D$ to the SE-based reference $D_0$ (defined in Eq. \ref{['eq:ratio']}) as a function of temperature $T$. The symbols show the experimental data obtained from XPCS measurements, whereas the solid line represents the prediction of the fluctuating--friction model based on Eq. \ref{['eq:fluctuating_friction']}, where $\delta = \Delta\gamma / \gamma_0$ corresponds to the relative amplitude of local friction fluctuations.