Coherent X-rays reveal anomalous molecular diffusion and cage effects in crowded protein solutions

TL;DR

Anomalous diffusion of ferritin is revealed, linking hydrodynamic and direct interactions to cage-trapping at microsecond time scales, with potential applications for optimizing ferritin-based drug delivery, where protein diffusion is the rate-limiting step.

Abstract

Understanding protein motion within the cell is crucial for predicting reaction rates and macromolecular transport in the cytoplasm. A key question is how crowded environments affect protein dynamics through hydrodynamic and direct interactions at molecular length scales. Using megahertz X-ray Photon Correlation Spectroscopy (MHz-XPCS) at the European X-ray Free Electron Laser (EuXFEL), we investigate ferritin diffusion at microsecond time scales. Our results reveal anomalous diffusion, indicated by the non-exponential decay of the intensity autocorrelation function $g_2(q,t)$ at high concentrations. This behavior is consistent with the presence of cage-trapping in between the short- and long-time protein diffusion regimes. Modeling with the $δγ$-theory of hydrodynamically interacting colloidal spheres successfully reproduces the experimental data by including a scaling factor linked to the protein direct interactions. These findings offer new insights into the complex molecular motion in crowded protein solutions, with potential applications for optimizing ferritin-based drug delivery, where protein diffusion is the rate-limiting step.

Figures (12)

• Figure 1: Capturing protein diffusion across different length scales and time scales with MHz-XPCS. (a) Conceptual representation of ferritin protein molecular dynamics at different time scales. The panels depict the short-time diffusion (top), cage effects (middle) and long-time diffusion (bottom). These different regimes are characterised by the interaction time, $\tau_i=R_h^2/(6D_s)$, where $R_h$ is the hydrodynamic radius and $D_s$ the self-diffusion coefficient. The ferritin ferritin images are rendered with Protein Data Bank (PDB file 6PXM [doi:10.2210/pdb6PXM/pdb]). (b) Schematic of the Megahertz X-ray Photon Correlation Spectroscopy (MHz-XPCS) experiment. Incident X-ray pulses are scattered from the ferritin protein solutions contained in a capillary. The scattered photons are detected per-pulse with an area detector (AGIPD 1M), capable of recording frames at MHz rate. The scattering intensity as a function of momentum transfer, $I(q)$, is obtained by azimuthal integration, while the intensity autocorrelation function $g_2(q,t)$ is determined by correlating the intensity across frames over time.
• Figure 2: Small-angle X-ray scattering (SAXS) of ferritin solutions. (a) Scattering intensity as a function of momentum transfer, $I(q)$, for different protein concentrations ($c=$ 9 mg/ml to $c=$ 730 mg/ml) obtained at the European XFEL (EuXFEL). The $I(q)$ curves are background-subtracted and normalized by the respective concentration $c$. (b) The structure factor as a function of momentum transfer, $S(q)$, obtained from the experimental data collected at the EuXFEL (empty symbols) shows excellent agreement with the $S(q)$ obtained at the European Synchrotron Radiation Facility (ESRF, solid lines).
• Figure 3: X-ray Photon Correlation Spectroscopy (XPCS) data of ferritin solutions obtained at EuXFEL. The intensity autocorrelation function, $g_2(q,t)$, for different protein concentrations (a) $c=$ 70 mg/ml, (b) $c=$ 180 mg/ml, (c) $c=$ 400 mg/ml and (d) $c=$ 730 mg/ml. Data in panels (a-c) where measured in water-glycerol (with glycerol volume fraction $\nu_{\textrm{glyc}}=0.55$), while panel (d) presents data measured in water to reach the desired protein concentration ($c=~730$ mg/ml). The different colors represent different $q$-values, changing from lighter to darker green for $q$ increasing from $q=$ 0.225 nm$^{-1}$ to $q=$ 0.625 nm$^{-1}$ with equal spacing of $dq=$ 0.05 nm$^{-1}$. Solid lines represent stretched exponential fits, with the corresponding Kohlrausch-Williams-Watts (KWW) exponent $\alpha$ shown in the legend. The error bars on the KWW exponents are estimated from the stretched exponential fit . The error bars on $g_2(q,t)$ shown correspond to the standard error, estimated as described in the SI.
• Figure 4: Average decorrelation rate $\Gamma(q)$ and diffusion coefficient $D(q)$ at different protein concentrations. (a) Decorrelation rate $\Gamma(q)$ as a function of momentum transfer $q$. Solid lines represent fits with $\Gamma(q)=Dq^2$, while shaded areas highlight deviations of the experimental values from the fit. (b) Diffusion coefficient $D(q)=\Gamma(q)/q^2$ as a function of momentum transfer $q$. Solid lines are model fits using $\delta\gamma$-theory. The error bars are estimated from the stretched exponential fit including standard error propagation.
• Figure 5: $D(q)S(q)/D_0$ and self-diffusion coefficient $D_s$ for different concentrations. (a) $D(q)S(q)/D_0$ as a function of momentum transfer $q$ (empty symbols) and model results using the $\delta\gamma$-theory (solid lines). In the inset is shown a zoom in for $c=$ 730 mg/ml. The error bars are estimated from the stretched exponential fit including standard error propagation. (b) The ratio of the self-diffusion coefficients over the dilute-limit diffusion coefficients, $D_s/D_0$, as a function of the hydrodynamic volume fraction $\phi_h=\phi \frac{R_h^3}{R_p^3}$. The lines represent the expected volume fraction dependence of the short-time self-diffusion coefficient $D_s^{short}/D_0$beenakker_diffusion_1983 (dotted line) and the long-time self-diffusion coefficient $D_s^{long}/D_0$blaaderen_longtime_1992 (solid line). The error bars are estimated from the fit of the scaling factor including standard error propagation and, if not visible, they are smaller than the symbol.