Probing Cage Relaxation in Concentrated Protein Solutions by X-Ray Photon Correlation Spectroscopy

Diffusion of proteins on length scales of their size is crucial for understanding the machinery of living cells. X-ray photon correlation spectroscopy (XPCS) is currently the only way to access long-time collective diffusion on these length scales, but radiation damage so far limits the use in biological systems. We apply a new approach to use XPCS to measure cage relaxation in crowded $\alpha$-crystallin solutions. This allows us to correct for radiation effects, obtain missing information on long time diffusion, and support the fundamental analogy between protein and colloid dynamical arrest.

Figure 1

Inverse of the relative position $q_{D=0}^{*}/q^{*}$ of the peak in the structure factor $S(q)$, where $q_{D=0}^{*}$ is the extrapolated zero-dose limit, as a function of deposited dose and dose rate for $\alpha$-cystallin solutions at different volume fractions $\varphi$. The guides to the eye (gray dashed) are exponential decays.

Figure 2

Observed dynamical characteristics of $\alpha$-crystallin solutions dependent on the dose and dose rates at volume fractions: $\varphi =0.55$ (left), $\varphi =0.58$ (center), $\varphi =0.61$ (right). Top: measured normalized intensity correlation functions. Dashed lines are fits with the KWW expression. Middle: the average relaxation time $⟨{\tau }_r⟩$ is decreased by both dose rate and dose. Inset: the relaxation rate as a function of the dose rate. Bottom: the exponent parameter $\beta$ evidences a transition from stretched exponential decay in the weakly affected fluid state to compressed decay for the strongly affected state.

Figure 3

Relative zero-shear viscosity ${\eta }_r$ of $\alpha$-crystallin solutions as a function of volume fraction $\varphi$ obtained from rheology (data from [3]) and microrheology (data from [18]) and normalized relaxation times obtained from XPCS (red squares).