Coherent X-ray Scattering Reveals Nanoscale Fluctuations in Hydrated Proteins

Hydrated proteins undergo a transition in the deeply supercooled regime, which is attributed to rapid changes in hydration water and protein structural dynamics. Here, we investigate the nanoscale stress–relaxation in hydrated lysozyme proteins stimulated and probed by X-ray Photon Correlation Spectroscopy (XPCS). This approach allows us to access the nanoscale dynamics in the deeply supercooled regime (T = 180 K), which is typically not accessible through equilibrium methods. The observed stimulated dynamic response is attributed to collective stress–relaxation as the system transitions from a jammed granular state to an elastically driven regime. The relaxation time constants exhibit Arrhenius temperature dependence upon cooling with a minimum in the Kohlrausch–Williams–Watts exponent at T = 227 K. The observed minimum is attributed to an increase in dynamical heterogeneity, which coincides with enhanced fluctuations observed in the two-time correlation functions and a maximum in the dynamic susceptibility quantified by the normalized variance χT. The amplification of fluctuations is consistent with previous studies of hydrated proteins, which indicate the key role of density and enthalpy fluctuations in hydration water. Our study provides new insights into X-ray stimulated stress–relaxation and the underlying mechanisms behind spatiotemporal fluctuations in biological granular materials.

: Wide-angle X-ray Scattering (WAXS) 2D intensity for the hydrated proteins at T = 290 K (left) and T = 175 K (right). The latter shows sharp rings, feature of crystallization. Figure S2: a) Layout of the performed azimuthal dependence analysis. The image depicts the different Q-bins as well as the azimuthal angles. b) The autocorrelation functions g 2 calculated for the horizontal component (black) and the vertical component (orange). The corresponding areas in the detector are marked with the same colors in panel a. The analysis shows no major difference between the horizontal and the vertical component.

Temperature increase
The transmission of lysozyme (T lys = 0.495) for the current experimental conditions (photon energy E = 12.4 keV, sample thickness d s = 1.5 mm) is calculated by using the molecular formula C 125 H 196 N 40 O 36 S 2 based on the known atomic data tables [1]. The total sample transmission is estimated by averaging the transmission of lysozyme with that of water (T w = 0.673) weighted by the corresponding mass fraction (h = 0.3).
The absorbed energy dQ for a given exposure time t e is calculated by including the incident beam flux I (in µJ s −1 ) and the sample transmission, which gives dQ = (1 − T r ) · I · t e . This estimation corresponds to a maximum temperature increase of T max (t) = dQ/m/c p where m is the mass and c p the heat capacity. Here we used the following values for the lysozyme: isobaric heat capacity c p = 1260 J kg −1 K −1 [2], density ρ = 2200 kg m −1 [3] and heat conductivity k w = 0.42 W K −1 m −1 [4]. The heat dissipation time [5] is calculated by where a is the beamsize (30 µm). The corresponding temperature rise [5] is This estimation gives values below ∆T = 10 K for the highest flux used here, I = 4 · 10 9 ph s −1 .

Dose
In order to quantify the amount of energy absorbed by the sample, we calculate the dose D absorbed by the system by where F denotes the flux, E the photon energy, A is the absorption, t e the exposure time, a the beam size, d s the sample thickness, and ρ w the weighted averaged density. The values utilized are summarized in Table S1. The calculated dose is D = 1.58 kGy.
The absorption is computed from the transmission as A = 2 − log(%T lys ), with T lys = 0.495 (see previous paragraph), which is calculated from atomic data tables and is in agreement with the transmission measurements performed during the experiment. Furthermore, the weighted average density ρ w is computed based on the mass fraction h = 0.28. In particular, S4 and the weights w i are calculated from h = m wat m lys = ρ wat V wat ρ lys V lys .