We propose a Ginzurg-Landau-type model to describe the kinetics of mixtures undergoing a sol-gel transition (nonconserved order parameter) simultaneously with phase separation (conserved order parameter). We compute the temporal development of the structure factor and determine the wave vector q max at which the structure factor is maximal. We find that after a certain time t f , q max saturates at a final value q f , and we calculate the temperature dependence of both t f and q f . The predictions of this zeroth-order model agree remarkably well with recent kinetic measurements in gelatin-water-methanol mixtures

Interference of phase separation and gelation : a zeroth-order kinetic model

We demonstrate that continuous time random walks in which successive waiting times are correlated by Gaussian statistics lead to anomalous diffusion with mean squared displacement ~t^{2/3}. Long-ranged correlations of the waiting times with power-law exponent alpha (0 ~t^{alpha/(1+alpha)}. In contrast correlations in the jump lengths are shown to produce superdiffusion. We show that in both cases weak ergodicity breaking occurs. Our results are in excellent agreement with simulations.

Anomalous diffusion in correlated continuous time random walks

Intrinsic thermodynamic fluctuations within biomolecules are crucial for their function, and flexibility is one of the strategies that evolution has developed to adapt to extreme environments. In this regard, pressure perturbation is an important tool for mechanistically exploring the causes and effects of volume fluctuations in biomolecules and biomolecular assemblies, their role in biomolecular interactions and reactions, and how they are affected by the solvent properties. High hydrostatic pressure is also a key parameter in the context of deep-sea and subsurface biology and the study of the origin and physical limits of life. We discuss the role of pressure-axis experiments in revealing intrinsic structural fluctuations as well as high-energy conformational substates of proteins and other biomolecular systems that are important for their function and provide some illustrative examples. We show that the structural and dynamic information obtained from such pressure-axis studies improves our understanding of biomolecular function, disease, biological evolution, and adaptation.

Harnessing Pressure-Axis Experiments to Explore Volume Fluctuations, Conformational Substates, and Solvation of Biomolecular Systems.

Prion diseases are characterized by prion protein (PrP) transmissible aggregation and toxicity in the brain. The physiological function of PrP seems related to sequestering and internalization of redox-active Cu2+. It is unclear whether Cu2+ contributes to PrP aggregation, recently shown to be mediated by PrP condensation. We investigated the role of Cu2+ and oxidation in PrP condensation and aggregation using multiple biophysical and biochemical methods. We find that Cu2+ promotes PrP condensation at the cell surface and in vitro through co-partitioning. Molecularly, Cu2+ inhibited PrP β-structure and hydrophobic residues exposure. Oxidation, induced by H2O2, triggered liquid-to-solid transition of PrP:Cu2+ condensates and promoted amyloid-like PrP aggregation. In cells, overexpression of PrPC initially protected against Cu2+ cytotoxicity but led to PrPC aggregation upon extended copper exposure. Our data suggest that PrP condensates function as a buffer for copper that prevent copper toxicity but can transition into PrP aggregation at prolonged oxidative stress.

/pdf/copper-drives-prion-protein-phase-separation-and-modulates-3c6hm0g8.pdf

Copper drives prion protein phase separation and modulates aggregation

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.

https://pubs.acs.org/doi/pdf/10.1021/acs.jpcb.3c02492

Coherent X-ray Scattering Reveals Nanoscale Fluctuations in Hydrated Proteins

Employing X-ray photon correlation spectroscopy we measure the kinetics and dynamics of a pressure-induced liquid-liquid phase separation (LLPS) in a water-lysozyme solution. Scattering invariants and kinetic information provide evidence that the system reaches the phase boundary upon pressure-induced LLPS with no sign of arrest. The coarsening slows down with increasing quench depths. The $g_2$-functions display a two-step decay with a gradually increasing non-ergodicity parameter typical for gelation. We observe fast superdiffusive ($\gamma \geq 3/2$) and slow subdiffusive ($\gamma < 0.6$) motion associated with fast viscoelastic fluctuations of the network and a slow viscous coarsening process, respectively. The dynamics age linear with time $\tau \propto t_\mathrm{w}$ and we observe the onset of viscoelastic relaxation for deeper quenches. Our results suggest that the protein solution gels upon reaching the phase boundary.

M. Moron

Papers

Gelation dynamics upon pressure-induced liquid-liquid phase separation in a water-lysozyme solution