Protein-rich clusters of steady submicron size and narrow size distribution exist in protein solutions in apparent violation of the classical laws of phase equilibrium. Even though they contain a ...minor fraction of the total protein, evidence suggests that they may serve as essential precursors for the nucleation of ordered solids such as crystals, sickle-cell hemoglobin polymers, and amyloid fibrils. The cluster formation mechanism remains elusive. We use the highly basic protein lysozyme at nearly neutral and lower pH as a model and explore the response of the cluster population to the electrostatic forces, which govern numerous biophysical phenomena, including crystallization and fibrillization. We tune the strength of intermolecular electrostatic forces by varying the solution ionic strength I and pH and find that despite the weaker repulsion at higher I and pH, the cluster size remains constant. Cluster responses to the presence of urea and ethanol demonstrate that cluster formation is controlled by hydrophobic interactions between the peptide backbones, exposed to the solvent after partial protein unfolding that may lead to transient protein oligomers. These findings reveal that the mechanism of the mesoscopic clusters is fundamentally different from those underlying the two main classes of ordered protein solid phases, crystals and amyloid fibrils, and partial unfolding of the protein chain may play a significant role.
Theory of aging in structural glasses Lubchenko, Vassiliy; Wolynes, Peter G
The Journal of chemical physics,
08/2004, Letnik:
121, Številka:
7
Journal Article
Recenzirano
Odprti dostop
The random first-order transition theory of the dynamics of supercooled liquids is extended to treat aging phenomena in nonequilibrium structural glasses. A reformulation of the idea of "entropic ...droplets" in terms of libraries of local energy landscapes is introduced which treats in a uniform way the supercooled liquid (reproducing earlier results) and glassy regimes. The resulting microscopic theory of aging makes contact with the Nayaranaswamy-Moynihan-Tool nonlinear relaxation formalism and the Hodge-Scherer extrapolation of the Adam-Gibbs formula, but deviations from both approaches are predicted and shown to be consistent with experiment. The nonlinearity of glassy relaxation is shown to quantitatively correlate with liquid fragility. The residual non-Arrhenius temperature dependence of relaxation observed in quenched glasses is explained. The broadening of relaxation spectra in the nonequilibrium glass with decreasing temperature is quantitatively predicted. The theory leads to the prediction of spatially fluctuating fictive temperatures in the long-aged glassy state, which have non-Gaussian statistics. This can give rise to "ultraslow" relaxations in systems after deep quenches.
Metastable clusters of mesoscopic dimensions composed of protein-rich liquid exist in protein solutions, both in the homogeneous region of the solution phase diagram and in the region supersaturated ...with respect to an ordered solid phase, such as crystals; in the latter region they are crucial nucleation sites for ordered solids. We monitor, using three optical techniques, the long-term evolution of the clusters in lysozyme solutions at conditions where no condensed phases, liquid or solid, are stable or present as long-lived metastable domains. We show that cluster formation is a reversible process and that the clusters are in near equilibrium with the solution, up to a capillary correction. In contrast to classical phase transformations, the solution concentration at cluster–solution equilibrium is close to its initial value; this is akin to chemical reaction equilibria and demonstrates the complex chemical composition of the clusters. However, similar to classical phase transformations, en route to full equilibration, the average cluster size grows with time following a universal law t 0.26±0.03, independent of the cluster volume fraction; the cluster size distribution is scale-invariant at all stages of cluster evolution. Despite the correspondence of these behaviors to the Lifshitz–Slyozov–Wagner (LSW) theory predictions, the cluster sizes are about 10× smaller than the LSW prediction, likely due to the complex cluster composition. The observed cluster evolution helps us to understand nucleation mysteries, such as nucleation rates lower by orders of magnitude than classical theory predictions, nucleation rate variable under steady conditions, and others.
We argue that the intrinsic glassy degrees of freedom in amorphous solids giving rise to the thermal conductivity plateau and the "boson peak" in the heat capacity at moderately low temperatures are ...directly connected to those motions giving rise to the two-level-like excitations seen at still lower temperatures. These degrees of freedom can be thought of as strongly anharmonic transitions between the local minima of the glassy energy landscape that are accompanied by ripplon-like domain wall motions of the glassy mosaic structure predicted to occur at Tgby the random first-order transition theory. The energy spectrum of the vibrations of the mosaic depends on the glass transition temperature, the Debye frequency, and the molecular length scale. The resulting spectrum reproduces the experimental low-temperature boson peak. The "nonuniversality" of the thermal conductivity plateau depends on$k_BT_g /\hslash \omega_D$and arises from calculable interactions with the phonons.
Toward quantitative description of protein aggregation, we develop a computationally efficient method to evaluate the potential of mean force between two folded protein molecules that allows for ...complete sampling of their mutual orientation. Our model is valid at moderate ionic strengths and accounts for the actual charge distribution on the surface of the molecules, the dielectric discontinuity at the protein-solvent interface, and the possibility of protonation or deprotonation of surface residues induced by the electric field due to the other protein molecule. We apply the model to the protein lysozyme, whose solutions exhibit both mesoscopic clusters of protein-rich liquid and liquid-liquid separation; the former requires that protein form complexes with typical lifetimes of approximately milliseconds. We find the electrostatic repulsion is typically lower than the prediction of the Derjaguin-Landau-Verwey-Overbeek theory. The Coulomb interaction in the lowest-energy docking configuration is nonrepulsive, despite the high positive charge on the molecules. Typical docking configurations barely involve protonation or deprotonation of surface residues. The obtained potential of mean force between folded lysozyme molecules is consistent with the location of the liquid-liquid coexistence, but produces dimers that are too short-lived for clusters to exist, suggesting lysozyme undergoes conformational changes during cluster formation.
We explore several potential issues that have been raised over the years regarding the “entropic droplet” scenario of activated transport in liquids, due to Wolynes and co-workers, with the aim of ...clarifying the status of various approximations of the random first-order transition theory (RFOT) of the structural glass transition. In doing so, we estimate the mismatch penalty between alternative aperiodic structures, above the glass transition; the penalty is equal to the typical magnitude of free energy fluctuations in the liquid. The resulting expressions for the activation barrier and the cooperativity length contain exclusively bulk, static properties; in their simplest form they contain only the bulk modulus and the configurational entropy per unit volume. The expressions are universal in that they do not depend explicitly on the molecular detail. The predicted values for the barrier and cooperativity length and, in particular, the temperature dependence of the barrier are in satisfactory agreement with observation. We thus confirm that the entropic droplet picture is indeed not only internally consistent but is also fully constructive, consistent with the apparent success of its many quantitative predictions. A simple view of a glassy liquid as a locally metastable, degenerate pattern of frozen-in stress emerges in the present description. Finally, we derive testable relationships between the bulk modulus and several characteristics of glassy liquids and peculiarities in low-temperature glasses.
The structural glass transition is often regarded as purely a problem of the classical theory of liquids. The dynamics of electrons enters only implicitly, through the interactions between ionic ...cores or molecules. Likewise, zero-point effects tied to the atomic masses hardly affect the typical barriers for liquid rearrangements. Yet, glasses do exhibit many quantum phenomenaelectronic, optical, and cryogenic peculiarities that seem to have universal characteristics. These anomalies of the glassy state are uncommon or strongly system dependent in crystals and amorphous solids not made by a quasi-equilibrium quench of a melt. These clearly quantum phenomena include midgap electronic states in amorphous semiconductors, the two-level systems, and the Boson peak. Here, we discuss how these quantum phenomena found in glasses are not merely consequences of any kind of disorder but have universal characteristics stemming from the structural dynamics inherent in the glass transition itself. The quantum dynamics at cryogenic temperatures and electronic dynamics are related to the transition states for relaxational motions above the glass transition temperature, which are partially frozen when the sample is quenched.
PDF
