Metastable Liquid-liquid Phase Separation Research Articles

Mechanistic study on metastable and stable liquid–liquid phase separation explored by molecular simulation and thermodynamic analysis

Liquid–liquid phase separation (LLPS) has been proven to play a key role in molecular self-assembly both in vivo and in vitro, and it is of great significance for life science and materials science. Comparative elucidation and research are essential for comprehensive understanding of different types of LLPS. Here, citicoline sodium was taken as model molecule to study stable and metastable LLPS. Process analytical technologies (PAT) were applied to characterize the process. Ternary phase diagrams and the solubility parameters of LLPS region were determined and discussed. Moreover, a combination of molecular simulations and spectroscopy was applied to analyze the mechanism of stable and metastable LLPS. Spectroscopy analyses showed that the solute molecules in metastable liquid intermediate were in a metastable state. And the MD simulation results indicated that LLPS was stable when the system was in the solvation-enhanced state, while metastable when the system was in the desolvation state.

Effect of Zr addition on metastable Liquid-Liquid Phase Separation of Cu-Fe alloys

The liquid-liquid phase separation (LLPS) behavior was investigated in Cu-Fe alloys that consisted of 60 wt % or 80 wt % Cu and balance iron, without or with addition of 1 wt% Zr. Both Zr-free alloys clearly showed LLPS at metastable spinodal temperatures prior to γ-Fe nucleation, whereas Zr-added showed γ-Fe phase evolution without LLPS. Addition of Zr was highly effective to activate γ-Fe nucleation by decreasing the mixing enthalpy and also accelerating heterogeneous nucleation. A combination of thermal instrumental analysis and classical nucleation theory yielded an effective assessment made of LLPS behavior below the liquidus temperature of Cu-Fe alloys. Furthermore, it was possible to control the solidification mechanism of Cu-Fe alloy by zirconium addition.

Enhanced protein adsorption upon bulk phase separation

In all areas related to protein adsorption, from medicine to biotechnology to heterogeneous nucleation, the question about its dominant forces and control arises. In this study, we used ellipsometry and quartz-crystal microbalance with dissipation (QCM-D), as well as density-functional theory (DFT) to obtain insight into the mechanism behind a wetting transition of a protein solution. We established that using multivalent ions in a net negatively charged globular protein solution (BSA) can either cause simple adsorption on a negatively charged interface, or a (diverging) wetting layer when approaching liquid-liquid phase separation (LLPS) by changing protein concentration (cp) or temperature (T). We observed that the water to protein ratio in the wetting layer is substantially larger compared to simple adsorption. In the corresponding theoretical model, we treated the proteins as limited-valence (patchy) particles and identified a wetting transition for this complex system. This wetting is driven by a bulk instability introduced by metastable LLPS exposed to an ion-activated attractive substrate.

Thermodynamic analysis of the stability of planar interfaces between coexisting phases and its application to supercooled water.

Two-phase simulations are commonly used to evaluate coexistence conditions, interfacial tensions, and other thermodynamic properties associated with first-order phase transitions. Calculation of these properties is often simplified when the interfaces between the two phases are flat or planar. Here, we derive a general thermodynamic criterion for selecting simulation cell dimensions to stabilize planar interfaces in phase-separated fluid-fluid systems with respect to homogeneous, single-phase states. The resulting expression is validated by analyzing the effects of simulation cell dimensions on the formation of planar liquid-vapor interfaces in the Lennard-Jones fluid and in the TIP4P/2005 model of water. We also perform large scale molecular dynamics simulations to study metastable liquid-liquid phase separation in the ST2 and TIP4P/2005 models of water under deeply supercooled conditions. Our simulations confirm the stability of a liquid-liquid interface in ST2, and they demonstrate that the corresponding interface for TIP4P/2005 can be stabilized by judiciously choosing the simulation cell aspect ratio in a manner consistent with the thermodynamic criterion. We posit that this sensitivity to the simulation cell aspect ratio may explain discrepancies between previous studies examining liquid-liquid separation in models of supercooled water.

Stable, metastable, and kinetically trapped amyloid aggregate phases.

Self-assembly of proteins into amyloid fibrils plays a key role in a multitude of human disorders that range from Alzheimer’s disease to type II diabetes. Compact oligomeric species, observed early during amyloid formation, are reported as the molecular entities responsible for the toxic effects of amyloid self-assembly. However, the relation between early-stage oligomeric aggregates and late-stage rigid fibrils, which are the hallmark structure of amyloid plaques, has remained unclear. We show that these different structures occupy well-defined regions in a peculiar phase diagram. Lysozyme amyloid oligomers and their curvilinear fibrils only form after they cross a salt and protein concentration-dependent threshold. We also determine a boundary for the onset of amyloid oligomer precipitation. The oligomeric aggregates are structurally distinct from rigid fibrils and are metastable against nucleation and growth of rigid fibrils. These experimentally determined boundaries match well with colloidal model predictions that account for salt-modulated charge repulsion. The model also incorporates the metastable and kinetic character of oligomer phases. Similarities and differences of amyloid oligomer assembly to metastable liquid–liquid phase separation of proteins and to surfactant aggregation are discussed.

Ion-activated attractive patches as a mechanism for controlled protein interactions.

The understanding of protein interactions to control phase and nucleation behavior of protein solutions is an important challenge for soft matter, biological and medical research. Here, we present ion bridges of multivalent cations between proteins as an ion-activated mechanism for patchy interaction that is directly supported by experimental findings in protein crystals. A deep understanding of experimentally observed phenomena in protein solutions—including charge reversal, reentrant condensation, metastable liquid-liquid phase separation, cluster formation and different pathways of crystallization—is gained by an analytic model that directly displays parameter dependencies and physical connections. The direct connection between experiment and theory provides a conceptual framework for future experimental, computational and theoretical research on topics such as rational design of phase behavior and crystallization pathways on the basis of the statistical physics of patchy particles.

The role of cluster formation and metastable liquid—liquid phase separation in protein crystallization

We discuss the phase behavior and in particular crystallization of a model globular protein (beta-lactoglobulin) in solution in the presence of multivalent electrolytes. It has been shown previously that negatively charged globular proteins at neutral pH in the presence of multivalent counterions undergo a “re-entrant condensation (RC)” phase behavior (Zhang et al., Phys. Rev. Lett., 2008, 101, 148101), i.e. a phase-separated regime occurs in between two critical salt concentrations, c* < c**, giving a metastable liquid–liquid phase separation (LLPS). Crystallization from the condensed regime has been observed to follow different mechanisms. Near c*, crystals grow following a classic nucleation and growth mechanism; near c**, the crystallization follows a two-step crystallization mechanism, i.e, crystal growth follows a metastable LLPS. In this paper, we focus on the two-step crystal growth near c**. SAXS measurements indicate that proteins form clusters in this regime and the cluster size increases approaching c**. Upon lowering the temperature, in situ SAXS studies indicate that the clusters can directly form both a dense liquid phase and protein crystals. During the crystal growth, the metastable dense liquid phase is dissolved. Based on our observations, we discuss a nucleation mechanism starting from clusters in the dilute phase from a metastable LLPS. These protein clusters behave as the building blocks for nucleation, while the dense phase acts as a reservoir ensuring constant protein concentration in the dilute phase during crystal growth.

Crystallization and dynamical arrest of attractive hard spheres

Crystallization of hard spheres interacting with a square well potential was investigated by numerical simulations using so-called Brownian cluster dynamics. The phase diagram was determined over a broad range of volume fractions. The crystallization rate was studied as a function of the interaction strength expressed in terms of the second virial coefficient. For volume fractions below about 0.3 the rate was found to increase abruptly with increasing attraction at the binodal of the metastable liquid-liquid phase separation. The rate increased until a maximum was reached after which it decreased with a power law dependence on the second virial coefficient. Above a critical percolation concentration, a transient system spanning network of connected particles was formed. Crystals were formed initially as part of the network, but eventually crystallization led to the breakup of the network. The lifetime of the transient gels increased very rapidly over a small range of interaction energies. Weak attraction destabilized the so-called repulsive crystals formed in pure hard sphere systems and shifted the coexistence line to higher volume fractions. Stronger attraction led to the formation of a denser, so-called attractive, crystalline phase. Nucleation of attractive crystals in the repulsive crystalline phase was observed close to the transition.

K2SO4-K2HPO4-H2O phase diagram in the region of heterogeneous supercritical fluids

Our experimental study of phase equilibria in the K2SO4-K2HPO4-H2O system at temperatures up to 500°C and pressures up to 100 MPa was directed to determine the sequence of phase transformations that generate heterogeneous supercritical fluids whose existence region propagates from the K2SO4-K2HPO4-H2O subsystem into the ternary system. We found that supercritical fluids become heterogeneous as a result of addition of K2HPO4 starting with l1-l2 critical phenomena in saturated solutions, with the attendant amalgamation of the stable immiscibility region that propagates from the K2HPO4-H2O system and the metastable liquid-liquid phase separation that originates from the K2SO4-H2O system. Our experimental results and the topological analysis of phase equilibria in the vicinity of the critical point of water gave us the full scenario of the phase behavior of the title ternary system in the region of the subcritical and supercritical parameters of state.

Kinetics and equilibria of lysozyme precipitation and crystallization in concentrated ammonium sulfate solutions

The kinetics and thermodynamics of lysozyme precipitation in ammonium sulfate solutions at pH 4 and 8 and room temperature were studied. X-ray powder diffraction (XRD) was used to characterize the structure of lysozyme precipitates. It was found that, if sufficient time was allowed, microcrystals developed following an induction period after initial lysozyme precipitation, even up to ionic strengths of 8 m and at acidic pH, where lysozyme is refractory to crystallization in ammonium sulfate. The full set of precipitation and crystallization data allowed construction of a phase diagram of lysozyme, showing the ammonium sulfate dependence. It suggests that precipitation may reflect a frustrated metastable liquid-liquid phase separation, which would allow this process to be understood within the framework of the generic phase diagram for proteins. The results also demonstrate that XRD, more frequently used for characterizing inorganic and organic polycrystalline materials, is useful both in characterizing the presence of crystals in the dense phase and in verifying the crystal form of proteins.

Calculation of kinetics of metastable liquid-liquid phase separation for the model with simultaneous nucleation of particles

The questions of calculation of phase separation kinetics in the case of nucleation and growth type processes are discussed. The model with diffusion-limited growth of ‘simultaneously nucleated’ spherical particles is considered in detail. This model corresponds to the case where the nuclei have been formed previously (intentionally or unintentionally) in the process of material preparation. The conditions are determined under which the stage of growth from supersaturated solution may be observed without appreciable Ostwald ripening and the description of this stage is given. Using the conditions arising in the system towards the end of growth stage as the initial conditions, computer simulation of Ostwald ripening kinetics has been carried out. In particular, the computations show that the transition period from the growth stage to Ostwald ripening stage exists when the mean radius of particles does not vary and the size distribution is significantly transformed. The calculated results may be used for description of phase separation kinetics in glasses and other systems. Some results of experimental study of metastable liquid-liquid phase separation in glasses are reviewed which are in agreement with results of presented theoretical analysis.

Phase Transformations in ZrO2-SiO2 Gels

ABSTRACTTransparent sols and gels in the ZrO2-SiO2 system containing 25, 50 and 75 mole % ZrO2 were prepared using tetraethyl orthosilicate (TEOS) and Zr n-propoxide solution in the presence of acids. Heating the gels to 600°C yielded an amorphous product which at higher temperature crystallized with formation of tetragonal and monoclinic ZrO2 . Zircon crystallized slowly at 1600°C. The results are explained by metastable liquid-liquid phase separation in the studied system.