Jeremy C. Palmer

Metastable liquid-liquid transition in a molecular model of water

Liquid water’s isothermal compressibility and isobaric heat capacity, and the magnitude of its thermal expansion coefficient, increase sharply on cooling below the equilibrium freezing point. Many experimental, theoretical and computational studies have sought to understand the molecular origin and implications of this anomalous behaviour. Of the different theoretical scenarios put forward, one posits the existence of a first-order phase transition that involves two forms of liquid water and terminates at a critical point located at deeply supercooled conditions. Some experimental evidence is consistent with this hypothesis, but no definitive proof of a liquid–liquid transition in water has been obtained to date: rapid ice crystallization has so far prevented decisive measurements on deeply supercooled water, although this challenge has been overcome recently. Computer simulations are therefore crucial for exploring water’s structure and behaviour in this regime, and have shown that some water models exhibit liquid–liquid transitions and others do not. However, recent work has argued that the liquid–liquid transition has been mistakenly interpreted, and is in fact a liquid–crystal transition in all atomistic models of water. Here we show, by studying the liquid–liquid transition in the ST2 model of water with the use of six advanced sampling methods to compute the free-energy surface, that two metastable liquid phases and a stable crystal phase exist at the same deeply supercooled thermodynamic condition, and that the transition between the two liquids satisfies the thermodynamic criteria of a first-order transition. We follow the rearrangement of water’s coordination shell and topological ring structure along a thermodynamically reversible path from the low-density liquid to cubic ice. We also show that the system fluctuates freely between the two liquid phases rather than crystallizing. These findings provide unambiguous evidence for a liquid–liquid transition in the ST2 model of water, and point to the separation of time scales between crystallization and relaxation as being crucial for enabling it.

Liquid-liquid transition in ST2 water

We use the weighted histogram analysis method [S. Kumar, D. Bouzida, R. H. Swendsen, P. A. Kollman, and J. M. Rosenberg, J. Comput. Chem. 13, 1011 (1992)] to calculate the free energy surface of the ST2 model of water as a function of density and bond-orientational order. We perform our calculations at deeply supercooled conditions (T = 228.6 K, P = 2.2 kbar; T = 235 K, P = 2.2 kbar) and focus our attention on the region of bond-orientational order that is relevant to disordered phases. We find a first-order transition between a low-density liquid (LDL, ρ ≈ 0.9 g/cc) and a high-density liquid (HDL, ρ ≈ 1.15 g/cc), confirming our earlier sampling of the free energy surface of this model as a function of density [Y. Liu, A. Z. Panagiotopoulos, and P. G. Debenedetti, J. Chem. Phys. 131, 104508 (2009)]. We demonstrate the disappearance of the LDL basin at high pressure and of the HDL basin at low pressure, in agreement with independent simulations of the systems equation of state. Consistency between directly computed and reweighted free energies, as well as between free energy surfaces computed using different thermodynamic starting conditions, confirms proper equilibrium sampling. Diffusion and structural relaxation calculations demonstrate that equilibration of the LDL phase, which exhibits slow dynamics, is attained in the course of the simulations. Repeated flipping between the LDL and HDL phases in the course of long molecular dynamics runs provides further evidence of a phase transition. We use the Ewald summation with vacuum boundary conditions to calculate long-ranged Coulombic interactions and show that conducting boundary conditions lead to unphysical behavior at low temperatures.

On the molecular origin of high-pressure effects in nanoconfinement: The role of surface chemistry and roughness

Experiments and simulations both suggest that the pressure experienced by an adsorbed phase confined within a carbon nanoporous material can be several orders of magnitude larger than the bulk phase pressure in equilibrium with the system. To investigate this pressure enhancement, we report a molecular-simulation study of the pressure tensor of argon confined in slit-shaped nanopores with walls of various models, including carbon and silica materials. We show that the pressure is strongly enhanced by confinement, arising from the effect of strongly attractive wall forces; confinement within purely repulsive walls does not lead to such enhanced pressures. Simulations with both the Lennard-Jones and Barker-Fisher-Watts intermolecular potentials for argon-argon interactions give rise to similar results. We also show that an increase in the wall roughness significantly decreases the in-pore pressure due to its influence on the structure of the adsorbate. Finally, we demonstrate that the pressures calculated from the mechanical (direct pressure tensor calculations) and the thermodynamic (volume perturbation method) routes yield almost identical results, suggesting that both methods can be used to calculate the local pressure tensor components in the case of these planar geometries.

The liquid–liquid transition in supercooled ST2 water: a comparison between umbrella sampling and well-tempered metadynamics

We investigate the metastable phase behaviour of the ST2 water model under deeply supercooled conditions. The phase behaviour is examined using umbrella sampling (US) and well-tempered metadynamics (WT-MetaD) simulations to compute the reversible free energy surface parameterized by density and bond-orientation order. We find that free energy surfaces computed with both techniques clearly show two liquid phases in coexistence, in agreement with our earlier US and grand canonical Monte Carlo calculations [Y. Liu, J. C. Palmer, A. Z. Panagiotopoulos and P. G. Debenedetti, J Chem Phys, 2012, 137, 214505; Y. Liu, A. Z. Panagiotopoulos and P. G. Debenedetti, J Chem Phys, 2009, 131, 104508]. While we demonstrate that US and WT-MetaD produce consistent results, the latter technique is estimated to be more computationally efficient by an order of magnitude. As a result, we show that WT-MetaD can be used to study the finite-size scaling behaviour of the free energy barrier separating the two liquids for systems containing 192, 300 and 400 ST2 molecules. Although our results are consistent with the expected N(2/3) scaling law, we conclude that larger systems must be examined to provide conclusive evidence of a first-order phase transition and associated second critical point.

The structural validity of various thermodynamical models of supercooled water.

The thermodynamic response functions of water exhibit an anomalous increase upon cooling that becomes strongly amplified in the deeply supercooled regime due to structural fluctuations between disordered and tetrahedral local structures. Here, we compare structural data from recent x-ray laser scattering measurements of water at 1 bar and temperatures down to 227 K with structural properties computed for several different water models using molecular dynamics simulations. Based on this comparison, we critically evaluate four different thermodynamic scenarios that have been invoked to explain the unusual behavior of water. The critical point-free model predicts small variations in the tetrahedrality with decreasing temperature, followed by a stepwise change at the liquid-liquid transition around 228 K at ambient pressure. This scenario is not consistent with the experimental data that instead show a smooth and accelerated variation in structure from 320 to 227 K. Both the singularity-free model and ice coarsening hypothesis give trends that indirectly indicate an increase in tetrahedral structure with temperature that is too weak to be consistent with experiment. A model that includes an apparent divergent point (ADP) at high positive pressure, however, predicts structural development consistent with our experimental measurements. The terminology ADP, instead of the commonly used liquid-liquid critical point, is more general in that it focuses on the growing fluctuations, whether or not they result in true criticality. Extrapolating this model beyond the experimental data, we estimate that an ADP in real water may lie around 1500 ± 250 bars and 190 ± 6 K.

Liquid–liquid phase transition in an ionic model of silica

Recent equation of state calculations [E. Lascaris, Phys. Rev. Lett. 116, 125701 (2016)] for an ionic model of silica suggest that it undergoes a density-driven, liquid-liquid phase transition (LLPT) similar to the controversial transition hypothesized to exist in deeply supercooled water. Here, we perform extensive free energy calculations to scrutinize the models low-temperature phase behavior and confirm the existence of a first-order phase transition between two liquids with identical compositions but different densities. The low-density liquid (LDL) exhibits tetrahedral order, which is partially disrupted in the high-density liquid (HDL) by the intrusion of additional particles into the primary neighbor shell. Histogram reweighting methods are applied to locate conditions of HDL-LDL coexistence and the liquid spinodals that bound the two-phase region. Spontaneous liquid-liquid phase separation is also observed directly in large-scale molecular dynamics simulations performed inside the predicted two-phase region. Given its clear LLPT, we anticipate that this model may serve as a paradigm for understanding whether similar transitions occur in water and other tetrahedral liquids.

Computer Simulation of Water Sorption on Flexible Protein Crystals.

The first simulation study of water sorption on a flexible protein crystal is presented, along with a new computational approach for calculating sorption isotherms on compliant materials. The flexible ubiquitin crystal examined in the study exhibits appreciable sorption-induced swelling during fluid uptake, similar to that reported in experiments on protein powders. A completely rigid ubiquitin crystal is also examined to investigate the impact that this swelling behavior has on water sorption. The water isotherms for the flexible crystal exhibit Type II-like behavior with sorption hysteresis, which is consistent with experimental measurements on protein powders. Both of these behaviors, however, are absent in the rigid crystal, indicating that modeling flexibility is crucial for predicting water sorption behavior in protein systems. Changes in the enthalpy of adsorption, specific volume, and internal protein fluctuations that occur during sorption in the flexible crystal are also shown to compare favorably with experiment.

Density and bond-orientational relaxations in supercooled water

ABSTRACT Recent computational studies have reported evidence of a metastable liquid–liquid phase transition (LLPT) in molecular models of water under deeply supercooled conditions. A competing hypothesis suggests, however, that non-equilibrium artefacts associated with coarsening of the stable crystal phase have been mistaken for an LLPT in these models. Such artefacts are posited to arise due to a separation of time scales in which density fluctuations in the supercooled liquid relax orders of magnitude faster than those associated with bond-orientational order. Here, we use molecular simulation to investigate the relaxation of density and bond-orientational fluctuations in three molecular models of water (ST2, TIP5P and TIP4P/2005) in the vicinity of their reported LLPT. For each model, we find that density is the slowly relaxing variable under such conditions. We also observe similar behaviour in the coarse-grained mW model of water. Our findings, therefore, challenge the key physical assumption underlying the competing hypothesis.

Computational investigation of cold denaturation in the Trp-cage miniprotein

Significance The ubiquity of cold denaturation in globular proteins has broad implications for developing preservation strategies for biological materials and understanding the evolution of freeze-tolerant organisms. Because cold denaturation conditions typically lie below water’s freezing point, direct experimental investigation of this phenomenon is often frustrated by ice formation in the surrounding solvent. Coarse-grained lattice and off-lattice models have provided significant insight into protein cold denaturation, but they lack the structural resolution to fully elucidate the molecular mechanism involved in this process. We perform extensive replica exchange molecular dynamics simulations (324 μs total) to conduct a fully atomistic computational study of cold unfolding of an α-helical protein. The functional native states of globular proteins become unstable at low temperatures, resulting in cold unfolding and impairment of normal biological function. Fundamental understanding of this phenomenon is essential to rationalizing the evolution of freeze-tolerant organisms and developing improved strategies for long-term preservation of biological materials. We present fully atomistic simulations of cold denaturation of an α-helical protein, the widely studied Trp-cage miniprotein. In contrast to the significant destabilization of the folded structure at high temperatures, Trp-cage cold denatures at 210 K into a compact, partially folded state; major elements of the secondary structure, including the α-helix, are conserved, but the salt bridge between aspartic acid and arginine is lost. The stability of Trp-cage’s α-helix at low temperatures suggests a possible evolutionary explanation for the prevalence of such structures in antifreeze peptides produced by cold-weather species, such as Arctic char. Although the 310-helix is observed at cold conditions, its position is shifted toward Trp-cage’s C-terminus. This shift is accompanied by intrusion of water into Trp-cage’s interior and the hydration of buried hydrophobic residues. However, our calculations also show that the dominant contribution to the favorable energetics of low-temperature unfolding of Trp-cage comes from the hydration of hydrophilic residues.

A Computational Study of the Effect of Matrix Structural Order on Water Sorption by Trp-Cage Miniproteins

We present the first simulation study of the impact of protein matrix structure on water sorption along with a new computational method to hydrate and dehydrate protein systems reversibly. To understand the impact of the underlying structure of the protein matrix on the hydration process, we compare three types of protein substrates comprised of Trp-cage miniproteins with varying degrees of monomer translational and orientational order and monomer denaturation. We show that the water sorption isotherms are qualitatively and quantitatively very similar for the Trp-cage matrices independently of the underlying degree of disorder, which is consistent with the experimental observation that the qualitative features of water sorption isotherms are nearly universal for globular proteins. We also show that the Trp-cage matrices with varying disorder share similar trends in volumetric swelling, solvent accessibility, and protein-water hydrogen bonding during the sorption processes, while hydrogen bonding between protein molecules depends sensitively on the matrix characteristics (crystal, powder, and thermally denatured powder). Volumetric swelling, solvent accessibility, and protein-water hydrogen bonds exhibit no hysteresis when plotted as a function of hydration level and are thus controlled exclusively by the proteins water content.