Liquid-liquid transition and ice crystallization in a machine-learned coarse-grained water model.

Mounting experimental evidence supports the existence of a liquid-liquid transition (LLT) in high-pressure supercooled water. However, fast crystallization of supercooled water has impeded identification of the LLT line TLL(p) in experiments. While the most accurate all-atom (AA) water models display a LLT, their computational cost limits investigations of its interplay with ice formation. Coarse-grained (CG) models provide over 100-fold computational efficiency gain over AA models, enabling the study of water crystallization, but have not yet shown to have a LLT. Here, we demonstrate that the CG machine-learned water model Machine-Learned Bond-Order Potential (ML-BOP) has a LLT that ends in a critical point at pc = 170 ± 10 MPa and Tc = 181 ± 3 K. The TLL(p) of ML-BOP is almost identical to the one of TIP4P/2005, adding to the similarity in the equation of state of liquid water in both models. Cooling simulations reveal that ice crystallization is fastest at the LLT and its supercritical continuation of maximum heat capacity, supporting a mechanistic relationship between the structural transformation of water to a low-density liquid (LDL) and ice formation. We find no signature of liquid-liquid criticality in the ice crystallization temperatures. ML-BOP replicates the competition between formation of LDL and ice observed in ultrafast experiments of decompression of the high-density liquid (HDL) into the region of stability of LDL. The simulations reveal that crystallization occurs prior to the coarsening of the HDL and LDL domains, obscuring the distinction between the highly metastable first-order LLT and pronounced structural fluctuations along its supercritical continuation.

Functional aggregation of cell-free proteins enables fungal ice nucleation.

Biological ice nucleation plays a key role in the survival of cold-adapted organisms. Several species of bacteria, fungi, and insects produce ice nucleators (INs) that enable ice formation at temperatures above -10 °C. Bacteria and fungi produce particularly potent INs that can promote water crystallization above -5 °C. Bacterial INs consist of extended protein units that aggregate to achieve superior functionality. Despite decades of research, the nature and identity of fungal INs remain elusive. Here, we combine ice nucleation measurements, physicochemical characterization, numerical modeling, and nucleation theory to shed light on the size and nature of the INs from the fungus Fusarium acuminatum. We find ice-binding and ice-shaping activity of Fusarium IN, suggesting a potential connection between ice growth promotion and inhibition. We demonstrate that fungal INs are composed of small 5.3 kDa protein subunits that assemble into ice-nucleating complexes that can contain more than 100 subunits. Fusarium INs retain high ice-nucleation activity even when only the ~12 kDa fraction of size-excluded proteins are initially present, suggesting robust pathways for their functional aggregation in cell-free aqueous environments. We conclude that the use of small proteins to build large assemblies is a common strategy among organisms to create potent biological INs.

Nanobubble Stability and Formation on Solid-Liquid Interfaces in Open Environments.

Are surface nanobubbles transient or thermodynamically stable structures? This question remained controversial until recently, when the stability of gas nanobubbles at solid-liquid interfaces was demonstrated from thermodynamic arguments in closed systems, establishing that bubbles with radii of hundreds of nanometers can be stable at modest supersaturations if the gas amount is finite. Here we develop a grand-canonical description of bubble formation that predicts that nanobubbles can nucleate and remain thermodynamically stable in open boundaries at high supersaturations when pinned to hydrophobic supports as small as a few nanometers. While larger bubbles can also be stable at lower supersaturations, the corresponding barriers are orders of magnitude above kT, meaning that their formation cannot proceed via heterogeneous nucleation on a uniform solid interface but must follow some alternative path. Moreover, we conclude that a source of growth-limiting mechanism, such as pinning or gas availability, is necessary for the thermodynamic stabilization of surface bubbles.

Kinetics and Mechanisms of Pressure-Induced Ice Amorphization and Polyamorphic Transitions in a Machine-Learned Coarse-Grained Water Model.

Water glasses have attracted considerable attention due to their potential connection to a liquid-liquid transition in supercooled water. Here we use molecular simulations to investigate the formation and phase behavior of water glasses using the machine-learned bond-order parameter (ML-BOP) water model. We produce glasses through hyperquenching of water, pressure-induced amorphization (PIA) of ice, and pressure-induced polyamorphic transformations. We find that PIA of polycrystalline ice occurs at a lower pressure than that of monocrystalline ice and through a different mechanism. The temperature dependence of the amorphization pressure of polycrystalline ice for ML-BOP agrees with that in experiments. We also find that ML-BOP accurately reproduces the density, coordination number, and structural features of low-density (LDA), high-density (HDA), and very high-density (VHDA) amorphous water glasses. ML-BOP accurately reproduces the experimental radial distribution function of LDA but overpredicts the minimum between the first two shells in high-density glasses. We examine the kinetics and mechanism of the transformation between low-density and high-density glasses and find that the sharp nature of these transitions in ML-BOP is similar to that in experiments and all-atom water models with a liquid-liquid transition. Transitions between ML-BOP glasses occur through a spinodal-like mechanism, similar to ice crystallization from LDA. Both glass-to-glass and glass-to-ice transformations have Avrami-Kolmogorov kinetics with exponent n = 1.5 ± 0.2 in experiments and simulations. Importantly, ML-BOP reproduces the competition between crystallization and HDA→LDA transition above the glass transition temperature Tg, and separation of their time scales below Tg, observed also in experiments. These findings demonstrate the ability of ML-BOP to accurately reproduce water properties across various regimes, making it a promising model for addressing the competition between polyamorphic transitions and crystallization in water and solutions.

Oriented attachment kinetics for rod-like particles at a flat surface: Buffon's needle at the nanoscale.

The adsorption of large rod-like molecules or crystallites on a flat crystal face, similar to Buffon's needle, requires the rods to "land," with their binding sites in precise orientational alignment with matching sites on the surface. An example is provided by long, helical antifreeze proteins (AFPs), which bind at specific facets and orientations on the ice surface. The alignment constraint for adsorption, in combination with the loss in orientational freedom as the molecule diffuses toward the surface, results in an entropic barrier that hinders the adsorption. Prior kinetic models do not factor in the complete geometry of the molecule, nor explicitly enforce orientational constraints for adsorption. Here, we develop a diffusion-controlled adsorption theory for AFP molecules binding at specific orientations to flat ice surfaces. We formulate the diffusion equation with relevant boundary conditions and present analytical solutions to the attachment rate constant. The resulting rate constant is a function of the length and aspect ratio of the AFP, the distance threshold associated with binding, and solvent conditions such as temperature and viscosity. These results and methods of calculation may also be useful for predicting the kinetics of crystal growth through oriented attachment.

Stability and Metastability of Liquid Water in a Machine-Learned Coarse-Grained Model with Short-Range Interactions.

Coarse-grained water models are ∼100 times more efficient than all-atom models, enabling simulations of supercooled water and crystallization. The machine-learned monatomic model ML-BOP reproduces the experimental equation of state (EOS) and ice-liquid thermodynamics at 0.1 MPa on par with the all-atom TIP4P/2005 and TIP4P/Ice models. These all-atom models were parametrized using high-pressure experimental data and are either accurate for water's EOS (TIP4P/2005) or ice-liquid equilibrium (TIP4P/Ice). ML-BOP was parametrized from temperature-dependent ice and liquid experimental densities and melting data at 0.1 MPa; its only pressure training is from compression of TIP4P/2005 ice at 0 K. Here we investigate whether ML-BOP replicates the experimental EOS and ice-water thermodynamics along all pressures of ice I. We find that ML-BOP reproduces the temperature, enthalpy, entropy, and volume of melting of hexagonal ice up to 400 MPa and the EOS of water along the melting line with an accuracy that rivals that of both TIP4P/2005 and TIP4P/Ice. We interpret that the accuracy of ML-BOP originates from its ability to capture the shift between compact and open local structures to changes in pressure and temperature. ML-BOP reproduces the sharpening of the tetrahedral peak of the pair distribution function of water upon supercooling, and its pressure dependence. We characterize the region of metastability of liquid ML-BOP with respect to crystallization and cavitation. The accessibility of ice crystallization to simulations of ML-BOP, together with its accurate representation of the thermodynamics of water, makes it promising for investigating the interplay between anomalies, glass transition, and crystallization under conditions challenging to access through experiments.

AlphaFold2 models indicate that protein sequence determines both structure and dynamics.

AlphaFold 2 (AF2) has placed Molecular Biology in a new era where we can visualize, analyze and interpret the structures and functions of all proteins solely from their primary sequences. We performed AF2 structure predictions for various protein systems, including globular proteins, a multi-domain protein, an intrinsically disordered protein (IDP), a randomized protein, two larger proteins (> 1000 AA), a heterodimer and a homodimer protein complex. Our results show that along with the three dimensional (3D) structures, AF2 also decodes protein sequences into residue flexibilities via both the predicted local distance difference test (pLDDT) scores of the models, and the predicted aligned error (PAE) maps. We show that PAE maps from AF2 are correlated with the distance variation (DV) matrices from molecular dynamics (MD) simulations, which reveals that the PAE maps can predict the dynamical nature of protein residues. Here, we introduce the AF2-scores, which are simply derived from pLDDT scores and are in the range of [0, 1]. We found that for most protein models, including large proteins and protein complexes, the AF2-scores are highly correlated with the root mean square fluctuations (RMSF) calculated from MD simulations. However, for an IDP and a randomized protein, the AF2-scores do not correlate with the RMSF from MD, especially for the IDP. Our results indicate that the protein structures predicted by AF2 also convey information of the residue flexibility, i.e., protein dynamics.

What Is the Smallest Zeolite That Could Be Synthesized?

Zeolites with a few unit cells are promising as catalyst and adsorbents. The quest to synthesize the smallest zeolites has recently resulted in 4 to 8 nm nanozeolites, about 2 to 4 unit cells. These findings pose the question of what is the smallest zeolite that could be obtained by hydrothermal synthesis. Here we address this question using molecular simulations and thermodynamic analysis. The simulations predict that amorphous precursors as small as 4 nm can crystallize zeolites, in agreement with the experiments. We find that interfacial forces dominate the structure of smaller particles, resulting in size-dependent compact isomers that have ring and pore distributions different from open framework zeolites. The instability of zeolites smaller than 3±0.5 nm precludes a classical mechanism of nucleation from solution or through assembly of small nanoslabs.

Polymorph Selection in Zeolite Synthesis Occurs after Nucleation.

Zeolites are porous crystals with extensive polymorphism. The hydrothermal synthesis of zeolites is a multistage process involving amorphous precursors that evolve continuously in solubility and local order toward those of the crystal. These results pose several questions: Why does a first-order transition appear as a continuous transformation? At which stage is the polymorph selected? How large are the barriers and critical sizes for zeolite nucleation? Here we address these questions using nucleation theory with experimental data. We find that the nucleation barriers and critical zeolite nuclei are extremely small at temperatures of hydrothermal synthesis, resulting in spinodal-like crystallization that produces a mosaic of tiny zeolitic crystallites that compete to grow inside each glassy precursor nanoparticle. The subnanometer size of the critical nuclei reveals that the selection between zeolite polymorphs occurs after the nucleation stage, during the growth and coarsening of the crystals around the excluded volume of the structure-directing agents.

Is It Possible to Follow the Structural Evolution of Water in "No-Man's Land" Using a Pulsed-Heating Procedure?

The anomalous increase in compressibility and heat capacity of supercooled water has been attributed to its structural transformation of into a four-coordinated liquid. Experiments revealed that κT and Cp peak at TWthermo ≈ 229 K [Kim et al. Science 2017, 358, 1589; Pathak et al. Proc. Natl. Acad. Sci. 2021, 118, e2018379118]. Recently, a pulsed heating procedure (PHP) was employed to interrogate the structure of water, reporting a steep increase in tetrahedrality around TWPHP = 210 ± 3 K [Kringle et al. Science 2020, 369, 1490]. This discrepancy questions whether water structure and thermodynamics are decoupled, or if the shift in TW is an artifact of PHP. Here we implement PHP in molecular simulations. We find that the stationary states captured at the bottom of the pulse are not representative of the thermalized liquid or its inherent structure. Our analysis reveals a temperature-dependent distortion that shifts TWPHP to ∼20 K below TWthermo. We conclude that 2 orders of magnitude faster rates are required to sample water's inherent structure with PHP.

Diffusion Attachment Model for Long Helical Antifreeze Proteins to Ice.

Some of the most potent antifreeze proteins (AFPs) are approximately rigid helical structures that bind with one side in contact with the ice surface at specific orientations. These AFPs take random orientations in solution; however, most orientations become sterically inaccessible as the AFP approaches the ice surface. The effect of these inaccessible orientations on the rate of adsorption of AFP to ice has never been explored. Here, we present a diffusion-controlled theory of adsorption kinetics that accounts for these orientational restrictions to predict a rate constant for adsorption (kon, in m/s) as a function of the length and width of the AFP molecules. We find that kon decreases with length and diameter of the AFP and is almost proportional to the inverse of the area of the binding surface. We demonstrate that the restricted orientations create an entropic barrier to AFP adsorption, which we compute to be approximately 7 kBT for most AFPs and up to 9 kBT for Maxi, the largest known AFP. We compare the entropic resistance 1/kon to resistances for diffusion through boundary layers and across typical distances in the extracellular matrix and find that these entropic and diffusion resistances could become comparable in the small confined spaces of biological environments.

Is Ice Nucleation by Organic Crystals Nonclassical? An Assessment of the Monolayer Hypothesis of Ice Nucleation.

Potent ice nucleating organic crystals display an increase in nucleation efficiency with pressure and memory effect after pressurization that set them apart from inorganic nucleants. These characteristics were proposed to arise from an ordered water monolayer at the organic-water interface. It was interpreted that ordering of the monolayer is the limiting step for ice nucleation on organic crystals, rendering their mechanism of nucleation nonclassical. Despite the importance of organics in atmospheric ice nucleation, that explanation has never been investigated. Here we elucidate the structure of interfacial water and its role in ice nucleation at ambient pressure on phloroglucinol dihydrate, the paradigmatic example of outstanding ice nucleating organic crystal, using molecular simulations. The simulations confirm the existence of an interfacial monolayer that orders on cooling and becomes fully ordered upon ice formation. The monolayer does not resemble any ice face but seamlessly connects the distinct hydrogen-bonding orders of ice and the organic surface. Although large ordered patches develop in the monolayer before ice nucleates, we find that the critical step is the formation of the ice crystallite, indicating that the mechanism is classical. We predict that the fully ordered, crystalline monolayer nucleates ice above -2 °C and could be responsible for the exceptional ice nucleation by the organic crystal at high pressures. The lifetime of the fully ordered monolayer around 0 °C, however, is too short to account for the memory effect reported in the experiments. The latter could arise from an increase in the melting temperature of ice confined by strongly ice-binding surfaces.

Computationally efficient approach for the identification of ice-binding surfaces and how they bind ice.

Recognition and binding of ice by proteins, crystals, and other surfaces is key for their control of the nucleation and growth of ice. Docking is the state-of-the-art computational method to identify ice-binding surfaces (IBS). However, docking methods require a priori knowledge of the ice plane to which the molecules bind and either neglect the competition of ice and water for the IBS or are computationally expensive. Here we present and validate a robust methodology for the identification of the IBS of molecules and crystals that is easy to implement and a hundred times computationally more efficient than the most advanced ice-docking approaches. The methodology is based on biased sampling with an order parameter that drives the formation of ice. We validate the method using all-atom and coarse-grained models of organic crystals and proteins. To our knowledge, this approach is the first to simultaneously identify the ice-binding surface as well as the plane of ice to which it binds, without the use of structure search algorithms. We show that biased simulations even identify surfaces that are too small or too weak to heterogeneously nucleate ice. The biasing simulations can be used to identify of IBS of antifreeze and ice nucleating proteins and to equilibrate ice seeds bound to an IBS for the calculation of heterogeneous ice nucleation rates using classical nucleation theory.

Electrochemically Generated Nanobubbles: Invariance of the Current with Respect to Electrode Size and Potential.

Gas-producing electrochemical reactions are key to energy conversion and generation technologies. Bubble formation dramatically decreases gas-production rates on nanoelectrodes, by confining the reaction to the electrode boundary. This results in the collapse of the current to a stationary value independent of the potential. Startlingly, these residual currents also appear to be insensitive to the nanoelectrode diameter in the 5 to 500 nm range. These results are counterintuitive, as it may be expected that the current be proportional to the circumference of the electrode, i.e., the length of the three-phase line where the reaction occurs. Here, we use molecular simulations and a kinetic model to elucidate the origin of current insensitivity with respect to the potential and establish its relationship to the size of nanoelectrodes. We provide critical insights for the design and operation of nanoscale electrochemical devices and demonstrate that nanoelectrode arrays maximize conversion rates compared to macroscopic electrodes with same total area.

Slow Propagation of Ice Binding Limits the Ice-Recrystallization Inhibition Efficiency of PVA and Other Flexible Polymers.

Ice recrystallization inhibitors (IRI) are of critical importance in biology, cryopreservation of cells and organs, and frozen foods. Antifreeze glycoproteins (AFGPs) are the most potent IRI. Their cost and cytotoxicity drive the design of synthetic flexible polymers that mimic their function. Poly(vinyl alcohol) (PVA) is the most potent biomimetic found to date, although it is orders of magnitude less potent than AFGPs. A lack of molecular understanding of the factors that limit the IRI efficiency of PVA and other flexible ice-binding polymers hinders the design of more potent IRI. Here, we use molecular and numerical simulations to elucidate how the degree of polymerization (DP) and functionalization of PVA impact its IRI. Our simulations indicate that the onset of IRI activity of PVA occurs for 15 < DP < 20, in agreement with experiments. We predict that polymers with stronger binding to ice per monomer attain IRI activity at lower DP and identify this as a contributor to the higher IRI potency of AFGPs. The simulations reveal that the limiting step for binding of flexible molecules to ice is not the alignment of the molecule to the surface or the initiation of the binding but the propagation to reach its full binding potential. This distinguishes AFGPs and PVA from rigid antifreeze proteins and, we argue, is responsible for their different scaling of efficiencies with molecular size. We use the analysis of PVA to identify the factors that control the IRI activity of flexible polymers and assess the molecular characteristics that endow AFGPs with their exceptional IRI potency.

The end of ice I.

The appearance of ice I in the smallest possible clusters and the nature of its phase coexistence with liquid water could not thus far be unraveled. The experimental and theoretical infrared spectroscopic and free-energy results of this work show the emergence of the characteristic hydrogen-bonding pattern of ice I in clusters containing only around 90 water molecules. The onset of crystallization is accompanied by an increase of surface oscillator intensity with decreasing surface-to-volume ratio, a spectral indicator of nanoscale crystallinity of water. In the size range from 90 to 150 water molecules, we observe mixtures of largely crystalline and purely amorphous clusters. Our analysis suggests that the liquid-ice I transition in clusters loses its sharp 1st-order character at the end of the crystalline-size regime and occurs over a range of temperatures through heterophasic oscillations in time, a process without analog in bulk water.

Can clathrates heterogeneously nucleate ice?

Methane hydrates can be preserved at ambient pressure, beyond their region of thermodynamic stability, by storing them at temperatures from 240 to 270 K. The origin of this anomalous self-preservation is the formation of an ice coating that covers the clathrate particles and prevents further loss of gas. While there have been several studies on self-preservation, the question of what is the mechanism by which ice nucleates on the decomposing clathrate hydrates has not yet been fully explained. Here, we use molecular simulations, thermodynamic analysis, and nucleation theory to investigate possible scenarios for the nucleation of ice: heterogeneous nucleation at the clathrate/vapor or clathrate/liquid interfaces and homogeneous nucleation from supercooled water. Our results indicate that clathrates cannot heterogeneously nucleate ice and that ice nucleation is due to the cooling of water at the decomposing clathrate/liquid interface, which suffices to trigger homogeneous ice nucleation. We find that the (111) face of the sII structure clathrate can bind to the (111) plane of cubic ice or the basal plane of hexagonal ice through domain matching, resulting in a weak binding that-while insufficient to promote heterogeneous ice nucleation-suffices to produce epitaxy and alignment between these crystals. We use thermodynamic relations, theory, and the contact angles of ice at the (111) sII clathrate/liquid interface to determine-for the first time-the interfacial free energy of this most favorable ice-clathrate interface, 59 ± 5 mJ/m2. We discuss the implications of our results for the feasibility of heterogeneous nucleation of gas clathrates at ice/vapor interfaces.

Mechanisms of Nucleation and Stationary States of Electrochemically Generated Nanobubbles.

Gas evolving reactions are ubiquitous in the operation of electrochemical devices. Recent studies of individual gas bubbles on nanoelectrodes have resulted in unprecedented control and insights on their formation. The experiments, however, lack the spatial resolution to elucidate the molecular pathway of nucleation of nanobubbles and their stationary size and shape. Here we use molecular simulations with an algorithm that mimics the electrochemical formation of gas, to investigate the mechanisms of nucleation of gas bubbles on nanoelectrodes, and characterize their stationary states. The simulations reproduce the experimental currents in the induction and stationary stages, and indicate that surface nanobubbles nucleate through a classical mechanism. We identify three distinct regimes for bubble nucleation, depending on the binding free energy per area of bubble to the electrode, Δγbind. If Δγbind is negative, the nucleation is heterogeneous and the nanobubble remains bound to the electrode, resulting in a low-current stationary state. For very negative Δγ, the bubble fully wets the electrode, forming a one-layer-thick micropancake that nucleates without supersaturation. On the other hand, when Δγbind > 0 the nanobubble nucleates homogeneously close to the electrode, but never attaches to it. We conclude that all surface nanobubbles must nucleate heterogeneously. The simulations reveal that the size and contact angle of stationary nanobubbles increase with the reaction driving force, although their residual current is invariant. The myriad of driven nonequilibrium stationary states with the same rate of production of gas, but distinct bubble properties, suggests that these dissipative systems have attractors that control the stationary current.

Following the nucleation pathway from disordered liquid to gyroid mesophase.

Mesophases have order intermediate between liquids and crystals and arise in systems with frustration, such as surfactants, block copolymers, and Janus nanoparticles. The gyroid mesophase contains two interpenetrated, nonintersecting chiral networks that give it properties useful for photonics. It is challenging to nucleate a gyroid from the liquid. Elucidating the reaction coordinate for gyroid nucleation could assist in designing additives that facilitate the formation of the mesophase. However, the complexity of the gyroid structure and the extreme weakness of the first-order liquid to gyroid transition make this a challenging quest. Here, we investigate the pathway and transition states for the nucleation of a gyroid from the liquid in molecular simulations with a mesogenic binary mixture. We find that the gyroid nuclei at the transition states have a large degree of positional disorder and are not compact, consistent with the low surface free energy of the liquid-gyroid interface. A combination of bond-order parameters for the minor component is best to describe the passage from liquid to gyroid, among those we consider. The committor analyses, however, show that this best coordinate is not perfect and suggests that accounting for the relative ordering of the two interpenetrated networks in infant nuclei, as well as for signatures of ordering in the major component of the mesophase, would improve the accuracy of the reaction coordinate for gyroid formation and its use to evaluate nucleation barriers. To our knowledge, this study is the first to investigate the reaction coordinate and critical nuclei for the formation of any mesophase from an amorphous phase.

Hydrogen-Bonding and Hydrophobic Groups Contribute Equally to the Binding of Hyperactive Antifreeze and Ice-Nucleating Proteins to Ice.

Hyperactive insect antifreeze proteins and bacterial ice-nucleating proteins are arguably the most potent ice-binding molecules in nature. These highly effective proteins bind ice through amphiphilic ice-binding sites based on arrays of threonine residues. It remains poorly understood how hydrophilic and hydrophobic groups of the binding site contribute to the ice affinity of proteins. Here, we use molecular simulations to demonstrate that the hydrogen-bonding and hydrophobic groups at the ice-binding site of the antifreeze protein TmAFP of Tenebrio molitor and extended ice-nucleating protein surfaces contribute distinctively yet almost equally in magnitude to their binding free energy to ice. The methyl groups rigidize the ice-binding site, slow the water dynamics at the ice-binding surface, and stabilize the clathrate-like water in the anchored clathrate motif that binds these proteins to ice. We find that hydrophobic dehydration of the methyl group does not contribute to the binding free energy of the protein to ice. The role of the hydroxyl groups is to anchor the clathrate-like water through direct hydrogen-bonding, positioning and slowing the dynamics of water at the trough of the binding site. We uncover a correlation between slower dynamics of water at the binding site for the protein in solution and stronger free energy of binding of the protein to ice. The synergy between hydrophobic and hydrophilic groups unveiled by this study provides guidance for the design of synthetic ice-binding molecules with enhanced ice nucleation and antifreeze activity.