Sequence dependence of critical properties for two-letter chains.

Histogram-reweighting grand canonical Monte Carlo simulations are used to obtain the critical properties of lattice chains composed of solvophilic and solvophobic monomers. The model is a modification of one proposed by Larson et al. [J. Chem. Phys. 83, 2411 (1985)], lowering the "contrast" between beads of different types to prevent aggregation into finite-size micelles that would mask true phase separation between bulk high- and low-density phases. Oligomeric chains of lengths between 5 and 24 beads are studied. Mixed-field finite-size scaling methods are used to obtain the critical properties with typical relative accuracies of better than 10-4 for the critical temperature and 10-3 for the critical volume fraction. Diblock chains are found to have lower critical temperatures and volume fractions relative to the corresponding homopolymers. The addition of solvophilic blocks of increasing length to a fixed-length solvophobic segment results in a decrease of both the critical temperature and the critical volume fraction, with an eventual slow asymptotic approach to the long-chain limiting behavior. Moving a single solvophobic or solvophilic bead along a chain leads to a minimum or maximum in the critical temperature, with no change in the critical volume fraction. Chains of identical length and composition have a significant spread in their critical properties, depending on their precise sequence. The present study has implications for understanding biomolecular phase separation and for developing design rules for synthetic polymers with specific phase separation properties. It also provides data potentially useful for the further development of theoretical models for polymer and surfactant phase behavior.

Interfacial exchange dynamics of biomolecular condensates are highly sensitive to client interactions.

Phase separation of biomolecules can facilitate their spatiotemporally regulated self-assembly within living cells. Due to the selective yet dynamic exchange of biomolecules across condensate interfaces, condensates can function as reactive hubs by concentrating enzymatic components for faster kinetics. The principles governing this dynamic exchange between condensate phases, however, are poorly understood. In this work, we systematically investigate the influence of client-sticker interactions on the exchange dynamics of protein molecules across condensate interfaces. We show that increasing affinity between a model protein scaffold and its client molecules causes the exchange of protein chains between the dilute and dense phases to slow down and that beyond a threshold interaction strength, this slowdown in exchange becomes substantial. Investigating the impact of interaction symmetry, we found that chain exchange dynamics are also considerably slower when client molecules interact equally with different sticky residues in the protein. The slowdown of exchange is due to a sequestration effect, by which there are fewer unbound stickers available at the interface to which dilute phase chains may attach. These findings highlight the fundamental connection between client-scaffold interaction networks and condensate exchange dynamics.

Asymmetric oligomerization state and sequence patterning can tune multiphase condensate miscibility.

Endogenous biomolecular condensates, composed of a multitude of proteins and RNAs, can organize into multiphasic structures with compositionally distinct phases. This multiphasic organization is generally understood to be critical for facilitating their proper biological function. However, the biophysical principles driving multiphase formation are not completely understood. Here we use in vivo condensate reconstitution experiments and coarse-grained molecular simulations to investigate how oligomerization and sequence interactions modulate multiphase organization in biomolecular condensates. We demonstrate that increasing the oligomerization state of an intrinsically disordered protein results in enhanced immiscibility and multiphase formation. Interestingly, we find that oligomerization tunes the miscibility of intrinsically disordered proteins in an asymmetric manner, with the effect being more pronounced when the intrinsically disordered protein, exhibiting stronger homotypic interactions, is oligomerized. Our findings suggest that oligomerization is a flexible biophysical mechanism that cells can exploit to tune the internal organization of biomolecular condensates and their associated biological functions.

A first-principles machine-learning force field for heterogeneous ice nucleation on microcline feldspar.

The formation of ice in the atmosphere affects precipitation and cloud properties, and plays a key role in the climate of our planet. Although ice can form directly from liquid water under deeply supercooled conditions, the presence of foreign particles can aid ice formation at much warmer temperatures. Over the past decade, experiments have highlighted the remarkable efficiency of feldspar minerals as ice nuclei compared to other particles present in the atmosphere. However, the exact mechanism of ice formation on feldspar surfaces has yet to be fully understood. Here, we develop a first-principles machine-learning model for the potential energy surface aimed at studying ice nucleation at microcline feldspar surfaces. The model is able to reproduce with high-fidelity the energies and forces derived from density-functional theory (DFT) based on the SCAN exchange and correlation functional. Our training set includes configurations of bulk supercooled water, hexagonal and cubic ice, microcline, and fully-hydroxylated feldspar surfaces exposed to a vacuum, liquid water, and ice. We apply the machine-learning force field to study different fully-hydroxylated terminations of the (100), (010), and (001) surfaces of microcline exposed to a vacuum. Our calculations suggest that terminations that do not minimize the number of broken bonds are preferred in a vacuum. We also study the structure of supercooled liquid water in contact with microcline surfaces, and find that water density correlations extend up to around 10 Å from the surfaces. Finally, we show that the force field maintains a high accuracy during the simulation of ice formation at microcline surfaces, even for large systems of around 30 000 atoms. Future work will be directed towards the calculation of nucleation free-energy barriers and rates using the force field developed herein, and understanding the role of different microcline surfaces in ice nucleation.

Neural Network Water Model Based on the MB-Pol Many-Body Potential.

The MB-pol many-body potential accurately predicts many properties of water, including cluster, liquid phase, and vapor-liquid equilibrium properties, but its high computational cost can make applying it in large-scale simulations quite challenging. In order to address this limitation, we developed a "deep potential" neural network (DPMD) model based on the MB-pol potential for water. We find that a DPMD model trained on mostly liquid configurations yields a good description of the bulk liquid phase but severely underpredicts vapor-liquid coexistence densities. By contrast, adding cluster configurations to the neural network training set leads to a good agreement for the vapor coexistence densities. Liquid phase densities under supercooled conditions are also represented well, even though they were not included in the training set. These results confirm that neural network models can combine accuracy and transferability if sufficient attention is given to the construction of a representative training set for the target system.

Why Dissolving Salt in Water Decreases Its Dielectric Permittivity.

The dielectric permittivity of salt water decreases on dissolving more salt. For nearly a century, this phenomenon has been explained by invoking saturation in the dielectric response of the solvent water molecules. Herein, we employ an advanced deep neural network (DNN), built using data from density functional theory, to study the dielectric permittivity of sodium chloride solutions. Notably, the decrease in the dielectric permittivity as a function of concentration, computed using the DNN approach, agrees well with experiments. Detailed analysis of the computations reveals that the dominant effect, caused by the intrusion of ionic hydration shells into the solvent hydrogen-bond network, is the disruption of dipolar correlations among water molecules. Accordingly, the observed decrease in the dielectric permittivity is mostly due to increasing suppression of the collective response of solvent waters.

First-Principles-Based Machine Learning Models for Phase Behavior and Transport Properties of CO2.

In this work, we construct distinct first-principles-based machine-learning models of CO2, reproducing the potential energy surface of the PBE-D3, BLYP-D3, SCAN, and SCAN-rvv10 approximations of density functional theory. We employ the Deep Potential methodology to develop the models and consequently achieve a significant computational efficiency over ab initio molecular dynamics (AIMD) that allows for larger system sizes and time scales to be explored. Although our models are trained only with liquid-phase configurations, they are able to simulate a stable interfacial system and predict vapor-liquid equilibrium properties, in good agreement with results from the literature. Because of the computational efficiency of the models, we are also able to obtain transport properties, such as viscosity and diffusion coefficients. We find that the SCAN-based model presents a temperature shift in the position of the critical point, while the SCAN-rvv10-based model shows improvement but still exhibits a temperature shift that remains approximately constant for all properties investigated in this work. We find that the BLYP-D3-based model generally performs better for the liquid phase and vapor-liquid equilibrium properties, but the PBE-D3-based model is better suited for predicting transport properties.

A Deep Potential model for liquid-vapor equilibrium and cavitation rates of water.

Computational studies of liquid water and its phase transition into vapor have traditionally been performed using classical water models. Here, we utilize the Deep Potential methodology-a machine learning approach-to study this ubiquitous phase transition, starting from the phase diagram in the liquid-vapor coexistence regime. The machine learning model is trained on ab initio energies and forces based on the SCAN density functional, which has been previously shown to reproduce solid phases and other properties of water. Here, we compute the surface tension, saturation pressure, and enthalpy of vaporization for a range of temperatures spanning from 300 to 600 K and evaluate the Deep Potential model performance against experimental results and the semiempirical TIP4P/2005 classical model. Moreover, by employing the seeding technique, we evaluate the free energy barrier and nucleation rate at negative pressures for the isotherm of 296.4 K. We find that the nucleation rates obtained from the Deep Potential model deviate from those computed for the TIP4P/2005 water model due to an underestimation in the surface tension from the Deep Potential model. From analysis of the seeding simulations, we also evaluate the Tolman length for the Deep Potential water model, which is (0.091 ± 0.008) nm at 296.4 K. Finally, we identify that water molecules display a preferential orientation in the liquid-vapor interface, in which H atoms tend to point toward the vapor phase to maximize the enthalpic gain of interfacial molecules. We find that this behavior is more pronounced for planar interfaces than for the curved interfaces in bubbles. This work represents the first application of Deep Potential models to the study of liquid-vapor coexistence and water cavitation.

Phase separation and aggregation in multiblock chains.

This paper focuses on phase and aggregation behavior for linear chains composed of blocks of hydrophilic and hydrophobic segments. Phase and conformational transitions of patterned chains are relevant for understanding liquid-liquid separation of biomolecular condensates, which play a prominent role in cellular biophysics and for surfactant and polymer applications. Previous studies of simple models for multiblock chains have shown that, depending on the sequence pattern and chain length, such systems can fall into one of two categories: displaying either phase separation or aggregation into finite-size clusters. The key new result of this paper is that both formation of finite-size aggregates and phase separation can be observed for certain chain architectures at appropriate conditions of temperature and concentration. For such systems, a bulk dense liquid condenses from a dilute phase that already contains multi-chain finite-size aggregates. The computational approach used in this study involves several distinct steps using histogram-reweighting grand canonical Monte Carlo simulations, which are described in some level of detail.

Dynamics of Aqueous Electrolyte Solutions: Challenges for Simulations.

This Perspective article focuses on recent simulation work on the dynamics of aqueous electrolytes. It is well-established that full-charge, nonpolarizable models for water and ions generally predict solution dynamics that are too slow in comparison to experiments. Models with reduced (scaled) charges do better for solution diffusivities and viscosities but encounter issues describing other dynamic phenomena such as nucleation rates of crystals from solution. Polarizable models show promise, especially when appropriately parametrized, but may still miss important physical effects such as charge transfer. First-principles calculations are starting to emerge for these properties that are in principle able to capture polarization, charge transfer, and chemical transformations in solution. While direct ab initio simulations are still too slow for simulations of large systems over long time scales, machine-learning models trained on appropriate first-principles data show significant promise for accurate and transferable modeling of electrolyte solution dynamics.

Modeling Chemical Reactions in Alkali Carbonate-Hydroxide Electrolytes with Deep Learning Potentials.

We developed a deep potential machine learning model for simulations of chemical reactions in molten alkali carbonate-hydroxide electrolyte containing dissolved CO2, using an active learning procedure. We tested the deep neural network (DNN) potential and training procedure against reaction kinetics, chemical composition, and diffusion coefficients obtained from density functional theory (DFT) molecular dynamics calculations. The DNN potential was found to match DFT results for the structural, transport, and short-time chemical reactions in the melt. Using the DNN potential, we extended the time scales of observation to 2 ns in systems containing thousands of atoms, while preserving quantum chemical accuracy. This allowed us to reach chemical equilibrium with respect to several chemical species in the melt. The approach can be generalized for a broad spectrum of chemically reactive systems.

Homogeneous ice nucleation in an ab initio machine-learning model of water.

Molecular simulations have provided valuable insight into the microscopic mechanisms underlying homogeneous ice nucleation. While empirical models have been used extensively to study this phenomenon, simulations based on first-principles calculations have so far proven prohibitively expensive. Here, we circumvent this difficulty by using an efficient machine-learning model trained on density-functional theory energies and forces. We compute nucleation rates at atmospheric pressure, over a broad range of supercoolings, using the seeding technique and systems of up to hundreds of thousands of atoms simulated with ab initio accuracy. The key quantity provided by the seeding technique is the size of the critical cluster (i.e., a size such that the cluster has equal probabilities of growing or melting at the given supersaturation), which is used together with the equations of classical nucleation theory to compute nucleation rates. We find that nucleation rates for our model at moderate supercoolings are in good agreement with experimental measurements within the error of our calculation. We also study the impact of properties such as the thermodynamic driving force, interfacial free energy, and stacking disorder on the calculated rates.

Liquid-liquid criticality in the WAIL water model.

The hypothesis that the anomalous behavior of liquid water is related to the existence of a second critical point in deeply supercooled states has long been the subject of intense debate. Recent, sophisticated experiments designed to observe the transformation between the two subcritical liquids on nano- and microsecond time scales, along with demanding numerical simulations based on classical (rigid) models parameterized to reproduce thermodynamic properties of water, have provided support to this hypothesis. A stronger numerical proof requires demonstrating that the critical point, which occurs at temperatures and pressures far from those at which the models were optimized, is robust with respect to model parameterization, specifically with respect to incorporating additional physical effects. Here, we show that a liquid-liquid critical point can be rigorously located also in the WAIL model of water [Pinnick et al., J. Chem. Phys. 137, 014510 (2012)], a model parameterized using ab initio calculations only. The model incorporates two features not present in many previously studied water models: It is both flexible and polarizable, properties which can significantly influence the phase behavior of water. The observation of the critical point in a model in which the water-water interaction is estimated using only quantum ab initio calculations provides strong support to the viewpoint according to which the existence of two distinct liquids is a robust feature in the free energy landscape of supercooled water.

Anomalies and Local Structure of Liquid Water from Boiling to the Supercooled Regime as Predicted by the Many-Body MB-pol Model.

For the past 50 years, researchers have sought molecular models that can accurately reproduce water's microscopic structure and thermophysical properties across broad ranges of its complex phase diagram. Herein, molecular dynamics simulations with the many-body MB-pol model are performed to monitor the thermodynamic response functions and local structure of liquid water from the boiling point down to deeply supercooled temperatures at ambient pressure. The isothermal compressibility and isobaric heat capacity show maxima near 223 K, in excellent agreement with recent experiments, and the liquid density exhibits a minimum at ∼208 K. A local tetrahedral arrangement, where each water molecule accepts and donates two hydrogen bonds, is found to be the most probable hydrogen-bonding topology at all temperatures. This work suggests that MB-pol may provide predictive capability for studies of liquid water's physical properties across broad ranges of thermodynamic states, including the so-called water's "no man's land" which is difficult to probe experimentally.

Activity Coefficients and Solubilities of NaCl in Water-Methanol Solutions from Molecular Dynamics Simulations.

We obtain activity coefficients and solubilities of NaCl in water-methanol solutions at 298.15 K and 1 bar from molecular dynamics (MD) simulations with the Joung-Cheatham, SPC/E, and OPLS-AA force fields for NaCl, water, and methanol, respectively. The Lorentz-Berthelot combining rules were adopted for the unlike-pair interactions of Na+, Cl-, and the oxygen site in SPC/E water, and geometric combining rules were utilized for the remainder of the cross interactions. We found that the selection of appropriate combining rules is important in obtaining physically realistic solubilities. The solvent compositions studied range from pure water to pure methanol. Several salt concentrations were investigated at each solvent composition, from the lowest concentrations permitted by the system size used up to the experimental solubilities. We first calculated individual ion activity coefficients (IIACs) for Na+ and Cl- from the free energy change due to the gradual insertion of a single cation or anion into the solution, accompanied by a neutralizing background. We obtained the salt solubilities by comparing the chemical potentials in solution with solid NaCl chemical potentials calculated previously using the Einstein crystal method. Mean ionic activity coefficients obtained from the IIACs are in reasonable agreement with experimental data, with deviations increasing for solutions of higher methanol content. Predictions for the salt solubility are in surprisingly good agreement with experimental data, despite well-known challenges in the simultaneous calculation of activity coefficients and solubilities with classical MD simulations. The present study demonstrates that good predictions for these two important phase equilibrium properties can be obtained for mixed-solvent electrolyte solutions using existing nonpolarizable models and further suggests that the previously proposed single ion insertion technique can be extended to complex mixed-solvent solutions as well.

A deep potential model with long-range electrostatic interactions.

Machine learning models for the potential energy of multi-atomic systems, such as the deep potential (DP) model, make molecular simulations with the accuracy of quantum mechanical density functional theory possible at a cost only moderately higher than that of empirical force fields. However, the majority of these models lack explicit long-range interactions and fail to describe properties that derive from the Coulombic tail of the forces. To overcome this limitation, we extend the DP model by approximating the long-range electrostatic interaction between ions (nuclei + core electrons) and valence electrons with that of distributions of spherical Gaussian charges located at ionic and electronic sites. The latter are rigorously defined in terms of the centers of the maximally localized Wannier distributions, whose dependence on the local atomic environment is modeled accurately by a deep neural network. In the DP long-range (DPLR) model, the electrostatic energy of the Gaussian charge system is added to short-range interactions that are represented as in the standard DP model. The resulting potential energy surface is smooth and possesses analytical forces and virial. Missing effects in the standard DP scheme are recovered, improving on accuracy and predictive power. By including long-range electrostatics, DPLR correctly extrapolates to large systems the potential energy surface learned from quantum mechanical calculations on smaller systems. We illustrate the approach with three examples: the potential energy profile of the water dimer, the free energy of interaction of a water molecule with a liquid water slab, and the phonon dispersion curves of the NaCl crystal.

Transferability of data-driven, many-body models for CO2 simulations in the vapor and liquid phases.

Extending on the previous work by Riera et al. [J. Chem. Theory Comput. 16, 2246-2257 (2020)], we introduce a second generation family of data-driven many-body MB-nrg models for CO2 and systematically assess how the strength and anisotropy of the CO2-CO2 interactions affect the models' ability to predict vapor, liquid, and vapor-liquid equilibrium properties. Building upon the many-body expansion formalism, we construct a series of MB-nrg models by fitting one-body and two-body reference energies calculated at the coupled cluster level of theory for large monomer and dimer training sets. Advancing from the first generation models, we employ the charge model 5 scheme to determine the atomic charges and systematically scale the two-body energies to obtain more accurate descriptions of vapor, liquid, and vapor-liquid equilibrium properties. Challenges in model construction arise due to the anisotropic nature and small magnitude of the interaction energies in CO2, calling for the necessity of highly accurate descriptions of the multidimensional energy landscape of liquid CO2. These findings emphasize the key role played by the training set quality in the development of transferable, data-driven models, which, accurately representing high-dimensional many-body effects, can enable predictive computer simulations of molecular fluids across the entire phase diagram.

Dissolving salt is not equivalent to applying a pressure on water.

Salt water is ubiquitous, playing crucial roles in geological and physiological processes. Despite centuries of investigations, whether or not water's structure is drastically changed by dissolved ions is still debated. Based on density functional theory, we employ machine learning based molecular dynamics to model sodium chloride, potassium chloride, and sodium bromide solutions at different concentrations. The resulting reciprocal-space structure factors agree quantitatively with neutron diffraction data. Here we provide clear evidence that the ions in salt water do not distort the structure of water in the same way as neat water responds to elevated pressure. Rather, the computed structural changes are restricted to the ionic first solvation shells intruding into the hydrogen bond network, beyond which the oxygen radial-distribution function does not undergo major change relative to neat water. Our findings suggest that the widely cited pressure-like effect on the solvent in Hofmeister series ionic solutions should be carefully revisited.

Liquid-Liquid Transition in Water from First Principles.

A long-standing question in water research is the possibility that supercooled liquid water can undergo a liquid-liquid phase transition (LLT) into high- and low-density liquids. We used several complementary molecular simulation techniques to evaluate the possibility of an LLT in an ab initio neural network model of water trained on density functional theory calculations with the SCAN exchange correlation functional. We conclusively show the existence of a first-order LLT and an associated critical point in the SCAN description of water, representing the first definitive computational evidence for an LLT in water from first principles.

Activity coefficients of aqueous electrolytes from implicit-water molecular dynamics simulations.

We obtain activity coefficients in NaCl and KCl solutions from implicit-water molecular dynamics simulations, at 298.15 K and 1 bar, using two distinct approaches. In the first approach, we consider ions in a continuum with constant relative permittivity (ɛr) equal to that of pure water; in the other approach, we take into account the concentration-dependence of ɛr, as obtained from explicit-water simulations. Individual ion activity coefficients (IIACs) are calculated using gradual insertion of single ions with uniform neutralizing backgrounds to ensure electroneutrality. Mean ionic activity coefficients (MIACs) obtained from the corresponding IIACs in simulations with constant ɛr show reasonable agreement with experimental data for both salts. Surprisingly, large systematic negative deviations are observed for both IIACs and MIACs in simulations with concentration-dependent ɛr. Our results suggest that the absence of hydration structure in implicit-water simulations cannot be compensated by correcting for the concentration-dependence of the relative permittivity ɛr. Moreover, even in simulations with constant ɛr for which the calculated MIACs are reasonable, the relative positioning of IIACs of anions and cations is incorrect for NaCl. We conclude that there are severe inherent limitations associated with implicit-water simulations in providing accurate activities of aqueous electrolytes, a finding with direct relevance to the development of electrolyte theories and to the use and interpretation of implicit-solvent simulations.