Water-Driven Cavity–Ligand Binding: Comparison of Thermodynamic Signatures from Coarse-Grained and Atomic-Level Simulations

Thermodynamically Optimized Machine-Learned Reaction Coordinates for Hydrophobic Ligand Dissociation

Ligand unbinding is mediated by its free energy change, which has intertwined contributions from both energy and entropy. It is important, but not easy, to quantify their individual contributions to the free energy profile. We model hydrophobic ligand unbinding for two systems, a methane particle and a C60 fullerene, both unbinding from hydrophobic pockets in all-atom water. Using a modified deep learning framework, we learn a thermodynamically optimized reaction coordinate to describe the hydrophobic ligand dissociation for both systems. Interpretation of these reaction coordinates reveals the roles of entropic and enthalpic forces as the ligand and pocket sizes change. In both cases, we observe that the free-energy barrier to unbinding is dominated by entropy considerations. Furthermore, the process of methane unbinding is driven by methane solvation, while fullerene unbinding is driven first by pocket wetting and then fullerene wetting. For both solutes, the direct importance of the distance from the binding pocket to the learned reaction coordinate is present, but low. Our framework and subsequent feature important analysis thus give useful thermodynamic insight into hydrophobic ligand dissociation problems that are otherwise difficult to glean.

Molecular recognition with soft biomaterials

Biomacromolecules and engineered materials can achieve molecular recognition if they engage their ligand with properly oriented and chemically complementary moieties. Recently, there has been significant interest in fabricating recognitive soft materials, which possess specific affinity for biological analytes. We present a summary and evaluation of current recognitive materials for biosensing, drug delivery, and regenerative medicine applications. We highlight the impact of material composition on the extent and specificity of ligand adsorption, citing new theoretical and empirical evidence. We conclude with a guide for synthesizing and characterizing novel recognitive materials, as well as recommendations for ligand selection and experimental design.

Water access and ligand dissociation at the binding site of proteins

Although water is undoubtedly an essential mediator of protein-ligand interactions, whether or not such water molecules are critical for the progress of ligand dissociation remains unclear. To gain a more complete understanding, molecular dynamics simulations are performed with two molecular systems, rigid model binding sites and trypsin-benzamidine. Free-energy landscapes are calculated with a suitably chosen solvent coordinate, which well describes water access to the ligand binding site. The results of free energy provided clear description of water-ligand exchange process, where two different mechanisms appear depending on whether the binding site is buried or not. As the site is more buried, water access is more difficult. When water does not access the site, ligand dissociation produces a large energy barrier, i.e., slow dissociation kinetics. This indicates that control of ligand dissociation kinetics becomes possible with burying the binding site. However, the results also showed that appropriate burying is important because burying reduces not only water access but also ligand binding. The role of the protein structural change is also discussed; it likely plays a similar role to water access because during ligand dissociation, it can make new coordination with the ligand binding site like water. These results contribute to the future pharmaceutical drug design and will be useful for fundamental exploration of various molecular events.

Molecular Insights into the Unusual Structure of an Antifreeze Protein with a Hydrated Core

The primary driving force for protein folding is the formation of a well-packed, anhydrous core. However, recently, the crystal structure of an antifreeze protein, maxi, has been resolved where the core of the protein is filled with water, which apparently contradicts the existing notion of protein folding. Here, we have performed standard molecular dynamics (MD) simulation, replica exchange MD (REMD) simulation, and umbrella sampling using TIP4P water at various temperatures (300, 260, and 240 K) to explore the origin of this unusual structural feature. It is evident from standard MD and REMD simulations that the protein is found to be stable at 240 K in its unusual state. The core of protein has two layers of semi-clathrate water separating the methyl groups of alanine residues from different helical strands. However, with increasing temperature (260 and 300 K), the stability decreases as the core becomes dehydrated, and methyl groups of alanine are tightly packed driven by hydrophobic interactions. Calculation of the potential of mean force by an umbrella sampling technique between a pair of model hydrophobes resembling maxi protein at 240 K shows the stabilization of second solvent-separated minima (SSM), which provides a thermodynamic rationale of the unusual structural feature in terms of weakening of the hydrophobic interaction. Because the stabilization of SSMs is implicated for cold denaturation, it suggests that the maxi protein is so designed by nature where the cold denatured-like state becomes the biologically active form as it works near or below the freezing point of water.

Why Is It So Difficult to Identify the Onset of Ice Premelting?

Premelting of ice at temperatures below 0 °C is of fundamental importance for environmental processes. Various experimental techniques have been used to investigate the temperature at which liquid-like water first appears at the ice-vapor interface, reporting onset temperatures from -160 to -2 °C. The signals that identify liquid-like order at the ice-vapor interface in these studies, however, do not show a sharp initiation with temperature. That is at odds with the expected first-order nature of surface phase transitions, and consistent with recent large-scale molecular simulations that show the first premelted layer to be sparse and to develop continuously over a wide range of temperatures. Here we perform a thermodynamic analysis to elucidate the origin of the continuous formation of the first layer of liquid at the ice-vapor interface. We conclude that a negative value of the line tension of the ice-liquid-vapor three-phase contact line is responsible for the continuous character of the transition and the sparse nature of the liquid-like domains in the incomplete first layer.

Ice-Liquid Oscillations in Nanoconfined Water

Nanoscale confinement has a strong effect on the phase behavior of water. Studies in the last two decades have revealed a wealth of novel crystalline and quasicrystalline structures for water confined in nanoslits. Less is known, however, about the nature of ice-liquid coexistence in extremely nanoconfined systems. Here, we use molecular simulations to investigate the ice-liquid equilibrium for water confined between two nanoscopic disks. We find that the nature of ice-liquid phase coexistence in nanoconfined water is different from coexistence in both bulk water and extended nanoslits. In highly nanoconfined systems, liquid water and ice do not coexist in space because the two-phase states are unstable. The confined ice and liquid phases coexist in time, through oscillations between all-liquid and all-crystalline states. The avoidance of spatial coexistence of ice and liquid originates on the non-negligible cost of the interface between confined ice and liquid in a small system. It is the result of the small number of water molecules between the plates and has no analogue in bulk water.

The Clathrate-Water Interface Is Oleophilic

The slow nucleation of clathrate hydrates is a central challenge for their use in the storage and transportation of natural gas. Molecules that strongly adsorb to the clathrate-water interface decrease the crystal-water surface tension, lowering the barrier for clathrate nucleation. Surfactants are widely used to promote the nucleation and growth of clathrate hydrates. It has been proposed that these amphiphilic molecules bind to the clathrate surface via hydrogen bonding. However, recent studies reveal that PVCap, an amphiphilic polymer, binds to clathrates through hydrophobic moieties. Here we use molecular dynamic simulations and theory to investigate the mode and strength of binding of surfactants to the clathrate-water interface and their effect on the nucleation rate. We find that the surfactants bind to the clathrate-water interface exclusively through their hydrophobic tails. The binding is strong, driven by the entropy of dehydration of the alkyl chain, as it penetrates empty cavities at the hydrate surface. The hydrophobic attraction of alkyl groups to the clathrate surface also results in strong adsorption of alkanes. We identify two regimes for the binding of surfactants as a function of their density at the hydrate surface, which we interpret to correspond to the two steps of the Langmuir adsorption isotherm observed in experiments. Our results indicate that hydrophobic attraction to the clathrate-water interface is key for the design of soluble additives that promote the nucleation of hydrates. We use the calculated adsorption coefficients to estimate the concentration of sodium dodecyl sulfate (SDS) required to reach nucleation rates for methane hydrate consistent with those measured in experiments. To our knowledge, this study is the first to quantify the effect of surfactant concentration in the nucleation rate of clathrate hydrates.

Ice-Nucleating and Antifreeze Proteins Recognize Ice through a Diversity of Anchored Clathrate and Ice-like Motifs

Cold-adapted organisms produce antifreeze and ice-nucleating proteins to prevent and promote ice formation. The crystal structure of hyperactive bacterial antifreeze protein (AFP) MpAFP suggests that this protein binds ice through an anchored clathrate motif. It is not known whether other hyperactive AFPs and ice-nucleating proteins (INPs) use the same motif to recognize or nucleate ice. Here we use molecular simulations to elucidate the ice-binding motifs of hyperactive insect AFPs and a model INP of Pseudomonas syringae. We find that insect AFPs recognize ice through anchored clathrate motifs distinct from that of MpAFP. By performing simulations of ice nucleation by PsINP, we identify two distinct ice-binding sites on opposite sides of the β-helix. The ice-nucleating sequences identified in the simulations agree with those previously proposed for the closely related INP of Pseudomonas borealis based on the structure of the protein. The simulations indicate that these sites have comparable ice-nucleating efficiency, but distinct binding motifs, controlled by the amino acid sequence: one is an anchored clathrate and the other ice-like. We conclude that anchored clathrate and ice-like motifs can be equally effective for binding proteins to ice and promoting ice nucleation.

Is Water at the Graphite Interface Vapor-like or Ice-like?

Graphitic surfaces are the main component of soot, a major constituent of atmospheric aerosols. Experiments indicate that soots of different origins display a wide range of abilities to heterogeneously nucleate ice. The ability of pure graphite to nucleate ice in experiments, however, seems to be almost negligible. Nevertheless, molecular simulations with the monatomic water model mW with water-carbon interactions parameterized to reproduce the experimental contact angle of water on graphite predict that pure graphite nucleates ice. According to classical nucleation theory, the ability of a surface to nucleate ice is controlled by the binding free energy between ice immersed in liquid water and the surface. To establish whether the discrepancy in freezing efficiencies of graphite in mW simulations and experiments arises from the coarse resolution of the model or can be fixed by reparameterization, it is important to elucidate the contributions of the water-graphite, water-ice, and ice-water interfaces to the free energy, enthalpy, and entropy of binding for both water and the model. Here we use thermodynamic analysis and free energy calculations to determine these interfacial properties. We demonstrate that liquid water at the graphite interface is not ice-like or vapor-like: it has similar free energy, entropy, and enthalpy as water in the bulk. The thermodynamics of the water-graphite interface is well reproduced by the mW model. We find that the entropy of binding between graphite and ice is positive and dominated, in both experiments and simulations, by the favorable entropy of reducing the ice-water interface. Our analysis indicates that the discrepancy in freezing efficiencies of graphite in experiments and the simulations with mW arises from the inability of the model to simultaneously reproduce the contact angle of liquid water on graphite and the free energy of the ice-graphite interface. This transferability issue is intrinsic to the resolution of the model, and arises from its lack of rotational degrees of freedom.

Parameterization of a coarse-grained model with short-ranged interactions for modeling fuel cell membranes with controlled water uptake

The coarse-grained model FF_pvap reproduces the experimental activity coefficient of water in tetramethylammonium chloride solutions over a wide range of concentrations, with a hundred-fold gain in computing efficiency with respect to atomistic models.

Van der Waals Perspective on Coarse-Graining: Progress toward Solving Representability and Transferability Problems

Low-resolution coarse-grained (CG) models provide the necessary efficiency for simulating phenomena that are inaccessible to more detailed models. However, in order to realize their considerable promise, CG models must accurately describe the relevant physical forces and provide useful predictions. By formally integrating out the unnecessary details from an all-atom (AA) model, "bottom-up" approaches can, at least in principle, quantitatively reproduce the structural and thermodynamic properties of the AA model that are observable at the CG resolution. In practice, though, bottom-up approaches only approximate this "exact coarse-graining" procedure. The resulting models typically reproduce the intermolecular structure of AA models at a single thermodynamic state point but often describe other state points less accurately and, moreover, tend to provide a poor description of thermodynamic properties. These two limitations have been coined the "transferability" and "representability" problems, respectively. Perhaps, the simplest and most commonly discussed manifestation of the representability problem regards the tendency of structure-based CG models to dramatically overestimate the pressure. Furthermore, when these models are adjusted to reproduce the pressure, they provide a poor description of the compressibility. More generally, it is sometimes suggested that CG models are fundamentally incapable of reproducing both structural and thermodynamic properties. After all, there is no such thing as a "free lunch"; any significant gain in computational efficiency should come at the cost of significant model limitations. At least in the case of structural and thermodynamic properties, though, we optimistically propose that this may be a false dichotomy. Accordingly, we have recently re-examined the "exact coarse-graining" procedure and investigated the intrinsic consequences of representing an AA model in reduced resolution. These studies clarify the origin and inter-relationship of representability and transferability problems. Both arise as consequences of transferring thermodynamic information from the high resolution configuration space and encoding this information into the many-body potential of mean force (PMF), that is, the potential that emerges from an exact coarse-graining procedure. At least in principle, both representability and transferability problems can be resolved by properly addressing this thermodynamic information. In particular, we have demonstrated that "pressure-matching" provides a practical and rigorous means for addressing the density dependence of the PMF. The resulting bottom-up models accurately reproduce the structure, equilibrium density, compressibility, and pressure equation of state for AA models of molecular liquids. Additionally, we have extended this approach to develop transferable potentials that provide similar accuracy for heptane-toluene mixtures. Moreover, these potentials provide predictive accuracy for modeling concentrations that were not considered in their parametrization. More generally, this work suggests a "van der Waals" perspective on coarse-graining, in which conventional structure-based methods accurately describe the configuration dependence of the PMF, while independent variational principles infer the thermodynamic information that is necessary to resolve representability and transferability problems.

What Determines the Ice Polymorph in Clouds?

Ice crystals in the atmosphere nucleate from supercooled liquid water and grow by vapor uptake. The structure of the ice polymorph grown has strong impact on the morphology and light scattering of the ice crystals, modulates the amount of water vapor in ice clouds, and can impact the molecular uptake and reactivity of atmospheric aerosols. Experiments and molecular simulations indicate that ice nucleated and grown from deeply supercooled liquid water is metastable stacking disordered ice. The ice polymorph grown from vapor has not yet been determined. Here we use large-scale molecular simulations to determine the structure of ice that grows as a result of uptake of water vapor in the temperature range relevant to cirrus and mixed-phase clouds, elucidate the molecular mechanism of the formation of ice at the vapor interface, and compute the free energy difference between cubic and hexagonal ice interfaces with vapor. We find that vapor deposition results in growth of stacking disordered ice only under conditions of extreme supersaturation, for which a nonequilibrium liquid layer completely wets the surface of ice. Such extreme conditions have been used to produce stacking disordered frost ice in experiments and may be plausible in the summer polar mesosphere. Growth of ice from vapor at moderate supersaturations in the temperature range relevant to cirrus and mixed-phase clouds, from 200 to 260 K, produces exclusively the stable hexagonal ice polymorph. Cubic ice is disfavored with respect to hexagonal ice not only by a small penalty in the bulk free energy (3.6 ± 1.5 J mol(-1) at 260 K) but also by a large free energy penalty at the ice-vapor interface (89.7 ± 12.8 J mol(-1) at 260 K). The latter originates in higher vibrational entropy of the hexagonal-terminated ice-vapor interface. We predict that the free energy penalty against the cubic ice interface should decrease strongly with temperature, resulting in some degree of stacking disorder in ice grown from vapor in the tropical tropopause layer, and in polar stratospheric and noctilucent clouds. Our findings support and explain the evolution of the morphology of ice crystals from hexagonal to trigonal symmetry with decreasing temperature, as reported by experiments and in situ measurements in clouds. We conclude that selective growth of the elusive cubic ice polymorph by manipulation of the interfacial properties can likely be achieved at the ice-liquid interface but not at the ice-vapor interface.

The impact of resolution upon entropy and information in coarse-grained models

By eliminating unnecessary degrees of freedom, coarse-grained (CG) models tremendously facilitate numerical calculations and theoretical analyses of complex phenomena. However, their success critically depends upon the representation of the system and the effective potential that governs the CG degrees of freedom. This work investigates the relationship between the CG representation and the many-body potential of mean force (PMF), W, which is the appropriate effective potential for a CG model that exactly preserves the structural and thermodynamic properties of a given high resolution model. In particular, we investigate the entropic component of the PMF and its dependence upon the CG resolution. This entropic component, SW, is a configuration-dependent relative entropy that determines the temperature dependence of W. As a direct consequence of eliminating high resolution details from the CG model, the coarsening process transfers configurational entropy and information from the configuration space into SW. In order to further investigate these general results, we consider the popular Gaussian Network Model (GNM) for protein conformational fluctuations. We analytically derive the exact PMF for the GNM as a function of the CG representation. In the case of the GNM, -TSW is a positive, configuration-independent term that depends upon the temperature, the complexity of the protein interaction network, and the details of the CG representation. This entropic term demonstrates similar behavior for seven model proteins and also suggests, in each case, that certain resolutions provide a more efficient description of protein fluctuations. These results may provide general insight into the role of resolution for determining the information content, thermodynamic properties, and transferability of CG models. Ultimately, they may lead to a rigorous and systematic framework for optimizing the representation of CG models.

Hydrogen-Bond Heterogeneity Boosts Hydrophobicity of Solid Interfaces

Experimental and theoretical studies suggest that the hydrophobicity of chemically heterogeneous surfaces may present important nonlinearities as a function of composition. In this article, this issue is systematically explored using molecular simulations. The hydrophobicity is characterized by computing the contact angle of water on flat interfaces and the desorption pressure of water from cylindrical nanopores. The studied interfaces are binary mixtures of hydrophilic and hydrophobic sites, with and without the ability to form hydrogen bonds with water, intercalated at different scales. Water is described with the mW coarse-grained potential, where hydrogen-bonds are modeled in the absence of explicit hydrogen atoms, via a three-body term that favors tetrahedral coordination. We found that the combination of particles exhibiting the same kind of coordination with water gives rise to a linear dependence of contact angle with respect to composition, in agreement with the Cassie model. However, when only the hydrophilic component can form hydrogen bonds, unprecedented deviations from linearity are observed, increasing the contact angle and the vapor pressure above their values in the purely hydrophobic interface. In particular, the maximum enhancement is seen when a 35% of hydrogen bonding molecules is randomly scattered on a hydrophobic background. This effect is very sensitive to the heterogeneity length-scale, being significantly attenuated when the hydrophilic domains reach a size of 2 nm. The observed behavior may be qualitatively rationalized via a simple modification of the Cassie model, by assuming a different microrugosity for hydrogen bonding and non-hydrogen bonding interfaces.

Perspective: Coarse-grained models for biomolecular systems

By focusing on essential features, while averaging over less important details, coarse-grained (CG) models provide significant computational and conceptual advantages with respect to more detailed models. Consequently, despite dramatic advances in computational methodologies and resources, CG models enjoy surging popularity and are becoming increasingly equal partners to atomically detailed models. This perspective surveys the rapidly developing landscape of CG models for biomolecular systems. In particular, this review seeks to provide a balanced, coherent, and unified presentation of several distinct approaches for developing CG models, including top-down, network-based, native-centric, knowledge-based, and bottom-up modeling strategies. The review summarizes their basic philosophies, theoretical foundations, typical applications, and recent developments. Additionally, the review identifies fundamental inter-relationships among the diverse approaches and discusses outstanding challenges in the field. When carefully applied and assessed, current CG models provide highly efficient means for investigating the biological consequences of basic physicochemical principles. Moreover, rigorous bottom-up approaches hold great promise for further improving the accuracy and scope of CG models for biomolecular systems.

Prediction of Small Molecule Hydration Thermodynamics with Grid Cell Theory

An efficient methodology has been developed to quantify water energetics by analysis of explicit solvent molecular simulations of organic and biomolecular systems. The approach, grid cell theory (GCT), relies on a discretization of the cell theory methodology on a three-dimensional grid to spatially resolve the density, enthalpy, and entropy of water molecules in the vicinity of solute(s) of interest. Entropies of hydration are found to converge more efficiently than enthalpies of hydration. GCT predictions of free energies of hydration on a data set of small molecules are strongly correlated with thermodynamic integration predictions. Agreement with the experiment is comparable for both approaches. A key advantage of GCT is its ability to provide from a single simulation insightful graphical analyses of spatially resolved components of the enthalpies and entropies of hydration.

Entropy-enthalpy compensation: role and ramifications in biomolecular ligand recognition and design

Recent calorimetric studies of interactions between small molecules and biomolecular targets have generated renewed interest in the phenomenon of entropy-enthalpy compensation. In these studies, entropic and enthalpic contributions to binding are observed to vary substantially and in an opposing manner as the ligand or protein is modified, whereas the binding free energy varies little. In severe examples, engineered enthalpic gains can lead to completely compensating entropic penalties, frustrating ligand design. Here, we examine the evidence for compensation, as well as its potential origins, prevalence, severity, and ramifications for ligand engineering. We find the evidence for severe compensation to be weak in light of the large magnitude of and correlation between errors in experimental measurements of entropic and enthalpic contributions to binding, though a limited form of compensation may be common. Given the difficulty of predicting or measuring entropic and enthalpic changes to useful precision, or using this information in design, we recommend ligand engineering efforts instead focus on computational and experimental methodologies to directly assess changes in binding free energy.