Enthalpy−Entropy and Cavity Decomposition of Alkane Hydration Free Energies: Numerical Results and Implications for Theories of Hydrophobic Solvation

The Joint Solvation Interaction

The solvent-induced interactions (SIIs) between flexible solutes can be separated into two distinct components: the solvation-induced conformational effect and the joint solvation interaction (JSI). The JSI quantifies the thermodynamic effect of the solvent simultaneously accommodating the solutes, generalizing the typical notion of the hydrophobic interaction. We present a formal definition of the JSI within the framework of the mixture expansion, demonstrate that this definition is equivalent to the SII between rigid solutes, and propose a method, partially connected molecular dynamics, which allows one to compute the interaction with existing free energy algorithms. We also compare the JSI to the more natural generalization of the hydrophobic interaction, the indirect solvent-mediated interaction, and argue that JSI is a more useful quantity for studying solute binding thermodynamics. Direct calculation of the JSI may prove useful in developing our understanding of solvent effects in self-assembly, protein aggregation, and protein folding, for which the isolation of the JSI from the conformational component of the SII becomes important due to the intra-species flexibility.

Structural Order in the Hydration Shell of Nonpolar Groups versus that in Bulk Water

The poor solubility of nonpolar compounds in water around room temperature is governed by a large and negative entropy change, whose molecular cause is still debated. Since the Frank and Evans original proposal in 1945, the large and negative entropy change is usually attributed to the formation of ordered structures in the hydration shell of nonpolar groups. However, the existence of such ordered structures has never been proven. The present study is aimed at providing available structural results and thermodynamic arguments disproving the existence of ordered structures in the hydration shell of nonpolar groups.

Molecular-Scale Liquid Density Fluctuations and Cavity Thermodynamics

Equilibrium density fluctuations at the molecular level produce cavities in a liquid and can be analyzed to shed light on the statistics of the number of molecules occupying observation volumes of increasing radius. An information theory approach led to the conclusion that these probabilities should follow a Gaussian distribution. Computer simulations confirmed this prediction across various liquid models if the size of the observation volume is not large. The reversible work required to create a cavity and the chance of finding no molecules in a fixed observation volume are directly correlated. The Gaussian formula for the latter probability is scrutinized to derive the changes in enthalpy and entropy, which arise from the cavity creation. The reversible work of cavity creation has a purely entropic origin as a consequence of the solvent-excluded volume effect produced by the inaccessibility of a region of the configurational space. The consequent structural reorganization leads to a perfect compensation of enthalpy and entropy changes. Such results are coherent with those obtained from Lee in his direct statistical mechanical study.

Computation of Overhauser dynamic nuclear polarization processes reveals fundamental correlation between water dynamics, structure, and solvent restructuring entropy

Hydration water dynamics, structure, and thermodynamics are crucially important to understand and predict water-mediated properties at molecular interfaces. Yet experimentally and directly quantifying water behavior locally near interfaces at the sub-nanometer scale is challenging, especially at interfaces submerged in biological solutions. Overhauser dynamic nuclear polarization (ODNP) experiments measure equilibrium hydration water dynamics within 8-15 angstroms of a nitroxide spin probe on instantaneous timescales (10 picoseconds to nanoseconds), making ODNP a powerful tool for probing local water dynamics in the vicinity of the spin probe. As with other spectroscopic techniques, concurrent computational analysis is necessary to gain access to detailed molecular level information about the dynamic, structural, and thermodynamic properties of water from experimental ODNP data. We chose a model system that can systematically tune the dynamics of water, a water-glycerol mixture with compositions ranging from 0 to 0.3 mole fraction glycerol. We demonstrate the ability of molecular dynamics (MD) simulations to compute ODNP spectroscopic quantities, and show that translational, rotational, and hydrogen bonding dynamics of hydration water align strongly with spectroscopic ODNP parameters. Moreover, MD simulations show tight correlations between the dynamic properties of water that ODNP captures and the structural and thermodynamic behavior of water. Hence, experimental ODNP readouts of varying water dynamics suggest changes in local structural and thermodynamic hydration water properties.

Soil processes modify the composition of volatile organic compounds (VOCs) from CO2- and CH4-dominated geogenic and landfill gases: A comprehensive study

Degradation mechanisms affecting non-methane volatile organic compounds (VOCs) during gas uprising from different hypogenic sources to the surface were investigated through extensive sampling surveys in areas encompassing a high enthalpy hydrothermal system associated with active volcanism, a CH4-rich sedimentary basin and a municipal waste landfill. For a comprehensive framework, published data from medium-to-high enthalpy hydrothermal systems were also included. The investigated systems were characterised by peculiar VOC suites that reflected the conditions of the genetic environments in which temperature, contents of organic matter, and gas fugacity had a major role. Differences in VOC patterns between source (gas vents and landfill gas) and soil gases indicated VOC transformations in soil. Processes acting in soil preferentially degraded high-molecular weight alkanes with respect to the low-molecular weight ones. Alkenes and cyclics roughly behaved like alkanes. Thiophenes were degraded to a larger extent with respect to alkylated benzenes, which were more reactive than benzene. Furan appeared less degraded than its alkylated homologues. Dimethylsulfoxide was generally favoured with respect to dimethylsulfide. Limonene and camphene were relatively unstable under aerobic conditions, while α-pinene was recalcitrant. O-bearing organic compounds (i.e., aldehydes, esters, ketones, alcohols, organic acids and phenol) acted as intermediate products of the ongoing VOC degradations in soil. No evidence for the degradation of halogenated compounds and benzothiazole was observed. This study pointed out how soil degradation processes reduce hypogenic VOC emissions and the important role played by physicochemical and biological parameters on the effective VOC attenuation capacity of the soil.

The role of charge in microdroplet redox chemistry

In charged water microdroplets, which occur in nature or in the lab upon ultrasonication or in electrospray processes, the thermodynamics for reactive chemistry can be dramatically altered relative to the bulk phase. Here, we provide a theoretical basis for the observation of accelerated chemistry by simulating water droplets of increasing charge imbalance to create redox agents such as hydroxyl and hydrogen radicals and solvated electrons. We compute the hydration enthalpy of OH- and H+ that controls the electron transfer process, and the corresponding changes in vertical ionization energy and vertical electron affinity of the ions, to create OH• and H• reactive species. We find that at ~ 20 - 50% of the Rayleigh limit of droplet charge the hydration enthalpy of both OH- and H+ have decreased by >50 kcal/mol such that electron transfer becomes thermodynamically favorable, in correspondence with the more favorable vertical electron affinity of H+ and the lowered vertical ionization energy of OH-. We provide scaling arguments that show that the nanoscale calculations and conclusions extend to the experimental microdroplet length scale. The relevance of the droplet charge for chemical reactivity is illustrated for the formation of H2O2, and has clear implications for other redox reactions observed to occur with enhanced rates in microdroplets.

Bridging the Gap in Cryopreservation Mechanism: Unraveling the Interplay between Structure, Dynamics, and Thermodynamics in Cryoprotectant Aqueous Solutions

Cryoprotectants play a crucial role in preserving biological material, ensuring their viability during storage and facilitating crucial applications such as the conservation of medical compounds, tissues, and organs for transplantation. However, the precise mechanism by which cryoprotectants modulate the thermodynamic properties of water to impede the formation and growth of ice crystals, thus preventing long-term damage, remains elusive. This is evident in the use of empirically optimized recipes for mixtures that typically contain DMSO, glycerol, and various sugar constituents. Here, we use terahertz calorimetry, Overhauser nuclear polarization, and molecular dynamics simulations to show that DMSO exhibits a robust structuring effect on water around its methyl groups, reaching a maximum at a DMSO mole fraction of XDMSO = 0.33. In contrast, glycerol exerts a smaller water-structuring effect, even at higher concentrations (Scheme 1). These results potentially suggest that the wrapped water around DMSO's methyl group, which can be evicted upon ligand binding, may render DMSO a more surface-active cryoprotectant than glycerol, while glycerol may participate more as a viscogen that acts on the entire sample. These findings shed light on the molecular intricacies of cryoprotectant solvation behavior and have potentially significant implications for optimizing cryopreservation protocols.

Free Energy Density of a Fluid and Its Role in Solvation and Binding

The concept that a fluid has a position-dependent free energy density appears in the literature but has not been fully developed or accepted. We set this concept on an unambiguous theoretical footing via the following strategy. First, we set forth four desiderata that should be satisfied by any definition of the position-dependent free energy density, f(R), in a system comprising only a fluid and a rigid solute: its volume integral, plus the fixed internal energy of the solute, should be the system free energy; it deviates from its bulk value, fbulk, near a solute but should asymptotically approach fbulk with increasing distance from the solute; it should go to zero where the solvent density goes to zero; and it should be well-defined in the most general case of a fluid made up of flexible molecules with an arbitrary interaction potential. Second, we use statistical thermodynamics to formulate a definition of the free energy density that satisfies these desiderata. Third, we show how any free energy density satisfying the desiderata may be used to analyze molecular processes in solution. In particular, because the spatial integral of f(R) equals the free energy of the system, it can be used to compute free energy changes that result from the rearrangement of solutes as well as the forces exerted on the solutes by the solvent. This enables the use of a thermodynamic analysis of water in protein binding sites to inform ligand design. Finally, we discuss related literature and address published concerns regarding the thermodynamic plausibility of a position-dependent free energy density. The theory presented here has applications in theoretical and computational chemistry and may be further generalizable beyond fluids, such as to solids and macromolecules.

S.O.S: Shape, orientation, and size tune solvation in electrocatalysis

Current models to understand the reactivity of metal/aqueous interfaces in electrochemistry, e.g., volcano plots, are based on the adsorption free energies of reactants and products, which are often small hydrophobic molecules (such as in CO2 and N2 reduction). Calculations played a major role in the quantification and comprehension of these free energies in terms of the interactions that the reactive species form with the surface. However, solvation free energies also come into play in two ways: (i) by modulating the adsorption free energy together with solute-surface interactions, as the solute has to penetrate the water adlayer in contact with the surface and get partially desolvated (which costs free energy); (ii) by regulating transport across the interface, i.e., the free energy profile from the bulk to the interface, which is strongly non-monotonic due to the unique nature of metal/aqueous interfaces. Here, we use constant potential molecular dynamics to study the solvation contributions, and we uncover huge effects of the shape and orientation (on top of the already known size effect) of small hydrophobic and amphiphilic solutes on their adsorption free energy. We propose a minimal theoretical model, the S.O.S. model, that accounts for size, orientation, and shape effects. These novel aspects are rationalized by recasting the concepts at the base of the Lum-Chandler-Weeks theory of hydrophobic solvation (for small solutes in the so-called volume-dominated regime) into a layer-by-layer form, where the properties of each interfacial region close to the metal are explicitly taken into account.

From Local Hydration Motifs in Aqueous Acetic Acid Solutions to Macroscopic Mixing Thermodynamics: A Quantitative Connection from THz-Calorimetry

We report the results of THz measurements (30-440 cm-1) of aqueous acetic acid solutions over the full mixing range (XAcAc = 0-1). We recorded spectroscopic observables as a function of the acetic acid concentration in the frequency range of the intermolecular stretch at 150 cm-1 and of the librational modes at 350-440 cm-1. This allowed us to unravel changes in hydrophobic and hydrophilic hydration motifs, respectively. By means of a novel THz-calorimetry approach, we quantitatively correlated these changes in local hydration motifs to excess mixing entropy and enthalpy. We find that ΔHmix is determined by both hydrophobic and hydrophilic solvation contributions. In contrast, ΔSmix is governed by hydrophobic cavity formation. Our results further suggest that acetic acid-water mixtures are systems at the edge of phase separation due to endothermic contributions from both hydrophilic and hydrophobic solvation in a large portion of the miscibility range. Our work establishes a quantitative relationship between the balance of local hydrophobic and hydrophilic solvation motifs and the macroscopic mixing thermodynamic properties.

Hydration makes a difference! How to tune protein complexes between liquid-liquid and liquid-solid phase separation

Understanding how protein rich condensates formed upon liquid-liquid phase separation (LLPS) evolve into solid aggregates is of fundamental importance for several medical applications, since these are suspected to be hot-spots for many neurotoxic diseases. This requires developing experimental approaches to observe in real-time both LLPS and liquid-solid phase separation (LSPS), and to unravel the delicate balance of protein and water interactions dictating the free energy differences between the two. We present a vibrational THz spectroscopy approach that allows doing so from the point of view of hydration water. We focus on a cellular prion protein of high medical relevance, which we can drive to undergo either LLPS or LSPS with few mutations. We find that it is a subtle balance of hydrophobic and hydrophilic solvation contributions that allows tuning between LLPS and LSPS. Hydrophobic hydration provides an entropic driving force to phase separation, through the release of hydration water into the bulk. Water hydrating hydrophilic groups provides an enthalpic driving force to keep the condensates in a liquid state. As a result, when we modify the protein by a few mutations to be less hydrophilic, we shift from LLPS to LSPS. This molecular understanding paves the way for a rational design of proteins.

A generalized Kirkwood implicit solvent for the polarizable AMOEBA protein model

Computational simulation of biomolecules can provide important insights into protein design, protein-ligand binding interactions, and ab initio biomolecular folding, among other applications. Accurate treatment of the solvent environment is essential in such applications, but the use of explicit solvents can add considerable cost. Implicit treatment of solvent effects using a dielectric continuum model is an attractive alternative to explicit solvation since it is able to describe solvation effects without the inclusion of solvent degrees of freedom. Previously, we described the development and parameterization of implicit solvent models for small molecules. Here, we extend the parameterization of the generalized Kirkwood (GK) implicit solvent model for use with biomolecules described by the AMOEBA force field via the addition of corrections to the calculation of effective radii that account for interstitial spaces that arise within biomolecules. These include element-specific pairwise descreening scale factors, a short-range neck contribution to describe the solvent-excluded space between pairs of nearby atoms, and finally tanh-based rescaling of the overall descreening integral. We then apply the AMOEBA/GK implicit solvent to a set of ten proteins and achieve an average coordinate root mean square deviation for the experimental structures of 2.0 Å across 500 ns simulations. Overall, the continued development of implicit solvent models will help facilitate the simulation of biomolecules on mechanistically relevant timescales.

Water model for hydrophobic cavities: structure and energy from quantum-chemical calculations

This ab initio study aims to design a series of large water clusters having a hollow clathrate-like cage able to host hydrophobic solutes of various sizes. Starting from the (H₂O)_n (n = 18, 20, 24 and 28) hollow cages, water layers have been added in a stepwise manner in order to model the configuration of water molecules beyond the primary shell. The large (H₂O)₁₀₀, (H₂O)₁₂₀ and (H₂O)₁₄₀ clusters complete the hydrogen bonding network of the cage with optimal and regular tiling of the do-, tetra-decahedron and hexa-decahedron, respectively. This study is corroborated by an investigation of dense water clusters up to the (H₂O)₁₂₃ one, being highly consistent with experimental data on ice concerning the electronic and zero-point energies for aggregate formation at 0 K and enthalpy and entropy at 273 K. The cavity creation profoundly alters the orientation of water molecules compared with those found in dense clusters. Nevertheless, such a large reorganization is necessary to maximize the water-water attraction by making it similar to the one found in dense clusters. The cage formation is an endothermic process; however, the computed values are large compared with previous reports for hydrocarbon aqueous solutions. Larger clusters are required for a more fruitful comparison.

Liquid-Liquid Phase Separation? Ask the Water!

Water is more than an inert spectator during liquid-liquid phase separation (LLPS), the reversible compartmentalization of protein solutions into a protein-rich and a dilute phase. We show that LLPS is driven by changes in hydration entropy and enthalpy. Tuning LLPS by adjusting experimental parameters, e.g., addition of co-solutes, is a major goal for biological and medical applications. This requires a general model to quantify thermodynamic driving forces. Here, we develop such a model based on the measured amplitudes of characteristic THz-features of two hydration populations: "Cavity-wrap" water hydrating hydrophobic patches is released during LLPS leading to an increase in entropy. "Bound" water hydrating hydrophilic patches is retained since it is enthalpically favorable. We introduce a THz-phase diagram mapping these spectroscopic/thermodynamic changes. This provides not only a precise understanding of hydrophobic and hydrophilic hydration driving forces as a function of temperature and concentration but also a rational means to tune LLPS.

Understanding the Hydration Thermodynamics of Cationic Quaternary Ammonium and Charge-Neutral Amine Surfactants

Aqueous solubility and interfacial adsorption of surfactants are important for numerous applications. Using molecular dynamics, we have studied the effect of the type of the polar headgroup (cationic quaternary ammonium and charge-neutral amine) and length of the alkyl tail on the hydration free energy of surfactants in infinite dilution. In addition, we have studied the effect of replacing the terminal methyl group of the alkyl tail with a more polar hydroxyl group on the hydration free energy. Quaternary ammonium surfactants have strongly favorable hydration free energies, whereas charge-neutral amine surfactants have unfavorable hydration free energies. The contribution of the quaternary ammonium group in reducing the hydration free energy is estimated to be as large as ∼63 k_BT and that of the charge-neutral amine group to be 3 k_BT. Both surfactants and their corresponding alkanes have minima in the free energy at the air-water interface. The quaternary ammonium group contributes to a 6 k_BT decrease in the free energy of transfer from air-water interface to bulk aqueous phase (termed henceforth as interface transfer free energy). The amine group, on the other hand, has a net zero interface transfer free energy. The interface transfer free energies of surfactants are both enthalpically and entropically unfavorable. The enthalpic penalty is attributed to the loss of water-water interactions. Interestingly, surfactant molecules gain entropy upon their transfer from the air-water interface to the aqueous phase, but this increase is more than compensated by the loss in the entropy of water molecules, presumably due to the ordering of water molecules around the surfactants. Replacing the terminal methyl group of the alkyl tail with a hydroxyl group in quat surfactants reduces their hydration free energy by 10 k_BT, thus making them more soluble in water. Attaching a hydroxyl group to the alkyl tail also inhibits their micelle forming tendency in the bulk aqueous phase. Overall, this work reveals how tuning the molecular characteristics of surfactants can help to achieve the desirable aqueous solubility, interfacial properties, and micellization tendency of surfactants.

Computer simulation of molecular recognition in biomolecular system: from in silico screening to generalized ensembles

Prediction of ligand-receptor complex structure is important in both the basic science and the industry such as drug discovery. We report various computation molecular docking methods: fundamental in silico (virtual) screening, ensemble docking, enhanced sampling (generalized ensemble) methods, and other methods to improve the accuracy of the complex structure. We explain not only the merits of these methods but also their limits of application and discuss some interaction terms which are not considered in the in silico methods. In silico screening and ensemble docking are useful when one focuses on obtaining the native complex structure (the most thermodynamically stable complex). Generalized ensemble method provides a free-energy landscape, which shows the distribution of the most stable complex structure and semi-stable ones in a conformational space. Also, barriers separating those stable structures are identified. A researcher should select one of the methods according to the research aim and depending on complexity of the molecular system to be studied.

Dependence of Vaporization Enthalpy on Molecular Surfaces and Temperature: Thermodynamically Effective Molecular Surfaces

Approximation of molecular surfaces is of central importance in numerous scientific fields. In this study we theoretically derive a physical model to relate phase-change thermodynamics to molecular surfaces. The model allows accurately predicting vaporization enthalpy of compounds for a wide temperature range without requiring any empirical parameter. Through the new model, we conceptualize thermodynamically effective molecular surfaces and show that they, although only marginally different than van der Waals surfaces, substantially improve predictability of multiple thermodynamic quantities.

Solvation Thermodynamics of Solutes in Water and Ionic Liquids Using the Multiscale Solvation-Layer Interface Condition Continuum Model

Molecular assembly processes are generally driven by thermodynamic properties in solutions. Atomistic modeling can be very helpful in designing and understanding complex systems, except that bulk solvent is very inefficient to treat explicitly as discrete molecules. In this work, we develop and assess two multiscale solvation models for computing solvation thermodynamic properties. The new SLIC/CDC model combines continuum solvent electrostatics based on the solvent layer interface condition (SLIC) with new statistical thermodynamic models for hydrogen bonding and nonpolar modes: cavity formation, dispersion interactions, combinatorial mixing (CDC). Given the structures of 500 solutes, the SLIC/CDC model predicts Gibbs energies of solvation in water with an average accuracy better than 1 kcal/mol, when compared to experimental measurements, and better than 0.8 kcal/mol, when compared to explicit-solvent molecular dynamics simulations. The individual SLIC/CDC energy mode values agree quantitatively with those computed from explicit-solvent molecular dynamics. The previously published SLIC/SASA multiscale model combines the SLIC continuum electrostatic model with the solvent-accessible surface area (SASA) nonpolar energy mode. With our new, improved parametrization method, the SLIC/SASA model now predicts Gibbs energies of solvation with better than 1.4 kcal/mol average accuracy in aqueous systems, compared to experimental and explicit-solvent molecular dynamics, and better than 1.6 kcal/mol average accuracy in ionic liquids, compared to explicit-solvent molecular dynamics. Both models predict solvation entropies, and are the first implicit-solvation models capable of predicting solvation heat capacities.

Spectroscopic Fingerprints of Cavity Formation and Solute Insertion as a Measure of Hydration Entropic Loss and Enthalpic Gain

Hydration free energies are dictated by a subtle balance of hydrophobic and hydrophilic interactions. We present here a spectroscopic approach, which gives direct access to the two main contributions: Using THz-spectroscopy to probe the frequency range of the intermolecular stretch (150-200 cm-1 ) and the hindered rotations (450-600 cm-1 ), the local contributions due to cavity formation and hydrophilic interactions can be traced back. We show that via THz calorimetry these fingerprints can be correlated 1 : 1 with the group specific solvation entropy and enthalpy. This allows to deduce separately the hydrophobic (i.e. cavity formation) and hydrophilic contributions to thermodynamics, as shown for hydrated alcohols as a case study. Accompanying molecular dynamics simulations quantitatively support our experimental results. In the future our approach will allow to dissect hydration contributions in inhomogeneous mixtures and under non-equilibrium conditions.

Hydration of Linear Alkanes is Governed by the Small Length-Scale Hydrophobic Effect

Length-scale dependence of the hydrophobic effect is well understood for apolar spherical solutes: for small solutes (diameter, d ≲ 0.8 nm), the hydration free energy is entropically driven, while for larger solutes (d ≳ 2 nm), it is enthalpically driven. The nature of the hydrophobic effect in the case of anisotropic molecules such as linear alkanes is not understood yet. In this work, we have calculated the hydration free energy of linear alkanes going from methane to octadecane and of a spherical decane droplet of d ≈ 3 nm using molecular simulations. We show that the hydration free energies of alkanes, irrespective of their size, are governed by the small length-scale hydrophobic effect. That is, unlike the case of large spherical solutes, the hydration free energies of linear alkanes are entropically driven.

Solubility of Hydrophobes into Macrocyclic Hosts

The intrinsic nature of macrocyclic molecules to preferentially absorb a specific solute has been opening up supramolecular chemistry. Nevertheless, the determinant factor with molecular perspectives in promoting host-guest complexations remains inconclusive, due to the lack of rigorous thermodynamic examination on the guest solubility inside the host. Here, we quantify the solute-solvent energetic and entropic contributions between the end states and on the docking route during inclusion of noble gases in cucurbit[5]uril, cucurbit[6]uril, and α-cyclodextrin, using molecular dynamics simulations in combination with the potential distribution theorem. Results show that in all of the pairs examined both the solute-solvent energy and entropy favor the inclusion, while the former is rather dominant. The frequency of interior drying, which pertains to the entropic contribution, differs between the hosts and is controlled by the existence of lid water at portal and the flexibility of host framework. Moreover, the hosts exhibit various types of absorption manners, involving non-, single-, and double-free-energy barriers.

Quantum Vibrational Spectroscopy of Explicitly Solvated Thymidine in Semiclassical Approximation

In this paper, we demonstrate the possibility to perform spectroscopy simulations of solvated biological species taking into consideration quantum effects and explicit solvation. We achieve this goal by interfacing our recently developed divide-and-conquer approach for semiclassical initial value representation molecular dynamics with the polarizable AMOEBABIO18 force field. The method is applied to the study of solvation of the thymidine nucleoside in two different polar solvents, water and N,N-dimethylformamide. Such systems are made of up to 2476 atoms. Experimental evidence concerning the different behavior of thymidine in the two solvents is well reproduced by our study, even though quantitative estimates are hampered by the limited accuracy of the classical force field employed. Overall, this study shows that semiclassically approximate quantum dynamical studies of explicitly solvated biological systems are both computationally affordable and insightful.

On the size, shape and energetics of the hydration shell around alkanes

A large number of clathrate-like cages have been proposed as the very first hydration shell of alkanes. The cages include canonical structures commonly found in clathrate hydrates and many others, not previously reported, derived from the carbon fullerene cavities. These structures have a rich and variegated form, which can adapt to the shape and conformation of the solute. They avoid "wasting" hydrogen bonds, while minimizing the volume cage and maximizing the solute-solvent van der Waals interactions. DFT/M06-2X and MP2 ab initio calculations give comparable structural and energetic results although the latter predicts slightly larger cages for a given solute. It is shown that the van der Waals interactions are substantial and the large exoenergetic values found for isobutane and cyclopentane provide an explanation for the surprising high melting points of related hydrates at room pressure. The encaging enthalpy for various hydrocarbons is similar to the enthalpy of solution measured at a temperature just above the melting point of aqueous hydrocarbon solutions, thus indicating that water molecules should not deviate too much from the configuration with O-H bonds tangentially oriented with respect to the solute surface. The computed trend differs from the enthalpy of solution measured at room temperature, thus the very first hydration shell departs, up to a certain degree, from the clathrate-like structures.

Implicit Solvents for the Polarizable Atomic Multipole AMOEBA Force Field

Computational protein design, ab initio protein/RNA folding, and protein-ligand screening can be too computationally demanding for explicit treatment of solvent. For these applications, implicit solvent offers a compelling alternative, which we describe here for the polarizable atomic multipole AMOEBA force field based on three treatments of continuum electrostatics: numerical solutions to the nonlinear and linearized versions of the Poisson-Boltzmann equation (PBE), the domain-decomposition conductor-like screening model (ddCOSMO) approximation to the PBE, and the analytic generalized Kirkwood (GK) approximation. The continuum electrostatics models are combined with a nonpolar estimator based on novel cavitation and dispersion terms. Electrostatic model parameters are numerically optimized using a least-squares style target function based on a library of 103 small-molecule solvation free energy differences. Mean signed errors for the adaptive Poisson-Boltzmann solver (APBS), ddCOSMO, and GK models are 0.05, 0.00, and 0.00 kcal/mol, respectively, while the mean unsigned errors are 0.70, 0.63, and 0.58 kcal/mol, respectively. Validation of the electrostatic response of the resulting implicit solvents, which are available in the Tinker (or Tinker-HP), OpenMM, and Force Field X software packages, is based on comparisons to explicit solvent simulations for a series of proteins and nucleic acids. Overall, the emergence of performative implicit solvent models for polarizable force fields opens the door to their use for folding and design applications.

Per|Mut: Spatially Resolved Hydration Entropies from Atomistic Simulations

The hydrophobic effect is essential for many biophysical phenomena and processes. It is governed by a fine-tuned balance between enthalpy and entropy contributions from the hydration shell. Whereas enthalpies can in principle be calculated from an atomistic simulation trajectory, calculating solvation entropies by sampling the extremely large configuration space is challenging and often impossible. Furthermore, to qualitatively understand how the balance is affected by individual side chains, chemical groups, or the protein topology, a local description of the hydration entropy is required. In this study, we present and assess the new method “Per|Mut”, which uses a permutation reduction to alleviate the sampling problem by a factor of N! and employs a mutual information expansion to the third order to obtain spatially resolved hydration entropies. We tested the method on an argon system, a series of solvated n-alkanes, and solvated octanol.

Protein Denaturation, Zero Entropy Temperature, and the Structure of Water around Hydrophobic and Amphiphilic Solutes

The hydrophobic effect plays a key role in many chemical and biological processes, including protein folding. Nonetheless, a comprehensive picture of the effect of temperature on hydrophobic hydration and protein denaturation remains elusive. Here, we study the effect of temperature on the hydration of model hydrophobic and amphiphilic solutes, through molecular dynamics, aiming at getting insight on the singular behavior of water, concerning the zero-entropy temperature, T_S, and entropy convergence, T_S^*, also observed for some proteins, upon denaturation. We show that, similar to hydrocarbons, polar amphiphilic solutes exhibit a T_S, although strongly dependent on solute-water interactions, opposite to hydrocarbons. Further, the temperature dependence of the hydration entropy, normalized by the solvent accessible surface area, is shown to be nearly solute size independent for hydrophobic but not for amphiphilic solutes, for similar reasons. These results are further discussed in the light of information theory (IT) and the structure of water around hydrophobic groups. The latter shows that the tetrahedral enhancement of some water molecules around hydrophobic groups, associated with the reduction of water defects, leads to the strengthening of the weakest hydrogen bonds, relative to bulk water. In addition, a larger tetrahedrality is found in low density water populations, demonstrating that pure water has encoded structural information, similar to that associated with hydrophobic hydration. The reversal of the hydration entropy dependence on the solute size, above T_S^*, is also analyzed and shown to be associated with a greater loss of water molecules exhibiting enhanced orientational order, in the coordination sphere of large solutes. Finally, the source of the differences between Kauzmann's "hydrocarbon model" on protein denaturation and hydrophobic hydration is discussed, with relatively large amphiphilic hydrocarbons seemingly displaying a more similar behavior to some globular proteins than aliphatic hydrocarbons.

Why Purine Nucleoside Phosphorylase Ribosylates 2,6-Diamino-8-azapurine in Noncanonical Positions? A Molecular Modeling Study

Protein nucleoside phosphorylase (PNP) is an enzyme that catalyzes a reversible conversion process (ribosylation and phosphorolysis) between nucleobases (purines) and their nucleosides. Experimental studies showed that calf PNP ribosylates purine analogues in specific positions: 2,6-diamino-8-azapurine in position 7 or 8 and 8-azaguanine in position 9 of the triazole ring. The reason for this phenomenon can be a result of different expositions of purine substrates to the channel leading to the binding site. This hypothesis was verified by the application of molecular modeling techniques to two complexes of purine analogues 2,6-diamino-azapurine, calf PNP (pdb-code: 1LVU), and 8-azaguanine, calf PNP (pdb-code: 2AI1). The results obtained with a combination of quantum chemistry, docking, and molecular dynamics methods showed qualitative validity of our hypothesis. Binding free energies of protein-ligand systems showed that most probable binding poses expose N8 nitrogen for 2,6-diamino-8-azapurine and N9 nitrogen for 8-azaguanine into the binding channel and ruled out the exposition of N9 for 2,6-diamino-8-azapurine and N7 for 8-azaguanine, partially in agreement with the experimental data. The other important result obtained in this study is a significantly higher population of the protonated form of crucial residue Glu-201 present in the binding pocket, compared to the standard protonation of free glutamic acid in solution. This result combined with populations of tautomeric forms of both investigated systems strongly suggests that 2,6-diamino-8-azapurine and 8-azaguanine are recognized by proteins with deprotonated and protonated Glu-201 residues, respectively. A comparison of computed binding poses of the investigated ligands to the inhibitors present in crystal structures suggests that the modification of the (S)-PMPDAP inhibitor, in which a 2-(phosphonomethoxy)propyl chain is attached at position 8 instead of position 9, might increase its binding affinity.

Spontaneously Forming Dendritic Voids in Liquid Water Can Host Small Polymers

Some liquids are characterized by the presence of large voids with dendritic shapes and for this reason are dubbed transiently porous. By using a battery of data analysis tools, we demonstrate that liquid water and methane are both characterized by transient porosity. We show that the thermodynamics of porosity is distinct from that associated with cavitation á la classical nucleation theory. The shapes of dendritic voids in both liquids with very different chemistries resemble those of small polymers. We further show, using free energy calculations, that the cost of solvating small hydrophobic polymers in water is consistent with the work associated with creating dendritic voids. The entropic and enthalpic contributions associated with hosting these polymers can thus be rationalized by the thermodynamics of fluctuations in bulk water.

Molecular modeling studies on the interactions of 7-methoxytacrine-4-pyridinealdoxime, 4-PA, 2-PAM, and obidoxime with VX-inhibited human acetylcholinesterase: a near attack conformation approach

7-methoxytacrine-4-pyridinealdoxime (7-MEOTA-4-PA, named hybrid 5C) is a compound formerly synthesized and evaluated in vitro, together with 4-pyridine aldoxime (4-PA) and commercial reactivators of acetylcholinesterase (AChE). This compound was designed with the purpose of being a prophylactic reactivator, capable of interacting with different subdomains of the active site of AChE. To investigate these interactions, theoretical results from docking were first compared with experimental data of hybrid 5C, 4-PA, and two commercial oximes, on the reactivation of human AChE (HssAChE) inhibited by VX. Then, further docking studies, molecular dynamics simulations, and molecular mechanics Poisson–Boltzmann surface area calculations, were carried out to investigate reactivation performances, considering the near attack conformation (NAC) approach, prior to the nucleophilic substitution mechanism. Our results helped to elucidate the interactions of such molecules with the different subdomains of the active site of HssAChE. Additionally, NAC poses of each oxime were suggested for further theoretical studies on the reactivation reaction.

A grid-based algorithm in conjunction with a gaussian-based model of atoms for describing molecular geometry

A novel grid-based method is presented, which in conjunction with a smooth Gaussian-based model of atoms, is used to compute molecular volume (MV) and surface area (MSA). The MV and MSA are essential for computing nonpolar component of free energies. The objective of our grid-based approach is to identify solute atom pairs that share overlapping volumes in space. Once completed, this information is used to construct a rooted tree using depth-first method to yield the final volume and SA by using the formulations of the Gaussian model described by Grant and Pickup (J. Phys Chem, 1995, 99, 3503). The method is designed to function uninterruptedly with the grid-based finite-difference method implemented in Delphi, a popular and open-source package used for solving the Poisson-Boltzmann equation (PBE). We demonstrate the time efficacy of the method while also validating its performance in terms of the effect of grid-resolution, positioning of the solute within the grid-map and accuracy in identification of overlapping atom pairs. We also explore and discuss different aspects of the Gaussian model with key emphasis on its physical meaningfulness. This development and its future release with the Delphi package are intended to provide a physically meaningful, fast, robust and comprehensive tool for MM/PBSA based free energy calculations. © 2019 Wiley Periodicals, Inc.

Free Energy Calculations Based on Coupling Proximal Distribution Functions and Thermodynamic Cycles

Techniques to calculate the free energy changes of a system are very useful in the study of biophysical and biochemical properties. In practice, free energy changes can be described with thermodynamic cycles, and the free energy change of an individual process can be computed by sufficiently sampling the corresponding configurations. However, this is still time-consuming especially for large biomolecular systems. Previously, we have shown that by utilizing precomputed solute-solvent correlations, so-called proximal distribution functions (pDF), we are capable of reconstructing the solvent environment near solute atoms, thus estimating the solute-solvent interactions and solvation free energies of molecules. In this contribution, we apply the technique of pDF-reconstructions to calculate chemical potentials and use this information in thermodynamic cycles. This illustrates how free energy changes of nontrivial chemical processes in aqueous solution systems can be rapidly estimated.

Contrasting the hydration thermodynamics of methane and methanol

The hydration thermodynamics of methane and methanol depend on the cavity creation work and energy of van der Waals and H-bonding attractions.

Thermodynamics of Reactions Affected by Medium Reorganization

We present a thermodynamic analysis of the activation barrier for reactions which can be monitored through the difference in the energies of reactants and products defined as the reaction coordinate (electron and atom transfer, enzyme catalysis, etc.). The free-energy surfaces along the reaction coordinate are separated into the enthalpy and entropy surfaces. For the Gaussian statistics of the reaction coordinate, the free-energy surfaces are parabolas, and the entropy surface is an inverted parabola. Its maximum coincides with the transition state for reactions with zero value of the reaction free energy. Maximum entropic depression of the activation barrier, anticipated by the concept of transition-state ensembles, can be achieved for such reactions. From Onsager's reversibility, the entropy of equilibrium fluctuations encodes the entropic component of the activation barrier. The reorganization entropy thus becomes the critical parameter of the theory reducing the problem of activation entropy to the problem of reorganization entropy. Standard solvation theories do not allow reorganization entropy sufficient for the barrier depression. Complex media, characterized by many relaxation processes, need to be involved. Proteins provide several routes for achieving large entropic effects through incomplete (nonergodic) sampling of the complex energy landscape and by facilitating an active role of water in the reaction mechanism.

Interfacial structural crossover and hydration thermodynamics of charged C60 in water

Classical molecular dynamics simulations of the hydration thermodynamics, structure, and dynamics of water in hydration shells of charged buckminsterfullerenes are presented in this study. Charging of fullerenes leads to a structural transition in the hydration shell, accompanied by creation of a significant population of dangling O-H bonds pointing toward the solute. In contrast to the well accepted structure-function paradigm, this interfacial structural transition causes nearly no effect on either the dynamics of hydration water or on the solvation thermodynamics. Linear response to the solute charge is maintained despite significant structural changes in the hydration shell, and solvation thermodynamic potentials are nearly insensitive to the altering structure. Only solvation heat capacities, which are higher thermodynamic derivatives of the solvation free energy, indicate some sensitivity to the local hydration structure. We have separated the solvation thermodynamic potentials into direct solute-solvent interactions and restructuring of the hydration shell and analyzed the relative contributions of electrostatic and nonpolar interactions to the solvation thermodynamics.

Fast Pairwise Approximation of Solvent Accessible Surface Area for Implicit Solvent Simulations of Proteins on CPUs and GPUs

We propose a pairwise and readily parallelizable SASA-based nonpolar solvation approach for protein simulations, inspired by our previous pairwise GB polar solvation model development. In this work, we developed a novel function to estimate the atomic and molecular SASAs of proteins, which results in comparable accuracy as the LCPO algorithm in reproducing numerical icosahedral-based SASA values. Implemented in Amber software and tested on consumer GPUs, our pwSASA method reasonably reproduces LCPO simulation results, but accelerates MD simulations up to 30 times compared to the LCPO implementation, which is greatly desirable for protein simulations facing sampling challenges. The value of incorporating the nonpolar term in implicit solvent simulations is explored on a peptide fragment containing the hydrophobic core of HP36 and evaluating thermal stability profiles of four small proteins.

Explicit ions/implicit water generalized Born model for nucleic acids

The ion atmosphere around highly charged nucleic acid molecules plays a significant role in their dynamics, structure, and interactions. Here we utilized the implicit solvent framework to develop a model for the explicit treatment of ions interacting with nucleic acid molecules. The proposed explicit ions/implicit water model is based on a significantly modified generalized Born (GB) model and utilizes a non-standard approach to define the solute/solvent dielectric boundary. Specifically, the model includes modifications to the GB interaction terms for the case of multiple interacting solutes-disconnected dielectric boundary around the solute-ion or ion-ion pairs. A fully analytical description of all energy components for charge-charge interactions is provided. The effectiveness of the approach is demonstrated by calculating the potential of mean force for Na⁺-Cl^- ion pair and by carrying out a set of Monte Carlo (MC) simulations of mono- and trivalent ions interacting with DNA and RNA duplexes. The monovalent (Na⁺) and trivalent (CoHex³⁺) counterion distributions predicted by the model are in close quantitative agreement with all-atom explicit water molecular dynamics simulations used as reference. Expressed in the units of energy, the maximum deviations of local ion concentrations from the reference are within k _B T. The proposed explicit ions/implicit water GB model is able to resolve subtle features and differences of CoHex distributions around DNA and RNA duplexes. These features include preferential CoHex binding inside the major groove of the RNA duplex, in contrast to CoHex biding at the "external" surface of the sugar-phosphate backbone of the DNA duplex; these differences in the counterion binding patters were earlier shown to be responsible for the observed drastic differences in condensation propensities between short DNA and RNA duplexes. MC simulations of CoHex ions interacting with the homopolymeric poly(dA·dT) DNA duplex with modified (de-methylated) and native thymine bases are used to explore the physics behind CoHex-thymine interactions. The simulations suggest that the ion desolvation penalty due to proximity to the low dielectric volume of the methyl group can contribute significantly to CoHex-thymine interactions. Compared to the steric repulsion between the ion and the methyl group, the desolvation penalty interaction has a longer range and may be important to consider in the context of methylation effects on DNA condensation.

Extracavity Effect in Cyclodextrin/Surfactant Complexation

Cyclodextrin (CD) complexation is a convenient method to sequester surfactants in a controllable way, for example, during membrane-protein reconstitution. Interestingly, the equilibrium stability of CD/surfactant inclusion complexes increases with the length of the nonpolar surfactant chain even beyond the point where all hydrophobic contacts within the canonical CD cavity are saturated. To rationalize this observation, we have dissected the inclusion complexation equilibria of a structurally well-defined CD, that is, heptakis(2,6-di- O-methyl)-β-CD (DIMEB), and a homologous series of surfactants, namely, n-alkyl- N, N-dimethyl-3-ammonio-1-propanesulfonates (SB3- x) with chain lengths ranging from x = 8 to 14. Thermodynamic parameters obtained by isothermal titration calorimetry and structural insights derived from nuclear magnetic resonance spectroscopy and molecular dynamics simulations revealed that, upon inclusion, long-chain surfactants with x = ≥10 extend beyond the canonical CD cavity. This enables the formation of hydrophobic contacts between long surfactant chains and the extracavity parts of DIMEB, which make additional favorable contributions to the stability of the inclusion complex. These results explain the finding that the stability of CD/surfactant inclusion complexes monotonously increases with the surfactant chain length even for long chains that completely fill the canonical CD cavity.

The Excess Chemical Potential of Water at the Interface with a Protein from End Point Simulations

We use end point simulations to estimate the excess chemical potential of water in the homogeneous liquid and at the interface with a protein in solution. When the pure liquid is taken as the reference, the excess chemical potential of interfacial water is the difference between the solvation free energy of a water molecule at the interface and in the bulk. Using the homogeneous liquid as an example, we show that the solvation free energy for growing a water molecule can be estimated by applying UWHAM to the simulation data generated from the initial and final states (i.e., "the end points") instead of multistate free energy perturbation simulations because of the possible overlaps of the configurations sampled at the end points. Then end point simulations are used to estimate the solvation free energy of water at the interface with a protein in solution. The estimate of the solvation free energy at the interface from two simulations at the end points agrees with the benchmark using 32 states within a 95% confidence interval for most interfacial locations. The ability to accurately estimate the excess chemical potential of water from end point simulations facilitates the statistical thermodynamic analysis of diverse interfacial phenomena. Our focus is on analyzing the excess chemical potential of water at protein receptor binding sites with the goal of using this information to assist in the design of tight binding ligands.