Spatial Decomposition of Translational Water-Water Correlation Entropy in Binding Pockets

Thermodynamic consequences of stapling side-chains on a peptide ligand using a lactam-bridge: A theoretical study on anti-angiogenic peptides targeting VEGF

Peptides are promising therapeutic agents for various biological targets due to their high efficacy and low toxicity, and the design of peptide ligands with high binding affinity to the target of interest is of utmost importance in peptide-based drug design. Introducing a conformational constraint to a flexible peptide ligand using a side-chain lactam-bridge is a convenient and efficient method to improve its binding affinity to the target. However, in general, such a small structural modification to a flexible ligand made with the intent of lowering the configurational entropic penalty for binding may have unintended consequences in different components of the binding enthalpy and entropy, including the configurational entropy component, which are still not clearly understood. Toward probing this, we examine different components of the binding enthalpy and entropy as well as the underlying structure and dynamics, for a side-chain lactam-bridged peptide inhibitor and its flexible analog forming complexes with vascular endothelial growth factor (VEGF), using all-atom molecular dynamics simulations. It is found that introducing a side-chain lactam-bridge constraint into the flexible peptide analog led to a gain in configurational entropy change but losses in solvation entropy, solute internal energy, and solvation energy changes upon binding, pinpointing the opportunities and challenges in drug design. The present study features an interplay between configurational and solvation entropy changes, as well as the one between binding enthalpy and entropy, in ligand-target binding upon imposing a conformational constraint into a flexible ligand.

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.

Discovery of Novel Inhibitors of BRD4 for Treating Prostate Cancer: A Comprehensive Case Study for Considering Water Networks in Virtual Screening and Drug Design

Androgen receptor (AR) is the primary target for treating prostate cancer (PCa), which inevitably progresses due to drug-resistant mutations. Bromodomain-containing protein 4 (BRD4) has been a new potential drug target for PCa treatment. Herein, we report the rational design and discovery of novel BRD4 inhibitors through computer-aided drug design (CADD), and a hit compound SQ-1 (IC50 = 676 nM) was identified by structure-based virtual screening (SBVS) with the conserved water network. To optimize the structure of SQ-1, the free energy landscape was constructed, and the binding mechanism was explored by characterizing the water profile and the dissociation mechanism. Finally, the compound SQ-17 with improved inhibitory activity (IC50 < 100 nM) was discovered, which showed potent antiproliferative activity against LNCaP. These data highlighted a successful attempt to identify and optimize a small molecule by comprehensive CADD application and provided essential clues for developing novel therapeutics for PCa treatment.

Solvation free energy arithmetic for small organic molecules

Solvent-mediated interactions contribute to ligand binding affinities in computational drug design and provide a challenge for theoretical predictions. In this study, we analyze the solvation free energy of benzene derivatives in water to guide the development of predictive models for solvation free energies and solvent-mediated interactions. We use a spatially resolved analysis of local solvation free energy contributions and define solvation free energy arithmetic, which enable us to construct additive models to describe the solvation of complex compounds. The substituents analyzed in this study are carboxyl and nitro-groups due to their similar sterical requirements but distinct interactions with water. We find that nonadditive solvation free energy contributions are primarily attributed to electrostatics, which are qualitatively reproduced with computationally efficient continuum models. This suggests a promising route for the development of efficient and accurate models for the solvation of complex molecules with varying substitution patterns using solvation arithmetic.

Grid inhomogeneous solvation theory for cross-solvation in rigid solvents

Grid Inhomogeneous Solvation Theory (GIST) has proven useful to calculate localized thermodynamic properties of water around a solute. Numerous studies have leveraged this information to enhance structure-based binding predictions. We have recently extended GIST toward chloroform as a solvent to allow the prediction of passive membrane permeability. Here, we further generalize the GIST algorithm toward all solvents that can be modeled as rigid molecules. This restriction is inherent to the method and is already present in the inhomogeneous solvation theory. Here, we show that our approach can be applied to various solvent molecules by comparing the results of GIST simulations with thermodynamic integration (TI) calculations and experimental results. Additionally, we analyze and compare a matrix consisting of 100 entries of ten different solvent molecules solvated within each other. We find that the GIST results are highly correlated with TI calculations as well as experiments. For some solvents, we find Pearson correlations of up to 0.99 to the true entropy, while others are affected by the first-order approximation more strongly. The enthalpy-entropy splitting provided by GIST allows us to extend a recently published approach, which estimates higher order entropies by a linear scaling of the first-order entropy, to solvents other than water. Furthermore, we investigate the convergence of GIST in different solvents. We conclude that our extension to GIST reliably calculates localized thermodynamic properties for different solvents and thereby significantly extends the applicability of this widely used method.

Spatially Resolved Hydration Thermodynamics in Biomolecular Systems

Water is essential for the structure, dynamics, energetics, and thus the function of biomolecules. It is a formidable challenge to elicit, in microscopic detail, the role of the solvation-related driving forces of biomolecular processes, such as the enthalpy and entropy contributions to the underlying free-energy landscape. In this Perspective, we discuss recent developments and applications of computational methods that provide a spatially resolved map of hydration thermodynamics in biomolecular systems and thus yield atomic-level insights to guide the interpretation of experimental observations. An emphasis is on the challenge of quantifying the hydration entropy, which requires characterization of both the motions of the biomolecules and of the water molecules in their surrounding.

Explicit solvation thermodynamics in ionic solution: extending grid inhomogeneous solvation theory to solvation free energy of salt-water mixtures

Hydration thermodynamics play a fundamental role in fields ranging from the pharmaceutical industry to environmental research. Numerous methods exist to predict solvation thermodynamics of compounds ranging from small molecules to large biomolecules. Arguably the most precise methods are those based on molecular dynamics (MD) simulations in explicit solvent. One theory that has seen increased use is inhomogeneous solvation theory (IST). However, while many applications require accurate description of salt-water mixtures, no implementation of IST is currently able to estimate solvation properties involving more than one solvent species. Here, we present an extension to grid inhomogeneous solvation theory (GIST) that can take salt contributions into account. At the example of carbazole in 1 M NaCl solution, we compute the solvation energy as well as first and second order entropies. While the effect of the first order ion entropy is small, both the water-water and water-ion entropies contribute strongly. We show that the water-ion entropies are efficiently approximated using the Kirkwood superposition approximation. However, this approach cannot be applied to the water-water entropy. Furthermore, we test the quantitative validity of our method by computing salting-out coefficients and comparing them to experimental data. We find a good correlation to experimental salting-out constants, while the absolute values are overpredicted due to the approximate second order entropy. Since ions are frequently used in MD, either to neutralize the system or as a part of the investigated process, our method greatly extends the applicability of GIST. The use-cases range from biopharmaceuticals, where many assays require high salt concentrations, to environmental research, where solubility in sea water is important to model the fate of organic substances.

An ATPase with a twist: A unique mechanism underlies the activity of the bacterial tyrosine kinase, Wzc

BY-kinases constitute a protein tyrosine kinase family that encodes unique catalytic domains that deviate from those of eukaryotic kinases resembling P-loop nucleotide triphosphatases (NTPases) instead. We have used computational and supporting biochemical approaches using the catalytic domain of the Escherichia coli BY-kinase, Wzc, to illustrate mechanistic divergences between BY-kinases and NTPases despite their deployment of similar catalytic motifs. In NTPases, the “arginine finger” drives the reactive conformation of ATP while also displacing its solvation shell, thereby making favorable enthalpic and entropic contributions toward βγ-bond cleavage. In BY-kinases, the reactive state of ATP is enabled by ATP·Mg²⁺-induced global conformational transitions coupled to the conformation of the Walker-A lysine. While the BY-kinase arginine finger does promote the desolvation of ATP, it does so indirectly by generating an ordered active site in combination with other structural elements. Bacteria, using these mechanistic variations, have thus repurposed an ancient fold to phosphorylate on tyrosine.

Water molecules at protein-drug interfaces: computational prediction and analysis methods

The fundamental importance of water molecules at drug-protein interfaces is now widely recognised and a significant feature in structure-based drug design. Experimental methods for analysing the role of water in drug binding have many challenges, including the accurate location of bound water molecules in crystal structures, and problems in resolving specific water contributions to binding thermodynamics. Computational analyses of binding site water molecules provide an alternative, and in principle complete, structural and thermodynamic picture, and their use is now commonplace in the pharmaceutical industry. In this review, we describe the computational methodologies that are available and discuss their strengths and weaknesses. Additionally, we provide a critical analysis of the experimental data used to validate the methods, regarding the type and quality of experimental structural data. We also discuss some of the fundamental difficulties of each method and suggest directions for future study.

Spatially resolved free-energy contributions of native fold and molten-globule-like Crambin

The folding stability of a protein is governed by the free-energy difference between its folded and unfolded states, which results from a delicate balance of much larger but almost compensating enthalpic and entropic contributions. The balance can therefore easily be shifted by an external disturbance, such as a mutation of a single amino acid or a change of temperature, in which case the protein unfolds. Effects such as cold denaturation, in which a protein unfolds because of cooling, provide evidence that proteins are strongly stabilized by the solvent entropy contribution to the free-energy balance. However, the molecular mechanisms behind this solvent-driven stability, their quantitative contribution in relation to other free-energy contributions, and how the involved solvent thermodynamics is affected by individual amino acids are largely unclear. Therefore, we addressed these questions using atomistic molecular dynamics simulations of the small protein Crambin in its native fold and a molten-globule-like conformation, which here served as a model for the unfolded state. The free-energy difference between these conformations was decomposed into enthalpic and entropic contributions from the protein and spatially resolved solvent contributions using the nonparametric method Per|Mut. From the spatial resolution, we quantified the local effects on the solvent free-energy difference at each amino acid and identified dependencies of the local enthalpy and entropy on the protein curvature. We identified a strong stabilization of the native fold by almost 500 kJ mol-1 due to the solvent entropy, revealing it as an essential contribution to the total free-energy difference of (53 ± 84) kJ mol-1. Remarkably, more than half of the solvent entropy contribution arose from induced water correlations.

Solvent-mediated forces in protein dielectrophoresis

DEP is an established method to manipulate micrometer-sized particles, but standard continuum theories predict only negligible effects for nanometer-sized proteins despite contrary experimental evidence. A theoretical description of protein DEP needs to consider details on the molecular scale. Previous work toward this goal addressed the role of orientational polarization of static protein dipole moments for dielectrophoretic effects, which successfully predicts the general magnitude of dielectrophoretic forces on proteins but does not readily explain negative DEP forces observed for proteins in some experiments. However, contributions to the protein chemical potential due to protein-water interactions have not yet been considered in this context. Here, we utilize atomistic molecular dynamics simulations to evaluate polarization-induced changes in the protein solvation free energy, which result in a solvent-mediated contribution to dielectrophoretic forces. We quantify solvent-mediated dielectrophoretic forces for two proteins and a small peptide in water, which follow expectations for protein-water dipole-dipole interactions. The magnitude of solvent-mediated dielectrophoretic forces exceeds predictions of nonmolecular continuum theories, but plays a minor role for the total dielectrophoretic force for the simulated proteins due to dominant contributions from the orientational polarization of their static protein dipoles. However, we extrapolate that solvent-mediated contributions to negative protein DEP forces will become increasingly relevant for multidomain proteins, complexes and aggregates with large protein-water interfaces, as well as for high electric field frequencies, which provides a potential mechanism for corresponding experimental observations of negative protein DEP.

Spectrally Resolved Estimation of Water Entropy in the Active Site of Human Carbonic Anhydrase II

A major challenge in understanding ligand binding to biomacromolecules lies in dissecting the underlying thermodynamic driving forces at the atomic level. Quantifying the contributions of water molecules is often especially demanding, although they can play important roles in biomolecular recognition and binding processes. One example is human carbonic anhydrase II, whose active site harbors a conserved network of structural water molecules that are essential for enzymatic catalysis. Inhibitor binding disrupts this water network and changes the hydrogen-bonding patterns in the active site. Here, we use atomistic molecular dynamics simulations to compute the absolute entropy of the individual water molecules confined in the active site of hCAII using a spectrally resolved estimation (SRE) approach. The entropy decrease of water molecules that remain in the active site upon binding of a dorzolamide inhibitor is caused by changes in hydrogen bonding and stiffening of the hydrogen-bonding network. Overall, this entropy decrease is overcompensated by the gain due to the release of three water molecules from the active site upon inhibitor binding. The spectral density calculations enable the assignment of the changes to certain vibrational modes. In addition, the range of applicability of the SRE approximation is systematically explored by exploiting the gradually changing degree of immobilization of water molecules as a function of the distance to a phospholipid bilayer surface, which defines an "entropy ruler". These results demonstrate the applicability of SRE to biomolecular solvation, and we expect it to become a useful method for entropy calculations in biomolecular systems.

Entropy of Two-Molecule Correlated Translational-Rotational Motions Using the kth Nearest Neighbor Method

The entropy associated with rotations, translations, and their coupled motions provides an important contribution to the free energy of many physicochemical processes such as association and solvation. The kth nearest neighbor method, which offers a convenient way to estimate the entropy in high-dimensional spaces, has been previously applied for translational-rotational entropy estimation. Here, we explore the possibility of extending the kth nearest neighbor method to the computation of the entropy of correlated translation-rotations of two molecules, i.e., in the product space of two translation-rotations, both referred to the same independent reference system, which is relevant for all cases in which the correlated translational-rotational motion of more than two molecules is involved. Numerical tests show that, albeit the relatively high dimensionality (12) of the space, the kth nearest neighbor approach provides an accurate estimate for the entropy of two correlated translational-rotational motions, even when computed from a limited number of samples.

Thermodynamic Decomposition of Solvation Free Energies with Particle Mesh Ewald and Long-Range Lennard-Jones Interactions in Grid Inhomogeneous Solvation Theory

Grid Inhomogeneous Solvation Theory (GIST) maps out solvation thermodynamic properties on a fine meshed grid and provides a statistical mechanical formalism for thermodynamic end-state calculations. However, differences in how long-range nonbonded interactions are calculated in molecular dynamics engines and in the current implementation of GIST have prevented precise comparisons between free energies estimated using GIST and those from other free energy methods such as thermodynamic integration (TI). Here, we address this by presenting PME-GIST, a formalism by which particle mesh Ewald (PME)-based electrostatic energies and long-range Lennard-Jones (LJ) energies are decomposed and assigned to individual atoms and the corresponding voxels they occupy in a manner consistent with the GIST approach. PME-GIST yields potential energy calculations that are precisely consistent with modern simulation engines and performs these calculations at a dramatically faster speed than prior implementations. Here, we apply PME-GIST end-state analyses to 32 small molecules whose solvation free energies are close to evenly distributed from 2 kcal/mol to -17 kcal/mol and obtain solvation energies consistent with TI calculations (R² = 0.99, mean unsigned difference 0.8 kcal/mol). We also estimate the entropy contribution from the second and higher order entropy terms that are truncated in GIST by the differences between entropies calculated in TI and GIST. With a simple correction for the high order entropy terms, PME-GIST obtains solvation free energies that are highly consistent with TI calculations (R² = 0.99, mean unsigned difference = 0.4 kcal/mol) and experimental results (R² = 0.88, mean unsigned difference = 1.4 kcal/mol). The precision of PME-GIST also enables us to show that the solvation free energy of small hydrophobic and hydrophilic molecules can be largely understood based on perturbations of the solvent in a region extending a few solvation shells from the solute. We have integrated PME-GIST into the open-source molecular dynamics analysis software CPPTRAJ.

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.

Mapping major SARS-CoV-2 drug targets and assessment of druggability using computational fragment screening: Identification of an allosteric small-molecule binding site on the Nsp13 helicase

The 2019 emergence of, SARS-CoV-2 has tragically taken an immense toll on human life and far reaching impacts on society. There is a need to identify effective antivirals with diverse mechanisms of action in order to accelerate preclinical development. This study focused on five of the most established drug target proteins for direct acting small molecule antivirals: Nsp5 Main Protease, Nsp12 RNA-dependent RNA polymerase, Nsp13 Helicase, Nsp16 2'-O methyltransferase and the S2 subunit of the Spike protein. A workflow of solvent mapping and free energy calculations was used to identify and characterize favorable small-molecule binding sites for an aromatic pharmacophore (benzene). After identifying the most favorable sites, calculated ligand efficiencies were compared utilizing computational fragment screening. The most favorable sites overall were located on Nsp12 and Nsp16, whereas the most favorable sites for Nsp13 and S2 Spike had comparatively lower ligand efficiencies relative to Nsp12 and Nsp16. Utilizing fragment screening on numerous possible sites on Nsp13 helicase, we identified a favorable allosteric site on the N-terminal zinc binding domain (ZBD) that may be amenable to virtual or biophysical fragment screening efforts. Recent structural studies of the Nsp12:Nsp13 replication-transcription complex experimentally corroborates ligand binding at this site, which is revealed to be a functional Nsp8:Nsp13 protein-protein interaction site in the complex. Detailed structural analysis of Nsp13 ZBD conformations show the role of induced-fit flexibility in this ligand binding site and identify which conformational states are associated with efficient ligand binding. We hope that this map of over 200 possible small-molecule binding sites for these drug targets may be of use for ongoing discovery, design, and drug repurposing efforts. This information may be used to prioritize screening efforts or aid in the process of deciphering how a screening hit may bind to a specific target protein.

Utilizing Grand Canonical Monte Carlo Methods in Drug Discovery

The concepts behind targeting waters for potency and selectivity gains have been well documented and explored, although maximizing such potential gains can prove to be challenging. This problem is exacerbated in cases where there are multiple interacting waters, wherein perturbation of one water can affect the free energy landscape of the remaining waters. Knowing the right modification a priori is challenging, and computational approaches are ideally suited to help answer the key question of which substitution is best to try. Here, we use Grand Canonical Monte Carlo and the recent Grand Canonical Alchemical Perturbation methods to both understand and predict the effect of ligand-mediated water displacement when more than one water molecule is involved, as well as to understand how exploiting water networks can help govern selectivity.

A molecular reconstruction approach to site-based 3D-RISM and comparison to GIST hydration thermodynamic maps in an enzyme active site

Computed, high-resolution, spatial distributions of solvation energy and entropy can provide detailed information about the role of water in molecular recognition. While grid inhomogeneous solvation theory (GIST) provides rigorous, detailed thermodynamic information from explicit solvent molecular dynamics simulations, recent developments in the 3D reference interaction site model (3D-RISM) theory allow many of the same quantities to be calculated in a fraction of the time. However, 3D-RISM produces atomic-site, rather than molecular, density distributions, which are difficult to extract physical meaning from. To overcome this difficulty, we introduce a method to reconstruct molecular density distributions from atomic-site density distributions. Furthermore, we assess the quality of the resulting solvation thermodynamics density distributions by analyzing the binding site of coagulation Factor Xa with both GIST and 3D-RISM. We find good qualitative agreement between the methods for oxygen and hydrogen densities as well as direct solute-solvent energetic interactions. However, 3D-RISM predicts lower energetic and entropic penalties for moving water from the bulk to the binding site.

Large-Scale Study of Hydration Environments through Hydration Sites

Hydration sites are locations of interest to water and they can be used to classify the behavior of water around chemical motifs commonly found on the surface of proteins. Inhomogeneous fluid solvation theory (IFST) is a method for calculating hydration free-energy changes from molecular dynamics (MD) trajectories. In this paper, hydration sites are identified from MD simulations of 380 diverse protein structures. The hydration free energies of the hydration sites are calculated using IFST and distributions of these free-energy changes are analyzed. The results show that for some hydration sites near features conventionally regarded as attractive to water, such as hydrogen bond donors, the water molecules are actually relatively weakly bound and are easily displaced. We also construct plots of the spatial density of hydration sites with high, medium, and low hydration free-energy changes which represent weakly and strongly bound hydration sites. It is found that these plots show consistent features around common polar amino acids for all of the proteins studied.

Characterizing hydration sites in protein-ligand complexes towards the design of novel ligands

Water is an essential part of protein binding sites and mediates interactions to ligands. Its displacement by ligand parts affects the free binding energy of resulting protein-ligand complexes. Therefore the characterization of solvation properties is important for design. Of particular interest is the propensity of localized water to be favorably displaced by a ligand. This review discusses two popular computational approaches addressing these questions, namely WaterMap based on statistical mechanics analysis of MD simulations and 3D RISM based on integral equation theory of liquids. The theoretical background and recent applications in structure-based design will be presented.

The Role of Interfacial Water in Protein-Ligand Binding: Insights from the Indirect Solvent Mediated Potential of Mean Force

Classical density functional theory (DFT) can be used to relate the thermodynamic properties of solutions to the indirect solvent mediated part of the solute-solvent potential of mean force (PMF). Standard, but powerful numerical methods can be used to estimate the solute-solvent PMF from which the indirect part can be extracted. In this work we show how knowledge of the direct and indirect parts of the solute-solvent PMF for water at the interface of a protein receptor can be used to gain insights about how to design tighter binding ligands. As we show, the indirect part of the solute-solvent PMF is equal to the sum of the 1-body (energy + entropy) terms in the inhomogeneous solvation theory (IST) expansion of the solvation free energy. To illustrate the effect of displacing interfacial water molecules with particular direct/indirect PMF signatures on the binding of ligands, we carry out simulations of protein binding with several pairs of congeneric ligands. We show that interfacial water locations that contribute favorably or unfavorably at the 1-body level (energy + entropy) to the solvation free energy of the solute can be targeted as part of the ligand design process. Water locations where the indirect PMF is larger in magnitude provide better targets for displacement when adding a functional group to a ligand core.

Solvation Structure and Thermodynamic Mapping (SSTMap): An Open-Source, Flexible Package for the Analysis of Water in Molecular Dynamics Trajectories

We have developed SSTMap, a software package for mapping structural and thermodynamic water properties in molecular dynamics trajectories. The package introduces automated analysis and mapping of local measures of frustration and enhancement of water structure. The thermodynamic calculations are based on Inhomogeneous Fluid Solvation Theory (IST), which is implemented using both site-based and grid-based approaches. The package also extends the applicability of solvation analysis calculations to multiple molecular dynamics (MD) simulation programs by using existing cross-platform tools for parsing MD parameter and trajectory files. SSTMap is implemented in Python and contains both command-line tools and a Python module to facilitate flexibility in setting up calculations and for automated generation of large data sets involving analysis of multiple solutes. Output is generated in formats compatible with popular Python data science packages. This tool will be used by the molecular modeling community for computational analysis of water in problems of biophysical interest such as ligand binding and protein function.

Validating the Water Flooding Approach by Comparing It to Grand Canonical Monte Carlo Simulations

The study of the function of proteins on a quantitative level requires consideration of the water molecules in and around the protein. This requirement presents a major computational challenge due to the fact that the insertion of water molecules can have a very high activation barrier and would require a long simulation time. Recently, we developed a water flooding (WF) approach which is based on a postprocessing Monte Carlo ranking of possible water configurations. This approach appears to provide a very effective way for assessing the insertion free energies and determining the most likely configurations of the internal water molecules. Although the WF approach was used effectively in modeling challenging systems that have not been addressed reliably by other microscopic approaches, it was not validated by a comparison to the more rigorous grand canonical Monte Carlo (GCMC) method. Here we validate the WF approach by comparing its performance to that of the GCMC method. It is found that the WF approach reproduces the GCMC results in well-defined test cases but does so much faster. This established the WF approach as a useful strategy for finding correct water configurations in proteins and thus to provide a powerful way for studies of the functions of proteins.

On the accuracy of one- and two-particle solvation entropies

Evaluating solvation entropies directly and combining with direct energy calculations is one way of calculating free energies of solvation and is used by Inhomogeneous Fluid Solvation Theory (IFST). The configurational entropy of a fluid is a function of the interatomic correlations and can thus be expressed in terms of correlation functions. The entropies in this work are directly calculated from a truncated series of integrals over these correlation functions. Many studies truncate all terms higher than the solvent-solute correlations. This study includes an additional solvent-solvent correlation term and assesses the associated free energy when IFST is applied to a fixed Lennard-Jones particle solvated in neon. The strength of the central potential is varied to imitate larger solutes. Average free energy estimates with both levels of IFST are able to reproduce the estimate made using the Free energy Perturbation (FEP) to within 0.16 kcal/mol. We find that the signal from the solvent-solvent correlations is very weak. Our conclusion is that for monatomic fluids simulated by pairwise classical potentials the correction term is relatively small in magnitude. This study shows it is possible to reproduce the free energy from a path based method like FEP, by only considering the endpoints of the path. This method can be directly applied to more complex solutes which break the spherical symmetry of this study.

Relationship between Solvation Thermodynamics from IST and DFT Perspectives

Inhomogeneous solvation theory (IST) and classical density functional theory (DFT) each provide a framework for relating distribution functions of solutions to their thermodynamic properties. As reviewed in this work, both IST and DFT can be formulated in a way that use two "end point" simulations, one of the pure solvent and the other of the solution, to determine the solute chemical potential and other thermodynamic properties of the solution and of subvolumes in regions local to the solute containing hydrating waters. In contrast to IST, where expressions for the excess energy and entropy of solution are the object of analysis, in the DFT end point formulation of the problem, the solute-solvent potential of mean force (PMF) plays a central role. The indirect part of the PMF corresponds to the lowest order (1-body) truncation of the IST expression. Because the PMF is a free energy function, powerful numerical methods can be used to estimate it. We show that the DFT expressions for the solute excess chemical potential can be written in a form which is local, involving integrals only over regions proximate to the solute. The DFT end point route to estimating solvation free energies provides an alternative path to that of IST for analyzing solvation effects on molecular recognition and conformational changes in solution, which can lead to new insights. In order to illustrate the kind of information that is contained in the solute-solvent PMF, we have carried out simulations of β-cyclodextrin in water. This solute is a well studied "host" molecule to which "guest" molecules bind; host-guest systems serve as models for molecular recognition. We illustrate the range of values the direct and indirect parts of the solute-solvent PMF can have as a water molecule is brought to the interface of β-cyclodextrin from the bulk; we discuss the "competition" between these two terms, and the role it plays in molecular recognition.

Enthalpic and Entropic Contributions to Hydrophobicity

Hydrophobic hydration plays a key role in a vast variety of biological processes, ranging from the formation of cells to protein folding and ligand binding. Hydrophobicity scales simplify the complex process of hydration by assigning a value describing the averaged hydrophobic character to each amino acid. Previously published scales were not able to calculate the enthalpic and entropic contributions to the hydrophobicity directly. We present a new method, based on Molecular Dynamics simulations and Grid Inhomogeneous Solvation Theory, that calculates hydrophobicity from enthalpic and entropic contributions. Instead of deriving these quantities from the temperature dependence of the free energy of hydration or as residual of the free energy and the enthalpy, we directly obtain these values from the phase space occupied by water molecules. Additionally, our method is able to identify regions with specific enthalpic and entropic properties, allowing to identify so-called "unhappy water" molecules, which are characterized by weak enthalpic interactions and unfavorable entropic constraints.