Quantifying the entropy of binding for water molecules in protein cavities by computing correlations

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.

W254 in furin functions as a molecular gate promoting anti-viral drug binding: Elucidation of putative drug tunneling and docking by non-equilibrium molecular dynamics

Furins are serine endoproteases that process precursor proteins into their biologically active forms, and they play essential roles in normal metabolism and disease presentation, including promoting expression of bacterial virulence factors and viral pathogenesis. Thus, furins represent vital targets for development of antimicrobial and antiviral therapeutics. Recent experimental evidence indicated that dichlorophenyl (DCP)-pyridine "BOS" drugs (e.g., BOS-318) competitively inhibit human furin by an induced-fit mechanism in which tryptophan W254 in the furin catalytic cleft (FCC) functions as a molecular gate, rotating nearly 180o through a steep energy barrier about its chi-1 dihedral to an "open" orientation, exposing a buried (i.e., cryptic) hydrophobic pocket 1. Once exposed, the non-polar DCP group of BOS-318, and similar halo-phenyl groups of analogs, enter the cryptic pocket, stabilizing drug binding. Here, we demonstrate flexible-receptor docking of BOS-318 (and various analogs) was unable to emulate the induced-fit motif, even when tryptophan was replaced with less bulky phenylalanine or glycine. While either substitution allowed access to the hydrophobic pocket for most ligands tested, optimal binding was observed only for W254, inferring a stabilizing effect of the indole sidechain. Furthermore, non-equilibrium steered molecular dynamics (sMD) in which the bound drugs (or their fragments) were extracted from the FCC did not cause closure of the open W254 gate, consistent with the thermodynamic stability of the open or closed W254 orientations. Finally, interactive molecular dynamics (iMD) revealed two putative conduits of drug entry and binding into the FCC, each coupled with W254 dihedral rotation and opening of the cryptic pocket. The iMD simulations further revealed ligand entry and binding in the FCC is likely driven in part by energy fluxes stemming from disruption and re-formation of ligand and protein solvation shells during drug migration from the solution phase into the FCC.

Heterogeneous and Allosteric Role of Surface Hydration for Protein-Ligand Binding

Atomistic-level understanding of surface hydration mediating protein-protein interactions and ligand binding has been a challenge due to the dynamic nature of water molecules near the surface. We develop a computational method to evaluate the solvation free energy based on the density map of the first hydration shell constructed from all-atom molecular dynamics simulation and use it to examine the binding of two intrinsically disordered ligands to their target protein domain. One ligand is from the human protein, and the other is from the 1918 Spanish flu virus. We find that the viral ligand incurs a 6.9 kcal/mol lower desolvation penalty upon binding to the target, which is consistent with its stronger binding affinity. The difference arises from the spatially fragmented and nonuniform water density profiles of the first hydration shell. In particular, residues that are distal from the ligand-binding site contribute to a varying extent to the desolvation penalty, among which the "entropy hotspot" residues contribute significantly. Thus, ligand binding alters hydration on remote sites in addition to affecting the binding interface. The nonlocal effect disappears when the conformational motion of the protein is suppressed. The present results elucidate the interplay between protein conformational dynamics and surface hydration. Our approach of measuring the solvation free energy based on the water density of the first hydration shell is tolerant of the conformational fluctuation of protein, and we expect it to be applicable to investigating a broad range of biomolecular interfaces.

Atomic Mechanisms of Transthyretin Tetramer Dissociation Studied by Molecular Dynamics Simulations

The dissociation of the transthyretin (TTR) tetramer into a monomer is closely related to various TTR amyloidoses in humans. While the tetramer dissociation has been reported to be the rate-limiting step for TTR aggregation, few details are known about the mechanism. Here, molecular dynamics (MD) simulations were performed by combining conventional MD and biased metadynamics to investigate the mechanism for the wild-type (WT) and mutant (T119M) structures. Both were found to have a great deal in common. Conventional MD simulations reveal that interfacial hydrophobic interactions contribute significantly to stabilize the tetramer. Interfacial residues including L17, V20, L110, and V121 with close contacts form a hydrophobic channel. Metadynamics simulations indicate that the mouth opening of the hydrophobic channel is the first and the most difficult step for dissociation. Interactions of V20 between opposing dimers lock four monomers into the tetramer, and disruption of the interactions is found to be involved in the final step. During the dissociation, an increasing extent of solvation was observed by calculating the radial distribution functions of water around interfacial hydrophobic residues, suggesting that water plays a role in driving the tetramer dissociation. Moreover, compared to T119, residue M119 has a longer side chain that extends into the hydrophobic channel, making solvation more difficult, consistent with a higher energy barrier for dissociation of the T119M tetramer. This result provides a good explanation for the protective role of the T119M mutation. Overall, this study can provide atomic-level insights to better understand the pathogenesis of TTR amyloidosis and guide rational drug design in the future.

Existence of two substates in the O intermediate of the bacteriorhodopsin photocycle

The proton pumping cycle of bacteriorhodopsin (bR) is initiated when the retinal chromophore with the 13-trans configuration is photo-isomerized into the 13-cis configuration. To understand the recovery processes of the initial retinal configuration that occur in the late stage of the photocycle, we have performed a comprehensive analysis of absorption kinetics data collected at various pH levels and at different salt concentrations. The result of analysis revealed the following features of the late stages of the trans photocycle. i) Two substates occur in the O intermediate. ii) The visible absorption band of the first substate (O1) appears at a much shorter wavelength than that of the late substate (O2). iii) O1 is in rapid equilibrium with the preceding state (N), but O1 becomes less stable than N when an ionizable residue (X₁) with a pKa value of 6.5 (in 2 M KCl) is deprotonated. iv) At a low pH and at a low salt concentration, the decay time constant of O2 is longer than those of the preceding states, but the relationship between these time constants is altered when the medium pH or the salt concentration is increased. On the basis of the present observations and previous studies on the structure of the chromophore in O, we suspect that the retinal chromophore in O1 takes on a distorted 13-cis configuration and the O1-to-O2 transition is accompanied by cis-to-trans isomerization about C13C14 bond.

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.

The ubiquitous buried water in the beta-trefoil architecture contributes to the folding nucleus and ~20% of the folding enthalpy

The beta-trefoil protein architecture is characterized by three repeating "trefoil" motifs related by rotational symmetry and postulated to have evolved via gene duplication and fusion events. Despite this apparent structural symmetry, the primary and secondary structural elements typically exhibit pronounced asymmetric features. A survey of this family of proteins has revealed that among the most conserved symmetric structural elements is a ubiquitous buried solvent which participates in a bridging H-bond with three different beta-strands in each of the trefoil motifs. A computational analysis reported that these waters are likely associated with a substantial enthalpic contribution to overall stability. In this report, a Pro mutation is used to disrupt one of the water H-bond interactions to a main chain amide, and the effects upon stability and folding kinetics are determined. Combined with Ala mutations, the separate effects upon side chain truncation and H-bond deletion are analyzed in terms of stability and folding kinetics. The results show that these buried waters act to assemble a central folding nucleus, and are responsible for ~20% of the overall favorable enthalpy of folding.

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.

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.

A Bit Stickier, a Bit Slower, a Lot Stiffer: Specific vs. Nonspecific Binding of Gal4 to DNA

Transcription factors regulate gene activity by binding specific regions of genomic DNA thanks to a subtle interplay of specific and nonspecific interactions that is challenging to quantify. Here, we exploit Reflective Phantom Interface (RPI), a label-free biosensor based on optical reflectivity, to investigate the binding of the N-terminal domain of Gal4, a well-known gene regulator, to double-stranded DNA fragments containing or not its consensus sequence. The analysis of RPI-binding curves provides interaction strength and kinetics and their dependence on temperature and ionic strength. We found that the binding of Gal4 to its cognate site is stronger, as expected, but also markedly slower. We performed a combined analysis of specific and nonspecific binding—equilibrium and kinetics—by means of a simple model based on nested potential wells and found that the free energy gap between specific and nonspecific binding is of the order of one kcal/mol only. We investigated the origin of such a small value by performing all-atom molecular dynamics simulations of Gal4–DNA interactions. We found a strong enthalpy–entropy compensation, by which the binding of Gal4 to its cognate sequence entails a DNA bending and a striking conformational freezing, which could be instrumental in the biological function of Gal4.

Solvation Thermodynamics from the Perspective of Endpoints DFT

Solvation thermodynamics is concerned with the evaluation and physical interpretation of solvation free energies. Endpoints DFT provides a framework for computing solvation free energies by combining molecular simulations with a version of the classical density-functional theory of solutions which focuses on ω, the indirect (solvent-mediated) part of the solute-solvent potential of mean force (indirect PMF). The simulations are performed at the endpoints of a hypothetical charging process which transforms the solvent density from the pure liquid state to that of the solution state. The endpoints DFT expression for solvation free energy can be shown to be equivalent to the standard expression for which the key quantity is the direct correlation function, but it has the advantage that the indirect term ω is more focused on the change in solvent-solvent correlations with respect to the pure liquid as the solute is inserted into the solution. In this Perspective, we review recent developments of endpoints DFT, highlighting a series of papers we have written together beginning in 2017. We emphasize the importance of dimensionality reduction as the key to the evaluation of endpoints DFT expressions and present a recently developed, spatially resolved version of the theory. The role of interfacial water at certain positions which stabilize or destabilize a solute in solution can be analyzed with the spatially resolved version, and it is of considerable interest to investigate how changes in solvation affect protein-ligand binding and conformational landscapes from an endpoints DFT perspective. Endpoints DFT can also be employed in materials science; an example involving the rational design strategy for polymer membrane separation is described. The endpoints DFT method is a scheme to evaluate the solvation free energy by introducing approximations to integrate the classical density functional over a charging parameter. We have further proposed a new functional which captures the correct dependence of the indirect PMF ω at both endpoints of the charging process, and we review how it might be employed in future work.

Conserved buried water molecules enable the β-trefoil architecture

Available high-resolution crystal structures for the family of β-trefoil proteins in the structural databank were queried for buried waters. Such waters were classified as either: (a) unique to a particular domain, family, or superfamily or (b) conserved among all β-trefoil folds. Three buried waters conserved among all β-trefoil folds were identified. These waters are related by the threefold rotational pseudosymmetry characteristic of this protein architecture (representing three instances of an identical structural environment within each repeating trefoil-fold motif). The structural properties of this buried water are remarkable and include: residing in a cavity space no larger than a single water molecule, exhibiting a positional uncertainty (i.e., normalized B-factor) substantially lower than the average Cα atom, providing essentially ideal H-bonding geometry with three solvent-inaccessible main chain groups, simultaneously serving as a bridging H-bond for three different β-strands at a point of secondary structure divergence, and orienting conserved hydrophobic side chains to form a nascent core-packing group. Other published work supports an interpretation that these interactions are key to the formation of an efficient folding nucleus and folded thermostability. The fundamental threefold symmetric structural element of the β-trefoil fold is therefore, surprisingly, a buried water molecule.

A Role for Monosaccharides in Nucleation Inhibition and Transport of Collagen

Background: Collagenous tissues are composed of precisely oriented, tightly packed collagen fibril bundles to confer the maximal strength within the smallest volume. While this compact form benefits mobility, it consequentially restricts vascularity and cell density to a minimally viable level in some regions. These tissues reside in a homeostatic state with an unstable equilibrium, where perturbations to structure or molecular milieu cause descension into a long-term compromised state. Several studies have shown that glycosaminoglycans are key molecules required for healthy tissue maintenance. Our long-term goal is to determine if glycosaminoglycans serve a critical function of stabilizing soluble monomeric collagen in the interstitial fluid that bathes tissue for immediate availability in tissue development and repair in vivo. Materials and Methods: To test glycosaminoglycan and collagen interactions at the most fundamental level, we have explored the effect of the monosaccharides that populate the glycosaminoglycans of the extracellular matrix on collagen assembly kinetics, pre-established matrix stability, and collagen incorporation into a preassembled matrix. Results: Results showed that monosaccharides increased the threshold concentration required for spontaneous polymerization by at least three orders of magnitude. When the monosaccharides were introduced to a pre-existing collagen network, fibrillar dissociation was undetectable. Fluorescent-labeling studies illustrated that in the presence of the saccharide solution, soluble collagen maintains the functional capacity to integrate into a pre-existing network. Conclusion: This work demonstrates a feasible role for glycosaminoglycans in supporting tissue remodeling and highlights the potential importance of age-related deterioration of glycosaminoglycan biosynthesis in reference to the homeostasis of collagen-based tissues.

Entropic bonding of the type 1 pilus from experiment and simulation

The type 1 pilus is a bacterial filament consisting of a long coiled proteic chain of subunits joined together by non-covalent bonding between complementing β -strands. Its strength and structural stability are critical for its anchoring function in uropathogenic Escherichia coli bacteria. The pulling and unravelling of the FimG subunit of the pilus was recently studied by atomic force microscopy experiments and steered molecular dynamics simulations (Alonso-Caballero et al. 2018 Nat. Commun. 9, 2758. (doi:10.1038/s41467-018-05107-6)). In this work, we perform a quantitative comparison between experiment and simulation, showing a good agreement in the underlying work values for the unfolding. The simulation results are then used to estimate the free energy difference for the detachment of FimG from the complementing strand of the neighbouring subunit in the chain, FimF. Finally, we show that the large free energy difference for the unravelling and detachment of the subunits which leads to the high stability of the chain is entirely entropic in nature.

A Binary Arginine Methylation Switch on Histone H3 Arginine 2 Regulates Its Interaction with WDR5

Histone H3 arginine 2 (H3R2) is post-translationally modified in three different states by "writers" of the protein arginine methyltransferase (PRMT) family. H3R2 methylarginine isoforms include PRMT5-catalyzed monomethylation (me1) and symmetric dimethylation (me2s) and PRMT6-catalyzed me1 and asymmetric dimethylation (me2a). WD-40 repeat-containing protein 5 (WDR5) is an epigenetic "reader" protein that interacts with H3R2. Previous studies suggested that H3R2me2s specified a high-affinity interaction with WDR5. However, our prior biological data prompted the hypothesis that WDR5 may also interact with H3R2me1. Here, using highly accurate quantitative binding analysis combined with high-resolution crystal structures of WDR5 in complex with unmodified (me0) and me1/me2s l-arginine amino acids and in complex with the H3R2me1 peptide, we provide a rigorous biochemical study and address long-standing discrepancies of this important biological interaction. Despite modest structural differences at the binding interface, our study supports an interaction model regulated by a binary arginine methylation switch: H3R2me2a prevents interaction with WDR5, whereas H3R2me0, -me1, and -me2s are equally permissive.

Strong Adverse Contribution of Conformational Dynamics to Streptavidin-Biotin Binding

Molecular dynamics plays an important role for the biological function of proteins. For protein ligand interactions, changes of conformational entropy of protein and hydration layer are relevant for the binding process. Quasielastic neutron scattering (QENS) was used to investigate differences in protein dynamics and conformational entropy of ligand-bound and ligand-free streptavidin. Protein dynamics were probed both on the fast picosecond time scale using neutron time-of-flight spectroscopy and on the slower nanosecond time scale using high-resolution neutron backscattering spectroscopy. We found the internal equilibrium motions of streptavidin and the corresponding mean square displacements (MSDs) to be greatly reduced upon biotin binding. On the basis of the observed MSDs, we calculated the difference of conformational entropy ΔS_conf of the protein component between ligand-bound and ligand-free streptavidin. The rather large negative ΔS_conf value (-2 kJ mol^-1 K^-1 on the nanosecond time scale) obtained for the streptavidin tetramer seems to be counterintuitive, given the exceptionally high affinity of streptavidin-biotin binding. Literature data on the total entropy change ΔS observed upon biotin binding to streptavidin, which includes contributions from both the protein and the hydration water, suggest partial compensation of the unfavorable ΔS_conf by a large positive entropy gain of the surrounding hydration layer and water molecules that are displaced during ligand binding.

A Fragmenting Protocol with Explicit Hydration for Calculation of Binding Enthalpies of Target-Ligand Complexes at a Quantum Mechanical Level

Optimization of the enthalpy component of binding thermodynamics of drug candidates is a successful pathway of rational molecular design. However, the large size and missing hydration structure of target-ligand complexes often hinder such optimizations with quantum mechanical (QM) methods. At the same time, QM calculations are often necessitated for proper handling of electronic effects. To overcome the above problems, and help the QM design of new drugs, a protocol is introduced for atomic level determination of hydration structure and extraction of structures of target-ligand complex interfaces. The protocol is a combination of a previously published program MobyWat, an engine for assigning explicit water positions, and Fragmenter, a new tool for optimal fragmentation of protein targets. The protocol fostered a series of fast calculations of ligand binding enthalpies at the semi-empirical QM level. Ligands of diverse chemistry ranging from small aromatic compounds up to a large peptide helix of a molecular weight of 3000 targeting a leukemia protein were selected for systematic investigations. Comparison of various combinations of implicit and explicit water models demonstrated that the presence of accurately predicted explicit water molecules in the complex interface considerably improved the agreement with experimental results. A single scaling factor was derived for conversion of QM reaction heats into binding enthalpy values. The factor links molecular structure with binding thermodynamics via QM calculations. The new protocol and scaling factor will help automated optimization of binding enthalpy in future molecular design projects.

Positive Cooperativity in Substrate Binding by Human Thymidylate Synthase

Thymidylate synthase (TS) catalyzes the production of the nucleotide dTMP from deoxyuridine monophosphate (dUMP), making the enzyme necessary for DNA replication and consequently a target for cancer therapeutics. TSs are homodimers with active sites separated by ∼30 Å. Reports of half-the-sites activity in TSs from multiple species demonstrate the presence of allosteric communication between the active sites of this enzyme. A simple explanation for the negative allosteric regulation occurring in half-the-sites activity would be that the two substrates bind with negative cooperativity. However, previous work on Escherichia coli TS revealed that dUMP substrate binds without cooperativity. To gain further insight into TS allosteric function, binding cooperativity in human TS is examined here. Isothermal titration calorimetry and two-dimensional lineshape analysis of NMR titration spectra are used to characterize the thermodynamics of dUMP binding, with a focus on quantification of cooperativity between the two substrate binding events. We find that human TS binds dUMP with ∼9-fold entropically driven positive cooperativity (ρ_ITC = 9 ± 1, ρ_NMR = 7 ± 1), in contrast to the apparent strong negative cooperativity reported previously. Our work further demonstrates the necessity of globally fitting isotherms collected under various conditions, as well as accurate determination of binding competent protein concentration, for calorimetric characterization of homotropic cooperative binding. Notably, an initial curvature of the isotherm is found to be indicative of positively cooperative binding. Two-dimensional lineshape analysis NMR is also found to be an informative tool for quantifying binding cooperativity, particularly in cases in which bound intermediates yield unique resonances.

A super-Gaussian Poisson-Boltzmann model for electrostatic free energy calculation: smooth dielectric distribution for protein cavities and in both water and vacuum states

Calculations of electrostatic potential and solvation free energy of macromolecules are essential for understanding the mechanism of many biological processes. In the classical implicit solvent Poisson-Boltzmann (PB) model, the macromolecule and water are modeled as two-dielectric media with a sharp border. However, the dielectric property of interior cavities and ion-channels is difficult to model realistically in a two-dielectric setting. In fact, the detection of water molecules in a protein cavity remains to be an experimental challenge. This introduces an uncertainty, which affects the subsequent solvation free energy calculation. In order to compensate this uncertainty, a novel super-Gaussian dielectric PB model is introduced in this work, which devices an inhomogeneous dielectric distribution to represent the compactness of atoms and characterizes empty cavities via a gap dielectric value. Moreover, the minimal molecular surface level set function is adopted so that the dielectric profile remains to be smooth when the protein is transferred from water phase to vacuum. An important feature of this new model is that as the order of super-Gaussian function approaches the infinity, the dielectric distribution reduces to a piecewise constant of the two-dielectric model. Mathematically, an effective dielectric constant analysis is introduced in this work to benchmark the dielectric model and select optimal parameter values. Computationally, a pseudo-time alternative direction implicit (ADI) algorithm is utilized for solving the super-Gaussian PB equation, which is found to be unconditionally stable in a smooth dielectric setting. Solvation free energy calculation of a Kirkwood sphere and various proteins is carried out to validate the super-Gaussian model and ADI algorithm. One macromolecule with both water filled and empty cavities is employed to demonstrate how the cavity uncertainty in protein structure can be bypassed through dielectric modeling in biomolecular electrostatic analysis.

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.

Spatially-Decomposed Free Energy of Solvation Based on the Endpoint Density-Functional Method

A spatially resolved version of the density-functional method for solvation thermodynamics is presented by extending the free-energy functional previously established in the one-dimensional, energy representation and formulating a new expression in a mixed four-dimensional representation (three dimensions for position and one dimension for energy). The space was further divided into a set of discrete regions with respect to the relative position of a solvent molecule from the solute, and the spatially decomposed energetics of solvation were analyzed for small molecules with a methyl, amine, or hydroxyl group and alanine dipeptide in solvent water. It was observed that the density of the solvation free energy is weakly dependent on the solute site in the excluded-volume region and is distinctively favorable in the first shells of the solute atoms that can readily form hydrogen bonds with water. The solvent-reorganization term reduces faster with the separation from the solute than the direct interaction between the solute and solvent, and the latter governs the energetics in the second shell and outer regions. The sum of the contributions to the free energy from the excluded volume and first shell was found to deviate significantly from the total sum over all the regions, implying that the solvation free energy is not spatially localized near the solute in a quantitative sense. Still, a local description was shown to be valid as confirmed by the correlation of the total value of free energy with the corresponding value obtained by integrating the free-energy density to the second shell. The theoretical framework developed in the present work to spatially decompose the solvation free energy can thus be useful to identify stabilizing or destabilizing regions of solvent proximate to a solute and to analyze the role that the displacement of interfacial water plays in the thermodynamics of molecular association.

Affinity Improvement of a Cancer-Targeted Antibody through Alanine-Induced Adjustment of Antigen-Antibody Interface

To investigate favorable single amino acid substitutions that improve antigen-antibody interactions, alanine (Ala) mutagenesis scanning of the interfacial residues of a cancer-targeted antibody, B5209B, was performed based on X-ray crystallography analysis. Two substitutions were shown to significantly enhance the binding affinity for the antigen, by up to 30-fold. One substitution improved the affinity by a gain of binding enthalpy, whereas the other substitution improved the affinity by a gain of binding entropy. Molecular dynamics simulations showed that the enthalpic improvement could be attributed to the stabilization of distant salt bridges located at the periphery of the antigen-antibody interface. The entropic improvement was due to the release of water molecules that were stably trapped in the antigen-antibody interface of the wild-type antibody. Importantly, these effects of the Ala substitutions were caused by subtle adjustments of the binding interface. These results will be helpful to design high-affinity antibodies with avoiding entropy-enthalpy compensation.

Functional Role of Solvent Entropy and Conformational Entropy of Metal Binding in a Dynamically Driven Allosteric System

Allostery is a regulatory phenomenon whereby ligand binding to one site influences the binding of the same or a different ligand to another site on a macromolecule. The physical origins of allosteric regulation remain under intense investigation. In general terms, ligand-induced structural changes, perturbations of residue-specific dynamics, and surrounding solvent molecules all potentially contribute to the global energetics of allostery. While the role of solvent is generally well understood in regulatory events associated with major protein structural rearrangements, the degree to which protein dynamics impact solvent degrees of freedom is unclear, particularly in cases of dynamically driven allostery. With the aid of new crystal structures, extensive calorimetric and residue-specific dynamics studies over a range of time scales and temperatures, we dissect for the first time the relative degree to which changes in solvent entropy and residue-specific dynamics impact dynamically driven, allosteric inhibition of DNA binding by Zn in the zinc efflux repressor, CzrA (chromosomal zinc-regulated repressor). We show that non-native residue-specific dynamics in allosterically impaired CzrA mutants are accompanied by significant perturbations in solvent entropy that cannot be predicted from crystal structures. We conclude that functional dynamics are not necessarily restricted to protein residues but involve surface water molecules that may be responding to ligand (Zn)-mediated perturbations in protein internal motions that define the conformational ensemble, rather than major structural rearrangements.

Dynamics and Thermodynamics of Transthyretin Association from Molecular Dynamics Simulations

Molecular dynamics simulations are used in this work to probe the structural stability and the dynamics of engineered mutants of transthyretin (TTR), i.e., the double mutant F87M/L110M (MT-TTR) and the triple mutant F87M/L110M/S117E (3M-TTR), in relation to wild-type. Free energy analysis from end-point simulations and statistical effective energy functions are used to analyze trajectories, revealing that mutations do not have major impact on protein structure but rather on protein association, shifting the equilibria towards dissociated species. The result is confirmed by the analysis of 3M-TTR which shows dissociation within the first 10 ns of the simulation, indicating that contacts are lost at the dimer-dimer interface, whereas dimers (formed by monomers which pair to form two extended β-sheets) appear fairly stable. Overall the simulations provide a detailed view of the dynamics and thermodynamics of wild-type and mutant transthyretins and a rationale of the observed effects.

Kinase inhibitors: the road ahead

Receptor tyrosine kinase signalling pathways have been successfully targeted to inhibit proliferation and angiogenesis for cancer therapy. However, kinase deregulation has been firmly demonstrated to play an essential role in virtually all major disease areas. Kinase inhibitor drug discovery programmes have recently broadened their focus to include an expanded range of kinase targets and therapeutic areas. In this Review, we provide an overview of the novel targets, biological processes and disease areas that kinase-targeting small molecules are being developed against, highlight the associated challenges and assess the strategies and technologies that are enabling efficient generation of highly optimized kinase inhibitors.

Quantitative metrics for drug-target ligandability

Ligandability is a prerequisite for druggability and is a much easier concept to understand, model and predict because it does not depend on the complex pharmacodynamic and pharmacokinetic mechanisms in the human body. In this review, we consider a metric for quantifying ligandability from experimental data. We discuss ligandability in terms of the balance between effort and reward. The metric is evaluated for a standard set of well-studied drug targets - some traditionally considered to be ligandable and some regarded as difficult. We suggest that this metric should be used to systematically improve computational predictions of ligandability, which can then be applied to novel drug targets to predict their tractability.

Dielectric Properties of a Protein Probed by Reversal of a Buried Ion Pair

Thirty years ago, Hwang and Warshel suggested that a microenvironment preorganized to stabilize an ion pair would be incapable of reorganizing to stabilize the reverse ion pair. The implications were that (1) proteins have a limited capacity to reorganize, even under the influence of strong interactions, such as those present when ionizable groups are buried in the hydrophobic interior of a protein, and (2) the inability of proteins to tolerate the reversal of buried ion pairs demonstrates the limitations inherent to continuum electrostatic models of proteins. Previously we showed that when buried individually in the interior of staphylococcal nuclease, Glu23 and Lys36 have p K_a values near pH 7, but when buried simultaneously, they establish a strong interaction of ∼5 kcal/mol and have p K_a values shifted toward more normal values. Here, using equilibrium thermodynamic measurements, crystal structures, and NMR spectroscopy experiments, we show that although the reversed, individual substitutions-Lys23 and Glu36-also have p K_a values near 7, when buried together, they neither establish a strong interaction nor promote reorganization of their microenvironment. These experiments both confirm Warshel's original hypothesis and expand it by showing that it applies to reorganization, as demonstrated by our artificial ion pairs, as well as to preorganization as is commonly argued for motifs that stabilize naturally occurring ion pairs in polar microenvironments. These data constitute a challenging benchmark useful to test the ability of structure-based algorithms to reproduce the compensation between self-energy, Coulomb and polar interactions in hydrophobic environments of proteins.

Free Energy, Enthalpy and Entropy from Implicit Solvent End-Point Simulations

Free energy is the key quantity to describe the thermodynamics of biological systems. In this perspective we consider the calculation of free energy, enthalpy and entropy from end-point molecular dynamics simulations. Since the enthalpy may be calculated as the ensemble average over equilibrated simulation snapshots the difficulties related to free energy calculation are ultimately related to the calculation of the entropy of the system and in particular of the solvent entropy. In the last two decades implicit solvent models have been used to circumvent the problem and to take into account solvent entropy implicitly in the solvation terms. More recently outstanding advancement in both implicit solvent models and in entropy calculations are making the goal of free energy estimation from end-point simulations more feasible than ever before. We review briefly the basic theory and discuss the advancements in light of practical applications.

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.

Protein conformational flexibility modulates kinetics and thermodynamics of drug binding

Structure-based drug design has often been restricted by the rather static picture of protein-ligand complexes presented by crystal structures, despite the widely accepted importance of protein flexibility in biomolecular recognition. Here we report a detailed experimental and computational study of the drug target, human heat shock protein 90, to explore the contribution of protein dynamics to the binding thermodynamics and kinetics of drug-like compounds. We observe that their binding properties depend on whether the protein has a loop or a helical conformation in the binding site of the ligand-bound state. Compounds bound to the helical conformation display slow association and dissociation rates, high-affinity and high cellular efficacy, and predominantly entropically driven binding. An important entropic contribution comes from the greater flexibility of the helical relative to the loop conformation in the ligand-bound state. This unusual mechanism suggests increasing target flexibility in the bound state by ligand design as a new strategy for drug discovery.

Enhancing Structure Prediction and Design of Soluble and Membrane Proteins with Explicit Solvent-Protein Interactions

Solvent molecules interact intimately with proteins and can profoundly regulate their structure and function. However, accurately and efficiently modeling protein solvation effects at the molecular level has been challenging. Here, we present a method that improves the atomic-level modeling of soluble and membrane protein structures and binding by efficiently predicting de novo protein-solvent molecule interactions. The method predicted with unprecedented accuracy buried water molecule positions, solvated protein conformations, and challenging mutational effects on protein binding. When applied to homology modeling, solvent-bound membrane protein structures, pockets, and cavities were recapitulated with near-atomic precision even from distant homologs. Blindly refined atomic-level structures of evolutionary distant G protein-coupled receptors imply strikingly different functional roles of buried solvent between receptor classes. The method should prove useful for refining low-resolution protein structures, accurately modeling drug-binding sites in structurally uncharacterized receptors, and designing solvent-mediated protein catalysis, recognition, ligand binding, and membrane protein signaling.

The Binding Mode of the Sonic Hedgehog Inhibitor Robotnikinin, a Combined Docking and QM/MM MD Study

Erroneous activation of the Hedgehog pathway has been linked to a great amount of cancerous diseases and therefore a large number of studies aiming at its inhibition have been carried out. One leverage point for novel therapeutic strategies targeting the proteins involved, is the prevention of complex formation between the extracellular signaling protein Sonic Hedgehog and the transmembrane protein Patched 1. In 2009 robotnikinin, a small molecule capable of binding to and inhibiting the activity of Sonic Hedgehog has been identified, however in the absence of X-ray structures of the Sonic Hedgehog-robotnikinin complex, the binding mode of this inhibitor remains unknown. In order to aid with the identification of novel Sonic Hedgehog inhibitors, the presented investigation elucidates the binding mode of robotnikinin by performing an extensive docking study, including subsequent molecular mechanical as well as quantum mechanical/molecular mechanical molecular dynamics simulations. The attained configurations enabled the identification of a number of key protein-ligand interactions, aiding complex formation and providing stabilizing contributions to the binding of the ligand. The predicted structure of the Sonic Hedgehog-robotnikinin complex is provided via a PDB file as Supplementary Material and can be used for further reference.

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.

The Roles of Water in the Protein Matrix: A Largely Untapped Resource for Drug Discovery

The value of thoroughly understanding the thermodynamics specific to a drug discovery/design study is well known. Over the past decade, the crucial roles of water molecules in protein structure, function, and dynamics have also become increasingly appreciated. This Perspective explores water in the biological environment by adopting its point of view in such phenomena. The prevailing thermodynamic models of the past, where water was seen largely in terms of an entropic gain after its displacement by a ligand, are now known to be much too simplistic. We adopt a set of terminology that describes water molecules as being "hot" and "cold", which we have defined as being easy and difficult to displace, respectively. The basis of these designations, which involve both enthalpic and entropic water contributions, are explored in several classes of biomolecules and structural motifs. The hallmarks for characterizing water molecules are examined, and computational tools for evaluating water-centric thermodynamics are reviewed. This Perspective's summary features guidelines for exploiting water molecules in drug discovery.

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.

Solvent effects on ligand binding to a serine protease

ITC experiments and MD simulations reveal the mechanism behind enthalpy/entropy compensation upon trypsin-benzamidine binding at different solvation conditions.

Binding thermodynamics discriminates fragments from druglike compounds: a thermodynamic description of fragment-based drug discovery

Small is beautiful - reducing the size and complexity of chemical starting points for drug design allows better sampling of chemical space, reveals the most energetically important interactions within protein-binding sites and can lead to improvements in the physicochemical properties of the final drug. The impact of fragment-based drug discovery (FBDD) on recent drug discovery projects and our improved knowledge of the structural and thermodynamic details of ligand binding has prompted us to explore the relationships between ligand-binding thermodynamics and FBDD. Information on binding thermodynamics can give insights into the contributions to protein-ligand interactions and could therefore be used to prioritise compounds with a high degree of specificity in forming key interactions.

Assessment of Hydration Thermodynamics at Protein Interfaces with Grid Cell Theory

Molecular dynamics simulations have been analyzed with the Grid Cell Theory (GCT) method to spatially resolve the binding enthalpies and entropies of water molecules at the interface of 17 structurally diverse proteins. Correlations between computed energetics and structural descriptors have been sought to facilitate the development of simple models of protein hydration. Little correlation was found between GCT-computed binding enthalpies and continuum electrostatics calculations. A simple count of contacts with functional groups in charged amino acids correlates well with enhanced water stabilization, but the stability of water near hydrophobic and polar residues depends markedly on its coordination environment. The positions of X-ray-resolved water molecules correlate with computed high-density hydration sites, but many unresolved waters are significantly stabilized at the protein surfaces. A defining characteristic of ligand-binding pockets compared to nonbinding pockets was a greater solvent-accessible volume, but average water thermodynamic properties were not distinctive from other interfacial regions. Interfacial water molecules are frequently stabilized by enthalpy and destabilized entropy with respect to bulk, but counter-examples occasionally occur. Overall detailed inspection of the local coordinating environment appears necessary to gauge the thermodynamic stability of water in protein structures.

Studying the role of cooperative hydration in stabilizing folded protein states

Understanding and modelling protein folding remains a key scientific and engineering challenge. Two key questions in protein folding are (1) why many proteins adopt a folded state and (2) how these proteins transition from the random coil ensemble to a folded state. In this paper we employ molecular dynamics simulations to address the first of these questions. Computational methods are well-placed to address this issue due to their ability to analyze systems at atomic-level resolution. Traditionally, the stability of folded proteins has been ascribed to the balance of two types of intermolecular interactions: hydrogen-bonding interactions and hydrophobic contacts. In this study, we explore a third type of intermolecular interaction: cooperative hydration of protein surface residues. To achieve this, we consider multiple independent simulations of the villin headpiece domain to quantify the contributions of different interactions to the energy of the native and fully extended states. In addition, we consider whether these findings are robust with respect to the protein forcefield, the water model, and the presence of salt. In all cases, we identify many cooperatively hydrated interactions that are transient but energetically favor the native state. Whilst further work on additional protein structures, forcefields, and water models is necessary, these results suggest a role for cooperative hydration in protein folding that should be explored further. Rational design of cooperative hydration on the protein surface could be a viable strategy for increasing protein stability.

Exploring the role of water in molecular recognition: predicting protein ligandability using a combinatorial search of surface hydration sites

The interaction between any two biological molecules must compete with their interaction with water molecules. This makes water the most important molecule in medicine, as it controls the interactions of every therapeutic with its target. A small molecule binding to a protein is able to recognize a unique binding site on a protein by displacing bound water molecules from specific hydration sites. Quantifying the interactions of these water molecules allows us to estimate the potential of the protein to bind a small molecule. This is referred to as ligandability. In the study, we describe a method to predict ligandability by performing a search of all possible combinations of hydration sites on protein surfaces. We predict ligandability as the summed binding free energy for each of the constituent hydration sites, computed using inhomogeneous fluid solvation theory. We compared the predicted ligandability with the maximum observed binding affinity for 20 proteins in the human bromodomain family. Based on this comparison, it was determined that effective inhibitors have been developed for the majority of bromodomains, in the range from 10 to 100 nM. However, we predict that more potent inhibitors can be developed for the bromodomains BPTF and BRD7 with relative ease, but that further efforts to develop inhibitors for ATAD2 will be extremely challenging. We have also made predictions for the 14 bromodomains with no reported small molecule K d values by isothermal titration calorimetry. The calculations predict that PBRM1(1) will be a challenging target, while others such as TAF1L(2), PBRM1(4) and TAF1(2), should be highly ligandable. As an outcome of this work, we assembled a database of experimental maximal K d that can serve as a community resource assisting medicinal chemistry efforts focused on BRDs. Effective prediction of ligandability would be a very useful tool in the drug discovery process.

On the positional and orientational order of water and methanol around indole: a study on the microscopic origin of solubility

The increase in solubility for indole in methanol water solutions relative to pure water is a result methanol −OH–π interactions. In addition, excess entropy calculations suggest that this process is enthalpically rather than entropically driven.