The electrostatic response of water to neutral polar solutes: implications for continuum solvent modeling

Inclusion of Water Multipoles into the Implicit Solvation Framework Leads to Accuracy Gains

The current practical "workhorses" of the atomistic implicit solvation─the Poisson-Boltzmann (PB) and generalized Born (GB) models─face fundamental accuracy limitations. Here, we propose a computationally efficient implicit solvation framework, the Implicit Water Multipole GB (IWM-GB) model, that systematically incorporates the effects of multipole moments of water molecules in the first hydration shell of a solute, beyond the dipole water polarization already present at the PB/GB level. The framework explicitly accounts for coupling between polar and nonpolar contributions to the total solvation energy, which is missing from many implicit solvation models. An implementation of the framework, utilizing the GAFF force field and AM1-BCC atomic partial charges model, is parametrized and tested against the experimental hydration free energies of small molecules from the FreeSolv database. The resulting accuracy on the test set (RMSE ∼ 0.9 kcal/mol) is 12% better than that of the explicit solvation (TIP3P) treatment, which is orders of magnitude slower. We also find that the coupling between polar and nonpolar parts of the solvation free energy is essential to ensuring that several features of the IWM-GB model are physically meaningful, including the sign of the nonpolar contributions.

Electrostatic Interactions in Protein Structure, Folding, Binding, and Condensation

Charged and polar groups, through forming ion pairs, hydrogen bonds, and other less specific electrostatic interactions, impart important properties to proteins. Modulation of the charges on the amino acids, e.g., by pH and by phosphorylation and dephosphorylation, have significant effects such as protein denaturation and switch-like response of signal transduction networks. This review aims to present a unifying theme among the various effects of protein charges and polar groups. Simple models will be used to illustrate basic ideas about electrostatic interactions in proteins, and these ideas in turn will be used to elucidate the roles of electrostatic interactions in protein structure, folding, binding, condensation, and related biological functions. In particular, we will examine how charged side chains are spatially distributed in various types of proteins and how electrostatic interactions affect thermodynamic and kinetic properties of proteins. Our hope is to capture both important historical developments and recent experimental and theoretical advances in quantifying electrostatic contributions of proteins.

Explicit Solvent Hydration Benchmark for Proteins with Application to the PBSA Method

Explicit and implicit solvent models have a proven record of delivering hydration free energies of small, druglike solutes in reasonable agreement with experiment. Hydration of macromolecules, such as proteins, is to a large extent uncharted territory, with few results shedding light on quantitative consistency between different solvent models, let alone their ability to reproduce real water. In this work, based on extensive explicit solvent simulations employing TIP3P and SPC/E water models we analyze hydration free energy changes between fixed conformations of 5 diverse proteins, including large multidomain structures. For the two solvent models we find better agreement in electrostatic rather than nonpolar contributions (RMSE of 2.3 and 2.7 kcal/mol, respectively), even though absolute values of the latter are typically an order of magnitude smaller. We also highlight the importance of finite size corrections to relative protein hydration free energies, which turn out to be rather large, on the order of several kcal/mol, and are necessary for proper interpretation of results obtained under periodic boundary conditions. We further compare gathered data with predictions of the implicit solvent approach based on the Poisson equation and the surface or volume based nonpolar term. We find definitely lesser consistency than between the two explicit models (RMSE between implicit and TIP3 results of 11.3 and 8.4 kcal/mol for electrostatic and nonpolar contributions, respectively). In the process we determine the value of the protein dielectric constant and the geometric model for the dielectric boundary that provide for the best agreement. Finally, we evaluate the usefulness of surface and volume based models of nonpolar contributions to hydration free energy of large biomolecules.

Hydration thermodynamics beyond the linear response approximation

The solvation energetics associated with the transformation of a solute molecule at infinite dilution in water from an initial state A to a final state B is reconsidered. The two solute states have different potentials energies of interaction, [Formula: see text] and [Formula: see text], with the solvent environment. Throughout the A [Formula: see text] B transformation of the solute, the solvation system is described by a Hamiltonian [Formula: see text] that changes linearly with the coupling parameter ξ. By focusing on the characterization of the probability density [Formula: see text] that the dimensionless perturbational solute-solvent interaction energy [Formula: see text] has numerical value y when the coupling parameter is ξ, we derive a hierarchy of differential equation relations between the ξ-dependent cumulant functions of various orders in the expansion of the appropriate cumulant generating function. On the basis of this theoretical framework we then introduce an inherently nonlinear solvation model for which we are able to find analytical results for both [Formula: see text] and for the solvation thermodynamic functions. The solvation model is based on the premise that there is an upper or a lower bound (depending on the nature of the interactions considered) to the amplitude of the fluctuations of Y in the solution system at equilibrium. The results reveal essential differences in behavior for the model when compared with the linear response approximation to solvation, particularly with regards to the probability density [Formula: see text]. The analytical expressions for the solvation properties show, however, that the linear response behavior is recovered from the new model when the room for the thermal fluctuations in Y is not restricted by the existence of a nearby bound. We compare the predictions of the model with the results from molecular dynamics computer simulations for aqueous solvation, in which either (1) the solute-solvent electrostatic interactions, or (2) the shorter-range attractive interactions are switched-on in the A [Formula: see text] B process.

Recent Progress in Treating Protein-Ligand Interactions with Quantum-Mechanical Methods

We review the first successes and failures of a “new wave” of quantum chemistry-based approaches to the treatment of protein/ligand interactions. These approaches share the use of “enhanced”, dispersion (D), and/or hydrogen-bond (H) corrected density functional theory (DFT) or semi-empirical quantum mechanical (SQM) methods, in combination with ensemble weighting techniques of some form to capture entropic effects. Benchmark and model system calculations in comparison to high-level theoretical as well as experimental references have shown that both DFT-D (dispersion-corrected density functional theory) and SQM-DH (dispersion and hydrogen bond-corrected semi-empirical quantum mechanical) perform much more accurately than older DFT and SQM approaches and also standard docking methods. In addition, DFT-D might soon become and SQM-DH already is fast enough to compute a large number of binding modes of comparably large protein/ligand complexes, thus allowing for a more accurate assessment of entropic effects.

Enhanced semiempirical QM methods for biomolecular interactions

Recent successes and failures of the application of 'enhanced' semiempirical QM (SQM) methods are reviewed in the light of the benefits and backdraws of adding dispersion (D) and hydrogen-bond (H) correction terms. We find that the accuracy of SQM-DH methods for non-covalent interactions is very often reported to be comparable to dispersion-corrected density functional theory (DFT-D), while computation times are about three orders of magnitude lower. SQM-DH methods thus open up a possibility to simulate realistically large model systems for problems both in life and materials science with comparably high accuracy.

Thermodynamics of binding of di- and tetrasubstituted naphthalene diimide ligands to DNA G-quadruplex

Naphthalene diimide ligands have the potential to stabilize human telomeric G-quadruplex DNA via noncovalent interactions. Stabilization of G-quadruplex high order structures has become an important strategy to develop novel anticancer therapeutics. In this study four naphthalene diimide based ligands were analyzed in order to elucidate the principal factors determining contributions to G-quadruplex-ligand binding. Three possible modes of binding and their respective Gibbs free energies for two naphthalene diimide based di-N-alkylpyridinium substituted ligands have been determined using a molecular docking technique and compared to experimental results. The structures obtained from the molecular docking calculations, were analyzed using the ab initio based fragment molecular orbital (FMO) method in order to determine the major enthalpic contributions to the binding and types of interactions between the ligand and specific residues of the G-quadruplex. A computational methodology for the efficient and inexpensive ligand optimization as compared to fully ab initio methods based on the estimation of binding affinities of the naphthalene diimide derived ligands to G-quadruplex is proposed.

Introducing Charge Hydration Asymmetry into the Generalized Born Model

The effect of charge hydration asymmetry (CHA)-non-invariance of solvation free energy upon solute charge inversion-is missing from the standard linear response continuum electrostatics. The proposed charge hydration asymmetric-generalized Born (CHA-GB) approximation introduces this effect into the popular generalized Born (GB) model. The CHA is added to the GB equation via an analytical correction that quantifies the specific propensity of CHA of a given water model; the latter is determined by the charge distribution within the water model. Significant variations in CHA seen in explicit water (TIP3P, TIP4P-Ew, and TIP5P-E) free energy calculations on charge-inverted "molecular bracelets" are closely reproduced by CHA-GB, with the accuracy similar to models such as SEA and 3D-RISM that go beyond the linear response. Compared against reference explicit (TIP3P) electrostatic solvation free energies, CHA-GB shows about a 40% improvement in accuracy over the canonical GB, tested on a diverse set of 248 rigid small neutral molecules (root mean square error, rmse = 0.88 kcal/mol for CHA-GB vs 1.24 kcal/mol for GB) and 48 conformations of amino acid analogs (rmse = 0.81 kcal/mol vs 1.26 kcal/mol). CHA-GB employs a novel definition of the dielectric boundary that does not subsume the CHA effects into the intrinsic atomic radii. The strategy leads to finding a new set of intrinsic atomic radii optimized for CHA-GB; these radii show physically meaningful variation with the atom type, in contrast to the radii set optimized for GB. Compared to several popular radii sets used with the original GB model, the new radii set shows better transferability between different classes of molecules.

Blind prediction of SAMPL4 cucurbit[7]uril binding affinities with the mining minima method

Accurate methods for predicting protein-ligand binding affinities are of central interest to computer-aided drug design for hit identification and lead optimization. Here, we used the mining minima (M2) method to predict cucurbit[7]uril binding affinities from the SAMPL4 blind prediction challenge. We tested two different energy models, an empirical classical force field, CHARMm with VCharge charges, and the Poisson-Boltzmann surface area solvation model; and a semiempirical quantum mechanical (QM) Hamiltonian, PM6-DH+, coupled with the COSMO solvation model and a surface area term for nonpolar solvation free energy. Binding affinities based on the classical force field correlated strongly with the experiments with a correlation coefficient (R(2)) of 0.74. On the other hand, binding affinities based on the QM energy model correlated poorly with experiments (R(2) = 0.24), due largely to two major outliers. As we used extensive conformational search methods, these results point to possible inaccuracies in the PM6-DH+ energy model or the COSMO solvation model. Furthermore, the different binding free energy components, solute energy, solvation free energy, and configurational entropy showed significant deviations between the classical M2 and quantum M2 calculations. Comparison of different classical M2 free energy components to experiments show that the change in the total energy, i.e. the solute energy plus the solvation free energy, is the key driving force for binding, with a reasonable correlation to experiment (R(2) = 0.56); however, accounting for configurational entropy further improves the correlation.

The SAMPL4 host-guest blind prediction challenge: an overview

Prospective validation of methods for computing binding affinities can help assess their predictive power and thus set reasonable expectations for their performance in drug design applications. Supramolecular host-guest systems are excellent model systems for testing such affinity prediction methods, because their small size and limited conformational flexibility, relative to proteins, allows higher throughput and better numerical convergence. The SAMPL4 prediction challenge therefore included a series of host-guest systems, based on two hosts, cucurbit[7]uril and octa-acid. Binding affinities in aqueous solution were measured experimentally for a total of 23 guest molecules. Participants submitted 35 sets of computational predictions for these host-guest systems, based on methods ranging from simple docking, to extensive free energy simulations, to quantum mechanical calculations. Over half of the predictions provided better correlations with experiment than two simple null models, but most methods underperformed the null models in terms of root mean squared error and linear regression slope. Interestingly, the overall performance across all SAMPL4 submissions was similar to that for the prior SAMPL3 host-guest challenge, although the experimentalists took steps to simplify the current challenge. While some methods performed fairly consistently across both hosts, no single approach emerged as consistent top performer, and the nonsystematic nature of the various submissions made it impossible to draw definitive conclusions regarding the best choices of energy models or sampling algorithms. Salt effects emerged as an issue in the calculation of absolute binding affinities of cucurbit[7]uril-guest systems, but were not expected to affect the relative affinities significantly. Useful directions for future rounds of the challenge might involve encouraging participants to carry out some calculations that replicate each others' studies, and to systematically explore parameter options.

The SAMPL4 hydration challenge: evaluation of partial charge sets with explicit-water molecular dynamics simulations

We used blind predictions of the 47 hydration free energies in the SAMPL4 challenge to test multiple partial charge models in the context of explicit solvent free energy simulations with the general AMBER force field. One of the partial charge models, IPolQ-Mod, is a fast continuum solvent-based implementation of the IPolQ approach. The AM1-BCC, restrained electrostatic potential (RESP) and IpolQ-Mod approaches all perform reasonably well (R(2) > 0.8), while VCharge, though faster, gives less accurate results (R(2) of 0.5). The AM1-BCC results are more accurate than those of RESP for tertiary amines and nitrates, but the overall difference in accuracy between these methods is not statistically significant. Interestingly, the IPolQ-Mod method is found to yield partial charges in very close agreement with RESP. This observation suggests that the success of RESP may be attributed to its fortuitously approximating the arguably more rigorous IPolQ approach.