Comment on the validation of continuum electrostatics models

An ABSINTH-Based Protocol for Predicting Binding Affinities between Proteins and Small Molecules

The core task in computational drug discovery is to accurately predict binding free energies in receptor-ligand systems for large libraries of putative binders. Here, the ABSINTH implicit solvent model and force field are extended to describe small, organic molecules and their interactions with proteins. We show that an automatic pipeline based on partitioning arbitrary molecules into substructures corresponding to model compounds with known free energies of solvation can be combined with the CHARMM general force field into a method that is successful at the two important challenges a scoring function faces in virtual screening work flows: it ranks known binders with correlation values rivaling that of comparable state-of-the-art methods and it enriches true binders in a set of decoys. Our protocol introduces innovative modifications to common virtual screening workflows, notably the use of explicit ions as competitors and the integration over multiple protein and ligand species differing in their protonation states. We demonstrate the value of modifications to both the protocol and ABSINTH itself. We conclude by discussing the limitations of high-throughput implicit methods such as the one proposed here.

Multiscale generalized born modeling of ligand binding energies for virtual database screening

Generalized Born (GB) models are widely used to study the electrostatic energetics of solute molecules including proteins. Previous work demonstrates that GB models may produce satisfactory solvation energies if accurate effective Born radii are computed for all atoms. Our previous study showed that a GB model which reproduces the solvation energy may not necessarily be suitable for ligand binding calculations. In this work, we studied binding energetics using the exact GB model, in which Born radii are computed from the Poisson-Boltzmann (PB) equation. Our results showed that accurate Born radii lead to very good agreement between GB and PB in electrostatic calculations for ligand binding. However, recently developed GB models with high Born radii accuracy, when used in large database screening, may suffer from time constraints which make accurate, large-scale Born radii calculations impractical. We therefore present a multiscale GB approach in which atoms are divided into two groups. For atoms in the first group, those few atoms which are most likely to be critical to binding electrostatics, the Born radii are computed accurately at the sacrifice of speed. We propose two alternative approaches for atoms in the second group. The Born radii of these atoms may simply be computed by a fast GB method. Alternatively, the Born radii of these atoms may be computed accurately in the free state, and then, a variational form of a fast GB method may be used to compute the change in Born radii experienced by these atoms during binding. This strategy provides an accuracy advantage while still being fast enough for use in the virtual screening of large databases.

FACTS: Fast analytical continuum treatment of solvation

An efficient method for calculating the free energy of solvation of a (macro)molecule embedded in a continuum solvent is presented. It is based on the fully analytical evaluation of the volume and spatial symmetry of the solvent that is displaced from around a solute atom by its neighboring atoms. The two measures of solvent displacement are combined in empirical equations to approximate the atomic (or self) electrostatic solvation energy and the solvent accessible surface area. The former directly yields the effective Born radius, which is used in the generalized Born (GB) formula to calculate the solvent-screened electrostatic interaction energy. A comparison with finite-difference Poisson data shows that atomic solvation energies, pair interaction energies, and their sums are evaluated with a precision comparable to the most accurate GB implementations. Furthermore, solvation energies of a large set of protein conformations have an error of only 1.5%. The solvent accessible surface area is used to approximate the nonpolar contribution to solvation. The empirical approach, called FACTS (Fast Analytical Continuum Treatment of Solvation), is only four times slower than using the vacuum energy in molecular dynamics simulations of proteins. Notably, the folded state of structured peptides and proteins is stable at room temperature in 100-ns molecular dynamics simulations using FACTS and the CHARMM force field.

Balancing an accurate representation of the molecular surface in generalized born formalisms with integrator stability in molecular dynamics simulations

Different integrator time steps in NVT and NVE simulations of protein and nucleic acid systems are tested with the GBMV (Generalized Born using Molecular Volume) and GBSW (Generalized Born with simple SWitching) methods. The simulation stability and energy conservation is investigated in relation to the agreement with the Poisson theory. It is found that very close agreement between generalized Born methods and the Poisson theory based on the commonly used sharp molecular surface definition results in energy drift and simulation artifacts in molecular dynamics simulation protocols with standard 2-fs time steps. New parameters are proposed for the GBMV method, which maintains very good agreement with the Poisson theory while providing energy conservation and stable simulations at time steps of 1 to 1.5 fs.

Electrostatics of ligand binding: parametrization of the generalized Born model and comparison with the Poisson-Boltzmann approach

An accurate and fast evaluation of the electrostatics in ligand-protein interactions is crucial for computer-aided drug design. The pairwise generalized Born (GB) model, a fast analytical method originally developed for studying the solvation of organic molecules, has been widely applied to macromolecular systems, including ligand-protein complexes. However, this model involves several empirical scaling parameters, which have been optimized for the solvation of organic molecules, peptides, and nucleic acids but not for energetics of ligand binding. Studies have shown that a good solvation energy does not guarantee a correct model of solvent-mediated interactions. Thus, in this study, we have used the Poisson-Boltzmann (PB) approach as a reference to optimize the GB model for studies of ligand-protein interactions. Specifically, we have employed the pairwise descreening approximation proposed by Hawkins et al.(1) for GB calculations and DelPhi for PB calculations. The AMBER all-atom force field parameters have been used in this work. Seventeen protein-ligand complexes have been used as a training database, and a set of atomic descreening parameters has been selected with which the pairwise GB model and the PB model yield comparable results on atomic Born radii, the electrostatic component of free energies of ligand binding, and desolvation energies of the ligands and proteins. The energetics of the 15 test complexes calculated with the GB model using this set of parameters also agrees well with the energetics calculated with the PB method. This is the first time that the GB model has been parametrized and thoroughly compared with the PB model for the electrostatics of ligand binding.

Evaluation of Poisson solvation models using a hybrid explicit/implicit solvent method

Implicit solvent methods have become popular tools in the field of protein dynamics simulations, yet evaluation of their validity has been primarily limited to comparisons with experimental and theoretical data for small molecules. In this paper, we use a recently developed hybrid explicit/implicit solvent methodology to evaluate the accuracy of several Poisson-based implicit solvent models. Specifically, we focus on the calculation of electrostatic solvation free energies of various fixed conformations for two proteins. We show that, among various dielectric boundary definitions, the Lee-Richards molecular surface has the best agreement with hybrid solvent results. Furthermore, certain modifications of the molecular surface Poisson protocol provide varied results. For instance, simple modifications of atomic radii on charged residues generally improve absolute errors but do not significantly reduce relative errors among conformations. On the other hand, using a water-probe radius of 1.0 A, as opposed to the standard value of 1.4 A, to generate the molecular surface, moderately improves both absolute and relative results.

One- and two-body decomposable Poisson-Boltzmann methods for protein design calculations

Successfully modeling electrostatic interactions is one of the key factors required for the computational design of proteins with desired physical, chemical, and biological properties. In this paper, we present formulations of the finite difference Poisson-Boltzmann (FDPB) model that are pairwise decomposable by side chain. These methods use reduced representations of the protein structure based on the backbone and one or two side chains in order to approximate the dielectric environment in and around the protein. For the desolvation of polar side chains, the two-body model has a 0.64 kcal/mol RMSD compared to FDPB calculations performed using the full representation of the protein structure. Screened Coulombic interaction energies between side chains are approximated with an RMSD of 0.13 kcal/mol. The methods presented here are compatible with the computational demands of protein design calculations and produce energies that are very similar to the results of traditional FDPB calculations.

On the transferability of hydration-parametrized continuum electrostatics models to solvated binding calculations

Using molecular mechanics force field partial atomic charges, we show the nonuniqueness of the parametrization of continuum electrostatics models with respect to solute atomic radii and interior dielectric constant based on hydration (vacuum-to-water transfer) free energy data available for small molecules. Moreover, parameter sets that are optimal and equivalent for hydration free energy calculations lead to large variations of calculated absolute and relative electrostatic binding free energies. Hence, parametrization of solvation effects based on hydration data, although a necessary condition, is not sufficient to guarantee its transferability to the calculation of binding free energies in solution.

Fragment-Based flexible ligand docking by evolutionary optimization

A new computational approach for the efficient docking of flexible ligands in a rigid protein is presented. It exploits the binding modes of functional groups determined by an exhaustive search with solvation. The search in ligand conformational space is performed by a genetic algorithm whose scoring function approximates steric effects and intermolecular hydrogen bonds. Ligand conformations generated by the genetic algorithm are docked in the protein binding site by optimizing the fit of their fragments to optimal positions of chemically related functional groups. We show that the use of optimal binding modes of molecular fragments allows to dock known inhibitors with about ten rotatable bonds in the active site of the uncomplexed and complexed conformations of thrombin and HIV-1 protease.

Solvation energy density occlusion approximation for evaluation of desolvation penalties in biomolecular interactions

In calculations involving many displacements of an interacting pair of biomolecules, such as brownian dynamics, the docking of a substrate/ligand to an enzyme/receptor, or the screening of a large number of ligands as prospective inhibitors for a particular receptor site, there is a need for rapid evaluation of the desolvation penalties of the interacting pair. Although continuum electrostatic treatments with distinct dielectric constants for solute and solvent provide an account of the electrostatics of solvation and desolvation, it is necessary to re-solve the Poisson equation, at considerable computational cost, for each displacement of the interacting pair. We present a new method that uses a formulation of continuum electrostatic solvation in terms of the solvation energy density and approximates desolvation in terms of the occlusion of this density. We call it the SEDO approximation. It avoids the need to re-solve the Poisson equation, as desolvation is now estimated by an integral over the occluded volume. Test calculations are presented for some simple model systems and for some real systems that have previously been studied using the Poisson equation approach: MHC class I protein-peptide complexes and a congeneric series of human immunodeficiency virus type 1 (HIV-1) protease--ligand complexes. For most of the systems considered, the trends and magnitudes of the desolvation component of interaction energies obtained using the SEDO approximation are in reasonable correlation with those obtained by re-solving the Poisson equation. In most cases, the error introduced by the SEDO approximation is much less than that of the often-used test-charge approximation for the charge-charge components of intermolecular interactions. Proteins 2001;43:12-27.

Generalized born models of macromolecular solvation effects

It would often be useful in computer simulations to use a simple description of solvation effects, instead of explicitly representing the individual solvent molecules. Continuum dielectric models often work well in describing the thermodynamic aspects of aqueous solvation, and approximations to such models that avoid the need to solve the Poisson equation are attractive because of their computational efficiency. Here we give an overview of one such approximation, the generalized Born model, which is simple and fast enough to be used for molecular dynamics simulations of proteins and nucleic acids. We discuss its strengths and weaknesses, both for its fidelity to the underlying continuum model and for its ability to replace explicit consideration of solvent molecules in macromolecular simulations. We focus particularly on versions of the generalized Born model that have a pair-wise analytical form, and therefore fit most naturally into conventional molecular mechanics calculations.

Efficient electrostatic solvation model for protein-fragment docking

A method is presented for the fast evaluation of the binding energy of a protein-small molecule complex with electrostatic solvation. It makes use of a fast preprocessing step based on the assumption that the main contribution to electrostatic desolvation upon ligand binding originates from the displacement of the first shell of water molecules. For a rigid protein, the precomputation of the energy contributions on a set of grids allows the estimation of the energy in solution of about 300 protein-fragment binding modes per second on a personal computer. The docking procedure is applied to five rigid binding sites whose size ranges from 17 residues to a whole protein of 107 amino acids. Using a library of 70 mainly rigid molecules, known micromolar inhibitors or close analogs are docked and prioritized correctly. The docking based rank-ordering of the library requires about 5 h and is proposed as a complementary approach to structure-activity relationships by nuclear magnetic resonance. Proteins 2001;42:256-268.