Optimization of the GBMV2 implicit solvent force field for accurate simulation of protein conformational equilibria.

Accurate treatment of solvent environment is critical for reliable simulations of protein conformational equilibria. Implicit treatment of solvation, such as using the generalized Born (GB) class of models arguably provides an optimal balance between computational efficiency and physical accuracy. Yet, GB models are frequently plagued by a tendency to generate overly compact structures. The physical origins of this drawback are relatively well understood, and the key to a balanced implicit solvent protein force field is careful optimization of physical parameters to achieve a sufficient level of cancellation of errors. The latter has been hampered by the difficulty of generating converged conformational ensembles of non-trivial model proteins using the popular replica exchange sampling technique. Here, we leverage improved sampling efficiency of a newly developed multi-scale enhanced sampling technique to re-optimize the generalized-Born with molecular volume (GBMV2) implicit solvent model with the CHARMM36 protein force field. Recursive optimization of key GBMV2 parameters (such as input radii) and protein torsion profiles (via the CMAP torsion cross terms) has led to a more balanced GBMV2 protein force field that recapitulates the structures and stabilities of both helical and ß-hairpin model peptides. Importantly, this force field appears to be free of the over-compaction bias, and can generate structural ensembles of several intrinsically disordered proteins of various lengths that seem highly consistent with available experimental data. © 2017 Wiley Periodicals, Inc.

Halorhodopsin pumps Cl- and bacteriorhodopsin pumps protons by a common mechanism that uses conserved electrostatic interactions.

Key mutations differentiate the functions of homologous proteins. One example compares the inward ion pump halorhodopsin (HR) and the outward proton pump bacteriorhodopsin (BR). Of the nine essential buried ionizable residues in BR, six are conserved in HR. However, HR changes three BR acids, D85 in a central cluster of ionizable residues, D96, nearer the intracellular, and E204, nearer the extracellular side of the membrane to the small, neutral amino acids T111, V122, and T230, respectively. In BR, acidic amino acids are stationary anions whose proton affinity is modulated by conformational changes, establishing a sequence of directed binding and release of protons. Multiconformation continuum electrostatics calculations of chloride affinity and residue protonation show that, in reaction intermediates where an acid is ionized in BR, a Cl(-) is bound to HR in a position near the deleted acid. In the HR ground state, Cl(-) binds tightly to the central cluster T111 site and weakly to the extracellular T230 site, recovering the charges on ionized BR-D85 and neutral E204 in BR. Imposing key conformational changes from the BR M intermediate into the HR structure results in the loss of Cl(-) from the central T111 site and the tight binding of Cl(-) to the extracellular T230 site, mirroring the changes that protonate BR-D85 and ionize E204 in BR. The use of a mobile chloride in place of D85 and E204 makes HR more susceptible to the environmental pH and salt concentrations than BR. These studies shed light on how ion transfer mechanisms are controlled through the interplay of protein and ion electrostatics.

Electrostatic free energies in translational GTPases: Classic allostery and the rest.

GTPases typically switch between an inactive, OFF conformation and an active, ON conformation when a GDP ligand is replaced by GTP. Their ON/OFF populations and activity thus depend on the stabilities of four protein complexes, two apo-protein forms, and GTP/GDP in solution. A complete characterization is usually not possible experimentally and poses major challenges for simulations. We review the most important methodological challenges and we review thermodynamic data for two GTPases involved in translation of the genetic code: archaeal Initiation Factors 2 and 5B (aIF2, aIF5B). One main challenge is the multiplicity of states and conformations, including those of GTP/GDP in solution. Another is force field accuracy, especially for interactions of GTP/GDP with co-bound divalent Mg(2+) ions. The calculation of electrostatic free energies also poses specific challenges, and requires careful protocols. For aIF2, experiments and earlier simulations showed that it is a "classic" GTPase, with distinct ON/OFF conformations that prefer to bind GTP and GDP, respectively. For aIF5B, we recently proposed a non-classic mechanism, where the ON/OFF states differ only in the protonation state of Glu81 in the nucleotide binding pocket. This model is characterized here using free energy simulations. The methodological analysis should help future studies, while the aIF2, aIF5B examples illustrate the diversity of ATPase/GTPase mechanisms. This article is part of a Special Issue entitled Recent developments of molecular dynamics.

Protein:Ligand binding free energies: A stringent test for computational protein design.

A computational protein design method is extended to allow Monte Carlo simulations where two ligands are titrated into a protein binding pocket, yielding binding free energy differences. These provide a stringent test of the physical model, including the energy surface and sidechain rotamer definition. As a test, we consider tyrosyl-tRNA synthetase (TyrRS), which has been extensively redesigned experimentally. We consider its specificity for its substrate l-tyrosine (l-Tyr), compared to the analogs d-Tyr, p-acetyl-, and p-azido-phenylalanine (ac-Phe, az-Phe). We simulate l- and d-Tyr binding to TyrRS and six mutants, and compare the structures and binding free energies to a more rigorous "MD/GBSA" procedure: molecular dynamics with explicit solvent for structures and a Generalized Born + Surface Area model for binding free energies. Next, we consider l-Tyr, ac- and az-Phe binding to six other TyrRS variants. The titration results are sensitive to the precise rotamer definition, which involves a short energy minimization for each sidechain pair to help relax bad contacts induced by the discrete rotamer set. However, when designed mutant structures are rescored with a standard GBSA energy model, results agree well with the more rigorous MD/GBSA. As a third test, we redesign three amino acid positions in the substrate coordination sphere, with either l-Tyr or d-Tyr as the ligand. For two, we obtain good agreement with experiment, recovering the wildtype residue when l-Tyr is the ligand and a d-Tyr specific mutant when d-Tyr is the ligand. For the third, we recover His with either ligand, instead of wildtype Gln.

Parameterization of the Hamiltonian Dielectric Solvent (HADES) Reaction-Field Method for the Solvation Free Energies of Amino Acid Side-Chain Analogs.

Optimization of the Hamiltonian dielectric solvent (HADES) method for biomolecular simulations in a dielectric continuum is presented with the goal of calculating accurate absolute solvation free energies while retaining the model's accuracy in predicting conformational free-energy differences. The solvation free energies of neutral and polar amino acid side-chain analogs calculated by using HADES, which may optionally include nonpolar contributions, were optimized against experimental data to reach a chemical accuracy of about 0.5 kcal mol(-1). The new parameters were evaluated for charged side-chain analogs. The HADES results were compared with explicit-solvent, generalized Born, Poisson-Boltzmann, and QM-based methods. The potentials of mean force (PMFs) between pairs of side-chain analogs obtained by using HADES and explicit-solvent simulations were used to evaluate the effects of the improved parameters optimized for solvation free energies on intermolecular potentials.

A new set of atomic radii for accurate estimation of solvation free energy by Poisson-Boltzmann solvent model.

The Poisson-Boltzmann implicit solvent (PB) is widely used to estimate the solvation free energies of biomolecules in molecular simulations. An optimized set of atomic radii (PB radii) is an important parameter for PB calculations, which determines the distribution of dielectric constants around the solute. We here present new PB radii for the AMBER protein force field to accurately reproduce the solvation free energies obtained from explicit solvent simulations. The presented PB radii were optimized using results from explicit solvent simulations of the large systems. In addition, we discriminated PB radii for N- and C-terminal residues from those for nonterminal residues. The performances using our PB radii showed high accuracy for the estimation of solvation free energies at the level of the molecular fragment. The obtained PB radii are effective for the detailed analysis of the solvation effects of biomolecules.

The electrostatic landscape of MHC-peptide binding revealed using inception networks.

Predictive modeling of macromolecular recognition and protein-protein complementarity represents one of the cornerstones of biophysical sciences. However, such models are often hindered by the combinatorial complexity of interactions at the molecular interfaces. Exemplary of this problem is peptide presentation by the highly polymorphic major histocompatibility complex class I (MHC-I) molecule, a principal component of immune recognition. We developed human leukocyte antigen (HLA)-Inception, a deep biophysical convolutional neural network, which integrates molecular electrostatics to capture non-bonded interactions for predicting peptide binding motifs across 5,821 MHC-I alleles. These predictions of generated motifs correlate strongly with experimental peptide binding and presentation data. Beyond molecular interactions, the study demonstrates the application of predicted motifs in analyzing MHC-I allele associations with HIV disease progression and patient response to immune checkpoint inhibitors. A record of this paper's transparent peer review process is included in the supplemental information.

Improved flexible refinement of protein docking in CAPRI rounds 22-27.

Since the fourth evaluation for critical assessment of prediction of interactions (CAPRI), we have made improvements in three major areas in our refinement approach, namely the treatment of conformational flexibility, the binding free energy model, and the search algorithm. First, we incorporated backbone flexibility into our previous approach, which only optimized rigid backbone poses with limited side-chain flexibility. Here, we formulated and solved the conformational search as a hierarchical optimization problem (involving rigid-body poses, backbone flexibility, and side-chain flexibility). Second, we used continuum electrostatic calculations to include solvation effects in the binding free energy model. Finally, we eliminated sloppy modes (directions in which the free energy is essentially constant) to improve the efficiency of the search. With these improvements, we produced correct predictions for 6 of the 10 latest CAPRI targets, including one high, three medium, and two acceptable accuracy predictions. Compared to our previous performance in CAPRI, substantial improvements have been made for targets requiring homology modeling.

Multiple drugs and multiple targets: an analysis of the electrostatic determinants of binding between non-nucleoside HIV-1 reverse transcriptase inhibitors and variants of HIV-1 RT.

We present a systematic, computational analysis of the electrostatic component of binding of three HIV-1 RT inhibitors-nevirapine (NVP), efavirenz (EFV), and the recently approved rilpivirine (RPV)-to wild-type (WT) and mutant variants of RT. Electrostatic charge optimization was applied to determine how suited each molecule's charge distribution is for binding WT and individual mutants of HIV-1 RT. Although the charge distributions of NVP and EFV are rather far from being optimal for tight binding, RPVs charge distribution is close to the theoretical, optimal charge distribution for binding WT HIV-1 RT, although slight changes in charge can dramatically impact binding energetics. Moreover, toward the L100I/K103N double mutant, RPVs charge distribution is quite far from optimal. We also determine the contributions of chemical moieties on each molecule toward the electrostatic component of binding and show that different regions of a drug molecule may be used for recognition by different RT variants. The electrostatic contributions of certain RT residues toward drug binding are also computed to highlight critical residues for each interaction. Finally, the charge distribution of RPV is optimized to promiscuously bind to three RT variants rather than to each one in turn, with the resulting charge distribution being a compromise between the optimal charge distributions to each individual variant. Taken together, this work demonstrates that even in a binding site considered quite hydrophobic, electrostatics play a subtle yet varying role that must be considered in designing next-generation molecules that recognize rapidly mutating targets.

Computational Approach for Probing Redox Potential for Iron-Sulfur Clusters in Photosystem I.

Photosystem I is a light-driven electron transfer device. Available X-ray crystal structure from Thermosynechococcus elongatus showed that electron transfer pathways consist of two nearly symmetric branches of cofactors converging at the first iron-sulfur cluster FX, which is followed by two terminal iron-sulfur clusters FA and FB. Experiments have shown that FX has lower oxidation potential than FA and FB, which facilitates the electron transfer reaction. Here, we use density functional theory and Multi-Conformer Continuum Electrostatics to explain the differences in the midpoint Em potentials of the FX, FA and FB clusters. Our calculations show that FX has the lowest oxidation potential compared to FA and FB due to strong pairwise electrostatic interactions with surrounding residues. These interactions are shown to be dominated by the bridging sulfurs and cysteine ligands, which may be attributed to the shorter average bond distances between the oxidized Fe ion and ligating sulfurs for FX compared to FA and FB. Moreover, the electrostatic repulsion between the 4Fe-4S clusters and the positive potential of the backbone atoms is lowest for FX compared to both FA and FB. These results agree with the experimental measurements from the redox titrations of low-temperature EPR signals and of room temperature recombination kinetics.

Poor Person's pH Simulation of Membrane Proteins.

pH conditions are central to the functioning of all biomolecules. However, implications of pH changes are nontrivial on a molecular scale. Though a rigorous microscopic definition of pH exists, its implementation in classical molecular dynamics (MD) simulations is cumbersome, and more so in large integral membrane systems. In this chapter, an integrative pipeline is described that combines Multi-Conformation Continuum Electrostatics (MCCE) computations with MD simulations to capture the effect of transient protonation states on the coupled conformational changes in transmembrane proteins. The core methodologies are explained, and all the software required to set up this pipeline are outlined with their key parameters. All associated analyses of structure and function are provided using two case studies, namely those of bioenergetic complexes: NADH dehydrogenase (complex I) and Vo domain of V-type ATPase. The hybrid MCCE-MD pipeline has allowed the discovery of hydrogen bond networks, ligand binding pathways, and disease-causing mutations.

A Simple PB/LIE Free Energy Function Accurately Predicts the Peptide Binding Specificity of the Tiam1 PDZ Domain.

PDZ domains generally bind short amino acid sequences at the C-terminus of target proteins, and short peptides can be used as inhibitors or model ligands. Here, we used experimental binding assays and molecular dynamics simulations to characterize 51 complexes involving the Tiam1 PDZ domain and to test the performance of a semi-empirical free energy function. The free energy function combined a Poisson-Boltzmann (PB) continuum electrostatic term, a van der Waals interaction energy, and a surface area term. Each term was empirically weighted, giving a Linear Interaction Energy or "PB/LIE" free energy. The model yielded a mean unsigned deviation of 0.43 kcal/mol and a Pearson correlation of 0.64 between experimental and computed free energies, which was superior to a Null model that assumes all complexes have the same affinity. Analyses of the models support several experimental observations that indicate the orientation of the α2 helix is a critical determinant for peptide specificity. The models were also used to predict binding free energies for nine new variants, corresponding to point mutants of the Syndecan1 and Caspr4 peptides. The predictions did not reveal improved binding; however, they suggest that an unnatural amino acid could be used to increase protease resistance and peptide lifetimes in vivo. The overall performance of the model should allow its use in the design of new PDZ ligands in the future.

Implicit solvent methods for free energy estimation.

Solvation is a fundamental contribution in many biological processes and especially in molecular binding. Its estimation can be performed by means of several computational approaches. The aim of this review is to give an overview of existing theories and methods to estimate solvent effects giving a specific focus on the category of implicit solvent models and their use in Molecular Dynamics. In many of these models, the solvent is considered as a continuum homogenous medium, while the solute can be represented at the atomic detail and at different levels of theory. Despite their degree of approximation, implicit methods are still widely employed due to their trade-off between accuracy and efficiency. Their derivation is rooted in the statistical mechanics and integral equations disciplines, some of the related details being provided here. Finally, methods that combine implicit solvent models and molecular dynamics simulation, are briefly described.

Modeling the partitioning of amino acids in aqueous two phase systems.

A new model to obtain fast prediction of partition coefficients in polymer/polymer aqueous two phase systems (ATPSs) is presented, using amino acids as test systems. In particular, the partitioning behavior of eleven amino acids (glycine, alanine, leucine, phenylalanine, lysine, arginine, histidine, aspartic acid, glutamic acid, glutamine and serine) has been studied in 6 polymer/polymer ATPSs, formed by different pairs of nonionic polymers, including polyethylene glycol (PEG), Dextran, Ucon and Ficoll at 0.15M NaCl in 0.01M sodium phosphate buffer. The partition coefficients of the amino acids in the different ATPSs under study showed linear correlations as described by the Collander equation. Based on continuum electrostatics (CE), a semi-empirical model was developed to study the partitioning behavior in ATPSs. The approach employs a thermodynamic cycle where the electrostatic and nonpolar contributions to the free energy of partition are assumed to be additive. Three systems were chosen for the modeling studies: PEG-Dextran, PEG-Ficoll and Ficoll-Dextran. In general, the model was found to correctly predict the preferred phase for the studied amino acids, and, except for the charged ones, a good quantitative correlation of the calculated and experimental partition free energies was also obtained (e.g., with RMSE values of 150Jmol(-1) for PEG-Ficoll). The model performance could be improved by grouping amino acids according to their electrostatic properties, resulting in very good quantitative partition coefficient predictions (e.g., RMSE values for nonpolar amino acids of 29, 16 and 0.4Jmol(-1) for PEG-Dextran, PEG-Ficoll and Ficoll-Dextran system, respectively). The good performance of the proposed model in predicting partition coefficients of amino acids, the building blocks of proteins, offers a good prospect to its application to protein molecules and complexes.

Progress in developing Poisson-Boltzmann equation solvers.

This review outlines the recent progress made in developing more accurate and efficient solutions to model electrostatics in systems comprised of bio-macromolecules and nano-objects, the last one referring to objects that do not have biological function themselves but nowadays are frequently used in biophysical and medical approaches in conjunction with bio-macromolecules. The problem of modeling macromolecular electrostatics is reviewed from two different angles: as a mathematical task provided the specific definition of the system to be modeled and as a physical problem aiming to better capture the phenomena occurring in the real experiments. In addition, specific attention is paid to methods to extend the capabilities of the existing solvers to model large systems toward applications of calculations of the electrostatic potential and energies in molecular motors, mitochondria complex, photosynthetic machinery and systems involving large nano-objects.