Improved treatment of cyclic β‐amino acids and successful prediction of β‐peptide secondary structure using a modified force field: AMBER*C

We added parameters to the AMBER* force field to model cyclic β‐amino acid derivatives more accurately within the commonly used MacroModel program. In an effort to generate an improved treatment of cyclohexane and cyclopentane conformational preferences, carbon–carbon torsional parameters were modified and incorporated into a force field we call AMBER*C. Simulation of trans‐2‐aminocyclohexanecarboxylic acid (trans‐ACHC) and trans‐2‐aminocyclopentanecarboxylic acid (trans‐ACPC) derivatives using AMBER*C produces more realistic energy differences between (pseudo)diaxial and (pseudo)diequatorial conformations than does simulation using AMBER*. AMBER*C molecular dynamics simulations more accurately reproduce the experimental hydrogen‐bonding tendencies of simple diamide derivatives of trans‐ACHC and trans‐ACPC than do simulations using the AMBER* force field. More importantly, this modified force field allows accurate qualitative prediction of the helical secondary structures adopted by β‐amino acid homo‐oligomers. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 763–773, 2000     

A fast method for large‐scale De Novo peptide and miniprotein structure prediction

Although peptides have many biological and biomedical implications, an accurate method predicting their equilibrium structural ensembles from amino acid sequences and suitable for large‐scale experiments is still missing. We introduce a new approach—PEP‐FOLD—to the de novo prediction of peptides and miniproteins. It first predicts, in the terms of a Hidden Markov Model‐derived structural alphabet, a limited number of local conformations at each position of the structure. It then performs their assembly using a greedy procedure driven by a coarse‐grained energy score. On a benchmark of 52 peptides with 9–23 amino acids, PEP‐FOLD generates lowest‐energy conformations within 2.8 and 2.3 Å Cα root‐mean‐square deviation from the full nuclear magnetic resonance structures (NMR) and the NMR rigid cores, respectively, outperforming previous approaches. For 13 miniproteins with 27–49 amino acids, PEP‐FOLD reaches an accuracy of 3.6 and 4.6 Å Cα root‐mean‐square deviation for the most‐native and lowest‐energy conformations, using the nonflexible regions identified by NMR. PEP‐FOLD simulations are fast—a few minutes only—opening therefore, the door to in silico large‐scale rational design of new bioactive peptides and miniproteins. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Computational studies on carbohydrates: I. Density functional ab initio geometry optimization on maltose conformations

Ab initio geometry optimization was carried out on 10 selected conformations of maltose and two 2‐methoxytetrahydropyran conformations using the density functional denoted B3LYP combined with two basis sets. The 6‐31G* and 6‐311++G** basis sets make up the B3LYP/6‐31G* and B3LYP/6‐311++G** procedures. Internal coordinates were fully relaxed, and structures were gradient optimized at both levels of theory. Ten conformations were studied at the B3LYP/6‐31G* level, and five of these were continued with full gradient optimization at the B3LYP/6‐311++G** level of theory. The details of the ab initio optimized geometries are presented here, with particular attention given to the positions of the atoms around the anomeric center and the effect of the particular anomer and hydrogen bonding pattern on the maltose ring structures and relative conformational energies. The size and complexity of the hydrogen‐bonding network prevented a rigorous search of conformational space by ab initio calculations. However, using empirical force fields, low‐energy conformers of maltose were found that were subsequently gradient optimized at the two ab initio levels of theory. Three classes of conformations were studied, as defined by the clockwise or counterclockwise direction of the hydroxyl groups, or a flipped conformer in which the ψ‐dihedral is rotated by ∼180°. Different combinations of ω side‐chain rotations gave energy differences of more than 6 kcal/mol above the lowest energy structure found. The lowest energy structures bear remarkably close resemblance to the neutron and X‐ray diffraction crystal structures. © 2000 John Wiley & Sons, Inc. * J Comput Chem 21: 1204–1219, 2000     

LEAP: Highly accurate prediction of protein loop conformations by integrating coarse‐grained sampling and optimized energy scores with all‐atom refinement of backbone and side chains

Prediction of protein loop conformations without any prior knowledge (ab initio prediction) is an unsolved problem. Its solution will significantly impact protein homology and template‐based modeling as well as ab initio protein‐structure prediction. Here, we developed a coarse‐grained, optimized scoring function for initial sampling and ranking of loop decoys. The resulting decoys are then further optimized in backbone and side‐chain conformations and ranked by all‐atom energy scoring functions. The final integrated technique called loop prediction by energy‐assisted protocol achieved a median value of 2.1 Å root mean square deviation (RMSD) for 325 12‐residue test loops and 2.0 Å RMSD for 45 12‐residue loops from critical assessment of structure‐prediction techniques (CASP) 10 target proteins with native core structures (backbone and side chains). If all side‐chain conformations in protein cores were predicted in the absence of the target loop, loop‐prediction accuracy only reduces slightly (0.2 Å difference in RMSD for 12‐residue loops in the CASP target proteins). The accuracy obtained is about 1 Å RMSD or more improvement over other methods we tested. The executable file for a Linux system is freely available for academic users at http://sparks‐lab.org . © 2013 Wiley Periodicals, Inc.     

Iterative method for finding the low‐energy conformations based on the concept of molecular volumes

The recently proposed overlapping spheres (OS) method (Raos, N. Croat Chem Acta 1999, 72, 727) finds low‐energy conformations by minimizing the repulsion potential dependent on the free molecular volume inside the sphere with radius R_v. The sphere is situated at the geometrical center of the molecule or at the center of a molecular segment. The method was checked on branched alkanes and cyclic molecules (1,4‐diethylcyclohexane and copper(II) monochelates with N‐alkylated amino acids), yielding in all cases stable conformations with usually lower conformational energy than the “seed” conformations. The simple rules for segmentation of a molecule, based mostly on the topological considerations, were derived from the results of successfull optimizations. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 1353–1360, 2000     

Computer simulations of ligand–protein binding with ensembles of protein conformations: A Monte Carlo study of HIV‐1 protease binding energy landscapes

We present the results of molecular docking simulations with HIV‐1 protease for the sb203386 and skf107457 inhibitors by Monte Carlo simulated annealing. A simplified piecewise linear energy function, the standard AMBER force field, and the AMBER force field with solvation and a soft‐core smoothing component are employed in simulations with a single‐protein conformation to determine the relationship between docking simulations with a simple energy function and more realistic force fields. The temperature‐dependent binding free energy profiles of the inhibitors interacting with a single protein conformation provide a detailed picture of relative thermodynamic stability and a distribution of ligand binding modes in agreement with experimental crystallographic data. Using the simplified piecewise linear energy function, we also performed Monte Carlo docking simulations with an ensemble of protein conformations employing preferential biased sampling of low‐energy protein conformations, and the results are analyzed in connection with the free energy profiles. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 72: 73–84, 1999     

Molecular dynamics simulations of fluid methane properties using ab initio intermolecular interaction potentials

Intermolecular interaction energy data for the methane dimer have been calculated at a spectroscopic accuracy and employed to construct an ab initio potential energy surface (PES) for molecular dynamics (MD) simulations of fluid methane properties. The full potential curves of the methane dimer at 12 symmetric conformations were calculated by the supermolecule counterpoise‐corrected second‐order Møller‐Plesset (MP2) perturbation theory. Single‐point coupled cluster with single and double and perturbative triple excitations [CCSD(T)] calculations were also carried out to calibrate the MP2 potentials. We employed Pople's medium size basis sets [up to 6‐311++G(3df, 3pd)] and Dunning's correlation consistent basis sets (cc‐pVXZ and aug‐cc‐pVXZ, X = D, T, Q). For each conformer, the intermolecular carbon–carbon separation was sampled in a step 0.1 Å for a range of 3–9 Å, resulting in a total of 732 configuration points calculated. The MP2 binding curves display significant anisotropy with respect to the relative orientations of the dimer. The potential curves at the complete basis set (CBS) limit were estimated using well‐established analytical extrapolation schemes. A 4‐site potential model with sites located at the hydrogen atoms was used to fit the ab initio potential data. This model stems from a hydrogen–hydrogen repulsion mechanism to explain the stability of the dimer structure. MD simulations using the ab initio PES show quantitative agreements on both the atom‐wise radial distribution functions and the self‐diffusion coefficients over a wide range of experimental conditions. © 2008 Wiley Periodicals, Inc. J Comput Chem 2009     

Accelerated molecular dynamics simulations of protein folding

Folding of four fast‐folding proteins, including chignolin, Trp‐cage, villin headpiece and WW domain, was simulated via accelerated molecular dynamics (aMD). In comparison with hundred‐of‐microsecond timescale conventional molecular dynamics (cMD) simulations performed on the Anton supercomputer, aMD captured complete folding of the four proteins in significantly shorter simulation time. The folded protein conformations were found within 0.2–2.1 Å of the native NMR or X‐ray crystal structures. Free energy profiles calculated through improved reweighting of the aMD simulations using cumulant expansion to the second‐order are in good agreement with those obtained from cMD simulations. This allows us to identify distinct conformational states (e.g., unfolded and intermediate) other than the native structure and the protein folding energy barriers. Detailed analysis of protein secondary structures and local key residue interactions provided important insights into the protein folding pathways. Furthermore, the selections of force fields and aMD simulation parameters are discussed in detail. Our work shows usefulness and accuracy of aMD in studying protein folding, providing basic references in using aMD in future protein‐folding studies. © 2015 Wiley Periodicals, Inc.     

Conformational Analysis of C‐Trehaloses Using Molecular Mechanics Calculations

Relaxed‐residue energy maps based on the MM3 force field were computed for the three C‐linked (1‐1) d‐glucosyl disaccharides, C‐trehaloses: the axial–axial linked α,α‐trehalose, the axial–equatorial α,β‐trehalose and the equatorial–equatorial linked β,β‐trehalose. Optimized structures were calculated on a 20°‐grid spacing of the torsional angles about the C‐glycosidic bonds. Boltzman weighted ³J coupling constants were calculated and compared to the experimental values; they are satisfactory. The general shape of the energy maps indicates that α,α‐trehalose is a quite rigid molecule adopting only one conformation around the C‐glycosidic linkage, whereas the other two isomers are rather flexible. Compared to the corresponding O‐disaccharides α,β‐ and β,β‐trehaloses exhibit a larger number of low energy conformers and a larger area of the map energy < 8 kcal/mol. The preferred conformations of the axial C‐glycosidic bond are in agreement with the exo‐anomeric effect. Equatorial C‐ glycosidic bonds are rather flexible, influenced by the polarity of the milieu and the formation of interresidue hydrogen bonds.     

Exploring the similarities between potential smoothing and simulated annealing

Simulated annealing and potential function smoothing are two widely used approaches for global energy optimization of molecular systems. Potential smoothing as implemented in the diffusion equation method has been applied to study partitioning of the potential energy surface (PES) for N‐Acetyl‐Ala‐Ala‐N‐Methylamide (CDAP) and the clustering of conformations on deformed surfaces. A deformable version of the united‐atom OPLS force field is described, and used to locate all local minima and conformational transition states on the CDAP surface. It is shown that the smoothing process clusters conformations in a manner consistent with the inherent structure of the undeformed PES. Smoothing deforms the original surface in three ways: structural shifting of individual minima, merging of adjacent minima, and energy crossings between unrelated minima. A master equation approach and explicit molecular dynamics trajectories are used to uncover similar features in the equilibrium probability distribution of CDAP minima as a function of temperature. Qualitative and quantitative correlations between the simulated annealing and potential smoothing approaches to enhanced conformational sampling are established. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 531–552, 2000     

Comparison between self-guided Langevin dynamics and molecular dynamics simulations for structure refinement of protein loop conformations

This article presents a comparative analysis of two replica‐exchange simulation methods for the structure refinement of protein loop conformations, starting from low‐resolution predictions. The methods are self‐guided Langevin dynamics (SGLD) and molecular dynamics (MD) with a Nosé–Hoover thermostat. We investigated a small dataset of 8‐ and 12‐residue loops, with the shorter loops placed initially from a coarse‐grained lattice model and the longer loops from an enumeration assembly method (the Loopy program). The CHARMM22 + CMAP force field with a generalized Born implicit solvent model (molecular‐surface parameterized GBSW2) was used to explore conformational space. We also assessed two empirical scoring methods to detect nativelike conformations from decoys: the all‐atom distance‐scaled ideal‐gas reference state (DFIRE‐AA) statistical potential and the Rosetta energy function. Among the eight‐residue loop targets, SGLD out performed MD in all cases, with a median of 0.48 Å reduction in global root‐mean‐square deviation (RMSD) of the loop backbone coordinates from the native structure. Among the more challenging 12‐residue loop targets, SGLD improved the prediction accuracy over MD by a median of 1.31 Å, representing a substantial improvement. The overall median RMSD for SGLD simulations of 12‐residue loops was 0.91 Å, yielding refinement of a median 2.70 Å from initial loop placement. Results from DFIRE‐AA and the Rosetta model applied to rescoring conformations failed to improve the overall detection calculated from the CHARMM force field. We illustrate the advantage of SGLD over the MD simulation model by presenting potential‐energy landscapes for several loop predictions. Our results demonstrate that SGLD significantly outperforms traditional MD in the generation and populating of nativelike loop conformations and that the CHARMM force field performs comparably to other empirical force fields in identifying these conformations from the resulting ensembles. Published 2011 Wiley Periodicals, Inc. J Comput Chem, 2011     

Effective protein conformational sampling based on predicted torsion angles

Protein structure prediction is a long‐standing problem in molecular biology. Due to lack of an accurate energy function, it is often difficult to know whether the sampling algorithm or the energy function is the most important factor for failure of locating near‐native conformations of proteins. This article examines the size dependence of sampling effectiveness by using a perfect “energy function”: the root‐mean‐squared distance from the target native structure. Using protein targets up to 460 residues from critical assessment of structure prediction techniques (CASP11, 2014), we show that the accuracy of near native structures sampled is relatively independent of protein sizes but strongly depends on the errors of predicted torsion angles. Even with 40% out‐of‐range angle prediction, 2 Å or less near‐native conformation can be sampled. The result supports that the poor energy function is one of the bottlenecks of structure prediction and predicted torsion angles are useful for overcoming the bottleneck by restricting the sampling space in the absence of a perfect energy function. © 2015 Wiley Periodicals, Inc.     

Theoretical studies on opioid receptors and ligands. I. Molecular modeling and QSAR studies on the interaction mechanism of fentanyl analogs binding to μ‐opioid receptor

Based on our previous result of the three‐dimensional model of the μ‐opioid receptor, binding conformations of 13 fentanyl analogs and three‐dimensional structures for the complexs of these analogs with μ‐opioid receptor were constructed employing the molecular modeling method and our binding conformation search program for ligands (BCSPL). Energetic calculation and quantitative structure–activity relationship (QSAR) analysis indicated a good correlation between the calculated binding energies of fentanyl analogs and their binding affinities, pK_i's and pK's, and analgesic activities, − log ED₅₀'s. Based on the three‐dimensional models, the possible interaction mechanism of fentanyl analogs with μ‐opioid receptor can be illustrated and the available structure–activity relationship of these analgesic agents can be explained reasonably. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 78: 285–293, 2000     

Complexes of a Zn‐metalloenzyme binding site with hydroxamate‐containing ligands. A case for detailed benchmarkings of polarizable molecular mechanics/dynamics potentials when the experimental binding structure is unknown

Zn‐metalloproteins are a major class of targets for drug design. They constitute a demanding testing ground for polarizable molecular mechanics/dynamics aimed at extending the realm of quantum chemistry (QC) to very long‐duration molecular dynamics (MD). The reliability of such procedures needs to be demonstrated upon comparing the relative stabilities of competing candidate complexes of inhibitors with the recognition site stabilized in the course of MD. This could be necessary when no information is available regarding the experimental structure of the inhibitor–protein complex. Thus, this study bears on the phosphomannose isomerase (PMI) enzyme, considered as a potential therapeutic target for the treatment of several bacterial and parasitic diseases. We consider its complexes with 5‐phospho‐d ‐arabinonohydroxamate and three analog ligands differing by the number and location of their hydroxyl groups. We evaluate the energy accuracy expectable from a polarizable molecular mechanics procedure, SIBFA. This is done by comparisons with ab initio quantum‐chemistry (QC) calculations in the following cases: (a) the complexes of the four ligands in three distinct structures extracted from the entire PMI‐ligand energy‐minimized structures, and totaling up to 264 atoms; (b) the solvation energies of several energy‐minimized complexes of each ligand with a shell of 64 water molecules; (c) the conformational energy differences of each ligand in different conformations characterized in the course of energy‐minimizations; and (d) the continuum solvation energies of the ligands in different conformations. The agreements with the QC results appear convincing. On these bases, we discuss the prospects of applying the procedure to ligand‐macromolecule recognition problems. © 2016 Wiley Periodicals, Inc.     

Reversible peptide folding: Dependence on molecular force field used

Temperature‐dependent nuclear magnetic resonance (NMR) and CD spectra of methanol solutions of a β‐heptapeptide have been interpreted in such a way that the secondary structure, a 3₁₄‐helix, is assumed to be stable in a temperature range of between 298 and 393 K. This is in contrast to the results of a 50‐ns molecular dynamics simulation using the GROMOS 96 force field, which found a melting temperature of about 340 K. This discrepancy is addressed by further computational studies using the OPLS‐AA force field. The conformational energetics of N‐formyl‐3‐aminobutanamide in vacuo are obtained using ab initio and density functional quantum‐mechanical calculations at the HF/6‐31G*, B3LYP/6‐31G*, and B3LYP/6‐311+G* levels of theory. The results permit development of torsional parameters for the OPLS‐AA force field that reproduce the conformational energetics of the monomer. By varying the development procedure, three parameter sets are obtained that focus on reproducing either low‐energy or high‐energy conformations. These parameter sets are tested by simulating the reversible folding of the β‐heptapeptide in methanol. The melting temperature of the helix formed (>360 K) is found to be higher than the one obtained from simulations using the GROMOS 96 force field (∼340 K). Differences in the potential energy functions of the latter two force fields are evaluated and point to the origins of the difference in stability. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 774–787, 2000     

Multidimensional umbrella sampling and replica‐exchange molecular dynamics simulations for structure prediction of transmembrane helix dimers

Structural information of a transmembrane (TM) helix dimer is useful in understanding molecular mechanisms of important biological phenomena such as signal transduction across the cell membrane. Here, we describe an umbrella sampling (US) scheme for predicting the structure of a TM helix dimer in implicit membrane using the interhelical crossing angle and the TM–TM relative rotation angles as the reaction coordinates. This scheme conducts an efficient conformational search on TM–TM contact interfaces, and its robustness is tested by predicting the structures of glycophorin A (GpA) and receptor tyrosine kinase EphA1 (EphA1) TM dimers. The nuclear magnetic resonance (NMR) structures of both proteins correspond to the global free‐energy minimum states in their free‐energy landscapes. In addition, using the landscape of GpA as a reference, we also examine the protocols of temperature replica‐exchange molecular dynamics (REMD) simulations for structure prediction of TM helix dimers in implicit membrane. A wide temperature range in REMD simulations, for example, 250–1000 K, is required to efficiently obtain a free‐energy landscape consistent with the US simulations. The interhelical crossing angle and the TM–TM relative rotation angles can be used as reaction coordinates in multidimensional US and be good measures for conformational sampling of REMD simulations. © 2013 Wiley Periodicals, Inc.     

Protein side chain modeling with orientation-dependent atomic force fields derived by series expansions

We describe the development of new force fields for protein side chain modeling called optimized side chain atomic energy (OSCAR). The distance‐dependent energy functions (OSCAR‐d) and side‐chain dihedral angle potential energy functions were represented as power and Fourier series, respectively. The resulting 802 adjustable parameters were optimized by discriminating the native side chain conformations from non‐native conformations, using a training set of 12,000 side chains for each residue type. In the course of optimization, for every residue, its side chain was replaced by varying rotamers, whereas conformations for all other residues were kept as they appeared in the crystal structure. Then, the OSCAR‐d were multiplied by an orientation‐dependent function to yield OSCAR‐o. A total of 1087 parameters of the orientation‐dependent energy functions (OSCAR‐o) were optimized by maximizing the energy gap between the native conformation and subrotamers calculated as low energy by OSCAR‐d. When OSCAR‐o with optimized parameters were used to model side chain conformations simultaneously for 218 recently released protein structures, the prediction accuracies were 88.8% for χ₁, 79.7% for χ_{1 + 2}, 1.24 Å overall root mean square deviation (RMSD), and 0.62 Å RMSD for core residues, respectively, compared with the next‐best performing side‐chain modeling program which achieved 86.6% for χ₁, 75.7% for χ_{1 + 2}, 1.40 Å overall RMSD, and 0.86 Å RMSD for core residues, respectively. The continuous energy functions obtained in this study are suitable for gradient‐based optimization techniques for protein structure refinement. A program with built‐in OSCAR for protein side chain prediction is available for download at http://sysimm.ifrec.osaka‐u.ac.jp/OSCAR/ . © 2011 Wiley Periodicals, Inc. J Comput Chem 2011     

Effective way of modeling chemical catalysis: Empirical valence bond picture of role of solvent and catalyst in alkylation reactions

A general methodology for the study of chemical catalysis is presented and demonstrated in a study of Friedel–Crafts‐type alkylation reactions that are constrained to collinear configurations. Ab initio potential energy surfaces in solution and relevant experimental results are used to calibrate general empirical valence bond (EVB) potential surfaces for studies of such reactions. The EVB surfaces allow one to interpolate the ab initio results to studies of the effect of different solvents, substituents, and catalysts on the alkylation reactions. This implicit approach introduces such effects by shifting the diagonal energies of the corresponding resonance structures. Such an EVB/shift approach appears valuable for assessing the effects of different catalysts and solvents on complex chemical reactions. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 607–625, 2000