A discriminative Ramachandran potential of mean force aimed at minimizing secondary structure bias

We introduce PMF*, a novel potential of mean force (PMF) for the Ramachandran ?/Ψ dihedral plot of the 20 standard amino acids and assess its relevance to the conformation of polypeptides by scoring structures in the protein data bank and decoy datasets. The new energy function is a linear combination of the conventional, unreferenced PMF and the ΔPMF relative to the free energy of all amino acids in the parameterization set of structures, effectively removing their respective biases toward α‐helix and β‐strand. It is shown that low‐resolution crystal structures, NMR structures, and theoretical models have on average significantly higher energies than high‐resolution crystal structures; also PMF* is more discriminative for structure quality than the individual PMF and ΔPMF energy functions. PMF* may be well suited for use as a restraint energy term in the refinement of experimental structures and theoretical models. © 2012 Wiley Periodicals, Inc.     

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     

Accurate assessment of the strain energy in a protein-bound drug using QM/MM X-ray refinement and converged quantum chemistry

An ongoing question regarding the energetics of protein‐ligand binding has been; what is the strain energy that a ligand pays (if any) when binding to its protein target? The traditional method to estimate strain energy uses force fields to calculate the energy difference between the ligand bound conformation and its nearest local minimum/global minimum on the gas‐phase or aqueous phase potential energy surface. This makes the implicit assumption that the underlying force field as well as the reference crystal structure is accurate. Herein, we use ibuprofen as a test case and compare MMFF and ab initio QM methods to identify the local and global minimum conformations. Nine low energy conformations were identified with HF/6‐31G* geometry optimization in vacuo. We also obtained highly accurate relative energies for ibuprofen's conformational energy surface based on M06/aug‐cc‐pVXZ (X = D and T), MP2/aug‐cc‐pVXZ (X = D and T) and the MP2/CBS method (with and without solvent corrections). Moreover, we curate and re‐refine the ibuprofen‐protein complex (PDB 2BXG) using QM/MM X‐ray refinement approaches (HF/6‐31G* was the QM method and the MM model was the AMBER force field ff99sb), which were compared with the low energy conformers to calculate the strain energy. The result indicates that there was an 88% reduction in ibuprofen conformation strain using the QM/MM refined structure versus the original PDB ibuprofen conformations. Furthermore, our results indicate that, due to its inherent limitations in estimating electrostatic interactions, force fields are not suitable to gauge strain energy for charged drug molecules like ibuprofen. The present work offers a carefully validated conformational potential energy surface for a drug molecule as well as a reliable QM/MM re‐refined X‐ray structure that can be used to test current structure‐based drug design approaches. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011     

Force field studies of cholesterol and cholesteryl acetate crystals and cholesterol–cholesterol intermolecular interactions

To model the physical properties of sterols and related species, an all-atom Class II force field has been derived based on the recently reported CFF93 force field for hydrocarbons. It has been tested using both energy minimization and molecular dynamics (MD) simulations of the low-temperature neutron-diffraction structure of cholesteryl acetate crystals and the X-ray diffraction crystal structure of cholesterol. Thus these studies test the techniques and limitations of high-accuracy crystal simulations as well. Employing energy minimization, all cell vectors and volumes were reproduced to within 2.4% of experimental values. For cholesteryl acetate, the root mean square (rms) deviations between the calculated and experimental bond lengths, angles, and torsions of nonhydrogen atoms are 0.013 Å, 1.2°, and 2.4°, respectively. The corresponding maximum deviations are also very small: 0.027 Å for bond length, 3.2° for angle, and 7.6° for torsion. For cholesterol, good agreement between the calculated and experimental structures was found only when the comparison was limited to atoms with relatively small thermal factors (B_eq < 15 Ų). It was found that for both systems, the MD averaged structures were in better agreement with the experimental ones than the energy minimized structures, since the rms deviations in atom positions are smaller for the MD-averaged structures (0.064 Å for cholesteryl acetate and 0.152 Å for cholesterol) than those for the minimized structures (0.178 Å for cholesteryl acetate and 0.189 Å for cholesterol). The force field was then applied to isolated molecules focusing on the rigidity of the cholesteryl ring and cholesterol–cholesterol interaction energies. It is concluded that the cholesteryl ring is fairly rigid since no major conformational change was observed during an MD simulation of a single cholesterol molecule in vacuo at 500 K, in agreement with condensed phase experiments. Calculations of cholesterol–cholesterol pairs suggest that there are only four low-energy configurations and that it is more useful to describe each molecule as having a plane (flat face) and two grooves rather than as having two (one flat and one rough) faces. This provides some insight into the equilibrium crystal structures. Limited results from a modified Class I (CVFF) force field are presented for comparison. © 1995 by John Wiley & Sons, Inc.     

Hydrogen ADPs with Cu Kα data? Invariom and Hirshfeld atom modelling of fluconazole

For the structure of fluconazole [systematic name: 2‐(2,4‐difluorophenyl)‐1,3‐bis(1H‐1,2,4‐triazol‐1‐yl)propan‐2‐ol] monohydrate, C₁₃H₁₂F₂N₆O·H₂O, a case study on different model refinements is reported, based on single‐crystal X‐ray diffraction data measured at 100 K with Cu Kα radiation to a resolution of sin θ/λ of 0.6 Å⁻¹. The structure, anisotropic displacement parameters (ADPs) and figures of merit from the independent atom model are compared to `invariom' and `Hirshfeld atom' refinements. Changing from a spherical to an aspherical atom model lowers the figures of merit and improves both the accuracy and the precision of the geometrical parameters. Differences between results from the two aspherical‐atom refinements are small. However, a refinement of ADPs for H atoms is only possible with the Hirshfeld atom density model. It gives meaningful results even at a resolution of 0.6 Å⁻¹, but requires good low‐order data.     

The gas-phase rotamers of 1,1,2,2-tetrafluoroethane - force field,vibrational amplitudes and geometry - a joint electron-diffraction and spectroscopic study

The gas-phase conformational mixture of the anti and gauche rotamers of 1,1,2,2-tetrafluoroethane has been subjected to an electron-diffraction study at 253 K. Effective least-squares refinement of the geometry and relative proportions of the conformers was achieved with vibrational amplitudes for both conformers fixed at values calculated from spectroscopic data. In order to calculate the amplitudes, a force field was deduced which reproduced the observed wave numbers for both conformers; the assignment of the modes proposed in the literature was modified slightly. At 253 K, the rotamer composition was found to be 84% anti : 16%gauche, which corresponds to an energy difference of 1170 cal mol^?1; the geometrical parameters (r_a values) and e.s.d. are C-C = 1.518 ± 0.005 Å, C-H = 1.098 ± 0.006 Å, C-F = 1.350 ± 0.002 Å. ∠CCF = 108.2 ± 0.3°, ∠FCF = 107.3 ± 0-3°, ∠ CCH = 110.3 ± 1.0δ, and the torsion angleτ _hcch in the gauche form is 78 ± 2°.     

Flexible ligand docking using a robust evolutionary algorithm

A flexible ligand docking protocol based on evolutionary algorithms is investigated. The proposed approach incorporates family competition and adaptive rules to integrate decreasing‐based mutations and self‐adaptive mutations to act as global and local search strategies, respectively. The method is applied to a dihydrofolate reductase enzyme with the anticancer drug methotrexate and two analogues of antibacterial drug trimethoprim. Conformations and orientations closed to the crystallographically determined structures are obtained, as well as alternative structures with low energy. Numerical results indicate that the new approach is very robust. The docked lowest‐energy structures have root‐mean‐square derivations ranging from 0.67 to 1.96 Å with respect to the corresponding crystal structures. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 988–998, 2000     

Binding pose and affinity prediction in the 2016 D3R Grand Challenge 2 using the Wilma-SIE method

The Farnesoid X receptor (FXR) exhibits significant backbone movement in response to the binding of various ligands and can be a challenge for pose prediction algorithms. As part of the D3R Grand Challenge 2, we tested Wilma-SIE, a rigid-protein docking method, on a set of 36 FXR ligands for which the crystal structures had originally been blinded. These ligands covered several classes of compounds. To overcome the rigid protein limitations of the method, we used an ensemble of publicly available structures for FXR from the PDB. The use of the ensemble allowed Wilma-SIE to predict poses with average and median RMSDs of 2.3 and 1.4 Å, respectively. It was quite clear, however, that had we used a single structure for the receptor the success rate would have been much lower. The most successful predictions were obtained on chemical classes for which one or more crystal structures of the receptor bound to a molecule of the same class was available. In the absence of a crystal structure for the class, observing a consensus binding mode for the ligands of the class using one or more receptor structures of other classes seemed to be indicative of a reasonable pose prediction. Affinity prediction proved to be more challenging with generally poor correlation with experimental IC50s (Kendall tau?~?0.3). Even when the 36 crystal structures were used the accuracy of the predicted affinities was not appreciably improved. A possible cause of difficulty is the internal energy strain arising from conformational differences in the receptor across complexes, which may need to be properly estimated and incorporated into the SIE scoring function.     

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     

A versatile method for systematic conformational searches: application to CheY

A novel molecular structure prediction method, the Z Method, is described. It provides a versatile platform for the development and use of systematic, grid‐based conformational search protocols, in which statistical information (i.e., rotamers) can also be included. The Z Method generates trial structures by applying many changes of the same type to a single starting structure, thereby sampling the conformation space in an unbiased way. The method, implemented in the CHARMM program as the Z Module, is applied here to an illustrative model problem in which rigid, systematic searches are performed in a 36‐dimensional conformational space that describes the relative positions of the 10 secondary structural elements of the protein CheY. A polar hydrogen representation with an implicit solvation term (EEF1) is used to evaluate successively larger fragments of the protein generated in a hierarchical build‐up procedure. After a final refinement stage, and a total computational time of about two‐and‐a‐half CPU days on AMD Opteron processors, the prediction is within 1.56 Å of the native structure. The errors in the predicted backbone dihedral angles are found to approximately cancel. Monte Carlo and simulated annealing trials on the same or smaller versions of the problem, using the same atomic model and energy terms, are shown to result in less accurate predictions. Although the problem solved here is a limited one, the findings illustrate the utility of systematic searches with atom‐based models for macromolecular structure prediction and the importance of unbiased sampling in structure prediction methods. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011     

From secondary structure to three-dimensional structure: Improved dihedral angle probability distribution function for use with energy searches for native structures of polypeptides and proteins

An improved scheme to help in the prediction of protein structure is presented. This procedure generates improved starting conformations of a protein suitable for energy minimization. Trivariate gaussian distribution functions for the π, ψ, and χ¹ dihedral angles have been derived, using conformational data from high resolution protein structures selected from the Protein Data Bank (PDB). These trivariate probability functions generate initial values for the π, ψ, and χ¹ dihedral angles which reflect the experimental values found in the PDB. These starting structures speed the search of the conformational space by focusing the search mainly in the regions of native proteins. The efficiency of the new trivariate probability distributions is demonstrated by comparing the results for the α-class polypeptide fragment, the mutant Antennapedia (C39 → S) homeodomain (2HOA), with those from two reference probability functions. The first reference probability function is a uniform or flat probability function and the second is a bivariate probability function for π and ψ. The trivariate gaussian probability functions are shown to search the conformational space more efficiently than the other two probability functions. The trivariate gaussian probability functions are also tested on the binding domain of Streptococcal protein G (2GB1), an α/β class protein. Since presently available energy functions are not accurate enough to identify the most native-like energy-minimized structures, three selection criteria were used to identify a native-like structure with a 1.90-Å rmsd from the NMR structure as the best structure for the Antennapedia fragment. Each individual selection criterion (ECEPP/3 energy, ECEPP/3 energy-plus-free energy of hydration, or a knowledge-based mean field method) was unable to identify a native-like structure, but simultaneous application of more than one selection criterion resulted in a successful identification of a native-like structure for the Antennapedia fragment. In addition to these tests, structure predictions are made for the Antennapedia polypeptide, using a Pattern Recognition-based Importance-Sampling Minimization (PRISM) procedure to predict the backbone conformational state of the mutant Antennapedia homeodomain. The ten most probable backbone conformational state predictions were used with the trivariate and bivariate gaussian dihedral angle probability distributions to generate starting structures (i.e., dihedral angles) suitable for energy minimization. The final energy-minimized structures show that neither the trivariate nor the bivariate gaussian probability distributions are able to overcome the inaccuracies in the backbone conformational state predictions to produce a native-like structure. Until highly accurate predictions of the backbone conformational states become available, application of these dihedral angle probability distributions must be limited to problems, such as homology modeling, in which only a limited portion of the backbone (e.g., surface loops) must be explored. © 1996 John Wiley & Sons, Inc.     

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.     

Three‐dimensional structure of cyclic antibiotic teicoplanin aglycone using NMR distance and dihedral angle restraints in a DMSO solvation model

The three‐dimensional solution conformation of teicoplanin aglycone was determined using NMR spectroscopy. A combination of NOE and dihedral angle restraints in a DMSO solvation model was used to calculate an ensemble of structures having a root mean square deviation of 0.17 Å. The structures were generated using systematic searches of conformational space for optimal satisfaction of distance and dihedral angle restraints. Comparison of the NMR‐derived structure of teicoplanin aglycone with the X‐ray structure of a teicoplanin aglycone analog revealed a common backbone conformation with deviation of two aromatic side chain substituents. Experimentally determined backbone ¹³C chemical shifts showed good agreement with those computed at the density functional level of theory, providing a cross validation of the backbone conformation. The flexible portion of the molecule was consistent with the region that changes conformation to accommodate protein binding. The results showed that a hydrogen‐bonded DMSO molecule in combination with NMR‐derived restraints together enabled calculation of structures that satisfied experimental data. Copyright © 2015 John Wiley & Sons, Ltd.     

Application of torsion angle molecular dynamics for efficient sampling of protein conformations

We investigate the application of torsion angle molecular dynamics (TAMD) to augment conformational sampling of peptides and proteins. Interesting conformational changes in proteins mainly involve torsional degrees of freedom. Carrying out molecular dynamics in torsion space does not only explicitly sample the most relevant degrees of freedom, but also allows larger integration time steps with elimination of the bond and angle degrees of freedom. However, the covalent geometry needs to be fixed during internal coordinate dynamics, which can introduce severe distortions to the underlying potential surface in the extensively parameterized modern Cartesian-based protein force fields. A "projection" approach (Katritch et al. J Comput Chem 2003, 24, 254-265) is extended to construct an accurate internal coordinate force field (ICFF) from a source Cartesian force field. Torsion crossterm corrections constructed from local molecular fragments, together with softened van der Waals and electrostatic interactions, are used to recover the potential surface and incorporate implicit bond and angle flexibility. MD simulations of dipeptide models demonstrate that full flexibility in both the backbone phi/psi and side chain chi1 angles are virtually restored. The efficacy of TAMD in enhancing conformational sampling is then further examined by folding simulations of small peptides and refinement experiments of protein NMR structures. The results show that an increase of several fold in conformational sampling efficiency can be reliably achieved. The current study also reveals some complicated intrinsic properties of internal coordinate dynamics, beyond energy conservation, that can limit the maximum size of the integration time step and thus the achievable gain in sampling efficiency.     

Triosmium clusters on a support: determination of structure by X-ray absorption spectroscopy and high-resolution microscopy

The structures of small, robust metal clusters on a solid support were determined by a combination of spectroscopic and microscopic methods: extended X‐ray absorption fine structure (EXAFS) spectroscopy, scanning transmission electron microscopy (STEM), and aberration‐corrected STEM. The samples were synthesized from [Os₃(CO)₁₂] on MgO powder to provide supported clusters intended to be triosmium. The results demonstrate that the supported clusters are robust in the absence of oxidants. Conventional high‐angle annular dark‐field (HAADF) STEM images demonstrate a high degree of uniformity of the clusters, with root‐mean‐square (rms) radii of 2.03±0.06 Å. The EXAFS Os? Os coordination number of 2.1±0.4 confirms the presence of triosmium clusters on average and correspondingly determines an average rms cluster radius of 2.02±0.04 Å. The high‐resolution STEM images show the individual Os atoms in the clusters, confirming the triangular structures of their frames and determining Os? Os distances of 2.80±0.14 Å, matching the EXAFS value of 2.89±0.06 Å. IR and EXAFS spectra demonstrate the presence of CO ligands on the clusters. This set of techniques is recommended as optimal for detailed and reliable structural characterization of supported clusters.     

Efficient sampling of protein conformational space using fast loop building and batch minimization on highly parallel computers

All‐atom sampling is a critical and compute‐intensive end stage to protein structural modeling. Because of the vast size and extreme ruggedness of conformational space, even close to the native structure, the high‐resolution sampling problem is almost as difficult as predicting the rough fold of a protein. Here, we present a combination of new algorithms that considerably speed up the exploration of very rugged conformational landscapes and are capable of finding heretofore hidden low‐energy states. The algorithm is based on a hierarchical workflow and can be parallelized on supercomputers with up to 128,000 compute cores with near perfect efficiency. Such scaling behavior is notable, as with Moore's law continuing only in the number of cores per chip, parallelizability is a critical property of new algorithms. Using the enhanced sampling power, we have uncovered previously invisible deficiencies in the Rosetta force field and created an extensive decoy training set for optimizing and testing force fields. © 2012 Wiley Periodicals, Inc.     

Hydrogen bonding in high-resolution protein structures: a new method to assess NMR protein geometry

An analysis of backbone hydrogen bonds has been performed on nine high-resolution protein X-ray crystal structures. Backbone hydrogen-bond geometry is compared in the context of X-ray crystal structure resolution. A strong correlation between the hydrogen-bond distance, R(HO), and the hydrogen-bond angle, theta(NHO), is observed when the X-ray crystal structure resolution is <1.00 A. Ab initio calculations were performed to substantiate these results. The angle and distance limits found in our correlation for the backbone hydrogen-bond geometry can be used to evaluate the quality of protein structures and for further NMR structure refinement.     

Crystal structure prediction of flexible molecules using parallel genetic algorithms with a standard force field

This article describes the application of our distributed computing framework for crystal structure prediction (CSP) the modified genetic algorithms for crystal and cluster prediction (MGAC), to predict the crystal structure of flexible molecules using the general Amber force field (GAFF) and the CHARMM program. The MGAC distributed computing framework includes a series of tightly integrated computer programs for generating the molecule's force field, sampling crystal structures using a distributed parallel genetic algorithm and local energy minimization of the structures followed by the classifying, sorting, and archiving of the most relevant structures. Our results indicate that the method can consistently find the experimentally known crystal structures of flexible molecules, but the number of missing structures and poor ranking observed in some crystals show the need for further improvement of the potential. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2009