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.     

Loop problem in proteins: Developments on Monte Carlo simulated annealing approach

Calculations of loop segments in bovine pancreatic trypsin inhibitor starting from random conformations are more efficient, reproducible, and reliable due to several program enhancements. Monte Carlo simulated annealing (MCSA) calculations of a five-residue α-helix N-terminus segment (H5) and β-strand segment (B5) in this study are compared to the corresponding loop calculations in our previous study. Characteristics of the calculations are: the lowest final total energy conformations (LECs) are within 5 kcal/mol; the average backbone deviations of the computed segments from the native X-ray conformations are 0.43 ± 0.15 Å for H5 and 0.68 ± 0.20 Å for B5; and all the native backbone-backbone hydrogen bonds (H bonds) are present in the best LECs. Compared to the previous study, the H5 and B5 calculations are about 3 and 24 times more efficient, respectively. In the analysis of the best H5 simulated annealing run, backbone-backbone H bonds appear between RT = 4 and 70 kcal/mol, where RT is the Boltzmann temperature factor. H bonds that involve side chains appear in the RT = 1–10 kcal/mol range. Program enhancements implemented are varying main chain versus side chain dihedral angle selection rate, varying ϕ/ψ and χ₁/χ₂ dihedral angles in pairs, the use of main chain and side chain rotamer libraries, and varying the location of the segment origin. © 1996 by John Wiley & Sons, Inc.     

GRID: A high‐resolution protein structure refinement algorithm

The energy‐based refinement of protein structures generated by fold prediction algorithms to atomic‐level accuracy remains a major challenge in structural biology. Energy‐based refinement is mainly dependent on two components: (1) sufficiently accurate force fields, and (2) efficient conformational space search algorithms. Focusing on the latter, we developed a high‐resolution refinement algorithm called GRID. It takes a three‐dimensional protein structure as input and, using an all‐atom force field, attempts to improve the energy of the structure by systematically perturbing backbone dihedrals and side‐chain rotamer conformations. We compare GRID to Backrub, a stochastic algorithm that has been shown to predict a significant fraction of the conformational changes that occur with point mutations. We applied GRID and Backrub to 10 high‐resolution (≤ 2.8 Å) crystal structures from the Protein Data Bank and measured the energy improvements obtained and the computation times required to achieve them. GRID resulted in energy improvements that were significantly better than those attained by Backrub while expending about the same amount of computational resources. GRID resulted in relaxed structures that had slightly higher backbone RMSDs compared to Backrub relative to the starting crystal structures. The average RMSD was 0.25 ± 0.02 Å for GRID versus 0.14 ± 0.04 Å for Backrub. These relatively minor deviations indicate that both algorithms generate structures that retain their original topologies, as expected given the nature of the algorithms. © 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     

sDFIRE: Sequence‐specific statistical energy function for protein structure prediction by decoy selections

An important unsolved problem in molecular and structural biology is the protein folding and structure prediction problem. One major bottleneck for solving this is the lack of an accurate energy to discriminate near‐native conformations against other possible conformations. Here we have developed sDFIRE energy function, which is an optimized linear combination of DFIRE (the Distance‐scaled Finite Ideal gas Reference state based Energy), the orientation dependent (polar‐polar and polar‐nonpolar) statistical potentials, and the matching scores between predicted and model structural properties including predicted main‐chain torsion angles and solvent accessible surface area. The weights for these scoring terms are optimized by three widely used decoy sets consisting of a total of 134 proteins. Independent tests on CASP8 and CASP9 decoy sets indicate that sDFIRE outperforms other state‐of‐the‐art energy functions in selecting near native structures and in the Pearson's correlation coefficient between the energy score and structural accuracy of the model (measured by TM‐score). © 2016 Wiley Periodicals, Inc.     

(−)‐3,7‐Dioxo‐5β‐cholanic acid: dual hydrogen‐bonding modes in a diketonic bile‐acid derivative

The asymmetric unit of the title compound, C₂₄H₃₆O₄, contains three mol­ecules, all differing in their side‐chain conformations and all linked by hydrogen bonding confined entirely within a three‐mol­ecule block. One connection is of the acid‐to‐ketone type [O⋯O = 2.7055 (19) Å and O—H⋯O = 180°] and the other involves carboxyl pairing [O⋯O = 2.6485 (18) and 2.6598 (18) Å, and O—H⋯O = 168 and 174°]. Numerous inter­molecular C—H⋯O close contacts connect neighbouring mol­ecules.     

The SAAP force field: Development of the single amino acid potentials for 20 proteinogenic amino acids and Monte Carlo molecular simulation for short peptides

Molecular simulation by using force field parameters has been widely applied in the fields of peptide and protein research for various purposes. We recently proposed a new all‐atom protein force field, called the SAAP force field, which utilizes single amino acid potentials (SAAPs) as the fundamental elements. In this article, whole sets of the SAAP force field parameters in vacuo, in ether, and in water have been developed by ab initio calculation for all 20 proteinogenic amino acids and applied to Monte Carlo molecular simulation for two short peptides. The side‐chain separation approximation method was employed to obtain the SAAP parameters for the amino acids with a long side chain. Monte Carlo simulation for Met‐enkephalin (CHO‐Tyr‐Gly‐Gly‐Phe‐Met‐NH₂) by using the SAAP force field revealed that the conformation in vacuo is mainly controlled by strong electrostatic interactions between the amino acid residues, while the SAAPs and the interamino acid Lennard‐Jones potentials are predominant in water. In ether, the conformation would be determined by the combination of the three components. On the other hand, the SAAP simulation for chignolin (H‐Gly‐Tyr‐Asp‐Pro‐Glu‐Thr‐Gly‐Thr‐Trp‐Gly‐OH) reasonably reproduced a native‐like β‐hairpin structure in water although the C‐terminal and side‐chain conformations were different from the native ones. It was suggested that the SAAP force field is a useful tool for analyzing conformations of polypeptides in terms of intrinsic conformational propensities of the single amino acid units. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2009     

New energy terms for reduced protein models implemented in an off‐lattice force field

Parameterization and test calculations of a reduced protein model with new energy terms are presented. The new energy terms retain the steric properties and the most significant degrees of freedom of protein side chains in an efficient way using only one to three virtual atoms per amino acid residue. The energy terms are implemented in a force field containing predefined secondary structure elements as constraints, electrostatic interaction terms, and a solvent‐accessible surface area term to include the effect of solvation. In the force field the main‐chain peptide units are modeled as electric dipoles, which have constant directions in α‐helices and β‐sheets and variable conformation‐dependent directions in loops. Protein secondary structures can be readily modeled using these dipole terms. Parameters of the force field were derived using a large set of experimental protein structures and refined by minimizing RMS errors between the experimental structures and structures generated using molecular dynamics simulations. The final average RMS error was 3.7 Å for the main‐chain virtual atoms (C_α atoms) and 4.2 Å for all virtual atoms for a test set of 10 proteins with 58–294 amino acid residues. The force field was further tested with a substantially larger test set of 608 proteins yielding somewhat lower accuracy. The fold recognition capabilities of the force field were also evaluated using a set of 27,814 misfolded decoy structures. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1229–1242, 2001     

Predicting helical hairpins from sequences by Monte Carlo simulations

The key problem in polypeptide‐structure prediction is with regard to thermodynamics. Two factors limit prediction in ab initio computer simulations. First, the thermodynamically dominant conformations must be found from an extremely large number of possible conformations. Second, these low‐energy forms must deviate little from the experimental structures. Here, we report on the application of the diffusion‐controlled Monte Carlo approach to predict four α‐helical hairpins with 34–38 residues by global optimization, using an energy optimized on other supersecondary structures. A total of seven simulations is carried out for each protein starting from fully extended conformations. Three proteins are correctly folded (within 3.0 Å rms from the experimental structures), but the fourth protein cannot distinguish between several equienergetic conformations. Possible improvement of the energy model is suggested. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 582–589, 2000     

MCCE2: Improving protein pKa calculations with extensive side chain rotamer sampling

Multiconformation continuum electrostatics (MCCE) explores different conformational degrees of freedom in Monte Carlo calculations of protein residue and ligand pK_as. Explicit changes in side chain conformations throughout a titration create a position dependent, heterogeneous dielectric response giving a more accurate picture of coupled ionization and position changes. The MCCE2 methods for choosing a group of input heavy atom and proton positions are described. The pK_as calculated with different isosteric conformers, heavy atom rotamers and proton positions, with different degrees of optimization are tested against a curated group of 305 experimental pK_as in 33 proteins. QUICK calculations, with rotation around Asn and Gln termini, sampling His tautomers and torsion minimum hydroxyls yield an RMSD of 1.34 with 84% of the errors being <1.5 pH units. FULL calculations adding heavy atom rotamers and side chain optimization yield an RMSD of 0.90 with 90% of the errors <1.5 pH unit. Good results are also found for pK_as in the membrane protein bacteriorhodopsin. The inclusion of extra side chain positions distorts the dielectric boundary and also biases the calculated pK_as by creating more neutral than ionized conformers. Methods for correcting these errors are introduced. Calculations are compared with multiple X‐ray and NMR derived structures in 36 soluble proteins. Calculations with X‐ray structures give significantly better pK_as. Results with the default protein dielectric constant of 4 are as good as those using a value of 8. The MCCE2 program can be downloaded from http://www.sci.ccny.cuny.edu/～mcce . © 2009 Wiley Periodicals, Inc. J Comput Chem, 2009     

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.     

Struktur und magnetische Eigenschaften von Bis{3‐amino‐1,2,4‐triazolium(1+)}pentafluoromanganat(III): (3‐atriazH)2[MnF5]

Structure and Magnetic Properties of Bis{3‐amino‐1,2,4‐triazolium(1+)}pentafluoromanganate(III): (3‐atriazH)₂[MnF₅] The crystal structure of (3‐atriazH)₂[MnF₅], space group P1, Z = 4, a = 8.007(1) Å, b = 11.390(1) Å, c = 12.788(1) Å, α = 85.19(1)°, β = 71.81(1)°, γ = 73.87(1)°, R = 0.034, is built by octahedral trans‐chain anions [MnF₅]^2–_∞ separated by the mono‐protonated organic amine cations. The [MnF₆] octahedra are strongly elongated along the chain axis (<Mn–F_ax> 2.135 Å, <Mn–F_eq> 1.842 Å), mainly due to the Jahn‐Teller effect, the chains are kinked with an average bridge angle Mn–F–Mn = 139.3°. Below 66 K the compound shows 1D‐antiferromagnetism with an exchange energy of J/k = –10.8 K. 3D ordering is observed at T_N = 9.0 K. In spite of the large inter‐chain separation of 8.2 Å a remarkable inter‐chain interaction with |J′/J| = 1.3 · 10^–5 is observed, mediated probably by H‐bonds. That as well as the less favourable D/J ratio of 0.25 excludes the existence of a Haldene phase possible for Mn³⁺ (S = 2).     

Glycosyl‐Substituted Dicarboxylates as Detergents for the Extraction,Overstabilization, and Crystallization of Membrane Proteins

To tackle the problems associated with membrane protein (MP) instability in detergent solutions, we designed a series of glycosyl‐substituted dicarboxylate detergents (DCODs) in which we optimized the polar head to clamp the membrane domain by including, on one side, two carboxyl groups that form salt bridges with basic residues abundant at the membrane–cytoplasm interface of MPs and, on the other side, a sugar to form hydrogen bonds. Upon extraction, the DCODs 8 b , 8 c , and 9 b preserved the ATPase function of BmrA, an ATP‐binding cassette pump, much more efficiently than reference or recently designed detergents. The DCODs 8 a , 8 b , 8 f , 9 a , and 9 b induced thermal shifts of 20 to 29 °C for BmrA and of 13 to 21 °C for the native version of the G‐protein‐coupled adenosine receptor A_2AR. Compounds 8 f and 8 g improved the diffraction resolution of BmrA crystals from 6 to 4 Å. DCODs are therefore considered to be promising and powerful tools for the structural biology of MPs.     

Glycosyl‐Substituted Dicarboxylates as Detergents for the Extraction,Overstabilization, and Crystallization of Membrane Proteins

To tackle the problems associated with membrane protein (MP) instability in detergent solutions, we designed a series of glycosyl‐substituted dicarboxylate detergents (DCODs) in which we optimized the polar head to clamp the membrane domain by including, on one side, two carboxyl groups that form salt bridges with basic residues abundant at the membrane–cytoplasm interface of MPs and, on the other side, a sugar to form hydrogen bonds. Upon extraction, the DCODs 8 b , 8 c , and 9 b preserved the ATPase function of BmrA, an ATP‐binding cassette pump, much more efficiently than reference or recently designed detergents. The DCODs 8 a , 8 b , 8 f , 9 a , and 9 b induced thermal shifts of 20 to 29 °C for BmrA and of 13 to 21 °C for the native version of the G‐protein‐coupled adenosine receptor A_2AR. Compounds 8 f and 8 g improved the diffraction resolution of BmrA crystals from 6 to 4 Å. DCODs are therefore considered to be promising and powerful tools for the structural biology of MPs.     

Exploring hierarchical refinement techniques for induced fit docking with protein and ligand flexibility

We present a series of molecular‐mechanics‐based protein refinement methods, including two novel ones, applied as part of an induced fit docking procedure. The methods used include minimization; protein and ligand sidechain prediction; a hierarchical ligand placement procedure similar to a‐priori protein loop predictions; and a minimized Monte Carlo approach using normal mode analysis as a move step. The results clearly indicate the importance of a proper opening of the active site backbone, which might not be accomplished when the ligand degrees of freedom are prioritized. The most accurate method consisted of the minimized Monte Carlo procedure designed to open the active site followed by a hierarchical optimization of the sidechain packing around a mobile flexible ligand. The methods have been used on a series of 88 protein‐ligand complexes including both cross‐docking and apo‐docking members resulting in complex conformations determined to within 2.0 Å heavy‐atom RMSD in 75% of cases where the protein backbone rearrangement upon binding is less than 1.0 Å α‐carbon RMSD. We also demonstrate that physics‐based all‐atom potentials can be more accurate than docking‐style potentials when complexes are sufficiently refined. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

A new method for side-chain conformation prediction using a Hopfield network and reproduced rotamers

We present a new side-chain prediction method based on energy minimization using a Hopfield network, focusing on the buried residues of proteins. In this method, the network is composed of automata assigned to each rotamer to restrict side-chain conformational space. We reproduced a rotamer library that enabled us to more widely cover the space for side-chain conformations than those previously produced. The accuracy of the side-chain modeling was estimated by three standards: root mean square deviations (rmsds) between the modeled and the crystal structures, the percentages of correctly predicted side-chain torsion angles, and the percentages of correctly predicted hydrogen bonds. The average rmsd for buried side chains of 21 proteins was 1.10 Å. The value was almost always improved relative to the previous works. The percentage of side-chain X₁ angles for buried residues was 87.3%. By considering the hydrogen bond energy, the average percentage of correctly predicted hydrogen bonds rose from 33% without hydrogen bond energy to 52% with the bond energy. We applied this method to homology modeling, where the protein backbone used to predict side-chain conformations deviates from the correct conformation, and could predict side-chain conformations as correctly as those using the correct backbones. © 1996 by John Wiley & Sons, Inc.