THEORETICAL APPROACHES TO PROTEIN STRUCTURE-FUNCTION ANALYSIS (Ⅰ)——DIRECTED PERTURBATION CONFORMATIONAL ANALYSIS

A new computational technique called directed perturbation conformational analysis has been developed for use in protein model building and structure-function studies. Designed to perform an efficient local search of a macromolecular potential energy surface, the algorithm can be used to locate multiple energy minimum conformers via low energy transition state structures from a single starting or trial structure. The algorithm contains developments to stabilize transition state optimizations for systems described by many degrees of freedom displaying anharmonic potential energy surfaces. It has been found to be efficient in the generation of alternative equilibrium structures from a given trial structure when compared with those generated from a standard molecular dynamics simulation of N-acetyl, N'-methyl-deca-L-alaninamide.     

Computational protocols for prediction of solute NMR relative chemical shifts. a case study of L-tryptophan in aqueous solution

In this study, we have applied two different spanning protocols for obtaining the molecular conformations of L-tryptophan in aqueous solution, namely a molecular dynamics simulation and a molecular mechanics conformational search with subsequent geometry re-optimization of the stable conformers using a quantum mechanically based method. These spanning protocols represent standard ways of obtaining a set of conformations on which NMR calculations may be performed. The results stemming from the solute-solvent configurations extracted from the MD simulation at 300 K are found to be inferior to the results stemming from the conformations extracted from the MM conformational search in terms of replicating an experimental reference as well as in achieving the correct sequence of the NMR relative chemical shifts of L-tryptophan in aqueous solution. We find this to be due to missing conformations visited during the molecular dynamics run as well as inaccuracies in geometrical parameters generated from the classical molecular dynamics simulations.     

A normal mode-based geometric simulation approach for exploring biologically relevant conformational transitions in proteins

A three-step approach for multiscale modeling of protein conformational changes is presented that incorporates information about preferred directions of protein motions into a geometric simulation algorithm. The first two steps are based on a rigid cluster normal-mode analysis (RCNMA). Low-frequency normal modes are used in the third step (NMSim) to extend the recently introduced idea of constrained geometric simulations of diffusive motions in proteins by biasing backbone motions of the protein, whereas side-chain motions are biased toward favorable rotamer states. The generated structures are iteratively corrected regarding steric clashes and stereochemical constraint violations. The approach allows performing three simulation types: unbiased exploration of conformational space; pathway generation by a targeted simulation; and radius of gyration-guided simulation. When applied to a data set of proteins with experimentally observed conformational changes, conformational variabilities are reproduced very well for 4 out of 5 proteins that show domain motions, with correlation coefficients r > 0.70 and as high as r = 0.92 in the case of adenylate kinase. In 7 out of 8 cases, NMSim simulations starting from unbound structures are able to sample conformations that are similar (root-mean-square deviation = 1.0-3.1 ?) to ligand bound conformations. An NMSim generated pathway of conformational change of adenylate kinase correctly describes the sequence of domain closing. The NMSim approach is a computationally efficient alternative to molecular dynamics simulations for conformational sampling of proteins. The generated conformations and pathways of conformational transitions can serve as input to docking approaches or as starting points for more sophisticated sampling techniques.     

Theoretical study of copper binding to GHK peptide

We report ligand field molecular mechanics, density functional theory and semi-empirical studies on the binding of Cu(II) to GlyHisLys (GHK) peptide. Following exhaustive conformational searching using molecular mechanics, we show that relative energy and geometry of conformations are in good agreement between GFN2-xTB semi-empirical and B3LYP-D DFT levels. Conventional molecular dynamics simulation of Cu-GHK shows the stability of the copper-peptide binding over 100 ps trajectory. Four equatorial bonds in 3N1O coordination remain stable throughout simulation, while a fifth in apical position from C-terminal carboxylate is more fluxional. We also show that the automated conformer and rotamer search algorithm CREST is able to correctly predict the metal binding position from a starting point consisting of separated peptide, copper and water.     

Kinetic barriers in the isomerization of substituted ureas: implications for computer-aided drug design

Urea derivatives are ubiquitously found in many chemical disciplines. N,N′-substituted ureas may show different conformational preferences depending on their substitution pattern. The high energetic barrier for isomerization of the cis and trans state poses additional challenges on computational simulation techniques aiming at a reproduction of the biological properties of urea derivatives. Herein, we investigate energetics of urea conformations and their interconversion using a broad spectrum of methodologies ranging from data mining, via quantum chemistry to molecular dynamics simulation and free energy calculations. We find that the inversion of urea conformations is inherently slow and beyond the time scale of typical simulation protocols. Therefore, extra care needs to be taken by computational chemists to work with appropriate model systems. We find that both knowledge-driven approaches as well as physics-based methods may guide molecular modelers towards accurate starting structures for expensive calculations to ensure that conformations of urea derivatives are modeled as adequately as possible.     

RNA unrestrained molecular dynamics ensemble improves agreement with experimental NMR data compared to single static structure: a test case

Nuclear magnetic resonance (NMR) provides structural and dynamic information reflecting an average, often non-linear, of multiple solution-state conformations. Therefore, a single optimized structure derived from NMR refinement may be misleading if the NMR data actually result from averaging of distinct conformers. It is hypothesized that a conformational ensemble generated by a valid molecular dynamics (MD) simulation should be able to improve agreement with the NMR data set compared with the single optimized starting structure. Using a model system consisting of two sequence-related self-complementary ribonucleotide octamers for which NMR data was available, 0.3 ns particle mesh Ewald MD simulations were performed in the AMBER force field in the presence of explicit water and counterions. Agreement of the averaged properties of the molecular dynamics ensembles with NMR data such as homonuclear proton nuclear Overhauser effect (NOE)-based distance constraints, homonuclear proton and heteronuclear ¹H–³¹P coupling constant (J) data, and qualitative NMR information on hydrogen bond occupancy, was systematically assessed. Despite the short length of the simulation, the ensemble generated from it agreed with the NMR experimental constraints more completely than the single optimized NMR structure. This suggests that short unrestrained MD simulations may be of utility in interpreting NMR results. As expected, a 0.5 ns simulation utilizing a distance dependent dielectric did not improve agreement with the NMR data, consistent with its inferior exploration of conformational space as assessed by 2-D RMSD plots. Thus, ability to rapidly improve agreement with NMR constraints may be a sensitive diagnostic of the MD methods themselves.     

Sequence-dependent conformational energy of DNA derived from molecular dynamics simulations: toward understanding the indirect readout mechanism in protein-DNA recognition

Sequence dependence of DNA conformation plays a crucial role in its recognition by proteins and ligands. To clarify the relationship between sequence and conformation, it is necessary to quantify the conformational energy and specificity of DNA. Here, we make a systematic analysis of dodecamer DNA structures including all the 136 unique tetranucleotide sequences at the center by molecular dynamics simulations. Using a simplified conformational model with six parameters to describe the geometry of adjacent base pairs and harmonic potentials along these coordinates, we estimated the equilibrium conformational parameters and the harmonic potentials of mean force for the central base-pair steps from many trajectories of the simulations. This enabled us to estimate the conformational energy and the specificity for any given DNA sequence and structure. We tested our method by using sequence-structure threading to estimate the conformational energy and the Z-score as a measure of specificity for many B-DNA and A-DNA crystal structures. The average Z-scores were negative for both kinds of structures, indicating that the potential of mean force from the simulation is capable of predicting sequence specificity for the crystal structures and that it may be used to study the sequence specificity of both types of DNA. We also estimated the positional distribution of conformational energy and Z-score within DNA and showed that they are strongly position dependent. This analysis enabled us to identify particular conformations responsible for the specificity. The presented results will provide an insight into the mechanisms of DNA sequence recognition by proteins and ligands.     

Molecular dynamics study of the influence of solvents on the chiral discrimination of alanine enantiomers by β-cyclodextrin

The influence of solvents on the separation of alanine enantiomers using β-cyclodextrin as a chiral selector was studied by means of a molecular dynamics simulation at a constant temperature. The potential energy of the interaction is modelled by the AMBER force field, where different polar and non-polar solvents are represented by the dielectric constant ? and two configurations for the amino acid derived from its electric charge distribution: the AMBER data base or its zwitterion state. The l enantiomer has more positions inside the cavity of a β-cyclodextrin where it is more stable than the d-enantiomer in vacuo and solution, except for solvents such as hydrocarbons in which most positions of the d-alanine inside and outside the cavity are more stable. In all cases, the greatest differences are located near the cavity walls. Molecular dynamics simulations show that Ala is able to form inclusion complexes with β-cyclodextrin in vacuo and in solvents such as hydrocarbons, benzene, acetone, ethanol or water. The chiral discrimination of Ala by β-cyclodextrin is mainly due to the adaptation of the guest to the host in the presence of non-polar agents, whereas the nonbonded interaction is the driving force for zwitterions. The elution order depends on the type of organic modifiers while a reversal of the enantiomeric elution order can be observed in solvents with higher dielectric constants.     

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     

Thermodynamics and kinetics of aggregation for the GNNQQNY peptide

The energy landscape of the monomer and dimer are explored for the amyloidogenic heptapeptide GNNQQNY from the N-terminal prion-determining domain of the yeast protein Sup35. The peptide is modeled by a united-atom potential and an implicit solvent representation. Replica exchange molecular dynamics is used to explore the conformational space, and discrete path sampling is employed to investigate the pathways that interconvert the most populated minima on the free energy surfaces. For the monomer, we find a rapid fluctuation between four different conformations, where a geometry intermediate between compact and extended structures is the most thermodynamically favorable. The GNNQQNY dimer forms three stable sheet structures, namely in-register parallel, off-register parallel, and antiparallel. The antiparallel dimer is stabilized by strong electrostatic interactions resulting from interpeptide hydrogen bonds, which restrict its conformational flexibility. The in-register parallel dimer, which is close to the amyloid beta-sheet structure, has fewer interpeptide hydrogen bonds, making hydrophobic interactions more important and increasing the conformational entropy compared to the antiparallel sheet. The estimated two-state rate constants indicate that the formation of dimers from monomers is fast and that the dimers are kinetically stable against dissociation at room temperature. Interconversions between the different dimers are feasible processes and are more likely than dissociation.     

Energy minimization of rigid-geometry polypeptides with exactly closed disulfide loops

A method has been developed for minimizing the energy of a polypeptide with rigid geometry while keeping all disulfide loops closed exactly. Exact closure of disulfide loops implies that some dihedral angles become implicit functions of the remaining dihedral angles in the polypeptide; the efficacy of the method is related to the manner in which the implicitly defined dihedral angles are chosen. The method has been used to find minimum-energy conformations of bovine pancreatic trypsin inhibitor, ribonuclease A, crambin, the defensin HNP3 dimer, and ω-conotoxin. For the first two proteins, the starting conformations for energy minimization had been derived previously from crystal structures using pseudopotentials to keep the disulfide loops almost closed. Starting conformations for the remaining three proteins were derived from their crystal or NMR structures by similar procedures. In all cases, the energy-minimized structures had a significantly and, in some cases, substantially, lower energy than the starting structures. The RMS deviations between the exactly closed energy- minimized structures and the crystal or NMR structures from which they were derived ranged from 0.9 Å to 1.9 Å, suggesting that the computed structures can serve as “regularized” native structures for these proteins. The energy of a ribonuclease derivative lacking the 65–72 disulfide bridge was minimized using the procedure; the result showed that this derivative has a low-energy structure with a conformation very close to that of native ribonuclease, and is consistent with its postulated role in the folding of ribonuclease. These results offer strong support for the validity of the rigid-geometry model in the studies of the conformational energy of proteins. © 1997 by John Wiley & Sons, Inc.     

Dependency of ligand free energy landscapes on charge parameters and solvent models

We performed replica-exchange molecular dynamics (REMD) simulations of six ligands to examine the dependency of their free energy landscapes on charge parameters and solvent models. Six different charge parameter sets for each ligand were first generated by RESP and AM1-BCC methods using three different conformations independently. RESP charges showed some conformational dependency. On the other hand, AM1-BCC charges did not show conformational dependency and well reproduced the overall trend of RESP charges. The free energy landscapes obtained from the REMD simulations of ligands in vacuum, Generalized-Born (GB), and TIP3P solutions were then analyzed. We found that even small charge differences can produce qualitatively different landscapes in vacuum condition, but the differences tend to be much smaller under GB and TIP3P conditions. The simulations in the GB model well reproduced the landscapes in the TIP3P model using only a fraction of the computational cost. The protein-bound ligand conformations were rarely the global minimum states, but similar conformations were found to exist in aqueous solution without proteins in regions close to the global minimum, local minimum or intermediate states.     

Are isolated nucleic acid bases really planar? A Car-Parrinello molecular dynamics study

Car-Parrinello molecular dynamics simulations of the flexibility of isolated DNA bases have been carried out. The comparison of lowest ring out-of-plane vibrations calculated by using MP2/cc-pvdz and BLYP/PW methods reveals that the DFT method with the plane wave basis set reasonably reproduces out-of-plane deformability of the pyrimidine ring in nucleic acid bases and could be used for reliable modeling of conformational flexibility of nucleobases. The conformational phase space of pyrimidine rings in thymine, cytosine, guanine, and adenine has been investigated by using the ab initio Car-Parrinello molecular dynamics method. It is demonstrated that all nucleic acid bases are highly flexible molecules and possess a nonplanar effective conformation of the pyrimidine ring despite the fact that the planar geometry corresponds to a minimum on the potential energy surface. The population of the planar geometry of the pyrimidine ring does not exceed 30%. Among the nonplanar conformations of the pyrimidine rings, the boat-like and half-chair conformations are the most populated.     

Quantum mechanical calculations of tryptophan and comparison with conformations in native proteins

We report a detailed analysis of the potential energy surface of N-acetyl-l-tryptophan-N-methylamide, (NATMA) both in the gas phase and in solution. The minima are identified using the density-functional-theory (DFT) with the 6-31g(d) basis set. The full potential energy surface in terms of torsional angles is spanned starting from various initial configurations. We were able to locate 77 distinct L-minima. The calculated energy maps correspond to the intrinsic conformational propensities of the individual NATMA molecule. We show that these conformations are essentially similar to the conformations of tryptophan in native proteins. For this reason, we compare the results of DFT calculations in the gas and solution phases with native state conformations of tryptophan obtained from a protein library. In native proteins, tryptophan conformations have strong preferences for the beta sheet, right-handed helix, tight turn, and bridge structures. The conformations calculated by DFT, the solution-phase results in particular, for the single tryptophan residue are in agreement with native state values obtained from the Protein Data Bank.     

Polystyrene models. II. Ab initio study of isobutylbenzene

The structure and stability of the various conformations of isobutylbenzene are studied using ab initio molecular orbital theory. The calculations show that coupling between the structural units is important. The results indicate that complete geometry optimization of the stable and transition structures of isobutylbenzene produce significant changes in geometrical parameters and charge distributions of this molecule when compared with the corresponding results obtained using the rigid-rotor approximation. These changes are particularly noticeable in one of the gauche conformations and in transition structures of isobutylbenzene generated by the phenyl group rotation. For polystyrene, these results present evidence that there is a strong coupling between the chain-backbone folding and the rotation of the phenyl group. Multidimensional potential energy surfaces are displayed using a topological representation. © 1992 John Wiley & Sons, Inc.     

Implementation of a protein reduced point charge model toward molecular dynamics applications

A reduced point charge model was developed in a previous work from the study of extrema in smoothed charge density distribution functions generated from the Amber99 molecular electrostatic potential. In the present work, such a point charge distribution is coupled with the Amber99 force field and implemented in the program TINKER to allow molecular dynamics (MD) simulations of proteins. First applications to two polypeptides that involve α-helix and β-sheet motifs are analyzed and compared to all-atom MD simulations. Two types of coarse-grained (CG)-based trajectories are generated using, on one hand, harmonic bond stretching terms and, on the other hand, distance restraints. Results show that the use of the unrestrained CG conditions are sufficient to preserve most of the secondary structure characteristics but restraints lead to a better agreement between CG and all-atom simulation results such as rmsd, dipole moment, and time-dependent mean square deviation functions.     

蒙特卡洛模拟退火与距离限制相结合的方法——在多肽溶液构象分析中的应用

Distance geometry and molecular dynamics are currently employed in determining molecular structures with interatomic distances from NMR NOESY experiment. Because of the flexibility of peptide, distances obtained from NMR are usually not sufficient to confine its structure. Both distance geometry and molecular dynamics will bias in the conformational space at this circumstance. Constraint Monte Carlo simulated annealing was established to solve this problem. Distance constraints were included into the ECEPP/2 force field by introducing a harmonic energy term. Conformational analysis of a pentapeptide with eight interatomic distances from NMR was carried out as a test. By comparison of the 100 conformers obtained from constraint simulated annealing and the 100 conformers from distance geometry calculation, it was found that constraint simulated annealing can cover the outcomes of distance geometry and at the same time give more con-formers fitting to the experimental data. The result shows that constraint Monte-Carlo simulated annealing is more valid in constructing peptide structures from NMR distances than currently employed methods when no sufficient distances from NMR are available.     

Conformational sampling and ensemble generation by molecular dynamics simulations: 18-Crown-6 as a test case

Using the crown ether 18-crown-6 as a test system, molecular dynamics has been evaluated as a technique for conformational searching and thermodynamic ensemble generation. By running a series of 200 ps and 2 ns simulations, an “optimum” temperature range for conformational searching, i.e., the temperature at which one finds the largest number of low energy structures, was demonstrated to be dependent on the time interval at which one examines the structure. By considering conformational degeneracy and entropy with the rigid rotor harmonic oscillator approximation we have been able to demonstrate that the ensemble generated approaches thermodynamic equilibrium in about 6 ns of simulation. To our knowledge this is the first time this has been demonstrated for a complex organic molecule and it highlights the power and usefulness of molecular dynamics as a method for thermodynamic ensemble generation and conformational searching.     

Can a physics‐based,all‐atom potential find a protein's native structure among misfolded structures? I. Large scale AMBER benchmarking

Recent work has shown that physics-based, all-atom energy functions (AMBER, CHARMM, OPLS-AA) and local minimization, when used in scoring, are able to discriminate among native and decoy structures. Yet, there have been only few instances reported of the successful use of physics based potentials in the actual refinement of protein models from a starting conformation to one that ends in structures, which are closer to the native state. An energy function that has a global minimum energy in the protein's native state and a good correlation between energy and native-likeness should be able to drive model structures closer to their native structure during a conformational search. Here, the possible reasons for the discrepancy between the scoring and refinement results for the case of AMBER potential are examined. When the conformational search via molecular dynamics is driven by the AMBER potential for a large set of 150 nonhomologous proteins and their associated decoys, often the native minimum does not appear to be the lowest free energy state. Ways of correcting the potential function in order to make it more suitable for protein model refinement are proposed.