Increasing the precision of comparative models with YASARA NOVA--a self-parameterizing force field

One of the conclusions drawn at the CASP4 meeting in Asilomar was that applying various force fields during refinement of template-based models tends to move predictions in the wrong direction, away from the experimentally determined coordinates. We have derived an all-atom force field aimed at protein and nucleotide optimization in vacuo (NOVA), which has been specifically designed to avoid this problem. NOVA resembles common molecular dynamics force fields but has been automatically parameterized with two major goals: (i) not to make high resolution X-ray structures worse and (ii) to improve homology models built by WHAT IF. Force-field parameters were not required to be physically correct; instead, they were optimized with random Monte Carlo moves in force-field parameter space, each one evaluated by simulated annealing runs of a 50-protein optimization set. Errors inherent to the approximate force-field equation could thus be canceled by errors in force-field parameters. Compared with the optimization set, the force field did equally well on an independent validation set and is shown to move in silico models closer to reality. It can be applied to modeling applications as well as X-ray and NMR structure refinement. A new method to assign force-field parameters based on molecular trees is also presented. A NOVA server is freely accessible at http://www.yasara.com/servers     

A geometry force field which converts low-resolution X-ray models to structures with properties found at ultra high resolution

A geometry optimization force field was developed using ultra high-resolution structures and tested using high- and low-resolution X-ray structures. Protein and small molecule X-ray data was used. When applied to ultra high-resolution structures the force field conserves the internal geometry and local strain energy. When applied to low-resolution structures there is a small change in geometry accompanied by a large drop in local strain energy. Although optimization causes only small structural changes in low-resolution X-ray models, it dramatically modifies profiles for hydrogen bonding, Van der Waals contact, bonded geometry, and local strain energy, making them almost indistinguishable from those found at high resolution. Further insight into the effect of the force field was obtained by comparing geometries of homologous proteins before and after geometry optimization. Optimization causes homologous regions of structures to become similar in internal geometry and energies. Once again, the changes only require small atomic movements. These findings provide insights into the structure of molecular complexes. The new force field contains only short-range interatomic potential functions. Its effectiveness shows that local geometries are determined by short-range interactions which are well modeled by the force field. Potential applications of this study include detection of possible structural errors, correction of errors with minimal change in geometry, improved understanding and prediction of the effects of modifying ligands or proteins, and computational addition of structural water.     

Refinement of the AMBER force field for nucleic acids: improving the description of alpha/gamma conformers

We present here the parmbsc0 force field, a refinement of the AMBER parm99 force field, where emphasis has been made on the correct representation of the alpha/gamma concerted rotation in nucleic acids (NAs). The modified force field corrects overpopulations of the alpha/gamma = (g+,t) backbone that were seen in long (more than 10 ns) simulations with previous AMBER parameter sets (parm94-99). The force field has been derived by fitting to high-level quantum mechanical data and verified by comparison with very high-level quantum mechanical calculations and by a very extensive comparison between simulations and experimental data. The set of validation simulations includes two of the longest trajectories published to date for the DNA duplex (200 ns each) and the largest variety of NA structures studied to date (15 different NA families and 97 individual structures). The total simulation time used to validate the force field includes near 1 mus of state-of-the-art molecular dynamics simulations in aqueous solution.     

Peptoid conformational free energy landscapes from implicit-solvent molecular simulations in AMBER

To test the accuracy of existing AMBER force field models in predicting peptoid conformation and dynamics, we simulated a set of model peptoid molecules recently examined by Butterfoss et al. (JACS 2009, 131, 16798-16807) using QM methods as well as three peptoid sequences with experimentally determined structures. We found that AMBER force fields, when used with a Generalized Born/Surface Area (GBSA) implicit solvation model, could accurately reproduce the peptoid torsional landscape as well as the major conformers of known peptoid structures. Enhanced sampling by replica exchange molecular dynamics (REMD) using temperatures from 300 to 800 K was used to sample over cis-trans isomerization barriers. Compared to (Nrch)5 and cyclo-octasarcosyl, the free energy of N-(2-nitro-3-hydroxyl phenyl)glycine-N-(phenyl)glycine has the most "foldable" free energy landscape, due to deep trans-amide minima dictated by N-aryl sidechains. For peptoids with (S)-N (1-phenylethyl) (Nspe) side chains, we observe a discrepancy in backbone dihedral propensities between molecular simulations and QM calculations, which may be due to force field effects or the inability to capture n --> n* interactions. For these residues, an empirical phi-angle biasing potential can "rescue" the backbone propensities seen in QM. This approach can serve as a general strategy for addressing force fields without resorting to a complete reparameterization. Overall, this study demonstrates the utility of implicit-solvent REMD simulations for efficient sampling to predict peptoid conformational landscapes, providing a potential tool for first-principles design of sequences with specific folding properties.     

Examination of the quality of various force fields and solvation models for the equilibrium simulations of GA88 and GB88

Elucidating the relationship between sequence and conformation is essential for the understanding of functions of proteins. While sharing 88 % sequence identity and differing by only seven residues, GA88 and GB88 have completely different structures and serve as ideal systems for investigating the relationship between sequence and function. Benefiting from the continuous advancement of the computational ability of modern computers, molecular dynamics (MD) simulation is now playing an increasingly important role in the study of proteins. However, the reliability of MD simulations is limited by the accuracy of the force fields and solvent model approximations. In this work, several AMBER force fields (AMBER03, AMBER99SB, AMBER12SB, AMBER14SB, AMBER96) and solvent models (TIP3P, IGB5, IGB7, IGB8) have been employed in the simulations of GA88 and GB88. The statistical results from 19 simulations show that GA88 and GB88 both adopt more compact structures than the native structures. GB88 is more stable than GA88 regardless of the force fields and solvent models utilized. Most of the simulations overestimated the salt bridge interaction. The combination of AMBER14SB force field and IGB8 solvent model shows the best overall performance in the simulations of both GA88 and GB88. AMBER03 and AMBER12SB also yield reasonable results but only in the TIP3P explicit solvent model.     

Homology modelling and molecular dynamics simulations: comparative studies of human aquaporin-1

The structures of the mammalian water transport protein Aqp1 and of its bacterial homologue GlpF enables us to test whether homology models can be used to explore relationships between structure, dynamics and function in mammalian transport proteins. Molecular dynamics simulations (totalling almost 40 ns) were performed starting from: the X-ray structure of Aqp1; a homology model of Aqp1 based on the GlpF structure; and intermediate resolution structures of Aqp1 derived from electron microscopy. Comparisons of protein RMSDs vs. time suggest that the homology models are of comparable conformational stability to the X-ray structure, whereas the intermediate resolution structures exhibit significant conformation drift. For simulations based on the X-ray structure and on homology models, the flexibility profile vs. residue number correlates well with the crystallographic B-values for each residue. In the simulations based on intermediate resolution structures, mobility of the highly conserved NPA loops is substantially higher than in the simulations based on the X-ray structure or the homology models. Pore radius profiles remained relatively constant in the X-ray and homology model simulations but showed substantial fluctuations (reflecting the higher NPA loop mobility) in the intermediate resolution simulations. The orientation of the dipoles of water molecules within the pore is of key importance in maintaining low proton permeability through Aqp1. This property seems to be quite robust to the starting model used in the simulation. These simulations suggest that homology models based on bacterial homologues may be used to derive functionally relevant information on the structural dynamics of mammalian transport proteins.     

Effects of force fields on the conformational and dynamic properties of amyloid β(1‐40) dimer explored by replica exchange molecular dynamics simulations

The conformational space and structural ensembles of amyloid beta (Aβ) peptides and their oligomers in solution are inherently disordered and proven to be challenging to study. Optimum force field selection for molecular dynamics (MD) simulations and the biophysical relevance of results are still unknown. We compared the conformational space of the Aβ(1‐40) dimers by 300 ns replica exchange MD simulations at physiological temperature (310 K) using: the AMBER‐ff99sb‐ILDN, AMBER‐ff99sb*‐ILDN, AMBER‐ff99sb‐NMR, and CHARMM22* force fields. Statistical comparisons of simulation results to experimental data and previously published simulations utilizing the CHARMM22* and CHARMM36 force fields were performed. All force fields yield sampled ensembles of conformations with collision cross sectional areas for the dimer that are statistically significantly larger than experimental results. All force fields, with the exception of AMBER‐ff99sb‐ILDN (8.8 ± 6.4%) and CHARMM36 (2.7 ± 4.2%), tend to overestimate the α‐helical content compared to experimental CD (5.3 ± 5.2%). Using the AMBER‐ff99sb‐NMR force field resulted in the greatest degree of variance (41.3 ± 12.9%). Except for the AMBER‐ff99sb‐NMR force field, the others tended to under estimate the expected amount of β‐sheet and over estimate the amount of turn/bend/random coil conformations. All force fields, with the exception AMBER‐ff99sb‐NMR, reproduce a theoretically expected β‐sheet‐turn‐β‐sheet conformational motif, however, only the CHARMM22* and CHARMM36 force fields yield results compatible with collapse of the central and C‐terminal hydrophobic cores from residues 17‐21 and 30‐36. Although analyses of essential subspace sampling showed only minor variations between force fields, secondary structures of lowest energy conformers are different.     

The use of the AMBER force field in conformational analysis of carbohydrate molecules: Determination of the solution conformation of methyl α-lactoside by NMR spectroscopy,assisted by molecular mechanics and dynamics calculations

The solution conformation of methyl α-lactoside has been studied through nmr spectroscopy and molecular mechanics calculations using the assisted model building with energy refinement (AMBER) force field. The nmr data have included nuclear Overhauser effect (NOE) measurements hot It in the laboratory and rotating frames, longitudinal relaxation times, and homonuclear and heteronuclear coupling constants. The steady-state and transient NOEs have been interpreted in terms of an ensemble average distribution of conformers, making use of the complete relaxation matrix approach. The molecular mechanics calculations have been performed at two dielectric constants [ε = 1 * r and 80 Debyes (D)] in an exhaustive way, and have been complemented with specific calculations at intermediate ε values. Relaxed energy maps and adiabatic surfaces have been generated for the different dielectric constants. The probability distribution of conformers has been estimated from these steric energy maps. Molecular dynamics simulations in vacuo have also been performed. The experimental results indicate that the β(1 → 4)-glycosidic linkage shows some fluctuations among three low energy regions, although spends ca. 85% of its lime in the region close to the global minimum. It is shown that the over estimation of the electrostatic contributions in AMBER is responsible for the failure of this force field to explain the experimental results when Used at low dielectric constant (ε < 20 D). The matching between the expected and observed facts increases for ε > 40 D. Different conditions have been tested to perform temperature constant molecular dynamics simulations in vacuo, which have indicated that, when used without explicit solvent, this force field should only be employed in a qualitatively way when analyzing dynamical properties of oligosaccharides. © 1995 John Wiley & Sons, Inc.     

Comparison of force fields for Alzheimer's A : A case study for intrinsically disordered proteins

Intrinsically disordered proteins are essential for biological processes such as cell signalling, but are also associated to devastating diseases including Alzheimer's disease, Parkinson's disease or type II diabetes. Because of their lack of a stable three‐dimensional structure, molecular dynamics simulations are often used to obtain atomistic details that cannot be observed experimentally. The applicability of molecular dynamics simulations depends on the accuracy of the force field chosen to represent the underlying free energy surface of the system. Here, we use replica exchange molecular dynamics simulations to test five modern force fields, OPLS, AMBER99SB, AMBER99SB*ILDN, AMBER99SBILDN‐NMR and CHARMM22*, in their ability to model Aβ₄₂, an intrinsically disordered peptide associated with Alzheimer's disease, and compare our results to nuclear magnetic resonance (NMR) experimental data. We observe that all force fields except AMBER99SBILDN‐NMR successfully reproduce local NMR observables, with CHARMM22* being slightly better than the other force fields.     

The nature of intermolecular interactions between aromatic amino acid residues

The nature of intermolecular interactions between aromatic amino acid residues has been investigated by a combination of molecular dynamics and ab initio methods. The potential energy surface of various interacting pairs, including tryptophan, phenilalanine, and tyrosine, was scanned for determining all the relevant local minima by a combined molecular dynamics and conjugate gradient methodology with the AMBER force field. For each of these minima, single-point correlated ab initio calculations of the binding energy were performed. The agreement between empirical force field and ab initio binding energies of the minimum energy structures is excellent. Aromatic-aromatic interactions can be rationalized on the basis of electrostatic and van der Waals interactions, whereas charge transfer or polarization phenomena are small for all intermolecular complexes and, particularly, for stacked structures. Proteins 2002;48:117-125.     

Structural equilibrium of DNA represented with different force fields.

We have recently indicated preliminary evidence of different equilibrium average structures with the CHARMM and AMBER force fields in explicit solvent molecular dynamics simulations on the DNA duplex d(C5T5) . d(A5G5) (Feig, M. and B.M. Pettitt, 1997, Experiment vs. Force Fields: DNA conformation from molecular dynamics simulations. J. Phys. Chem. B. (101:7361-7363). This paper presents a detailed comparison of DNA structure and dynamics for both force fields from extended simulation times of 10 ns each. Average structures display an A-DNA base geometry with the CHARMM force field and a base geometry that is intermediate between A- and B-DNA with the AMBER force field. The backbone assumes B form on both strands with the AMBER force field, while the CHARMM force field produces heterogeneous structures with the purine strand in A form and the pyrimidine strand in dynamical equilibrium between A and B conformations. The results compare well with experimental data for the cytosine/guanine part but fail to fully reproduce an overall B conformation in the thymine/adenine tract expected from crystallographic data, particularly with the CHARMM force field. Fluctuations between A and B conformations are observed on the nanosecond time scale in both simulations, particularly with the AMBER force field. Different dynamical behavior during the first 4 ns indicates that convergence times of several nanoseconds are necessary to fully establish a dynamical equilibrium in all structural quantities on the time scale of the simulations presented here.     

MolStruc: a force field calculation program allowing interactive modifications of the force field parameters

To analyze the influence of parameters and functions on the energy and geometry obtained through different force field calculations, we have developed program MolStruc. This software allows the user to choose between two sets of functions and parameters, MM2 and AMBER.The MM2 option of the program was developed to compute the coulombic energy in a dipole or monopole approximation. To establish comparisons between the energy values, the coulombic contribution is computed in the same way in the Amber and MM2 options of the program.The force field parameters can be handled interactively (through addition or modification).The program was used to study molecules of a representative sample displaying most of the problems encountered in molecular mechanics (MM).     

Force field parameters for S-nitrosocysteine and molecular dynamics simulations of S-nitrosated thioredoxin

Estimation of structural perturbation induced by S-nitrosation is important to understand the mode of cellular signal transduction mediated by nitric oxide. Crystal structures of S-nitrosated proteins have been solved only for a few cases, however, so that molecular dynamics simulation may provide an alternative tool for probing structural perturbation. In this study AMBER-99 force field parameters for S-nitrosocysteine were developed and applied to molecular dynamics simulations of S-nitrosated thioredoxin. Geometry optimization at the level of HF/6-31G∗ was followed by a restrained electrostatic potential charge-fitting to obtain the atomic charges of S-nitrosocysteine. Force constants for bonds and angles were obtained from generalized AMBER force field. Torsional force constants for CC-SN and CS-NO were determined by fitting the torsional profiles obtained from geometry optimization with those from molecular mechanical energy minimization. Finally molecular dynamics simulations were performed with theses parameters on oxidized and reduced thioredoxin with and without S-nitrosocysteine. In all cases the root-mean-square deviations of α-carbons yielded well-behaved trajectories. The CC-SH dihedral angle which fluctuated severely during the simulation became quiet upon S-nitrosation. In conclusion the force field parameters developed in this study for S-nitrosocysteine appear to be suitable for molecular dynamics simulations of S-nitrosated proteins.     

Determination method of the balance of the secondary-structure-forming tendencies of force fields

We propose a new method of optimisation of backbone torsion-energy parameters in the force field for molecular simulations of protein systems. This method is based on the idea of balancing the secondary-structure-forming tendencies, namely, those of α-helix and β-sheet structures. We perform a minimisation of the backbone dihedral angle-based root-mean-square deviation of the helix and β structure regions in many protein structures. As an example, we optimised the backbone torsion-energy parameters of AMBER parm96 force field using 100 protein molecules from the Protein Data Bank. We then performed folding simulations of α-helical and β-hairpin peptides, using the optimised force field. The results imply that the new force-field parameters give structures more consistent with the experimental implications than the original AMBER parm96 force field.     

Automated docking of ligands to antibodies: methods and applications

Many approaches to studying protein-ligand interactions by computational docking are currently available. Given the structures of a protein and a ligand, the ultimate goal of all docking methods is to predict the structure of the resulting complex. This requires a suitable representation of molecular structures and properties, search algorithms to efficiently scan the configuration space for favorable interaction geometries, and accurate scoring functions to evaluate and rank the generated orientations. For many of the available methods, tests on experimentally known antibody-antigen or antibody-hapten complexes have appeared in the literature. In addition, some of them have been used in predictive studies on antibody-ligand interactions to provide structural insights where adequate experimental information is missing. The AutoDock program is presented as example of a method for flexibly docking ligands to antibodies. Applying parameters of the second-generation AMBER force field, three antibody-hapten complexes (AN02, DB3, NC6.8) are used as new test cases to analyze the ability of the method to reproduce experimental findings. The X-ray structures could be reconstituted and the corresponding solutions were ranked with best energy score in all cases. Docking to the free instead of the complexed NC6.8 structure indicated the limits of the rigid protein treatment, although fairly good guesses about the location of the binding site and the contact residues could still be obtained if conformational flexibility was allowed at least in the ligand.     

Critical assessment of quantum mechanics based energy restraints in protein crystal structure refinement

A critical evaluation of the performance of X-ray refinement protocols using various energy functions is presented using the bovine pancreatic trypsin inhibitor (BPTI) protein. The four potential energy functions we explored include: (1) fully quantum mechanical calculations; (2) one based on an incomplete molecular mechanics (MM) energy function employed in the Crystallography and NMR System (CNS) with empirical parameters developed by Engh and Huber (EH), which lacks electrostatic and attractive van der Waals terms; (3) one based on a complete MM energy function (AMBER ff99 parameter set); and (4) the same as 3, with the addition of a Generalized Born (GB) implicit solvation term. The R, R (free), real space R values of the refined structures and deviations from the original experimental structure were used to assess the relative performance. It was found that at 1 Angstrom resolution the physically based energy functions 1, 3, and 4 performed better than energy function 2, which we attribute to the better representation of key interactions, particularly electrostatics. The observed departures from the experimental structure were similar for the refinements with physically based energy functions and were smaller than the structure refined with EH. A test refinement was also performed with the reflections truncated at a high-resolution cutoff of 2.5 Angstrom and with random perturbations introduced into the initial coordinates, which showed that low-resolution refinements with physically based energy functions held the structure closer to the experimental structure solved at 1 Angstrom resolution than the EH-based refinements.     

Investigations of the thermostability of rubredoxin models using molecular dynamics simulations.

The affects of differences in amino acid sequence on the temperature stability of the three-dimensional structure of the small beta-sheet protein, rubredoxin (Rd), was revealed when a set of homology models was subjected to molecular dynamics simulations at relatively high temperatures. Models of Rd from the hyperthermophile, Pyrococcus furiosus (Pf), an organism that grows optimally at 100 degrees C, were compared to three mesophilic Rds of known X-ray crystal structure. Simulations covering the limits of known Rd thermostabilities were carried out at temperatures of 300 K, 343 K, 373 K, and 413 K. They suggest that Rd stability is correlated with structural dynamics. Because the dynamic behavior of three Pf Rd models was consistently different from the dynamic behavior of the three mesophilic Rd structures, detailed analysis of the temperature-dependent dynamic behavior was carried out. The major differences between the models of the protein from the hyperthermophile and the others were: (1) an obvious temperature-dependent transition in the mesophilic structures not seen with the Pf Rd models, (2) consistent AMBER energy for the Pf Rd due to differences in nonbonded interaction terms, (3) less variation in the average conformations for the Pf Rd models with temperature, and (4) the presence of more extensive secondary structure for the Pf Rd models. These unsolvated dynamics simulations support a simple, general hypothesis to explain the hyperthermostability of Pf Rd. Its structure simplifies the conformational space to give a single minimum accessible over an extreme range of temperatures, whereas the mesophilic proteins sample a more complex conformational space with two or more minima over the same temperature range.     

Conformational transitions of flanking purines in HIV-1 RNA dimerization initiation site kissing complexes studied by CHARMM explicit solvent molecular dynamics

Dimerization of HIV-1 genomic RNA is initiated by kissing loop interactions at the Dimerization Initiation Site (DIS). Dynamics of purines that flank the 5' ends of the loop-loop helix in HIV-1 DIS kissing complex were explored using explicit solvent molecular dynamics (MD) simulations with the CHARMM force field. Multiple MD simulations (200 ns in total) of X-ray structures for HIV-1 DIS Subtypes A, B, and F revealed conformational variability of flanking purines. In particular, the flanking purines, which in the starting X-ray structures are bulged-out and stack in pairs, formed a consecutive stack of four bulged-out adenines at the beginning of several simulations. This conformation is seen in the crystal structure of DIS Subtype F with no interference from crystal packing, and was frequently reported in our preceding MD studies performed with the AMBER force field. However, as CHARMM simulations progressed, the four continuously stacked adenines showed conformational transitions from the bulged-out into the bulged-in geometries. Although such an arrangement has not been seen in any X-ray structure, it has been suggested by a recent NMR investigation. In CHARMM simulations, in the longer time scale, the flanking purines display the tendency to move to bulged-in conformations. This is in contrast with the AMBER simulations, which indicate a modest prevalence for bulged-out flanking base positions in line with the X-ray data. The simulations also suggest that the intermolecular stacking between purines from the opposite hairpins can additionally stabilize the kissing complex.