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

Pair Potentials as Machine Learning Features

Atom pairwise potential functions make up an essential part of many scoring functions for protein decoy detection. With the development of machine learning (ML) tools, there are multiple ways to combine potential functions to create novel ML models and methods. Potential function parameters can be easily extracted; however, it is usually hard to directly obtain the calculated atom pairwise energies from scoring functions. Amber, as one of the most popular suites of modeling programs, has an extensive history and library of force field potential functions. In this work, we directly used the force field parameters in ff94 and ff14SB from Amber and encoded them to calculate atom pairwise energies for different interactions. Two sets of structures (single amino acid set and a dipeptide set) were used to evaluate the performance of our encoded Amber potentials. From the comparison results between energy terms obtained from our encoding and Amber, we find energy difference within ±0.06 kcal/mol for all tested structures. Previously we have shown that the Random Forest (RF) model can help to emphasize more important atom pairwise interactions and ignore insignificant ones [Pei, J.; Zheng, Z.; Merz, K. M. J. Chem. Inf. Model. 2019, 59, 1919-1929]. Here, as an example of combining ML methods with traditional potential functions, we followed the same work flow to combine the RF models with force field potential functions from Amber. To determine the performance of our RF models with force field potential functions, 224 different protein native-decoy systems were used as our training and testing sets We find that the RF models with ff94 and ff14SB force field parameters outperformed all other scoring functions (RF models with KECSA2, RWplus, DFIRE, dDFIRE, and GOAP) considered in this work for native structure detection, and they performed similarly in detecting the best decoy. Through inclusion of best decoy to decoy comparisons in building our RF models, we were able to generate models that outperformed the score functions tested herein both on accuracy and best decoy detection, again showing the performance and flexibility of our RF models to tackle this problem. Finally, the importance of the RF algorithm and force field parameters were also tested and the comparison results suggest that both the RF algorithm and force field potentials are important with the ML scoring function achieving its best performance only by combining them together. All code and data used in this work are available at https://github.com/JunPei000/FFENCODER_for_Protein_Folding_Pose_Selection.

Molecular Dynamics Simulations of the Interactions between Glial Cell Line-Derived Neurotrophic Factor Family Receptor GFRα1 and Small-Molecule Ligands

The glial cell line-derived neurotrophic factor (GDNF) family ligands (GFLs) support the survival and functioning of various neuronal populations. Thus, they could be attractive therapeutic agents against a multitude of neurodegenerative diseases caused by progressive death of GFLs responsive neurons. Small-molecule ligands BT13 and BT18 show an effect on GDNF family receptor GFRα1 and RET receptor tyrosine kinase RetA function. Thus, their potential binding sites and interactions were explored in the GDNF-GFRα1-RetA complex using molecular docking calculations as well as molecular dynamics (MD) simulations. Three possible regions were examined: the interface between GDNF and GFRα1 (region A), the RetA interface with GFRα1 (region B), and a possible allosteric site in GFRα1 (region C). The results obtained by the docking calculations and the MD simulations indicate that the preferable binding occurs at the allosteric site. A less preferable binding site was detected on the RetA surface interfacing GFRα1. In the membrane-bound state of RetA this can enable compounds BT13 and BT18 to act as direct RetA agonists. The analysis of the MD simulations shows hydrogen bonds for BT13 and significant hydrophobic interactions with GFRα1 for BT13 and BT18 at the allosteric site.

Computational protein structure refinement: Almost there, yet still so far to go

Protein structures are essential in modern biology yet experimental methods are far from being able to catch up with the rapid increase in available genomic data. Computational protein structure prediction methods aim to fill the gap while the role of protein structure refinement is to take approximate initial template-based models and bring them closer to the true native structure. Current methods for computational structure refinement rely on molecular dynamics simulations, related sampling methods, or iterative structure optimization protocols. The best methods are able to achieve moderate degrees of refinement but consistent refinement that can reach near-experimental accuracy remains elusive. Key issues revolve around the accuracy of the energy function, the inability to reliably rank multiple models, and the use of restraints that keep sampling close to the native state but also limit the degree of possible refinement. A different aspect is the question of what exactly the target of high-resolution refinement should be as experimental structures are affected by experimental conditions and different biological questions require varying levels of accuracy. While improvement of the global protein structure is a difficult problem, high-resolution refinement methods that improves local structural quality such as favorable stereochemistry and the avoidance of atomic clashes are much more successful.

Structural characterization of MG and pre-MG states of proteins by MD simulations, NMR, and other techniques

Almost all proteins fold via a number of partially structured intermediates such as molten globule (MG) and pre-molten globule states. Understanding the structure of these intermediates at atomic level is often a challenge, as these states are observed under extreme conditions of pH, temperature, and chemical denaturants. Furthermore, several other processes such as chemical modification, site-directed mutagenesis (or point mutation), and cleavage of covalent bond of natural proteins often lead to MG like partially unfolded conformation. However, the dynamic nature of proteins in these states makes them unsuitable for most structure determination at atomic level. Intermediate states studied so far have been characterized mostly by circular dichroism, fluorescence, viscosity, dynamic light scattering measurements, dye binding, infrared techniques, molecular dynamics simulations, etc. There is a limited amount of structural data available on these intermediate states by nuclear magnetic resonance (NMR) and hence there is a need to characterize these states at the molecular level. In this review, we present characterization of equilibrium intermediates by biophysical techniques with special reference to NMR.

Detecting local residue environment similarity for recognizing near-native structure models

We developed a new representation of local amino acid environments in protein structures called the Side-chain Depth Environment (SDE). An SDE defines a local structural environment of a residue considering the coordinates and the depth of amino acids that locate in the vicinity of the side-chain centroid of the residue. SDEs are general enough that similar SDEs are found in protein structures with globally different folds. Using SDEs, we developed a procedure called PRESCO (Protein Residue Environment SCOre) for selecting native or near-native models from a pool of computational models. The procedure searches similar residue environments observed in a query model against a set of representative native protein structures to quantify how native-like SDEs in the model are. When benchmarked on commonly used computational model datasets, our PRESCO compared favorably with the other existing scoring functions in selecting native and near-native models.

ROTAS: a rotamer-dependent, atomic statistical potential for assessment and prediction of protein structures

Background

Multibody potentials accounting for cooperative effects of molecular interactions have shown better accuracy than typical pairwise potentials. The main challenge in the development of such potentials is to find relevant structural features that characterize the tightly folded proteins. Also, the side-chains of residues adopt several specific, staggered conformations, known as rotamers within protein structures. Different molecular conformations result in different dipole moments and induce charge reorientations. However, until now modeling of the rotameric state of residues had not been incorporated into the development of multibody potentials for modeling non-bonded interactions in protein structures.

Results

In this study, we develop a new multibody statistical potential which can account for the influence of rotameric states on the specificity of atomic interactions. In this potential, named “rotamer-dependent atomic statistical potential” (ROTAS), the interaction between two atoms is specified by not only the distance and relative orientation but also by two state parameters concerning the rotameric state of the residues to which the interacting atoms belong. It was clearly found that the rotameric state is correlated to the specificity of atomic interactions. Such rotamer-dependencies are not limited to specific type or certain range of interactions. The performance of ROTAS was tested using 13 sets of decoys and was compared to those of existing atomic-level statistical potentials which incorporate orientation-dependent energy terms. The results show that ROTAS performs better than other competing potentials not only in native structure recognition, but also in best model selection and correlation coefficients between energy and model quality.

Conclusions

A new multibody statistical potential, ROTAS accounting for the influence of rotameric states on the specificity of atomic interactions was developed and tested on decoy sets. The results show that ROTAS has improved ability to recognize native structure from decoy models compared to other potentials. The effectiveness of ROTAS may provide insightful information for the development of many applications which require accurate side-chain modeling such as protein design, mutation analysis, and docking simulation.

Electronic supplementary material

The online version of this article (doi:10.1186/1471-2105-15-307) contains supplementary material, which is available to authorized users.

Protein's native structure is dynamically stabilized by electronic polarization

In this paper, molecular dynamics (MD) simulations were performed for a number of benchmark proteins using both the standard assisted model building with energy refinement (AMBER) charge and the dynamically adjusted polarized protein-specific charge (DPPC) from quantum fragment calculations to provide accurate electrostatic interactions. Our result shows that proteins' dynamic structures drifted away from the native structures in simulations under standard (nonpolarizable) AMBER force field. For comparison, proteins' native structures were dynamically stable after a long time simulation under DPPC. The free energy landscape reveals that the native structure is the lowest energy conformation under DPPC, while it is not under standard AMBER charge. To further investigate the polarization effect on the stability of native structures of proteins, we restarted from some decoy structures generated from simulations using standard AMBER charges and then carried out further MD simulation using DPPC to refine those structures. Our study shows that the native structures from these decoy structures can be mostly recovered using DPPC and that the dynamic structures with the highest population in cluster analysis are in close agreement with the corresponding native structures. The current study demonstrates the importance of electronic polarization of protein in stabilizing the native structure.

ITScorePro: an efficient scoring program for evaluating the energy scores of protein structures for structure prediction

One important component in protein structure prediction is to evaluate the free energy of a given conformation. Given the enormous number of possible conformations for a sequence, it is extremely challenging to quickly and accurately score the energies of these conformations and predict a reasonable structure within a practical computational time. Here, we describe an efficient program for energy evaluation, referred to as ITScorePro (Copyright © 2012). The energy scoring function in the ITScorePro program is based on the distance-dependent, pairwise atomic potentials for protein structure prediction that we recently derived by using statistical mechanics principles (Huang and Zou, Proteins 79:2648-2661, 2011). ITScorePro is a stand-alone program and can also be easily implemented in other software suites for protein structure prediction.

Estimation of Interaction Potentials through the Configurational Temperature Formalism

Molecular interaction potentials are difficult to measure experimentally and hard to compute from first principles, especially for large systems such as proteins. It is therefore desirable to estimate the potential energy that underlies a thermodynamic ensemble from simulated or experimentally determined configurations. This inverse problem of statistical mechanics is challenging because the various potential energy terms can exhibit subtle indirect and correlated effects on the resulting ensemble. A direct approach would try to adapt the force field parameters such that the given configurations are highly probable in the resulting ensemble. But this would require a full simulation of the system whenever a parameter changes. We introduce an extension of the configurational temperature formalism that allows us to circumvent these difficulties and efficiently estimate interaction potentials from molecular configurations. We illustrate the approach for various systems including fluids and a coarse-grained protein model.

Application of replica exchange umbrella sampling to protein structure refinement of nontemplate models

We provide an assessment of a computational strategy for protein structure refinement that combines self-guided Langevin dynamics with umbrella-potential biasing replica exchange using the radius of gyration as a coordinate (Rg -ReX). Eight structurally nonredundant proteins and their decoys were examined by sampling conformational space at room temperature using the CHARMM22/GBMV2 force field to generate the ensemble of structures. Two atomic statistical potentials (RWplus and DFIRE) were analyzed for structure identification and compared to the simulation force-field potential. The results show that, while the Rg -ReX simulations were able to sample conformational basins that were more structurally similar to the X-ray crystallographic structures than the starting first-order ranked decoys, the potentials failed to detect these basins from refinement. Of the three potential functions, RWplus yielded the highest accuracy for recognition of structures that refined to an average of nearly 20% increase in native contacts relative to the starting decoys. The overall performance of Rg -ReX is compared to an earlier study of applying temperature-based replica exchange to refine the same decoy sets and highlights the general challenge of achieving consistently the sampling and detection threshold of 70% fraction of native contacts.

Structure refinement of protein model decoys requires accurate side-chain placement

In this study, the application of temperature-based replica-exchange (T-ReX) simulations for structure refinement of decoys taken from the I-TASSER dataset was examined. A set of eight nonredundant proteins was investigated using self-guided Langevin dynamics (SGLD) with a generalized Born implicit solvent model to sample conformational space. For two of the protein test cases, a comparison of the SGLD/T-ReX method with that of a hybrid explicit/implicit solvent molecular dynamics T-ReX simulation model is provided. Additionally, the effect of side-chain placement among the starting decoy structures, using alternative rotamer conformations taken from the SCWRL4 modeling program, was investigated. The simulation results showed that, despite having near-native backbone conformations among the starting decoys, the determinant of their refinement is side-chain packing to a level that satisfies a minimum threshold of native contacts to allow efficient excursions toward the downhill refinement regime on the energy landscape. By repacking using SCWRL4 and by applying the RWplus statistical potential for structure identification, the SGLD/T-ReX simulations achieved refinement to an average of 38% increase in the number of native contacts relative to the original I-TASSER decoy sets and a 25% reduction in values of C(α) root-mean-square deviation. The hybrid model succeeded in obtaining a sharper funnel to low-energy states for a modeled target than the implicit solvent SGLD model; yet, structure identification remained roughly the same. Without meeting a threshold of near-native packing of side chains, the T-ReX simulations degrade the accuracy of the decoys, and subsequently, refinement becomes tantamount to the protein folding problem.

Dynamic and Thermodynamic Signatures of Native and Non-Native Protein States with Application to the Improvement of Protein Structures

Accurate knowledge of the 3D structural ensemble of proteins is important for understanding of their biological function. We report here the application of microsecond all-atom molecular dynamics (MD) simulations in explicit solvent for the improvement of the quality of low-resolution structures obtained by protein structure prediction (decoys). Seventy MD simulations of ∼1 μs average duration were performed on 13 different protein systems starting from X-ray crystal structures and decoys. Their behavior can be divided into three groups: 22 trajectories converged toward the native state, 27 trajectories displayed a quasi-equilibrium by populating mainly a single non-native free energy basin, and 21 trajectories drifted away from their initial decoy structure transiently visiting multiple free energy minima. To determine whether the native structure can be identified among non-native ensembles, the free energy was determined for each basin by the MM/GBSA method together with the von Mises entropy estimator in dihedral angle space. For the proteins studied here, it is found that the ensembles belonging to free energy basins with the lowest free energies and the longest residence times are most native-like. The results demonstrate that explicit solvent microsecond MD simulations using the latest generation of protein force fields and free energy metrics are sufficiently accurate to permit positive identification of native state ensembles against low-resolution structural models and decoys. The approach can be applied to the direct refinement of predicted or experimental low-resolution protein structures.

Multi-LZerD: multiple protein docking for asymmetric complexes

The tertiary structures of protein complexes provide a crucial insight about the molecular mechanisms that regulate their functions and assembly. However, solving protein complex structures by experimental methods is often more difficult than single protein structures. Here, we have developed a novel computational multiple protein docking algorithm, Multi-LZerD, that builds models of multimeric complexes by effectively reusing pairwise docking predictions of component proteins. A genetic algorithm is applied to explore the conformational space followed by a structure refinement procedure. Benchmark on eleven hetero-multimeric complexes resulted in near-native conformations for all but one of them (a root mean square deviation smaller than 2.5Å). We also show that our method copes with unbound docking cases well, outperforming the methodology that can be directly compared with our approach. Multi-LZerD was able to predict near-native structures for multimeric complexes of various topologies.

Coarse-grain Protein Models

Coarse-graining is a powerful approach for modeling biomolecules that, over the last few decades, has been extensively applied to proteins. Coarse-grain models offer access to large systems and to slow processes without becoming computationally unmanageable. In addition, they are very versatile, enabling both the protein representation and the energy function to be adapted to the biological problem in hand. This review concentrates on modeling soluble proteins and their assemblies. It presents an overview of the coarse-grain representations, of the associated interaction potentials, and of the optimization procedures used to define them. It then shows how coarse-grain models have been used to understand processes involving proteins, from their initial folding to their functional properties, their binary interactions, and the assembly of large complexes.

Structure refinement of protein low resolution models using the GNEIMO constrained dynamics method

The challenge in protein structure prediction using homology modeling is the lack of reliable methods to refine the low resolution homology models. Unconstrained all-atom molecular dynamics (MD) does not serve well for structure refinement due to its limited conformational search. We have developed and tested the constrained MD method, based on the generalized Newton-Euler inverse mass operator (GNEIMO) algorithm for protein structure refinement. In this method, the high-frequency degrees of freedom are replaced with hard holonomic constraints and a protein is modeled as a collection of rigid body clusters connected by flexible torsional hinges. This allows larger integration time steps and enhances the conformational search space. In this work, we have demonstrated the use of torsional GNEIMO method without using any experimental data as constraints, for protein structure refinement starting from low-resolution decoy sets derived from homology methods. In the eight proteins with three decoys for each, we observed an improvement of ~2 Å in the rmsd in coordinates to the known experimental structures of these proteins. The GNEIMO trajectories also showed enrichment in the population density of native-like conformations. In addition, we demonstrated structural refinement using a "freeze and thaw" clustering scheme with the GNEIMO framework as a viable tool for enhancing localized conformational search. We have derived a robust protocol based on the GNEIMO replica exchange method for protein structure refinement that can be readily extended to other proteins and possibly applicable for high throughput protein structure refinement.

A scoring function based on solvation thermodynamics for protein structure prediction

We predict protein structure using our recently developed free energy function for describing protein stability, which is focused on solvation thermodynamics. The function is combined with the current most reliable sampling methods, i.e., fragment assembly (FA) and comparative modeling (CM). The prediction is tested using 11 small proteins for which high-resolution crystal structures are available. For 8 of these proteins, sequence similarities are found in the database, and the prediction is performed with CM. Fairly accurate models with average Cα root mean square deviation (RMSD) ∼ 2.0 Å are successfully obtained for all cases. For the rest of the target proteins, we perform the prediction following FA protocols. For 2 cases, we obtain predicted models with an RMSD ∼ 3.0 Å as the best-scored structures. For the other case, the RMSD remains larger than 7 Å. For all the 11 target proteins, our scoring function identifies the experimentally determined native structure as the best structure. Starting from the predicted structure, replica exchange molecular dynamics is performed to further refine the structures. However, we are unable to improve its RMSD toward the experimental structure. The exhaustive sampling by coarse-grained normal mode analysis around the native structures reveals that our function has a linear correlation with RMSDs < 3.0 Å. These results suggest that the function is quite reliable for the protein structure prediction while the sampling method remains one of the major limiting factors in it. The aspects through which the methodology could further be improved are discussed.

Molecular dynamics modeling of the sub-THz vibrational absorption of thioredoxin from E. coli

Sub-terahertz (THz) vibrational modes of the protein thioredoxin in a water environment were simulated using molecular dynamics (MD) in order to find the conditions needed for simulation convergence, improve the correlation between experimental and simulated absorption frequencies, and ultimately enhance the predictive capabilities of computational modeling. Thioredoxin from E. coli was used as a model molecule for protocol development and to optimize the simulation parameters. The empirically parameterized software packages Amber 8 and 10 were used in this work. Using atomic trajectories from the constant energy and volume MD simulations, thioredoxin's sub-THz vibrational spectra and absorption coefficients were calculated in a quasi-harmonic approximation. An optimal production run length ~100 ps was found, in agreement with experimental data on thioredoxin relaxation dynamics. At the same time, a new procedure was developed for averaging correlation matrices of atomic coordinates in MD simulations. In particular, the open source package ptraj was edited to improve a matrix-analyzing function. Averaging only six matrices gave much more consistent results, with absorption peak intensities exceeding those from the individual spectra and a rather good correlation between simulated vibrational frequencies and experimental data.

Statistical mechanics-based method to extract atomic distance-dependent potentials from protein structures

In this study, we have developed a statistical mechanics-based iterative method to extract statistical atomic interaction potentials from known, nonredundant protein structures. Our method circumvents the long-standing reference state problem in deriving traditional knowledge-based scoring functions, by using rapid iterations through a physical, global convergence function. The rapid convergence of this physics-based method, unlike other parameter optimization methods, warrants the feasibility of deriving distance-dependent, all-atom statistical potentials to keep the scoring accuracy. The derived potentials, referred to as ITScore/Pro, have been validated using three diverse benchmarks: the high-resolution decoy set, the AMBER benchmark decoy set, and the CASP8 decoy set. Significant improvement in performance has been achieved. Finally, comparisons between the potentials of our model and potentials of a knowledge-based scoring function with a randomized reference state have revealed the reason for the better performance of our scoring function, which could provide useful insight into the development of other physical scoring functions. The potentials developed in this study are generally applicable for structural selection in protein structure prediction.

Assessment of protein structure refinement in CASP9

We assess performance in the structure refinement category in CASP9. Two years after CASP8, the performance of the best groups has not improved. There are few groups that improve any of our assessment scores with statistical significance. Some predictors, however, are able to consistently improve the physicality of the models. Although we cannot identify any clear bottleneck in improving refinement, several points arise: (1) The refinement portion of CASP has too few targets to make many statistically meaningful conclusions. (2) Predictors are usually very conservative, limiting the possibility of large improvements in models. (3) No group is actually able to correctly rank their five submissions-indicating that potentially better models may be discarded. (4) Different sampling strategies work better for different refinement problems; there is no single strategy that works on all targets. In general, conservative strategies do better, while the greatest improvements come from more adventurous sampling-at the cost of consistency. Comparison with experimental data reveals aspects not captured by comparison to a single structure. In particular, we show that improvement in backbone geometry does not always mean better agreement with experimental data. Finally, we demonstrate that even given the current challenges facing refinement, the refined models are useful for solving the crystallographic phase problem through molecular replacement. Proteins 2011;. © 2011 Wiley-Liss, Inc.

Remote thioredoxin recognition using evolutionary conservation and structural dynamics

The thioredoxin family of oxidoreductases plays an important role in redox signaling and control of protein function. Not only are thioredoxins linked to a variety of disorders, but their stable structure has also seen application in protein engineering. Both sequence-based and structure-based tools exist for thioredoxin identification, but remote homolog detection remains a challenge. We developed a thioredoxin predictor using the approach of integrating sequence with structural information. We combined a sequence-based Hidden Markov Model (HMM) with a molecular dynamics enhanced structure-based recognition method (dynamic FEATURE, DF). This hybrid method (HMMDF) has high precision and recall (0.90 and 0.95, respectively) compared with HMM (0.92 and 0.87, respectively) and DF (0.82 and 0.97, respectively). Dynamic FEATURE is sensitive but struggles to resolve closely related protein families, while HMM identifies these evolutionary differences by compromising sensitivity. Our method applied to structural genomics targets makes a strong prediction of a novel thioredoxin.

Influence of the acetylcholinesterase active site protonation on omega loop and active site dynamics

Existence of alternative entrances in acetylcholinesterase (AChE) could explain the contrast between the very high AChE catalytic efficiency and the narrow and long access path to the active site revealed by X-ray crystallography. Alternative entrances could facilitate diffusion of the reaction products or at least water and ions from the active site. Previous molecular dynamics simulations identified side door and back door as the most probable alternative entrances. The simulations of non-inhibited AChE suggested that the back door opening events occur only rarely (0.8% of the time in the 10ns trajectory). Here we present a molecular dynamics simulation of non-inhibited AChE, where the back door opening appears much more often (14% of the time in the 12ns trajectory) and where the side door opening was observed quite frequently (78% of trajectory time). We also present molecular dynamics, where the back door does not open at all, or where large conformational changes of the AChE omega loop occur together with alternative passage opening events. All these differences in AChE dynamical behavior are caused by different protonation states of two glutamate residues located on bottom of the active site gorge (Glu202 and G450 in Mus musculus AChE). Our results confirm the results of previous molecular dynamics simulations, expand the view and suggest the probable reasons for the overall conformational behavior of AChE omega loop.

A practical introduction to molecular dynamics simulations: applications to homology modeling

In this chapter, practical concepts and guidelines are provided for the use of molecular dynamics (MD) simulation for the refinement of homology models. First, an overview of the history and a theoretical background of MD are given. Literature examples of successful MD refinement of homology models are reviewed before selecting the Cytochrome P450 2J2 structure as a case study. We describe the setup of a system for classical MD simulation in a detailed stepwise fashion and how to perform the refinement described in the publication of Li et al. (Proteins 71:938-949, 2008). This tutorial is based on version 11 of the AMBER Molecular Dynamics software package (http://ambermd.org/). However, the approach discussed is equally applicable to any condensed phase MD simulation environment.

Advances in implicit models of water solvent to compute conformational free energy and molecular dynamics of proteins at constant pH

Modern implicit solvent models for macromolecular simulations in water-proton bath are considered. The fundamental quantity that implicit models approximate is the solute potential of mean force, which is obtained by averaging over solvent degrees of freedom. The implicit solvent models suggest practical ways to calculate free energies of macromolecular conformations taking into account equilibrium interactions with water solvent and proton bath, while the explicit solvent approach is unable to do that due to the need to account for a large number of solvent degrees of freedom. The most advanced realizations of the implicit continuum models by different research groups are discussed, their accuracy are examined, and some applications of the implicit solvent models to macromolecular modeling, such as free energy calculations, protein folding, and constant pH molecular dynamics are highlighted.

Calculation of accurate small angle X-ray scattering curves from coarse-grained protein models

BACKGROUND

Genome sequencing projects have expanded the gap between the amount of known protein sequences and structures. The limitations of current high resolution structure determination methods make it unlikely that this gap will disappear in the near future. Small angle X-ray scattering (SAXS) is an established low resolution method for routinely determining the structure of proteins in solution. The purpose of this study is to develop a method for the efficient calculation of accurate SAXS curves from coarse-grained protein models. Such a method can for example be used to construct a likelihood function, which is paramount for structure determination based on statistical inference.

RESULTS

We present a method for the efficient calculation of accurate SAXS curves based on the Debye formula and a set of scattering form factors for dummy atom representations of amino acids. Such a method avoids the computationally costly iteration over all atoms. We estimated the form factors using generated data from a set of high quality protein structures. No ad hoc scaling or correction factors are applied in the calculation of the curves. Two coarse-grained representations of protein structure were investigated; two scattering bodies per amino acid led to significantly better results than a single scattering body.

CONCLUSION

We show that the obtained point estimates allow the calculation of accurate SAXS curves from coarse-grained protein models. The resulting curves are on par with the current state-of-the-art program CRYSOL, which requires full atomic detail. Our method was also comparable to CRYSOL in recognizing native structures among native-like decoys. As a proof-of-concept, we combined the coarse-grained Debye calculation with a previously described probabilistic model of protein structure, TorusDBN. This resulted in a significant improvement in the decoy recognition performance. In conclusion, the presented method shows great promise for use in statistical inference of protein structures from SAXS data.

Blind docking method combining search of low-resolution binding sites with ligand pose refinement by molecular dynamics-based global optimization

This study describes the development of a new blind hierarchical docking method, bhDock, its implementation, and accuracy assessment. The bhDock method uses two-step algorithm. First, a comprehensive set of low-resolution binding sites is determined by analyzing entire protein surface and ranked by a simple score function. Second, ligand position is determined via a molecular dynamics-based method of global optimization starting from a small set of high ranked low-resolution binding sites. The refinement of the ligand binding pose starts from uniformly distributed multiple initial ligand orientations and uses simulated annealing molecular dynamics coupled with guided force-field deformation of protein-ligand interactions to find the global minimum. Assessment of the bhDock method on the set of 37 protein-ligand complexes has shown the success rate of predictions of 78%, which is better than the rate reported for the most cited docking methods, such as AutoDock, DOCK, GOLD, and FlexX, on the same set of complexes.

Symmetry-restrained molecular dynamics simulations improve homology models of potassium channels

Most crystallized homo-oligomeric ion channels are highly symmetric, which dramatically decreases conformational space and facilitates building homology models (HMs). However, in molecular dynamics (MD) simulations channels deviate from ideal symmetry and accumulate thermal defects, which complicate the refinement of HMs using MD. In this work we evaluate the ability of symmetry constrained MD simulations to improve HMs accuracy, using an approach conceptually similar to Critical Assessment of techniques for protein Structure Prediction (CASP) competition: build HMs of channels with known structure and evaluate the efficiency of proposed methods in improving HMs accuracy (measured as deviation from experimental structure). Results indicate that unrestrained MD does not improve the accuracy of HMs, instantaneous symmetrization improves accuracy but not stability of HMs during subsequent unrestrained MD, while gradually imposing symmetry constraints improves both accuracy (by 5-50%) and stability of HMs. Moreover, accuracy and stability are strongly correlated, making stability a reliable criterion in predicting the accuracy of new HMs. Proteins 2010. (c) 2009 Wiley-Liss, Inc.

Simulating protein folding initiation sites using an alpha-carbon-only knowledge-based force field

Protein folding is a hierarchical process where structure forms locally first, then globally. Some short sequence segments initiate folding through strong structural preferences that are independent of their three-dimensional context in proteins. We have constructed a knowledge-based force field in which the energy functions are conditional on local sequence patterns, as expressed in the hidden Markov model for local structure (HMMSTR). Carbon-alpha force field (CALF) builds sequence specific statistical potentials based on database frequencies for alpha-carbon virtual bond opening and dihedral angles, pair-wise contacts and hydrogen bond donor-acceptor pairs, and simulates folding via Brownian dynamics. We introduce hydrogen bond donor and acceptor potentials as alpha-carbon probability fields that are conditional on the predicted local sequence. Constant temperature simulations were carried out using 27 peptides selected as putative folding initiation sites, each 12 residues in length, representing several different local structure motifs. Each 0.6 micros trajectory was clustered based on structure. Simulation convergence or representativeness was assessed by subdividing trajectories and comparing clusters. For 21 of the 27 sequences, the largest cluster made up more than half of the total trajectory. Of these 21 sequences, 14 had cluster centers that were at most 2.6 A root mean square deviation (RMSD) from their native structure in the corresponding full-length protein. To assess the adequacy of the energy function on nonlocal interactions, 11 full length native structures were relaxed using Brownian dynamics simulations. Equilibrated structures deviated from their native states but retained their overall topology and compactness. A simple potential that folds proteins locally and stabilizes proteins globally may enable a more realistic understanding of hierarchical folding pathways.

Assessment of the protein-structure refinement category in CASP8

Here, we summarize the assessment of protein structure refinement in CASP8. Twenty-four groups refined a total of 12 target proteins. Averaging over all groups and all proteins, there was no net improvement over the original starting models. However, there are now some individual research groups who consistently do improve protein structures relative to a starting starting model. We compare various measures of quality assessment, including (i) standard backbone-based methods, (ii) new methods from the Richardson group, and (iii) ensemble-based methods for comparing experimental structures, such as NMR NOE violations and the suitability of the predicted models to serve as templates for molecular replacement. On the whole, there is a general correlation among various measures. However, there are interesting differences. Sometimes a structure that is in better agreement with the experimental data is judged to be slightly worse by GDT-TS. This suggests that for comparing protein structures that are already quite close to the native, it may be preferable to use ensemble-based experimentally derived measures of quality, in addition to single-structure-based methods such as GDT-TS.

Splitting statistical potentials into meaningful scoring functions: testing the prediction of near-native structures from decoy conformations

Background

Recent advances on high-throughput technologies have produced a vast amount of protein sequences, while the number of high-resolution structures has seen a limited increase. This has impelled the production of many strategies to built protein structures from its sequence, generating a considerable amount of alternative models. The selection of the closest model to the native conformation has thus become crucial for structure prediction. Several methods have been developed to score protein models by energies, knowledge-based potentials and combination of both.

Results

Here, we present and demonstrate a theory to split the knowledge-based potentials in scoring terms biologically meaningful and to combine them in new scores to predict near-native structures. Our strategy allows circumventing the problem of defining the reference state. In this approach we give the proof for a simple and linear application that can be further improved by optimizing the combination of Zscores. Using the simplest composite score () we obtained predictions similar to state-of-the-art methods. Besides, our approach has the advantage of identifying the most relevant terms involved in the stability of the protein structure. Finally, we also use the composite Zscores to assess the conformation of models and to detect local errors.

Conclusion

We have introduced a method to split knowledge-based potentials and to solve the problem of defining a reference state. The new scores have detected near-native structures as accurately as state-of-art methods and have been successful to identify wrongly modeled regions of many near-native conformations.

Identifying native-like protein structures with scoring functions based on all-atom ECEPP force fields, implicit solvent models and structure relaxation

Availability of energy functions which can discriminate native-like from non-native protein conformations is crucial for theoretical protein structure prediction and refinement of low-resolution protein models. This article reports the results of benchmark tests for scoring functions based on two all-atom ECEPP force fields, that is, ECEPP/3 and ECEPP05, and two implicit solvent models for a large set of protein decoys. The following three scoring functions are considered: (i) ECEPP05 plus a solvent-accessible surface area model with the parameters optimized with a set of protein decoys (ECEPP05/SA); (ii) ECEPP/3 plus the solvent-accessible surface area model of Ooi et al. (Proc Natl Acad Sci USA 1987;84:3086-3090) (ECEPP3/OONS); and (iii) ECEPP05 plus an implicit solvent model based on a solution of the Poisson equation with an optimized Fast Adaptive Multigrid Boundary Element (FAMBEpH) method (ECEPP05/FAMBEpH). Short Monte Carlo-with-Minimization (MCM) simulations, following local energy minimization, are used as a scoring method with ECEPP05/SA and ECEPP3/OONS potentials, whereas energy calculation is used with ECEPP05/FAMBEpH. The performance of each scoring function is evaluated by examining its ability to distinguish between native-like and non-native protein structures. The results of the tests show that the new ECEPP05/SA scoring function represents a significant improvement over the earlier ECEPP3/OONS version of the force field. Thus, it is able to rank native-like structures with C(alpha) root-mean-square-deviations below 3.5 A as lowest-energy conformations for 76% and within the top 10 for 87% of the proteins tested, compared with 69 and 80%, respectively, for ECEPP3/OONS. The use of the FAMBEpH solvation model, which provides a more accurate description of the protein-solvent interactions, improves the discriminative ability of the scoring function to 89%. All failed tests in which the native-like structures cannot be discriminated as those with low energy, are due to omission of protein-protein interactions. The results of this study represent a benchmark in force-field development, and may be useful for evaluation of the performance of different force fields.

Force field bias in protein folding simulations

Long timescale (>1 micros) molecular dynamics simulations of protein folding offer a powerful tool for understanding the atomic-scale interactions that determine a protein's folding pathway and stabilize its native state. Unfortunately, when the simulated protein fails to fold, it is often unclear whether the failure is due to a deficiency in the underlying force fields or simply a lack of sufficient simulation time. We examine one such case, the human Pin1 WW domain, using the recently developed deactivated morphing method to calculate free energy differences between misfolded and folded states. We find that the force field we used favors the misfolded states, explaining the failure of the folding simulations. Possible further applications of deactivated morphing and implications for force field development are discussed.

Artefacts and biases affecting the evaluation of scoring functions on decoy sets for protein structure prediction

MOTIVATION

Decoy datasets, consisting of a solved protein structure and numerous alternative native-like structures, are in common use for the evaluation of scoring functions in protein structure prediction. Several pitfalls with the use of these datasets have been identified in the literature, as well as useful guidelines for generating more effective decoy datasets. We contribute to this ongoing discussion an empirical assessment of several decoy datasets commonly used in experimental studies.

RESULTS

We find that artefacts and sampling issues in the large majority of these data make it trivial to discriminate the native structure. This underlines that evaluation based on the rank/z-score of the native is a weak test of scoring function performance. Moreover, sampling biases present in the way decoy sets are generated or used can strongly affect other types of evaluation measures such as the correlation between score and root mean squared deviation (RMSD) to the native. We demonstrate how, depending on type of bias and evaluation context, sampling biases may lead to both over- or under-estimation of the quality of scoring terms, functions or methods.

AVAILABILITY

Links to the software and data used in this study are available at http://dbkgroup.org/handl/decoy_sets.

Protein structure prediction: when is it useful?

Computationally predicted three-dimensional structure of protein molecules has demonstrated the usefulness in many areas of biomedicine, ranging from approximate family assignments to precise drug screening. For nearly 40 years, however, the accuracy of the predicted models has been dictated by the availability of close structural templates. Progress has recently been achieved in refining low-resolution models closer to the native ones; this has been made possible by combining knowledge-based information from multiple sources of structural templates as well as by improving the energy funnel of physics-based force fields. Unfortunately, there has been no essential progress in the development of techniques for detecting remotely homologous templates and for predicting novel protein structures.

Solvent dramatically affects protein structure refinement

One of the most challenging problems in protein structure prediction is improvement of homology models (structures within 1-3 A C(alpha) rmsd of the native structure), also known as the protein structure refinement problem. It has been shown that improvement could be achieved using in vacuo energy minimization with molecular mechanics and statistically derived continuously differentiable hybrid knowledge-based (KB) potential functions. Globular proteins, however, fold and function in aqueous solution in vivo and in vitro. In this work, we study the role of solvent in protein structure refinement. Molecular dynamics in explicit solvent and energy minimization in both explicit and implicit solvent were performed on a set of 75 native proteins to test the various energy potentials. A more stringent test for refinement was performed on 729 near-native decoys for each native protein. We use a powerfully convergent energy minimization method to show that implicit solvent (GBSA) provides greater improvement for some proteins than the KB potential: 24 of 75 proteins showing an average improvement of >20% in C(alpha) rmsd from the native structure with GBSA, compared to just 7 proteins with KB. Molecular dynamics in explicit solvent moved the structures further away from their native conformation than the initial, unrefined decoys. Implicit solvent gives rise to a deep, smooth potential energy attractor basin that pulls toward the native structure.

Use of decoys to optimize an all-atom force field including hydration

A novel method of parameter optimization is proposed. It makes use of large sets of decoys generated for six nonhomologous proteins with different architecture. Parameter optimization is achieved by creating a free energy gap between sets of nativelike and nonnative conformations. The method is applied to optimize the parameters of a physics-based scoring function consisting of the all-atom ECEPP05 force field coupled with an implicit solvent model (a solvent-accessible surface area model). The optimized force field is able to discriminate near-native from nonnative conformations of the six training proteins when used either for local energy minimization or for short Monte Carlo simulated annealing runs after local energy minimization. The resulting force field is validated with an independent set of six nonhomologous proteins, and appears to be transferable to proteins not included in the optimization; i.e., for five out of the six test proteins, decoys with 1.7- to 4.0-A all-heavy-atom root mean-square deviations emerge as those with the lowest energy. In addition, we examined the set of misfolded structures created by Park and Levitt using a four-state reduced model. The results from these additional calculations confirm the good discriminative ability of the optimized force field obtained with our decoy sets.

Estimating quality of template-based protein models by alignment stability

The error in protein tertiary structure prediction is unavoidable, but it is not explicitly shown in most of the current prediction algorithms. Estimated error of a predicted structure is crucial information for experimental biologists to use the prediction model for design and interpretation of experiments. Here, we propose a method to estimate errors in predicted structures based on the stability of the optimal target-template alignment when compared with a set of suboptimal alignments. The stability of the optimal alignment is quantified by an index named the SuboPtimal Alignment Diversity (SPAD). We implemented SPAD in a profile-based threading algorithm and investigated how well SPAD can indicate errors in threading models using a large benchmark dataset of 5232 alignments. SPAD shows a very good correlation not only to alignment shift errors but also structure-level errors, the root mean square deviation (RMSD) of predicted structure models to the native structures (i.e. global errors), and local errors at each residue position. We have further compared SPAD with seven other quality measures, six from sequence alignment-based measures and one atomic statistical potential, discrete optimized protein energy (DOPE), in terms of the correlation coefficient to the global and local structure-level errors. In terms of the correlation to the RMSD of structure models, when a target and a template are in the same SCOP family, the sequence identity showed a best correlation to the RMSD; in the superfamily level, SPAD was the best; and in the fold level, DOPE was best. However, in a head-to-head comparison, SPAD wins over the other measures. Next, SPAD is compared with three other measures of local errors. In this comparison, SPAD was best in all of the family, the superfamily and the fold levels. Using the discovered correlation, we have also predicted the global and local error of our predicted structures of CASP7 targets by the SPAD. Finally, we proposed a sausage representation of predicted tertiary structures which intuitively indicate the predicted structure and the estimated error range of the structure simultaneously.

Fast procedure for reconstruction of full-atom protein models from reduced representations

We introduce PULCHRA, a fast and robust method for the reconstruction of full-atom protein models starting from a reduced protein representation. The algorithm is particularly suitable as an intermediate step between coarse-grained model-based structure prediction and applications requiring an all-atom structure, such as molecular dynamics, protein-ligand docking, structure-based function prediction, or assessment of quality of the predicted structure. The accuracy of the method was tested on a set of high-resolution crystallographic structures as well as on a set of low-resolution protein decoys generated by a protein structure prediction algorithm TASSER. The method is implemented as a standalone program that is available for download from http://cssb.biology.gatech.edu/skolnick/files/PULCHRA.

Prediction of protein loop conformations using multiscale modeling methods with physical energy scoring functions

This article examines ab initio methods for the prediction of protein loops by a computational strategy of multiscale conformational sampling and physical energy scoring functions. Our approach consists of initial sampling of loop conformations from lattice-based low-resolution models followed by refinement using all-atom simulations. To allow enhanced conformational sampling, the replica exchange method was implemented. Physical energy functions based on CHARMM19 and CHARMM22 parameterizations with generalized Born (GB) solvent models were applied in scoring loop conformations extracted from the lattice simulations and, in the case of all-atom simulations, the ensemble of conformations were generated and scored with these models. Predictions are reported for 25 loop segments, each eight residues long and taken from a diverse set of 22 protein structures. We find that the simulations generally sampled conformations with low global root-mean-square-deviation (RMSD) for loop backbone coordinates from the known structures, whereas clustering conformations in RMSD space and scoring detected less favorable loop structures. Specifically, the lattice simulations sampled basins that exhibited an average global RMSD of 2.21 +/- 1.42 A, whereas clustering and scoring the loop conformations determined an RMSD of 3.72 +/- 1.91 A. Using CHARMM19/GB to refine the lattice conformations improved the sampling RMSD to 1.57 +/- 0.98 A and detection to 2.58 +/- 1.48 A. We found that further improvement could be gained from extending the upper temperature in the all-atom refinement from 400 to 800 K, where the results typically yield a reduction of approximately 1 A or greater in the RMSD of the detected loop. Overall, CHARMM19 with a simple pairwise GB solvent model is more efficient at sampling low-RMSD loop basins than CHARMM22 with a higher-resolution modified analytical GB model; however, the latter simulation method provides a more accurate description of the all-atom energy surface, yet demands a much greater computational cost.

Protein model refinement using an optimized physics-based all-atom force field

One of the greatest challenges in protein structure prediction is the refinement of low-resolution predicted models to high-resolution structures that are close to the native state. Although contemporary structure prediction methods can assemble the correct topology for a large fraction of protein domains, such approximate models are often not of the resolution required for many important applications, including studies of reaction mechanisms and virtual ligand screening. Thus, the development of a method that could bring those structures closer to the native state is of great importance. We recently optimized the relative weights of the components of the Amber ff03 potential on a large set of decoy structures to create a funnel-shaped energy landscape with the native structure at the global minimum. Such an energy function might be able to drive proteins toward their native structure. In this work, for a test set of 47 proteins, with 100 decoy structures per protein that have a range of structural similarities to the native state, we demonstrate that our optimized potential can drive protein models closer to their native structure. Comparing the lowest-energy structure from each trajectory with the starting decoy, structural improvement is seen for 70% of the models on average. The ability to do such systematic structural refinements by using a physics-based all-atom potential represents a promising approach to high-resolution structure prediction.

Progress and challenges in protein structure prediction

Depending on whether similar structures are found in the PDB library, the protein structure prediction can be categorized into template-based modeling and free modeling. Although threading is an efficient tool to detect the structural analogs, the advancements in methodology development have come to a steady state. Encouraging progress is observed in structure refinement which aims at drawing template structures closer to the native; this has been mainly driven by the use of multiple structure templates and the development of hybrid knowledge-based and physics-based force fields. For free modeling, exciting examples have been witnessed in folding small proteins to atomic resolutions. However, predicting structures for proteins larger than 150 residues still remains a challenge, with bottlenecks from both force field and conformational search.

Ten-microsecond molecular dynamics simulation of a fast-folding WW domain

All-atom molecular dynamics (MD) simulations of protein folding allow analysis of the folding process at an unprecedented level of detail. Unfortunately, such simulations have not yet reached their full potential both due to difficulties in sufficiently sampling the microsecond timescales needed for folding, and because the force field used may yield neither the correct dynamical sequence of events nor the folded structure. The ongoing study of protein folding through computational methods thus requires both improvements in the performance of molecular dynamics programs to make longer timescales accessible, and testing of force fields in the context of folding simulations. We report a ten-microsecond simulation of an incipient downhill-folding WW domain mutant along with measurement of a molecular time and activated folding time of 1.5 microseconds and 13.3 microseconds, respectively. The protein simulated in explicit solvent exhibits several metastable states with incorrect topology and does not assume the native state during the present simulations.

Development of a physics-based force field for the scoring and refinement of protein models

The minimal requirements of a physics-based potential that can refine protein structures are the existence of a correlation between the energy with native similarity and the scoring of the native structure as the lowest in energy. To develop such a force field, the relative weights of the Amber ff03 all-atom potential supplemented by an explicit hydrogen-bond potential were adjusted by global optimization of energetic and structural criteria for a large set of protein decoys generated for a set of 58 nonhomologous proteins. The average correlation coefficient of the energy with TM-score significantly improved from 0.25 for the original ff03 potential to 0.65 for the optimized force field. The fraction of proteins for which the native structure had lowest energy increased from 0.22 to 0.90. Moreover, use of an explicit hydrogen-bond potential improves scoring performance of the force field. Promising preliminary results were obtained in applying the optimized potentials to refine protein decoys using only an energy criterion to choose the best decoy among sampled structures. For a set of seven proteins, 63% of the decoys improve, 18% get worse, and 19% are not changed.