Refinement of Peptide Conformational Ensembles by 2D IR Spectroscopy: Application to Ala‒Ala‒Ala

Characterizing ensembles of intrinsically disordered proteins is experimentally challenging because of the ill-conditioned nature of ensemble determination with limited data and the intrinsic fast dynamics of the conformational ensemble. Amide I two-dimensional infrared (2D IR) spectroscopy has picosecond time resolution to freeze structural ensembles as needed for probing disordered-protein ensembles and conformational dynamics. Also, developments in amide I computational spectroscopy now allow a quantitative and direct prediction of amide I spectra based on conformational distributions drawn from molecular dynamics simulations, providing a route to ensemble refinement against experimental spectra. We performed a Bayesian ensemble refinement method on Ala–Ala–Ala against isotope-edited Fourier-transform infrared spectroscopy and 2D IR spectroscopy and tested potential factors affecting the quality of ensemble refinements. We found that isotope-edited 2D IR spectroscopy provides a stringent constraint on Ala–Ala–Ala conformations and returns consistent conformational ensembles with the dominant ppII conformer across varying prior distributions from many molecular dynamics force fields and water models. The dominant factor influencing ensemble refinements is the systematic frequency uncertainty from spectroscopic maps. However, the uncertainty of conformer populations can be significantly reduced by incorporating 2D IR spectra in addition to traditional Fourier-transform infrared spectra. Bayesian ensemble refinement against isotope-edited 2D IR spectroscopy thus provides a route to probe equilibrium-complex protein ensembles and potentially nonequilibrium conformational dynamics.     

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. Proteins 2013. 2012 Published by Wiley Periodicals, Inc.     

Application of statistical potentials to protein structure refinement from low resolution ab initio models

Recently ab initio protein structure prediction methods have advanced sufficiently so that they often assemble the correct low resolution structure of the protein. To enhance the speed of conformational search, many ab initio prediction programs adopt a reduced protein representation. However, for drug design purposes, better quality structures are probably needed. To achieve this refinement, it is natural to use a more detailed heavy atom representation. Here, as opposed to costly implicit or explicit solvent molecular dynamics simulations, knowledge-based heavy atom pair potentials were employed. By way of illustration, we tried to improve the quality of the predicted structures obtained from the ab initio prediction program TOUCHSTONE by three methods: local constraint refinement, reduced predicted tertiary contact refinement, and statistical pair potential guided molecular dynamics. Sixty-seven predicted structures from 30 small proteins (less than 150 residues in length) representing different structural classes (alpha, beta, alpha;/beta) were examined. In 33 cases, the root mean square deviation (RMSD) from native structures improved by more than 0.3 A; in 19 cases, the improvement was more than 0.5 A, and sometimes as large as 1 A. In only seven (four) cases did the refinement procedure increase the RMSD by more than 0.3 (0.5) A. For the remaining structures, the refinement procedures changed the structures by less than 0.3 A. While modest, the performance of the current refinement methods is better than the published refinement results obtained using standard molecular dynamics.     

Folding simulations of Trp‐cage mini protein in explicit solvent using biasing potential replica‐exchange molecular dynamics simulations

Replica exchange molecular dynamics (RexMD) simulations are frequently used for studying structure formation and dynamics of peptides and proteins. A significant drawback of standard temperature RexMD is, however, the rapid increase of the replica number with increasing system size to cover a desired temperature range. A recently developed Hamiltonian RexMD method has been used to study folding of the Trp‐cage protein. It employs a biasing potential that lowers the backbone dihedral barriers and promotes peptide backbone transitions along the replica coordinate. In two independent applications of the biasing potential RexMD method including explicit solvent and starting from a completely unfolded structure the formation of near‐native conformations was observed after 30–40 ns simulation time. The conformation representing the most populated cluster at the final simulation stage had a backbone root mean square deviation of ～1.3 Å from the experimental structure. This was achieved with a very modest number of five replicas making it well suited for peptide and protein folding and refinement studies including explicit solvent. In contrast, during five independent continuous 70 ns molecular dynamics simulations formation of collapsed states but no near native structure formation was observed. The simulations predict a largely collapsed state with a significant helical propensity for the helical domain of the Trp‐cage protein already in the unfolded state. Hydrogen bonded bridging water molecules were identified that could play an active role by stabilizing the arrangement of the helical domain with respect to the rest of the chain already in intermediate states of the protein. Proteins 2009. © 2008 Wiley‐Liss, Inc.     

Interpreting Dynamically-Averaged Scalar Couplings in Proteins

The experimental determination of scalar three-bond coupling constants represents a powerful method to probe both the structure and dynamics of proteins. The detailed structural interpretation of such coupling constants is usually based on Karplus relationships, which allow the measured couplings to be related to the torsion angles of the molecules. As the measured couplings are sensitive to thermal fluctuations, the parameters in the Karplus relationships are better derived from ensembles representing the distributions of dihedral angles present in solution, rather than from single conformations. We present a method to derive such parameters that uses ensembles of conformations determined through dynamic-ensemble refinement – a method that provides structural ensembles that simultaneously represent both the structure and the associated dynamics of a protein.     

The MUMO (minimal under-restraining minimal over-restraining) method for the determination of native state ensembles of proteins

While reliable procedures for determining the conformations of proteins are available, methods for generating ensembles of structures that also reflect their flexibility are much less well established. Here we present a systematic assessment of the ability of ensemble-averaged molecular dynamics simulations with ensemble-averaged NMR restraints to simultaneously reproduce the average structure of proteins and their associated dynamics. We discuss the effects that under-restraining (overfitting) and over-restraining (underfitting) have on the structures generated in ensemble-averaged molecular simulations. We then introduce the MUMO (minimal under-restraining minimal over-restraining) method, a procedure in which different observables are averaged over a different number of molecules. As both over-restraining and under-restraining are significantly reduced in the MUMO method, it is possible to generate ensembles of conformations that accurately characterize both the structure and the dynamics of native states of proteins. The application of the MUMO method to the protein ubiquitin yields a high-resolution structural ensemble with an RDC Q-factor of 0.19.     

Distance-Based Metrics for Comparing Conformational Ensembles of Intrinsically Disordered Proteins

Intrinsically disordered proteins are proteins whose native functional states represent ensembles of highly diverse conformations. Such ensembles are a challenge for quantitative structure comparisons because their conformational diversity precludes optimal superimposition of the atomic coordinates necessary for deriving common similarity measures such as the root mean-square deviation of these coordinates. Here, we introduce superimposition-free metrics that are based on computing matrices of the Cα-Cα distance distributions within ensembles and comparing these matrices between ensembles. Differences between two matrices yield information on the similarity between specific regions of the polypeptide, whereas the global structural similarity is captured by the root mean-square difference between the medians of the Cα-Cα distance distributions of two ensembles. Together, our metrics enable rigorous investigations of structure-function relationships in conformational ensembles of intrinsically disordered proteins derived using experimental restraints or by molecular simulations and for proteins containing both structured and disordered regions.     

Discrete analyses of protein dynamics

Abstract

Protein structures are highly dynamic macromolecules. This dynamics is often analysed through experimental and/or computational methods only for an isolated or a limited number of proteins. Here, we explore large-scale protein dynamics simulation to observe dynamics of local protein conformations using different perspectives. We analysed molecular dynamics to investigate protein flexibility locally, using classical approaches such as RMSf, solvent accessibility, but also innovative approaches such as local entropy. First, we focussed on classical secondary structures and analysed specifically how β-strand, β–turns, and bends evolve during molecular simulations. We underlined interesting specific bias between β–turns and bends, which are considered as the same category, while their dynamics show differences. Second, we used a structural alphabet that is able to approximate every part of the protein structures conformations, namely protein blocks (PBs) to analyse (i) how each initial local protein conformations evolve during dynamics and (ii) if some exchange can exist among these PBs. Interestingly, the results are largely complex than simple regular/rigid and coil/flexible exchange. Abbreviations N_eq number of equivalent

PB Protein Blocks

PDB Protein DataBank

RMSf root mean square fluctuations

Communicated by Ramaswamy H. Sarma     

Statistical characterization of protein ensembles

When accounting for structural fluctuations or measurement errors, a single rigid structure may not be sufficient to represent a protein. One approach to solve this problem is to represent the possible conformations as a discrete set of observed conformations, an ensemble. In this work, we follow a different richer approach, and introduce a framework for estimating probability density functions in very high dimensions, and then apply it to represent ensembles of folded proteins. This proposed approach combines techniques such as kernel density estimation, maximum likelihood, cross-validation, and bootstrapping. We present the underlying theoretical and computational framework and apply it to artificial data and protein ensembles obtained from molecular dynamics simulations. We compare the results with those obtained experimentally, illustrating the potential and advantages of this representation.     

Monte Carlo replica‐exchange based ensemble docking of protein conformations

A replica‐exchange Monte Carlo (REMC) ensemble docking approach has been developed that allows efficient exploration of protein–protein docking geometries. In addition to Monte Carlo steps in translation and orientation of binding partners, possible conformational changes upon binding are included based on Monte Carlo selection of protein conformations stored as ordered pregenerated conformational ensembles. The conformational ensembles of each binding partner protein were generated by three different approaches starting from the unbound partner protein structure with a range spanning a root mean square deviation of 1–2.5 Å with respect to the unbound structure. Because MC sampling is performed to select appropriate partner conformations on the fly the approach is not limited by the number of conformations in the ensemble compared to ensemble docking of each conformer pair in ensemble cross docking. Although only a fraction of generated conformers was in closer agreement with the bound structure the REMC ensemble docking approach achieved improved docking results compared to REMC docking with only the unbound partner structures or using docking energy minimization methods. The approach has significant potential for further improvement in combination with more realistic structural ensembles and better docking scoring functions. Proteins 2017; 85:924–937. © 2016 Wiley Periodicals, Inc.     

Separating true positive predicted residue contacts from false positive ones in mainly alpha proteins, using constrained Metropolis MC simulations

We present a method that significantly improves the accuracy of predicted proximal residue pairs in protein molecules. Computational methods for predicting pairs of amino acids that are distant in the protein sequence but close in the protein 3D structure can benefit attempts to in silico recognize the fold of a protein molecule. Unfortunately, currently available methods suffer from low predictive accuracy. In this work, we use Monte Carlo simulations to fold protein molecules with proximal pair predictions used as additional energy constraints. To test our methods, we study molecules with known tertiary structures. With Monte Carlo, we generate ensembles of structures for each set of residues constraints. The distribution of the root mean square deviation of the folded structures from the known native structure reveals clear information about the accuracy of the constraint sets used. With recursive substitutions of constraints, false positive predictions are identified and filtered out and significant improvements in accuracy are observed.     

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.Proteins 2012; © 2012 Wiley Periodicals, Inc.     

Three-dimensional structure of the apo form of the N-terminal EGF-like module of blood coagulation factor X as determined by NMR spectroscopy and simulated folding.

The three-dimensional structure of a 42-residue fragment containing the N-terminal EGF-like module of blood coagulation factor X was determined by means of 2D NMR spectroscopy and computer simulation. The spectroscopic data consisted of 370 NOE distances and 27 dihedral angle constraints. These were used to generate peptide conformations by molecular dynamics simulation. The simulations used a novel functional form for the constraint potentials and were performed with two time steps to ensure rapid execution. Apart from preliminary runs to aid assignment of NOEs, 60 runs resulted in 13 accepted structures, which have two antiparallel beta sheets, no alpha helices, and five tight turns. There is no hydrophobic cluster. The root mean square deviation for the backbone of the 13 conformations is 0.65 +/- 0.11 A against their mean conformation. About half of the side chains have well-defined structure. The overall conformation is similar to that of murine EGF.     

A flexible docking scheme to explore the binding selectivity of PDZ domains

Modeling of protein binding site flexibility in molecular docking is still a challenging problem due to the large conformational space that needs sampling. Here, we propose a flexible receptor docking scheme: A dihedral restrained replica exchange molecular dynamics (REMD), where we incorporate the normal modes obtained by the Elastic Network Model (ENM) as dihedral restraints to speed up the search towards correct binding site conformations. To our knowledge, this is the first approach that uses ENM modes to bias REMD simulations towards binding induced fluctuations in docking studies. In our docking scheme, we first obtain the deformed structures of the unbound protein as initial conformations by moving along the binding fluctuation mode, and perform REMD using the ENM modes as dihedral restraints. Then, we generate an ensemble of multiple receptor conformations (MRCs) by clustering the lowest replica trajectory. Using ROSETTA LIGAND , we dock ligands to the clustered conformations to predict the binding pose and affinity. We apply this method to postsynaptic density‐95/Dlg/ZO‐1 (PDZ) domains; whose dynamics govern their binding specificity. Our approach produces the lowest energy bound complexes with an average ligand root mean square deviation of 0.36 Å. We further test our method on (i) homologs and (ii) mutant structures of PDZ where mutations alter the binding selectivity. In both cases, our approach succeeds to predict the correct pose and the affinity of binding peptides. Overall, with this approach, we generate an ensemble of MRCs that leads to predict the binding poses and specificities of a protein complex accurately.     

Constructing ensembles of flexible fragments in native proteins by iterative stochastic elimination is relevant to protein-protein interfaces

We investigate the extent to which ensembles of flexible fragments (FF), generated by our loop conformational search method, include conformations that are near experimental and reflect conformational changes that these FFs undergo when binary protein-protein complexes are formed. Twenty-eight FFs, which are located in protein-protein interfaces and have different conformations in the bound structure (BS) and unbound structure (UbS) were extracted. The conformational space of these fragments in the BS and UbS was explored with our method which is based on the iterative stochastic elimination (ISE) algorithm. Conformational search of BSs generated bound ensembles and conformational search of UbSs produced unbound ensembles. ISE samples conformations near experimental (less than 1.05 A root mean square deviation, RMSD) for 51 out of the 56 examined fragments in the bound and unbound ensembles. In 14 out of the 28 unbound fragments, it also samples conformations within 1.05 A from the BS in the unbound ensemble. Sampling the bound conformation in the unbound ensemble demonstrates the potential biological relevance of the predicted ensemble. The 10 lowest energy conformations are the best choice for docking experiments, compared with any other 10 conformations of the ensembles. We conclude that generating conformational ensembles for FFs with ISE is relevant to FF conformations in the UbS and BS. Forming ensembles of the isolated proteins with our method prior to docking represents more comprehensively their inherent flexibility and is expected to improve docking experiments compared with results obtained by docking only UbSs.     

Partition decoupling for multi-gene analysis of gene expression profiling data

Background

Molecular dynamics (MD) simulations are powerful tools to investigate the conformational dynamics of proteins that is often a critical element of their function. Identification of functionally relevant conformations is generally done clustering the large ensemble of structures that are generated. Recently, Self-Organising Maps (SOMs) were reported performing more accurately and providing more consistent results than traditional clustering algorithms in various data mining problems. We present a novel strategy to analyse and compare conformational ensembles of protein domains using a two-level approach that combines SOMs and hierarchical clustering.

Results

The conformational dynamics of the α-spectrin SH3 protein domain and six single mutants were analysed by MD simulations. The Cα's Cartesian coordinates of conformations sampled in the essential space were used as input data vectors for SOM training, then complete linkage clustering was performed on the SOM prototype vectors. A specific protocol to optimize a SOM for structural ensembles was proposed: the optimal SOM was selected by means of a Taguchi experimental design plan applied to different data sets, and the optimal sampling rate of the MD trajectory was selected. The proposed two-level approach was applied to single trajectories of the SH3 domain independently as well as to groups of them at the same time. The results demonstrated the potential of this approach in the analysis of large ensembles of molecular structures: the possibility of producing a topological mapping of the conformational space in a simple 2D visualisation, as well as of effectively highlighting differences in the conformational dynamics directly related to biological functions.

Conclusions

The use of a two-level approach combining SOMs and hierarchical clustering for conformational analysis of structural ensembles of proteins was proposed. It can easily be extended to other study cases and to conformational ensembles from other sources.     

Clustering biomolecular complexes by residue contacts similarity

Inaccuracies in computational molecular modeling methods are often counterweighed by brute-force generation of a plethora of putative solutions. These are then typically sieved via structural clustering based on similarity measures such as the root mean square deviation (RMSD) of atomic positions. Albeit widely used, these measures suffer from several theoretical and technical limitations (e.g., choice of regions for fitting) that impair their application in multicomponent systems (N > 2), large-scale studies (e.g., interactomes), and other time-critical scenarios. We present here a simple similarity measure for structural clustering based on atomic contacts--the fraction of common contacts--and compare it with the most used similarity measure of the protein docking community--interface backbone RMSD. We show that this method produces very compact clusters in remarkably short time when applied to a collection of binary and multicomponent protein-protein and protein-DNA complexes. Furthermore, it allows easy clustering of similar conformations of multicomponent symmetrical assemblies in which chain permutations can occur. Simple contact-based metrics should be applicable to other structural biology clustering problems, in particular for time-critical or large-scale endeavors.     

A comparative analysis of the equilibrium dynamics of a designed protein inferred from NMR,X‐ray,and computations

A detailed analysis of high‐resolution structural data and computationally predicted dynamics was carried out for a designed sugar‐binding protein. The mean‐square deviations in the positions of residues derived from nuclear magnetic resonance (NMR) models and those inferred from X‐ray crystallographic B‐factors for two different crystal forms were compared with the predictions based on the Gaussian Network Model (GNM) and the results from molecular dynamics (MD) simulations. GNM systematically yielded a higher correlation than MD, with experimental data, suggesting that the lack of atomistic details in the coarse‐grained GNM is more than compensated for by the mathematically exact evaluation of fluctuations using the native contacts topology. Evidence is provided that particular loop motions are curtailed by intermolecular contacts in the crystal environment causing a discrepancy between theory and experiments. Interestingly, the information conveyed by X‐ray crystallography becomes more consistent with NMR models and computational predictions when ensembles of X‐ray models are considered. Less precise (broadly distributed) ensembles indeed appear to describe the accessible conformational space under native state conditions better than B‐factors. Our results highlight the importance of using multiple conformations obtained by alternative experimental methods, and analyzing results from both coarse‐grained models and atomic simulations, for accurate assessment of motions accessible to proteins under native state conditions. Proteins 2009. © 2009 Wiley‐Liss, Inc.     

Computational techniques for efficient conformational sampling of proteins

In this review, we summarize the computational methods for sampling the conformational space of biomacromolecules. We discuss the methods applicable to find only lowest energy conformations (global minimization of the potential-energy function) and to generate canonical ensembles (canonical Monte Carlo method and canonical molecular dynamics method and their extensions). Special attention is devoted to the use of coarse-grained models that enable simulations to be enhanced by several orders of magnitude.     

Progress and challenges in high-resolution refinement of protein structure models

Achieving atomic level accuracy in de novo structure prediction presents a formidable challenge even in the context of protein models with correct topologies. High-resolution refinement is a fundamental test of force field accuracy and sampling methodology, and its limited success in both comparative modeling and de novo prediction contexts highlights the limitations of current approaches. We constructed four tests to identify bottlenecks in our current approach and to guide progress in this challenging area. The first three tests showed that idealized native structures are stable under our refinement simulation conditions and that the refinement protocol can significantly decrease the root mean square deviation (RMSD) of perturbed native structures. In the fourth test we applied the refinement protocol to de novo models and showed that accurate models could be identified based on their energies, and in several cases many of the buried side chains adopted native-like conformations. We also showed that the differences in backbone and side-chain conformations between the refined de novo models and the native structures are largely localized to loop regions and regions where the native structure has unusual features such as rare rotamers or atypical hydrogen bonding between beta-strands. The refined de novo models typically have higher energies than refined idealized native structures, indicating that sampling of local backbone conformations and side-chain packing arrangements in a condensed state is a primary obstacle.