Similarity Measures for Protein Ensembles

Analyses of similarities and changes in protein conformation can provide important information regarding protein function and evolution. Many scores, including the commonly used root mean square deviation, have therefore been developed to quantify the similarities of different protein conformations. However, instead of examining individual conformations it is in many cases more relevant to analyse ensembles of conformations that have been obtained either through experiments or from methods such as molecular dynamics simulations. We here present three approaches that can be used to compare conformational ensembles in the same way as the root mean square deviation is used to compare individual pairs of structures. The methods are based on the estimation of the probability distributions underlying the ensembles and subsequent comparison of these distributions. We first validate the methods using a synthetic example from molecular dynamics simulations. We then apply the algorithms to revisit the problem of ensemble averaging during structure determination of proteins, and find that an ensemble refinement method is able to recover the correct distribution of conformations better than standard single-molecule refinement.     

All-Atom Monte Carlo Approach to Protein-Peptide Binding

We develop a procedure for exploring the free energy landscape of protein-peptide binding at atomic detail and apply it to PDZ domain-peptide interactions. The procedure involves soft constraints on receptor proteins providing limited chain flexibility, including backbone motions. Peptide chains are left fully flexible and kept in spatial proximity of the protein through periodic boundary conditions. By extensive Monte Carlo simulations, full representative conformational ensembles at temperatures where bound and unbound states coexist are obtained. To make this approach computationally feasible, we develop an effective all-atom energy function centering on hydrophobicity, hydrogen bonding, and electrostatic interactions. Our initial focus is a set of 11 PDZ domain-peptide pairs with experimentally determined complex structures. Minimum-energy conformations are found to be highly similar to the respective native structures in eight of the cases (all-atom peptide RMSDs < 6 Å). Having achieved that, we turn to a more complete characterization of the bound peptide state through a clustering scheme applied on the full ensembles of peptide structures. We find a significant diversity among bound peptide conformations for several PDZ domains, in particular involving the N terminal side of the peptide chains. Our computational model is then tested further on a set of nine PDZ domain-peptide pairs where the peptides are not originally present in the experimentally determined structures. We find a similar success rate in terms of the nativeness of minimum-energy conformations. Finally, we investigate the ability of our approach to capture variations in binding affinities for different peptide sequences. This is done in particular for a set of related sequences binding to the third PDZ domain of PSD-95 with encouraging results.     

Multi‐scale characterization of the energy landscape of proteins with application to the C3D/Efb‐C complex

We present a novel multi‐level methodology to explore and characterize the low energy landscape and the thermodynamics of proteins. Traditional conformational search methods typically explore only a small portion of the conformational space of proteins and are hard to apply to large proteins due to the large amount of calculations required. In our multi‐scale approach, we first provide an initial characterization of the equilibrium state ensemble of a protein using an efficient computational conformational sampling method. We then enrich the obtained ensemble by performing short Molecular Dynamics (MD) simulations on selected conformations from the ensembles as starting points. To facilitate the analysis of the results, we project the resulting conformations on a low‐dimensional landscape to efficiently focus on important interactions and examine low energy regions. This methodology provides a more extensive sampling of the low energy landscape than an MD simulation starting from a single crystal structure as it explores multiple trajectories of the protein. This enables us to obtain a broader view of the dynamics of proteins and it can help in understanding complex binding, improving docking results and more. In this work, we apply the methodology to provide an extensive characterization of the bound complexes of the C3d fragment of human Complement component C3 and one of its powerful bacterial inhibitors, the inhibitory domain of Staphylococcus aureus extra‐cellular fibrinogen‐binding domain (Efb‐C) and two of its mutants. We characterize several important interactions along the binding interface and define low free energy regions in the three complexes. Proteins 2010. © 2009 Wiley‐Liss, Inc.     

Druggable Protein Interaction Sites Are More Predisposed to Surface Pocket Formation than the Rest of the Protein Surface

Despite intense interest and considerable effort via high-throughput screening, there are few examples of small molecules that directly inhibit protein-protein interactions. This suggests that many protein interaction surfaces may not be intrinsically “druggable” by small molecules, and elevates in importance the few successful examples as model systems for improving our fundamental understanding of druggability. Here we describe an approach for exploring protein fluctuations enriched in conformations containing surface pockets suitable for small molecule binding. Starting from a set of seven unbound protein structures, we find that the presence of low-energy pocket-containing conformations is indeed a signature of druggable protein interaction sites and that analogous surface pockets are not formed elsewhere on the protein. We further find that ensembles of conformations generated with this biased approach structurally resemble known inhibitor-bound structures more closely than equivalent ensembles of unbiased conformations. Collectively these results suggest that “druggability” is a property encoded on a protein surface through its propensity to form pockets, and inspire a model in which the crude features of the predisposed pocket(s) restrict the range of complementary ligands; additional smaller conformational changes then respond to details of a particular ligand. We anticipate that the insights described here will prove useful in selecting protein targets for therapeutic intervention.     

An evolutionary strategy for all-atom folding of the 60-amino-acid bacterial ribosomal protein l20

We have investigated an evolutionary algorithm for de novo all-atom folding of the bacterial ribosomal protein L20. We report results of two simulations that converge to near-native conformations of this 60-amino-acid, four-helix protein. We observe a steady increase of "native content" in both simulated ensembles and a large number of near-native conformations in their final populations. We argue that these structures represent a significant fraction of the low-energy metastable conformations, which characterize the folding funnel of this protein. These data validate our all-atom free-energy force field PFF01 for tertiary structure prediction of a previously inaccessible structural family of proteins. We also compare folding simulations of the evolutionary algorithm with the basin-hopping technique for the Trp-cage protein. We find that the evolutionary algorithm generates a dynamic memory in the simulated population, which leads to faster overall convergence.     

Assembly of polypeptide and protein backbone conformations from low energy ensembles of short fragments: development of strategies and construction of models for myoglobin, lysozyme, and thymosin beta 4.

Recently we developed methods for the construction of knowledge-based mean fields from a data base of known protein structures. As shown previously, this approach can be used to calculate ensembles of probable conformations for short fragments of polypeptide chains. Here we develop procedures for the assembly of short fragments to complete three-dimensional models of polypeptide chains. The amino acid sequence of a given protein is decomposed into all possible overlapping fragments of a given length, and an ensemble of probable conformations is calculated for each fragment. The fragments are assembled to a complete model by choosing appropriate conformations from the individual ensembles and by averaging over equivalent angles. Finally a consistent model is obtained by rebuilding the conformation from the average angles. From the average angles the local variability of the structure can be calculated, which is a useful criterion for the reliability of the model. The procedure is applied to the calculation of the local backbone conformations of myoglobin and lysozyme whose structures have been solved by X-ray analysis and thymosin beta 4, a polypeptide of 43 amino acid residues whose structure was recently investigated by NMR spectroscopy. We demonstrate that substantial fractions of the calculated local backbone conformations are similar to the experimentally determined structures.     

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.     

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.     

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.     

Ab initio construction of polypeptide fragments: efficient generation of accurate,representative ensembles

We describe a novel method to generate ensembles of conformations of the main-chain atoms [N, C(alpha), C, O, Cbeta] for a sequence of amino acids within the context of a fixed protein framework. Each conformation satisfies fundamental stereo-chemical restraints such as idealized geometry, favorable phi/psi angles, and excluded volume. The ensembles include conformations both near and far from the native structure. Algorithms for effective conformational sampling and constant time overlap detection permit the generation of thousands of distinct conformations in minutes. Unlike previous approaches, our method samples dihedral angles from fine-grained phi/psi state sets, which we demonstrate is superior to exhaustive enumeration from coarse phi/psi sets. Applied to a large set of loop structures, our method samples consistently near-native conformations, averaging 0.4, 1.1, and 2.2 A main-chain root-mean-square deviations for four, eight, and twelve residue long loops, respectively. The ensembles make ideal decoy sets to assess the discriminatory power of a selection method. Using these decoy sets, we conclude that quality of anchor geometry cannot reliably identify near-native conformations, though the selection results are comparable to previous loop prediction methods. In a subsequent study (de Bakker et al.: Proteins 2003;51:21-40), we demonstrate that the AMBER forcefield with the Generalized Born solvation model identifies near-native conformations significantly better than previous methods.     

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.     

Automated electron-density sampling reveals widespread conformational polymorphism in proteins

Although proteins populate large structural ensembles, X-ray diffraction data are traditionally interpreted using a single model. To search for evidence of alternate conformers, we developed a program, Ringer, which systematically samples electron density around the dihedral angles of protein side chains. In a diverse set of 402 structures, Ringer identified weak, nonrandom electron-density features that suggest of the presence of hidden, lowly populated conformations for >18% of uniquely modeled residues. Although these peaks occur at electron-density levels traditionally regarded as noise, statistically significant (P < 10⁻⁵) enrichment of peaks at successive rotameric χ angles validates the assignment of these features as unmodeled conformations. Weak electron density corresponding to alternate rotamers also was detected in an accurate electron density map free of model bias. Ringer analysis of the high-resolution structures of free and peptide-bound calmodulin identified shifts in ensembles and connected the alternate conformations to ligand recognition. These results show that the signal in high-resolution electron density maps extends below the traditional 1 σ cutoff, and crystalline proteins are more polymorphic than current crystallographic models. Ringer provides an objective, systematic method to identify previously undiscovered alternate conformations that can mediate protein folding and function.     

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.     

Ensemble models of proteins and protein domains based on distance distribution restraints

Conformational ensembles of intrinsically disordered peptide chains are not fully determined by experimental observations. Uncertainty due to lack of experimental restraints and due to intrinsic disorder can be distinguished if distance distributions restraints are available. Such restraints can be obtained from pulsed dipolar electron paramagnetic resonance (EPR) spectroscopy applied to pairs of spin labels. Here, we introduce a Monte Carlo approach for generating conformational ensembles that are consistent with a set of distance distribution restraints, backbone dihedral angle statistics in known protein structures, and optionally, secondary structure propensities or membrane immersion depths. The approach is tested with simulated restraints for a terminal and an internal loop and for a protein with 69 residues by using sets of sparse restraints for underlying well‐defined conformations and for published ensembles of a premolten globule‐like and a coil‐like intrinsically disordered protein. Proteins 2016; 84:544–560. © 2016 Wiley Periodicals, Inc.     

Interpretation of HDX Data by Maximum-Entropy Reweighting of Simulated Structural Ensembles

Hydrogen-deuterium exchange combined with mass spectrometry (HDX-MS) is a widely applied biophysical technique that probes the structure and dynamics of biomolecules without the need for site-directed modifications or bio-orthogonal labels. The mechanistic interpretation of HDX data, however, is often qualitative and subjective, owing to a lack of quantitative methods to rigorously translate observed deuteration levels into atomistic structural information. To help address this problem, we have developed a methodology to generate structural ensembles that faithfully reproduce HDX-MS measurements. In this approach, an ensemble of protein conformations is first generated, typically using molecular dynamics simulations. A maximum-entropy bias is then applied post hoc to the resulting ensemble such that averaged peptide-deuteration levels, as predicted by an empirical model, agree with target values within a given level of uncertainty. We evaluate this approach, referred to as HDX ensemble reweighting (HDXer), for artificial target data reflecting the two major conformational states of a binding protein. We demonstrate that the information provided by HDX-MS experiments and by the model of exchange are sufficient to recover correctly weighted structural ensembles from simulations, even when the relevant conformations are rarely observed. Degrading the information content of the target data—e.g., by reducing sequence coverage, by averaging exchange levels over longer peptide segments, or by incorporating different sources of uncertainty—reduces the structural accuracy of the reweighted ensemble but still allows for useful insights into the distinctive structural features reflected by the target data. Finally, we describe a quantitative metric to rank candidate structural ensembles according to their correspondence with target data and illustrate the use of HDXer to describe changes in the conformational ensemble of the membrane protein LeuT. In summary, HDXer is designed to facilitate objective structural interpretations of HDX-MS data and to inform experimental approaches and further developments of theoretical exchange models.     

Reweighting of molecular simulations with explicit-solvent SAXS restraints elucidates ion-dependent RNA ensembles

Small-angle X-ray scattering (SAXS) experiments are increasingly used to probe RNA structure. A number of forward models that relate measured SAXS intensities and structural features, and that are suitable to model either explicit-solvent effects or solute dynamics, have been proposed in the past years. Here, we introduce an approach that integrates atomistic molecular dynamics simulations and SAXS experiments to reconstruct RNA structural ensembles while simultaneously accounting for both RNA conformational dynamics and explicit-solvent effects. Our protocol exploits SAXS pure-solute forward models and enhanced sampling methods to sample an heterogenous ensemble of structures, with no information towards the experiments provided on-the-fly. The generated structural ensemble is then reweighted through the maximum entropy principle so as to match reference SAXS experimental data at multiple ionic conditions. Importantly, accurate explicit-solvent forward models are used at this reweighting stage. We apply this framework to the GTPase-associated center, a relevant RNA molecule involved in protein translation, in order to elucidate its ion-dependent conformational ensembles. We show that (a) both solvent and dynamics are crucial to reproduce experimental SAXS data and (b) the resulting dynamical ensembles contain an ion-dependent fraction of extended structures.     

Detection of native-like models for amino acid sequences of unknown three-dimensional structure in a data base of known protein conformations.

We present an approach which can be used to identify native-like folds in a data base of protein conformations in the absence of any sequence homology to proteins in the data base. The method is based on a knowledge-based force field derived from a set of known protein conformations. A given sequence is mounted on all conformations in the data base and the associated energies are calculated. Using several conformations and sequences from the globin family we show that the native conformation is identified correctly. In fact the resolution of the force field is high enough to discriminate between a native fold and several closely related conformations. We then apply the procedure to several globins of known sequence but unknown three dimensional structure. The homology of these sequences to globins of known structures in the data base ranges from 49 to 17%. With one exception we find that for all globin sequences one of the known globin folds is identified as the most favorable conformation. These results are obtained using a force field derived from a data base devoid of globins of known structure. We briefly discuss useful applications in protein structural research and future development of our approach.     

Modeling protein conformational ensembles: from missing loops to equilibrium fluctuations

Characterizing protein flexibility is an important goal for understanding the physical-chemical principles governing biological function. This paper presents a Fragment Ensemble Method to capture the mobility of a protein fragment such as a missing loop and its extension into a Protein Ensemble Method to characterize the mobility of an entire protein at equilibrium. The underlying approach in both methods is to combine a geometric exploration of conformational space with a statistical mechanics formulation to generate an ensemble of physical conformations on which thermodynamic quantities can be measured as ensemble averages. The Fragment Ensemble Method is validated by applying it to characterize loop mobility in both instances of strongly stable and disordered loop fragments. In each instance, fluctuations measured over generated ensembles are consistent with data from experiment and simulation. The Protein Ensemble Method captures the mobility of an entire protein by generating and combining ensembles of conformations for consecutive overlapping fragments defined over the protein sequence. This method is validated by applying it to characterize flexibility in ubiquitin and protein G. Thermodynamic quantities measured over the ensembles generated for both proteins are fully consistent with available experimental data. On these proteins, the method recovers nontrivial data such as order parameters, residual dipolar couplings, and scalar couplings. Results presented in this work suggest that the proposed methods can provide insight into the interplay between protein flexibility and function.     

The effect of a DeltaK280 mutation on the unfolded state of a microtubule-binding repeat in Tau

Tau is a natively unfolded protein that forms intracellular aggregates in the brains of patients with Alzheimer's disease. To decipher the mechanism underlying the formation of tau aggregates, we developed a novel approach for constructing models of natively unfolded proteins. The method, energy-minima mapping and weighting (EMW), samples local energy minima of subsequences within a natively unfolded protein and then constructs ensembles from these energetically favorable conformations that are consistent with a given set of experimental data. A unique feature of the method is that it does not strive to generate a single ensemble that represents the unfolded state. Instead we construct a number of candidate ensembles, each of which agrees with a given set of experimental constraints, and focus our analysis on local structural features that are present in all of the independently generated ensembles. Using EMW we generated ensembles that are consistent with chemical shift measurements obtained on tau constructs. Thirty models were constructed for the second microtubule binding repeat (MTBR2) in wild-type (WT) tau and a DeltaK280 mutant, which is found in some forms of frontotemporal dementia. By focusing on structural features that are preserved across all ensembles, we find that the aggregation-initiating sequence, PHF6*, prefers an extended conformation in both the WT and DeltaK280 sequences. In addition, we find that residue K280 can adopt a loop/turn conformation in WT MTBR2 and that deletion of this residue, which can adopt nonextended states, leads to an increase in locally extended conformations near the C-terminus of PHF6*. As an increased preference for extended states near the C-terminus of PHF6* may facilitate the propagation of beta-structure downstream from PHF6*, these results explain how a deletion at position 280 can promote the formation of tau aggregates.