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.     

Ab initio construction of polypeptide fragments: Accuracy of loop decoy discrimination by an all-atom statistical potential and the AMBER force field with the Generalized Born solvation model

The accuracy of model selection from decoy ensembles of protein loop conformations was explored by comparing the performance of the Samudrala-Moult all-atom statistical potential (RAPDF) and the AMBER molecular mechanics force field, including the Generalized Born/surface area solvation model. Large ensembles of consistent loop conformations, represented at atomic detail with idealized geometry, were generated for a large test set of protein loops of 2 to 12 residues long by a novel ab initio method called RAPPER that relies on fine-grained residue-specific phi/psi propensity tables for conformational sampling. Ranking the conformers on the basis of RAPDF scores resulted in selected conformers that had an average global, non-superimposed RMSD for all heavy mainchain atoms ranging from 1.2 A for 4-mers to 2.9 A for 8-mers to 6.2 A for 12-mers. After filtering on the basis of anchor geometry and RAPDF scores, ranking by energy minimization of the AMBER/GBSA potential energy function selected conformers that had global RMSD values of 0.5 A for 4-mers, 2.3 A for 8-mers, and 5.0 A for 12-mers. Minimized fragments had, on average, consistently lower RMSD values (by 0.1 A) than their initial conformations. The importance of the Generalized Born solvation energy term is reflected by the observation that the average RMSD accuracy for all loop lengths was worse when this term is omitted. There are, however, still many cases where the AMBER gas-phase minimization selected conformers of lower RMSD than the AMBER/GBSA minimization. The AMBER/GBSA energy function had better correlation with RMSD to native than the RAPDF. When the ensembles were supplemented with conformations extracted from experimental structures, a dramatic improvement in selection accuracy was observed at longer lengths (average RMSD of 1.3 A for 8-mers) when scoring with the AMBER/GBSA force field. This work provides the basis for a promising hybrid approach of ab initio and knowledge-based methods for loop modeling.     

Solution structure of Fe(II) cytochrome c551 from Pseudomonas aeruginosa as determined by two-dimensional 1H NMR.

The solution structure of Fe(II) cytochrome c551 from Pseudomonas aeruginosa based on 2D 1H NMR data is reported. Two sets of structure calculations were completed with a combination of simulated annealing and distance geometry calculations: one set of 20 structures included the heme-peptide covalent linkages, and one set of 10 structures excluded them. The main-chain atoms were well constrained within the two structural ensembles (1.30 and 1.35 A average RMSD, respectively) except for two regions spanning residues 30-40 and 60-70. The results were essentially the same when global fold comparisons were made between the ensembles with an average RMSD of 1.33 A. In total, 556 constraints were used, including 479 NOEs, 53 volume constraints, and 24 other distances. This report represents the first solution structure determination of a heme protein by 2D 1H NMR and should provide a basis for the application of these techniques to other proteins containing large prosthetic groups or cofactors.     

Clustering algorithms for identifying core atom sets and for assessing the precision of protein structure ensembles

An important open question in the field of NMR-based biomolecular structure determination is how best to characterize the precision of the resulting ensemble of structures. Typically, the RMSD, as minimized in superimposing the ensemble of structures, is the preferred measure of precision. However, the presence of poorly determined atomic coordinates and multiple "RMSD-stable domains"--locally well-defined regions that are not aligned in global superimpositions--complicate RMSD calculations. In this paper, we present a method, based on a novel, structurally defined order parameter, for identifying a set of core atoms to use in determining superimpositions for RMSD calculations. In addition we present a method for deciding whether to partition that core atom set into "RMSD-stable domains" and, if so, how to determine partitioning of the core atom set. We demonstrate our algorithm and its application in calculating statistically sound RMSD values by applying it to a set of NMR-derived structural ensembles, superimposing each RMSD-stable domain (or the entire core atom set, where appropriate) found in each protein structure under consideration. A parameter calculated by our algorithm using a novel, kurtosis-based criterion, the epsilon-value, is a measure of precision of the superimposition that complements the RMSD. In addition, we compare our algorithm with previously described algorithms for determining core atom sets. The methods presented in this paper for biomolecular structure superimposition are quite general, and have application in many areas of structural bioinformatics and structural biology.     

Characterizing molecular flexibility by combining least root mean square deviation measures

The root mean square deviation (RMSD) and the least RMSD are two widely used similarity measures in structural bioinformatics. Yet, they stem from global comparisons, possibly obliterating locally conserved motifs. We correct these limitations with the so-called combined RMSD, which mixes independent lRMSD measures, each computed with its own rigid motion. The combined RMSD is relevant in two main scenarios, namely to compare (quaternary) structures based on motifs defined from the sequence (domains and SSE) and to compare structures based on structural motifs yielded by local structural alignment methods. We illustrate the benefits of combined RMSD over the usual RMSD on three problems, namely (a) the assignment of quaternary structures for hemoglobin (scenario #1), (b) the calculation of structural phylogenies (case study: class II fusion proteins; scenario #1), and (c) the analysis of conformational changes based on combined RMSD of rigid structural motifs (case study: one class II fusion protein; scenario #2). Based on these illustrations, we argue that the combined RMSD is a tool of choice to perform positive and negative discrimination of degree of freedom, with applications to the design of move sets and collective coordinates. Executables to compute combined RMSD are available within the Structural Bioinformatics Library ( http://sbl.inria.fr ).     

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.     

Protein-protein docking by simulating the process of association subject to biochemical constraints

We present a computational procedure for modeling protein-protein association and predicting the structures of protein-protein complexes. The initial sampling stage is based on an efficient Brownian dynamics algorithm that mimics the physical process of diffusional association. Relevant biochemical data can be directly incorporated as distance constraints at this stage. The docked configurations are then grouped with a hierarchical clustering algorithm into ensembles that represent potential protein-protein encounter complexes. Flexible refinement of selected representative structures is done by molecular dynamics simulation. The protein-protein docking procedure was thoroughly tested on 10 structurally and functionally diverse protein-protein complexes. Starting from X-ray crystal structures of the unbound proteins, in 9 out of 10 cases it yields structures of protein-protein complexes close to those determined experimentally with the percentage of correct contacts >30% and interface backbone RMSD <4 A. Detailed examination of all the docking cases gives insights into important determinants of the performance of the computational approach in modeling protein-protein association and predicting of protein-protein complex structures.     

Structural prediction of peptides bound to MHC class I

An ab initio structure prediction approach adapted to the peptide-major histocompatibility complex (MHC) class I system is presented. Based on structure comparisons of a large set of peptide-MHC class I complexes, a molecular dynamics protocol is proposed using simulated annealing (SA) cycles to sample the conformational space of the peptide in its fixed MHC environment. A set of 14 peptide-human leukocyte antigen (HLA) A0201 and 27 peptide-non-HLA A0201 complexes for which X-ray structures are available is used to test the accuracy of the prediction method. For each complex, 1000 peptide conformers are obtained from the SA sampling. A graph theory clustering algorithm based on heavy atom root-mean-square deviation (RMSD) values is applied to the sampled conformers. The clusters are ranked using cluster size, mean effective or conformational free energies, with solvation free energies computed using Generalized Born MV 2 (GB-MV2) and Poisson-Boltzmann (PB) continuum models. The final conformation is chosen as the center of the best-ranked cluster. With conformational free energies, the overall prediction success is 83% using a 1.00 Angstroms crystal RMSD criterion for main-chain atoms, and 76% using a 1.50 Angstroms RMSD criterion for heavy atoms. The prediction success is even higher for the set of 14 peptide-HLA A0201 complexes: 100% of the peptides have main-chain RMSD values < or =1.00 Angstroms and 93% of the peptides have heavy atom RMSD values < or =1.50 Angstroms. This structure prediction method can be applied to complexes of natural or modified antigenic peptides in their MHC environment with the aim to perform rational structure-based optimizations of tumor vaccines.     

The building of protein structures from alpha-carbon coordinates

A procedure for the construction of complete protein structures from only alpha-carbon coordinates is described. This involves building the backbone by sequential addition of Pro, Gly, or Ala residues. This main chain structure is then refined using molecular dynamics. Side chains are constructed by sequential addition of atoms with intermediate molecular dynamics refinement. For alpha lytic protease (a structure that is mostly beta sheet) a backbone root mean square deviation (RMSD) of 0.19 A and an overall RMSD of 1.24 A from the crystallographic coordinates are attained. For troponin C (67% alpha-helix), where the coordinates are available only for the alpha-carbons, a backbone RMSD of 0.41 A and an overall RMSD of 1.68 A are attained (fits kindly provided by Dr. Michael James and Natalie Strynadka). For flavodoxin a backbone RMSD of 0.49 A and an overall RMSD of 1.64 A were attained.     

Ab initio modeling of small, medium, and large loops in proteins.

This study presents different procedures for ab initio modeling of peptide loops of different sizes in proteins. Small loops (up to 8--12 residues) were generated by a straightforward procedure with subsequent "averaging" over all the low-energy conformers obtained. The averaged conformer fairly represents the entire set of low-energy conformers, root mean square deviation (RMSD) values being from 1.01 A for a 4-residue loop to 1.94 A for an 8-residue loop. Three-dimensional (3D) structures for several medium loops (20--30 residues) and for two large loops (54 and 61 residues) were predicted using residue-residue contact matrices divided into variable parts corresponding to the loops, and into a constant part corresponding to the known core of the protein. For each medium loop, a very limited number of sterically reasonable C(alpha) traces (from 1 to 3) was found; RMSD values ranged from 2.4 to 5.9 A. Single C(alpha) traces predicted for each of the large loops possessed RMSD values of 4.5 A. Generally, ab initio loop modeling presented in this work combines elements of computational procedures developed both for protein folding and for peptide conformational analysis.     

DynaDock: A new molecular dynamics‐based algorithm for protein–peptide docking including receptor flexibility

Molecular docking programs play an important role in drug development and many well‐established methods exist. However, there are two situations for which the performance of most approaches is still not satisfactory, namely inclusion of receptor flexibility and docking of large, flexible ligands like peptides. In this publication a new approach is presented for docking peptides into flexible receptors. For this purpose a two step procedure was developed: first, the protein–peptide conformational space is scanned and approximate ligand poses are identified and second, the identified ligand poses are refined by a new molecular dynamics‐based method, optimized potential molecular dynamics (OPMD). The OPMD approach uses soft‐core potentials for the protein–peptide interactions and applies a new optimization scheme to the soft‐core potential. Comparison with refinement results obtained by conventional molecular dynamics and a soft‐core scaling approach shows significant improvements in the sampling capability for the OPMD method. Thus, the number of starting poses needed for successful refinement is much lower than for the other methods. The algorithm was evaluated on 15 protein–peptide complexes with 2–16mer peptides. Docking poses with peptide RMSD values <2.10 Å from the equilibrated experimental structures were obtained in all cases. For four systems docking into the unbound receptor structures was performed, leading to peptide RMSD values <2.12 Å. Using a specifically fitted scoring function in 11 of 15 cases the best scoring poses featured a peptide RMSD ≤2.10 Å. Proteins 2010. © 2009 Wiley‐Liss, Inc.     

Efficient substructure RMSD query algorithms.

Protein structure analysis is a very important research topic in the molecular biology of the post-genomic era. The root mean square deviation (RMSD) is the most frequently used measure for comparing two protein three-dimensional (3-D) structures. In this paper, we deal with two fundamental problems related to the RMSD. We first deal with a problem called the "range RMSD query" problem. Given an aligned pair of structures, the problem is to compute the RMSD between two aligned substructures of them without gaps. This problem has many applications in protein structure analysis. We propose a linear-time preprocessing algorithm that enables constant-time RMSD computation. Next, we consider a problem called the "substructure RMSD query" problem, which is a generalization of the above range RMSD query problem. It is a problem to compute the RMSD between any substructures of two unaligned structures without gaps. Based on the algorithm for the range RMSD problem, we propose an O(nm) preprocessing algorithm that enables constant-time RMSD computation, where n and m are the lengths of the given structures. Moreover, we propose O(nm log r/r)-time and O(nm/r)-space preprocessing algorithm that enables O(r) query, where r is an arbitrary integer such that 1 < or = r < or = min(n, m). We also show that our strategy also works for another measure called the unit-vector root mean square deviation (URMSD), which is a variant of the RMSD.     

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.     

Degradation of Alzheimer’s Amyloid-β by a Catalytically Inactive Insulin-Degrading Enzyme

It is known that insulin-degrading-enzyme (IDE) plays a crucial role in the clearance of Alzheimer’s amyloid-β (Aβ). The cysteine-free IDE mutant (cf-E111Q-IDE) is catalytically inactive against insulin, but its effect on Aβ degradation is unknown that would help in the allosteric modulation of the enzyme activity. Herein, the degradation of Aβ(1–40) by cf-E111Q-IDE via a non-chaperone mechanism is demonstrated by NMR and LC-MS, and the aggregation of fragmented peptides is characterized using fluorescence and electron microscopy. cf-E111Q-IDE presented a reduced effect on the aggregation kinetics of Aβ(1–40) when compared with the wild-type IDE. Whereas LC-MS and diffusion ordered NMR spectroscopy revealed the generation of Aβ fragments by both wild-type and cf-E111Q-IDE. The aggregation propensities and the difference in the morphological phenotype of the full-length Aβ(1–40) and its fragments are explained using multi-microseconds molecular dynamics simulations. Notably, our results reveal that zinc binding to Aβ(1–40) inactivates cf-E111Q-IDE’s catalytic function, whereas zinc removal restores its function as evidenced from high-speed AFM, electron microscopy, chromatography, and NMR results. These findings emphasize the catalytic role of cf-E111Q-IDE on Aβ degradation and urge the development of zinc chelators as an alternative therapeutic strategy that switches on/off IDE’s function.     

Frustration‐guided motion planning reveals conformational transitions in proteins

Proteins exist as conformational ensembles, exchanging between substates to perform their function. Advances in experimental techniques yield unprecedented access to structural snapshots of their conformational landscape. However, computationally modeling how proteins use collective motions to transition between substates is challenging owing to a rugged landscape and large energy barriers. Here, we present a new, robotics‐inspired motion planning procedure called dCC‐RRT that navigates the rugged landscape between substates by introducing dynamic, interatomic constraints to modulate frustration. The constraints balance non‐native contacts and flexibility, and instantaneously redirect the motion towards sterically favorable conformations. On a test set of eight proteins determined in two conformations separated by, on average, 7.5 Å root mean square deviation (RMSD), our pathways reduced the Cα atom RMSD to the goal conformation by 78%, outperforming peer methods. We then applied dCC‐RRT to examine how collective, small‐scale motions of four side‐chains in the active site of cyclophilin A propagate through the protein. dCC‐RRT uncovered a spatially contiguous network of residues linked by steric interactions and collective motion connecting the active site to a recently proposed, non‐canonical capsid binding site 25 Å away, rationalizing NMR and multi‐temperature crystallography experiments. In all, dCC‐RRT can reveal detailed, all‐atom molecular mechanisms for small and large amplitude motions. Source code and binaries are freely available at https://github.com/ExcitedStates/KGS/ .     

Robust probabilistic superposition and comparison of protein structures

Background  

Protein structure comparison is a central issue in structural bioinformatics. The standard dissimilarity measure for protein structures is the root mean square deviation (RMSD) of representative atom positions such as α-carbons. To evaluate the RMSD the structures under comparison must be superimposed optimally so as to minimize the RMSD. How to evaluate optimal fits becomes a matter of debate, if the structures contain regions which differ largely - a situation encountered in NMR ensembles and proteins undergoing large-scale conformational transitions.