A substitution matrix for structural alphabet based on structural alignment of homologous proteins and its applications

Analysis of protein structures based on backbone structural patterns known as structural alphabets have been shown to be very useful. Among them, a set of 16 pentapeptide structural motifs known as protein blocks (PBs) has been identified and upon which backbone model of most protein structures can be built. PBs allows simplification of 3D space onto 1D space in the form of sequence of PBs. Here, for the first time, substitution probabilities of PBs in a large number of aligned homologous protein structures have been studied and are expressed as a simplified 16 x 16 substitution matrix. The matrix was validated by benchmarking how well it can align sequences of PBs rather like amino acid alignment to identify structurally equivalent regions in closely or distantly related proteins using dynamic programming approach. The alignment results obtained are very comparable to well established structure comparison methods like DALI and STAMP. Other interesting applications of the matrix have been investigated. We first show that, in variable regions between two superimposed homologous proteins, one can distinguish between local conformational differences and rigid-body displacement of a conserved motif by comparing the PBs and their substitution scores. Second, we demonstrate, with the example of aspartic proteinases, that PBs can be efficiently used to detect the lobe/domain flexibility in the multidomain proteins. Lastly, using protein kinase as an example, we identify regions of conformational variations and rigid body movements in the enzyme as it is changed to the active state from an inactive state.     

Identification of local conformational similarity in structurally variable regions of homologous proteins using protein blocks

Structure comparison tools can be used to align related protein structures to identify structurally conserved and variable regions and to infer functional and evolutionary relationships. While the conserved regions often superimpose well, the variable regions appear non superimposable. Differences in homologous protein structures are thought to be due to evolutionary plasticity to accommodate diverged sequences during evolution. One of the kinds of differences between 3-D structures of homologous proteins is rigid body displacement. A glaring example is not well superimposed equivalent regions of homologous proteins corresponding to α-helical conformation with different spatial orientations. In a rigid body superimposition, these regions would appear variable although they may contain local similarity. Also, due to high spatial deviation in the variable region, one-to-one correspondence at the residue level cannot be determined accurately. Another kind of difference is conformational variability and the most common example is topologically equivalent loops of two homologues but with different conformations. In the current study, we present a refined view of the "structurally variable" regions which may contain local similarity obscured in global alignment of homologous protein structures. As structural alphabet is able to describe local structures of proteins precisely through Protein Blocks approach, conformational similarity has been identified in a substantial number of 'variable' regions in a large data set of protein structural alignments; optimal residue-residue equivalences could be achieved on the basis of Protein Blocks which led to improved local alignments. Also, through an example, we have demonstrated how the additional information on local backbone structures through protein blocks can aid in comparative modeling of a loop region. In addition, understanding on sequence-structure relationships can be enhanced through our approach. This has been illustrated through examples where the equivalent regions in homologous protein structures share sequence similarity to varied extent but do not preserve local structure.     

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.     

Exploring the dynamic information content of a protein NMR structure: Comparison of a molecular dynamics simulation with the NMR and X‐ray structures of Escherichia coli ribonuclease HI

The multiconformer nature of solution nuclear magnetic resonance (NMR) structures of proteins results from the effects of intramolecular dynamics, spin diffusion and an uneven distribution of structural restraints throughout the molecule. A delineation of the former from the latter two contributions is attempted in this work for an ensemble of 15 NMR structures of the protein Escherichia coli ribonuclease HI (RNase HI). Exploration of the dynamic information content of the NMR ensemble is carried out through correlation with data from two crystal structures and a 1.7‐ns molecular dynamics (MD) trajectory of RNase HI in explicit solvent. Assessment of the consistency of the crystal and mean MD structures with nuclear Overhauser effect (NOE) data showed that the NMR ensemble is overall more compatible with the high‐resolution (1.48 Å) crystal structure than with either the lower‐resolution (2.05 Å) crystal structure or the MD simulation. Furthermore, the NMR ensemble is found to span more conformational space than the MD simulation for both the backbone and the sidechains of RNase HI. Nonetheless, the backbone conformational variability of both the NMR ensemble and the simulation is especially consistent with NMR relaxation measurements of two loop regions that are putative sites of substrate recognition. Plausible side‐chain dynamic information is extracted from the NMR ensemble on the basis of (i) rotamericity and syn‐pentane character of variable torsion angles, (ii) comparison of the magnitude of atomic mean‐square fluctuations (msf) with those deduced from crystallographic thermal factors, and (iii) comparison of torsion angle conformational behavior in the NMR ensemble and the simulation. Several heterogeneous torsion angles, while adopting non‐rotameric/syn‐pentane conformations in the NMR ensemble, exist in a unique conformation in the simulation and display low X‐ray thermal factors. These torsions are identified as sites whose variability is likely to be an artifact of the NMR structure determination procedure. A number of other torsions show a close correspondence between the conformations sampled in the NMR and MD ensembles, as well as significant correlations among crystallographic thermal factors and atomic msf calculated from the NMR ensemble and the simulation. These results indicate that a significant amount of dynamic information is contained in the NMR ensemble. The relevance of the present findings for the biological function of RNase HI, protein recognition studies, and previous investigations of the motional content of protein NMR structures are discussed. Proteins 1999;36:87–110. © 1999 Wiley‐Liss, Inc.     

Ensembles from Ordered and Disordered Proteins Reveal Similar Structural Constraints during Evolution

The conformations accessible to proteins are determined by the inter-residue interactions between amino acid residues. During evolution, structural constraints that are required for protein function providing biologically relevant information can exist. Here, we studied the proportion of sites evolving under structural constraints in two very different types of ensembles, those coming from ordered and disordered proteins. Using a structurally constrained model of protein evolution, we found that both types of ensembles show comparable, near 40%, number of positions evolving under structural constraints. Among these sites, ~ 68% are in disordered regions and ~ 57% of them show long-range inter-residue contacts. Also, we found that disordered ensembles are redundant in reference to their structurally constrained evolutionary information and could be described on average with ~ 11 conformers. Despite the different complexity of the studied ensembles and proteins, the similar constraints reveal a comparable level of selective pressure to maintain their biological functions. These results highlight the importance of the evolutionary information to recover meaningful biological information to further characterize conformational ensembles.     

Structural dynamics shape the fitness window of alanine:glyoxylate aminotransferase

The conformational landscape of a protein is constantly expanded by genetic variations that have a minimal impact on the function(s) while causing subtle effects on protein structure. The wider the conformational space sampled by these variants, the higher the probabilities to adapt to changes in environmental conditions. However, the probability that a single mutation may result in a pathogenic phenotype also increases. Here we present a paradigmatic example of how protein evolution balances structural stability and dynamics to maximize protein adaptability and preserve protein fitness. We took advantage of known genetic variations of human alanine:glyoxylate aminotransferase (AGT1), which is present as a common major allelic form (AGT‐Ma) and a minor polymorphic form (AGT‐Mi) expressed in 20% of Caucasian population. By integrating crystallographic studies and molecular dynamics simulations, we show that AGT‐Ma is endowed with structurally unstable (frustrated) regions, which become disordered in AGT‐Mi. An in‐depth biochemical characterization of variants from an anticonsensus library, encompassing the frustrated regions, correlates this plasticity to a fitness window defined by AGT‐Ma and AGT‐Mi. Finally, co‐immunoprecipitation analysis suggests that structural frustration in AGT1 could favor additional functions related to protein–protein interactions. These results expand our understanding of protein structural evolution by establishing that naturally occurring genetic variations tip the balance between stability and frustration to maximize the ensemble of conformations falling within a well‐defined fitness window, thus expanding the adaptability potential of the protein.     

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     

Understanding the roles of amino acid residues in tertiary structure formation of chignolin by using molecular dynamics simulation

Chignolin is a 10-residue peptide (GYDPETGTWG) that forms a stable beta-hairpin structure in water. However, its design template, GPM12 (GYDDATKTFG), does not have a specific structure. To clarify which amino acids give it the ability to form the beta-hairpin structure, we calculated the folding free-energy landscapes of chignolin, GPM12, and their chimeric peptides using multicanonical molecular dynamics (MD) simulation. Cluster analysis of the conformational ensembles revealed that the native structure of chignolin was the lowest in terms of free energy while shallow local minima were widely distributed in the free energy landscape of GPM12, in agreement with experimental observations. Among the chimeric peptides, GPM12(D4P/K7G) stably formed the same beta-hairpin structure as that of chignolin in the MD simulation. This was confirmed by nuclear magnetic resonance (NMR) spectroscopy. A comparison of the free-energy landscapes showed that the conformational distribution of the Asp3-Pro4 sequence was inherently biased in a way that is advantageous both to forming hydrogen bonds with another beta-strand and to initiating loop structure. In addition, Gly7 helps stabilize the loop structure by having a left-handed alpha-helical conformation. Such a conformation is necessary to complete the loop structure, although it is not preferred by other amino acids. Our results suggest that the consistency between the short-range interactions that determine the local geometries and the long-range interactions that determine the global structure is important for stable tertiary structure formation.     

Exploring the Minimally Frustrated Energy Landscape of Unfolded ACBP

The unfolded state of globular proteins is not well described by a simple statistical coil due to residual structural features, such as secondary structure or transiently formed long-range contacts. The principle of minimal frustration predicts that the unfolded ensemble is biased toward productive regions in the conformational space determined by the native structure. Transient long-range contacts, both native-like and non-native-like, have previously been shown to be present in the unfolded state of the four-helix-bundle protein acyl co-enzyme binding protein (ACBP) as seen from both perturbations in nuclear magnetic resonance (NMR) chemical shifts and structural ensembles generated from NMR paramagnetic relaxation data. To study the nature of the contacts in detail, we used paramagnetic NMR relaxation enhancements, in combination with single-point mutations, to obtain distance constraints for the acid-unfolded ensemble of ACBP. We show that, even in the acid-unfolded state, long-range contacts are specific in nature and single-point mutations affect the free-energy landscape of the unfolded protein. Using this approach, we were able to map out concerted, interconnected, and productive long-range contacts. The correlation between the native-state stability and compactness of the denatured state provides further evidence for native-like contact formation in the denatured state. Overall, these results imply that, even in the earliest stages of folding, ACBP dynamics are governed by native-like contacts on a minimally frustrated energy landscape.     

Structure and dynamics in solution of the stop codon decoding N-terminal domain of the human polypeptide chain release factor eRF1

The high-resolution NMR structure of the N-domain of human eRF1, responsible for stop codon recognition, has been determined in solution. The overall fold of the protein is the same as that found in the crystal structure. However, the structures of several loops, including those participating in stop codon decoding, are different. Analysis of the NMR relaxation data reveals that most of the regions with the highest structural discrepancy between the solution and solid states undergo internal motions on the ps-ns and ms time scales. The NMR data show that the N-domain of human eRF1 exists in two conformational states. The distribution of the residues having the largest chemical shift differences between the two forms indicates that helices α2 and α3, with the NIKS loop between them, can switch their orientation relative to the β-core of the protein. Such structural plasticity may be essential for stop codon recognition by human eRF1.     

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.     

Characterizing RNA ensembles from NMR data with kinematic models

Functional mechanisms of biomolecules often manifest themselves precisely in transient conformational substates. Researchers have long sought to structurally characterize dynamic processes in non-coding RNA, combining experimental data with computer algorithms. However, adequate exploration of conformational space for these highly dynamic molecules, starting from static crystal structures, remains challenging. Here, we report a new conformational sampling procedure, KGSrna, which can efficiently probe the native ensemble of RNA molecules in solution. We found that KGSrna ensembles accurately represent the conformational landscapes of 3D RNA encoded by NMR proton chemical shifts. KGSrna resolves motionally averaged NMR data into structural contributions; when coupled with residual dipolar coupling data, a KGSrna ensemble revealed a previously uncharacterized transient excited state of the HIV-1 trans-activation response element stem–loop. Ensemble-based interpretations of averaged data can aid in formulating and testing dynamic, motion-based hypotheses of functional mechanisms in RNAs with broad implications for RNA engineering and therapeutic intervention.     

Modeling structurally variable regions in homologous proteins with rosetta

A major limitation of current comparative modeling methods is the accuracy with which regions that are structurally divergent from homologues of known structure can be modeled. Because structural differences between homologous proteins are responsible for variations in protein function and specificity, the ability to model these differences has important functional consequences. Although existing methods can provide reasonably accurate models of short loop regions, modeling longer structurally divergent regions is an unsolved problem. Here we describe a method based on the de novo structure prediction algorithm, Rosetta, for predicting conformations of structurally divergent regions in comparative models. Initial conformations for short segments are selected from the protein structure database, whereas longer segments are built up by using three- and nine-residue fragments drawn from the database and combined by using the Rosetta algorithm. A gap closure term in the potential in combination with modified Newton's method for gradient descent minimization is used to ensure continuity of the peptide backbone. Conformations of variable regions are refined in the context of a fixed template structure using Monte Carlo minimization together with rapid repacking of side-chains to iteratively optimize backbone torsion angles and side-chain rotamers. For short loops, mean accuracies of 0.69, 1.45, and 3.62 A are obtained for 4, 8, and 12 residue loops, respectively. In addition, the method can provide reasonable models of conformations of longer protein segments: predicted conformations of 3A root-mean-square deviation or better were obtained for 5 of 10 examples of segments ranging from 13 to 34 residues. In combination with a sequence alignment algorithm, this method generates complete, ungapped models of protein structures, including regions both similar to and divergent from a homologous structure. This combined method was used to make predictions for 28 protein domains in the Critical Assessment of Protein Structure 4 (CASP 4) and 59 domains in CASP 5, where the method ranked highly among comparative modeling and fold recognition methods. Model accuracy in these blind predictions is dominated by alignment quality, but in the context of accurate alignments, long protein segments can be accurately modeled. Notably, the method correctly predicted the local structure of a 39-residue insertion into a TIM barrel in CASP 5 target T0186.     

Conservation of Flexible Residue Clusters among Structural and Functional Enzyme Homologues

Conformational flexibility between structural ensembles is an essential component of enzyme function. Although the broad dynamical landscape of proteins is known to promote a number of functional events on multiple time scales, it is yet unknown whether structural and functional enzyme homologues rely on the same concerted residue motions to perform their catalytic function. It is hypothesized that networks of contiguous and flexible residue motions occurring on the biologically relevant millisecond time scale evolved to promote and/or preserve optimal enzyme catalysis. In this study, we use a combination of NMR relaxation dispersion, model-free analysis, and ligand titration experiments to successfully capture and compare the role of conformational flexibility between two structural homologues of the pancreatic ribonuclease family: RNase A and eosinophil cationic protein (or RNase 3). In addition to conserving the same catalytic residues and structural fold, both homologues show similar yet functionally distinct clusters of millisecond dynamics, suggesting that conformational flexibility can be conserved among analogous protein folds displaying low sequence identity. Our work shows that the reduced conformational flexibility of eosinophil cationic protein can be dynamically and functionally reproduced in the RNase A scaffold upon creation of a chimeric hybrid between the two proteins. These results support the hypothesis that conformational flexibility is partly required for catalytic function in homologous enzyme folds, further highlighting the importance of dynamic residue sectors in the structural organization of proteins.     

Structural and dynamics characterization of norovirus protease

Norovirus protease is an essential enzyme for proteolytic maturation of norovirus nonstructural proteins and has been implicated as a potential target for antiviral drug development. Although X‐ray structural studies of the protease give us wealth of structural information including interactions of the protease with its substrate and dimeric overall structure, the role of protein dynamics in the substrate recognition and the biological relevance of the protease dimer remain unclear. Here we determined the solution NMR structure of the 3C‐like protease from Norwalk virus (NV 3CLpro), a prototype strain of norovirus, and analyzed its backbone dynamics and hydrodynamic behavior in solution. ¹⁵N spin relaxation and analytical ultracentrifugation analyses demonstrate that NV 3CLpro is predominantly a monomer in solution. Solution structure of NV 3CLpro shows significant structural variation in C‐terminal domain compared with crystal structures and among lower energy structure ensembles. Also, ¹⁵N spin relaxation and Carr–Purcell–Meiboom–Gill (CPMG)‐based relaxation dispersion analyses reveal the dynamic properties of residues in the C‐terminal domain over a wide range of timescales. In particular, the long loop spanning residues T123–G133 show fast motion (ps‐ns), and the residues in the bII–cII region forming the large hydrophobic pocket (S2 site) undergo conformational exchanges on slower timescales (μs–ms), suggesting their important role in substrate recognition.     

Essential spaces defined by NMR structure ensembles and molecular dynamics simulation show significant overlap

Large concerted motions of proteins which span its “essential space,” are an important component of protein dynamics. We investigate to what extent structure ensembles generated with standard structure calculation techniques such as simulated annealing can capture these motions by comparing them to long-time molecular dynamics (MD) trajectories. The motions are analyzed by principal component analysis and compared using inner products of eigenvectors of the respective covariance matrices. Two very different systems are studied, the β-spectrin PH domain and the single-stranded DNA binding protein (ssDBP) from the filamentous phage Pf3. A comparison of the ensembles from NMR and MD shows significant overlap of the essential spaces, which in the case of ssDBP is extraordinarily high. The influence of variations in the specifications of distance restraints is investigated. We also study the influence of the selection criterion for the final structure ensemble on the definition of mobility. The results suggest a modified criterion that improves conformational sampling in terms of amplitudes of correlated motion. Proteins 31:370–382, 1998. © 1998 Wiley-Liss, Inc.     

In silico elucidation of the recognition dynamics of ubiquitin

Elucidation of the mechanism of biomacromolecular recognition events has been a topic of intense interest over the past century. The inherent dynamic nature of both protein and ligand molecules along with the continuous reshaping of the energy landscape during the binding process renders it difficult to characterize this process at atomic detail. Here, we investigate the recognition dynamics of ubiquitin via microsecond all-atom molecular dynamics simulation providing both thermodynamic and kinetic information. The high-level of consistency found with respect to experimental NMR data lends support to the accuracy of the in silico representation of the conformational substates and their interconversions of free ubiquitin. Using an energy-based reweighting approach, the statistical distribution of conformational states of ubiquitin is monitored as a function of the distance between ubiquitin and its binding partner Hrs-UIM. It is found that extensive and dense sampling of conformational space afforded by the μs MD trajectory is essential for the elucidation of the binding mechanism as is Boltzmann sampling, overcoming inherent limitations of sparsely sampled empirical ensembles. The results reveal a population redistribution mechanism that takes effect when the ligand is at intermediate range of 1-2 nm from ubiquitin. This mechanism, which may be depicted as a superposition of the conformational selection and induced fit mechanisms, also applies to other binding partners of ubiquitin, such as the GGA3 GAT domain.     

Improving the accuracy of protein stability predictions with multistate design using a variety of backbone ensembles

Multistate computational protein design (MSD) with backbone ensembles approximating conformational flexibility can predict higher quality sequences than single‐state design with a single fixed backbone. However, it is currently unclear what characteristics of backbone ensembles are required for the accurate prediction of protein sequence stability. In this study, we aimed to improve the accuracy of protein stability predictions made with MSD by using a variety of backbone ensembles to recapitulate the experimentally measured stability of 85 Streptococcal protein G domain β1 sequences. Ensembles tested here include an NMR ensemble as well as those generated by molecular dynamics (MD) simulations, by Backrub motions, and by PertMin, a new method that we developed involving the perturbation of atomic coordinates followed by energy minimization. MSD with the PertMin ensembles resulted in the most accurate predictions by providing the highest number of stable sequences in the top 25, and by correctly binning sequences as stable or unstable with the highest success rate (≈90%) and the lowest number of false positives. The performance of PertMin ensembles is due to the fact that their members closely resemble the input crystal structure and have low potential energy. Conversely, the NMR ensemble as well as those generated by MD simulations at 500 or 1000 K reduced prediction accuracy due to their low structural similarity to the crystal structure. The ensembles tested herein thus represent on‐ or off‐target models of the native protein fold and could be used in future studies to design for desired properties other than stability. Proteins 2014; 82:771–784. © 2013 Wiley Periodicals, Inc.