Tools and Databases to Analyze Protein Flexibility; Approaches to Mapping Implied Features onto Sequences

Factors correlating with significant differences between X-ray structures of myoglobin

Validation of general ideas about the origins of conformational differences in proteins is critical in order to arrive at meaningful functional insights. Here, principal component analysis (PCA) and distance difference matrices are used to validate some such ideas about the conformational differences between 291 myoglobin structures from sperm whale, horse and pig. Almost all of the horse and pig structures form compact PCA clusters with only minor coordinate differences and outliers that are easily explained. The 222 whale structures form a few dense clusters with multiple outliers. A few whale outliers with a prominent distortion of the GH loop are very similar to the cluster of horse structures, which all have a similar GH-loop distortion apparently owing to intermolecular crystal lattice hydrogen bonds to the GH loop from residues near the distal histidine His64. The variations of the GH-loop coordinates in the whale structures are likely to be owing to the observed alternative intermolecular crystal lattice bond, with the change to the GH loop distorting bonds correlated with the binding of specific `unusual' ligands. Such an alternative intermolecular bond is not observed in horse myoglobins, obliterating any correlation with the ligands. Intermolecular bonds do not usually cause significant coordinate differences and cannot be validated as their universal cause. Most of the native-like whale myoglobin structure outliers can be correlated with a few specific factors. However, these factors do not always lead to coordinate differences beyond the previously determined uncertainty thresholds. The binding of unusual ligands by myoglobin, leading to crystal-induced distortions, suggests that some of the conformational differences between the apo and holo structures might not be `functionally important' but rather artifacts caused by the binding of `unusual' substrate analogs. The causes of P6 symmetry in myoglobin crystals and the relationship between crystal and solution structures are also discussed.

Diversity of function-related conformational changes in proteins: coordinate uncertainty, fragment rigidity, and stability

It was found that the variety of function-related conformational changes ("movements") in proteins is beyond the earlier simple classifications. Here we offer biochemists a more comprehensive, transparent, and easy-to-use approach allowing a detailed and accurate interpretation of such conformational changes. It makes possible a more multifaceted characterization of protein flexibility via identification of rigidly and nonrigidly repositioned fragments, stable and nonstable fragments, and domain and nondomain repositioning. "Coordinate uncertainty thresholds" derived from computed differences between independently determined coordinates of the same molecules are used as the criteria for conformational identity. "Identical" rigid substructures are localized in the distance difference matrices (DDMs). A sequence of simple transformations determines whether a structural change occurs by rigid-body movements of fragments or largely through non-rigid-body deformations. We estimate the stability of protein fragments and compare stable and rigidly moving fragments. The motions computed with the coarse-grained elastic networks are also compared to those of their DDM analogues. We study and suggest a classification for 17 structural pairs, differing in their functional states. For five of the 17 proteins, conformational change cannot be accomplished by rigid-body transformations and requires significant non-rigid-body deformations. Stable fragments rarely coincide with rigidly moving fragments and often disagree with the CATH identifications of domains. Almost all monomeric apo chains, containing stable fragments and/or domains, indicate instability of the entire molecule, suggesting the importance of fragments and domains motions prior to stabilization by substrate binding or crystallization. Notably, kinases exhibit the greatest extent of nonrigidity among the proteins investigated.

Protein flexibility: coordinate uncertainties and interpretation of structural differences

Valid interpretations of conformational movements in protein structures determined by X-ray crystallography require that the movement magnitudes exceed their uncertainty threshold. Here, it is shown that such thresholds can be obtained from the distance difference matrices (DDMs) of 1014 pairs of independently determined structures of bovine ribonuclease A and sperm whale myoglobin, with no explanations provided for reportedly minor coordinate differences. The smallest magnitudes of reportedly functional motions are just above these thresholds. Uncertainty thresholds can provide objective criteria that distinguish between true conformational changes and apparent 'noise', showing that some previous interpretations of protein coordinate changes attributed to external conditions or mutations may be doubtful or erroneous. The use of uncertainty thresholds, DDMs, the newly introduced CDDMs (contact distance difference matrices) and a novel simple rotation algorithm allows a more meaningful classification and description of protein motions, distinguishing between various rigid-fragment motions and nonrigid conformational deformations. It is also shown that half of 75 pairs of identical molecules, each from the same asymmetric crystallographic cell, exhibit coordinate differences that range from just outside the coordinate uncertainty threshold to the full magnitude of large functional movements. Thus, crystallization might often induce protein conformational changes that are comparable to those related to or induced by the protein function.

Residue Level Three-dimensional Workspace Maps for Conformational Trajectory Planning of Proteins

The function of a protein macromolecule often requires conformational transitions between two native conformations. Understanding these transitions is essential to the understanding of how proteins function, as well as to the ability to design and manipulate protein-based nanomechanical systems. In this paper we propose a set of 3D Cartesian workspace maps for exploring protein pathways. These 3D maps are constructed in the Euclidean space for triads of chain segments of protein molecules that have been shown to have a high probability of occurrence in naturally observed proteins based on data obtained from more than 38,600 proteins from the Protein Data Bank (PDB). We show that the proposed 3D propensity maps are more effective navigation tools than the propensity maps constructed in the angle space. We argue that the main reason for this improved efficiency is the fact that, although there is a one-to-one mapping between the 2D dihedral angle maps and the 3D Cartesian maps, the propensity distributions are significantly different in the two spaces. Hence, the 3D maps allow the pathway planning to be performed directly in the 3D Euclidean space based on propensities computed in the same space, which is where protein molecules change their conformations.

A conformational transition state accompanies tryptophan activation by B. stearothermophilus tryptophanyl-tRNA synthetase

B. stearothermophilus tryptophanyl-tRNA synthetase catalysis proceeds via high-energy protein conformations. Unliganded MD trajectories of the pretransition-state complex with Mg(2+)ATP and the (post) transition-state analog complex with adenosine tetraphosphate relax rapidly in opposite directions, the former regressing, the latter progressing along the structural reaction coordinate. The two crystal structures (rmsd 0.7 A) therefore lie on opposite sides of a conformational free-energy maximum as the chemical transition state forms. SNAPP analysis illustrates the complexity of the associated long-range conformational coupling. Switching interactions in four nonpolar core regions are locally isoenergetic throughout the transition. Different configurations, however, propagate their effects to unfavorable, longer-range interactions at the molecular surface. Designed mutation shows that switching interactions enhance the rate, perhaps by destabilizing the ground state immediately before the transition state and limiting nonproductive diffusion before and after the chemical transition state, thereby reducing the activation entropy. This paradigm may apply broadly to energy-transducing enzymes.

FlexOracle: predicting flexible hinges by identification of stable domains

Background

Protein motions play an essential role in catalysis and protein-ligand interactions, but are difficult to observe directly. A substantial fraction of protein motions involve hinge bending. For these proteins, the accurate identification of flexible hinges connecting rigid domains would provide significant insight into motion. Programs such as GNM and FIRST have made global flexibility predictions available at low computational cost, but are not designed specifically for finding hinge points.

Results

Here we present the novel FlexOracle hinge prediction approach based on the ideas that energetic interactions are stronger within structural domains than between them, and that fragments generated by cleaving the protein at the hinge site are independently stable. We implement this as a tool within the Database of Macromolecular Motions, MolMovDB.org. For a given structure, we generate pairs of fragments based on scanning all possible cleavage points on the protein chain, compute the energy of the fragments compared with the undivided protein, and predict hinges where this quantity is minimal. We present three specific implementations of this approach. In the first, we consider only pairs of fragments generated by cutting at a single location on the protein chain and then use a standard molecular mechanics force field to calculate the enthalpies of the two fragments. In the second, we generate fragments in the same way but instead compute their free energies using a knowledge based force field. In the third, we generate fragment pairs by cutting at two points on the protein chain and then calculate their free energies.

Conclusion

Quantitative results demonstrate our method's ability to predict known hinges from the Database of Macromolecular Motions.

Hinge Atlas: relating protein sequence to sites of structural flexibility

Background

Relating features of protein sequences to structural hinges is important for identifying domain boundaries, understanding structure-function relationships, and designing flexibility into proteins. Efforts in this field have been hampered by the lack of a proper dataset for studying characteristics of hinges.

Results

Using the Molecular Motions Database we have created a Hinge Atlas of manually annotated hinges and a statistical formalism for calculating the enrichment of various types of residues in these hinges.

Conclusion

We found various correlations between hinges and sequence features. Some of these are expected; for instance, we found that hinges tend to occur on the surface and in coils and turns and to be enriched with small and hydrophilic residues. Others are less obvious and intuitive. In particular, we found that hinges tend to coincide with active sites, but unlike the latter they are not at all conserved in evolution. We evaluate the potential for hinge prediction based on sequence.

Motions play an important role in catalysis and protein-ligand interactions. Hinge bending motions comprise the largest class of known motions. Therefore it is important to relate the hinge location to sequence features such as residue type, physicochemical class, secondary structure, solvent exposure, evolutionary conservation, and proximity to active sites. To do this, we first generated the Hinge Atlas, a set of protein motions with the hinge locations manually annotated, and then studied the coincidence of these features with the hinge location. We found that all of the features have bearing on the hinge location. Most interestingly, we found that hinges tend to occur at or near active sites and yet unlike the latter are not conserved. Less surprisingly, we found that hinge residues tend to be small, not hydrophobic or aliphatic, and occur in turns and random coils on the surface. A functional sequence based hinge predictor was made which uses some of the data generated in this study. The Hinge Atlas is made available to the community for further flexibility studies.

Prediction of flexible/rigid regions from protein sequences using k-spaced amino acid pairs

Background

Traditionally, it is believed that the native structure of a protein corresponds to a global minimum of its free energy. However, with the growing number of known tertiary (3D) protein structures, researchers have discovered that some proteins can alter their structures in response to a change in their surroundings or with the help of other proteins or ligands. Such structural shifts play a crucial role with respect to the protein function. To this end, we propose a machine learning method for the prediction of the flexible/rigid regions of proteins (referred to as FlexRP); the method is based on a novel sequence representation and feature selection. Knowledge of the flexible/rigid regions may provide insights into the protein folding process and the 3D structure prediction.

Results

The flexible/rigid regions were defined based on a dataset, which includes protein sequences that have multiple experimental structures, and which was previously used to study the structural conservation of proteins. Sequences drawn from this dataset were represented based on feature sets that were proposed in prior research, such as PSI-BLAST profiles, composition vector and binary sequence encoding, and a newly proposed representation based on frequencies of k-spaced amino acid pairs. These representations were processed by feature selection to reduce the dimensionality. Several machine learning methods for the prediction of flexible/rigid regions and two recently proposed methods for the prediction of conformational changes and unstructured regions were compared with the proposed method. The FlexRP method, which applies Logistic Regression and collocation-based representation with 95 features, obtained 79.5% accuracy. The two runner-up methods, which apply the same sequence representation and Support Vector Machines (SVM) and Naïve Bayes classifiers, obtained 79.2% and 78.4% accuracy, respectively. The remaining considered methods are characterized by accuracies below 70%. Finally, the Naïve Bayes method is shown to provide the highest sensitivity for the prediction of flexible regions, while FlexRP and SVM give the highest sensitivity for rigid regions.

Conclusion

A new sequence representation that uses k-spaced amino acid pairs is shown to be the most efficient in the prediction of the flexible/rigid regions of protein sequences. The proposed FlexRP method provides the highest prediction accuracy of about 80%. The experimental tests show that the FlexRP and SVM methods achieved high overall accuracy and the highest sensitivity for rigid regions, while the best quality of the predictions for flexible regions is achieved by the Naïve Bayes method.

Identifying sequence regions undergoing conformational change via predicted continuum secondary structure

MOTIVATION

Conformational flexibility is essential to the function of many proteins, e.g. catalytic activity. To assist efforts in determining and exploring the functional properties of a protein, it is desirable to automatically identify regions that are prone to undergo conformational changes. It was recently shown that a probabilistic predictor of continuum secondary structure is more accurate than categorical predictors for structurally ambivalent sequence regions, suggesting that such models are suited to characterize protein flexibility.

RESULTS

We develop a computational method for identifying regions that are prone to conformational change directly from the amino acid sequence. The method uses the entropy of the probabilistic output of an 8-class continuum secondary structure predictor. Results for 171 unique amino acid sequences with well-characterized variable structure (identified in the 'Macromolecular movements database') indicate that the method is highly sensitive at identifying flexible protein regions, but false positives remain a problem. The method can be used to explore conformational flexibility of proteins (including hypothetical or synthetic ones) whose structure is yet to be determined experimentally.

AVAILABILITY

The predictor, sequence data and supplementary studies are available at http://pprowler.itee.uq.edu.au/sspred/ and are free for academic use.

The Database of Macromolecular Motions: new features added at the decade mark

The database of molecular motions, MolMovDB (), has been in existence for the past decade. It classifies macromolecular motions and provides tools to interpolate between two conformations (the Morph Server) and predict possible motions in a single structure. In 2005, we expanded the services offered on MolMovDB. In particular, we further developed the Morph Server to produce improved interpolations between two submitted structures. We added support for multiple chains to the original adiabatic mapping interpolation, allowing the analysis of subunit motions. We also added the option of using FRODA interpolation, which allows for more complex pathways, potentially overcoming steric barriers. We added an interface to a hinge prediction service, which acts on single structures and predicts likely residue points for flexibility. We developed tools to relate such points of flexibility in a structure to particular key residue positions, i.e. active sites or highly conserved positions. Lastly, we began relating our motion classification scheme to function using descriptions from the Gene Ontology Consortium.

Assessing local structural perturbations in proteins

Background

Protein structure research often deals with the comparison of two or more structures of the same protein, for instance when handling alternative structure models for the same protein, point mutants, molecule movements, structure predictions, etc. Often the difference between structures is small, restricted to a local neighborhood, and buried in structural "noise" due to trivial differences resulting from experimental artifacts. In such cases, whole-structure comparisons by means of structure superposition may be unsatisfactory and researchers have to perform a tedious process of manually superposing different segments individually and/or use different frames of reference, chosen roughly by educated guessing.

Results

We have developed an algorithm to compare local structural differences between alternative structures of the same protein. We have implemented the algorithm through a computer program that performs the numerical evaluation and allows inspecting visually the results of the structure comparison. We have tested the algorithm on different kinds of model systems. Here we present the algorithm and some results to illustrate its characteristics.

Conclusion

This program may provide an insight into the local structural changes produced in a protein structure by different interactions or modifications. It is convenient for the general user and it can be applied to standard or specific tasks on protein structure research.

Independent movement, dimerization and stability of tandem repeats of chicken brain alpha-spectrin

Previous X-ray crystal structures have shown that linkers of five amino acid residues connecting pairs of chicken brain alpha-spectrin and human erythroid beta-spectrin repeats can undergo bending without losing their alpha-helical structure. To test whether bending at one linker can influence bending at an adjacent linker, the structures of two and three repeat fragments of chicken brain alpha-spectrin have been determined by X-ray crystallography. The structure of the three-repeat fragment clearly shows that bending at one linker can occur independently of bending at an adjacent linker. This observation increases the possible trajectories of modeled chains of spectrin repeats. Furthermore, the three-repeat molecule crystallized as an antiparallel dimer with a significantly smaller buried interfacial area than that of alpha-actinin, a spectrin-related molecule, but large enough and of a type indicating biological specificity. Comparison of the structures of the spectrin and alpha-actinin dimers supports weak association of the former, which could not be detected by analytical ultracentrifugation, versus strong association of the latter, which has been observed by others. To correlate features of the structure with solution properties and to test a previous model of stable spectrin and dystrophin repeats, the number of inter-helical interactions in each repeat of several spectrin structures were counted and compared to their thermal stabilities. Inter-helical interactions, but not all interactions, increased in parallel with measured thermal stabilities of each repeat and in agreement with the thermal stabilities of two and three repeats and also partial repeats of spectrin.