Importance of long-range interactions in (α/β)8 barrel fold

Protein structures are stabilized by both local and long-range interactions. In this work, we analyzed the importance of long-range interactions in (α/β)₈ barrel proteins in terms of residue distances. We found that the residues occurring in the range of 21–30 residues apart contribute more toward long-range contacts. Indeed, about 50% of successive strands in these proteins are found to occur at a sequential distance of 21–30 residues. The aromatic amino acid residues Phe, Trp, and Tyr prefer the 4–10 range and all other residues prefer the 21–30 range. Hydrophobic-hydrophobic resideu pairs are the most preferred ones for long-range interactions and they may play a key role in the folding and stabilization of (α/β)₈ barrel proteins.     

Importance of long-range interactions in (α/β)8 barrel fold

Protein structures are stabilized by both local and long-range interactions. In this work, we analyzed the importance of long-range interactions in (α/β)₈ barrel proteins in terms of residue distances. We found that the residues occurring in the range of 21–30 residues apart contribute more toward long-range contacts. Indeed, about 50% of successive strands in these proteins are found to occur at a sequential distance of 21–30 residues. The aromatic amino acid residues Phe, Trp, and Tyr prefer the 4–10 range and all other residues prefer the 21–30 range. Hydrophobic-hydrophobic resideu pairs are the most preferred ones for long-range interactions and they may play a key role in the folding and stabilization of (α/β)₈ barrel proteins.     

Visualization of the nature of protein folding by a study of a distance constraint approach in two-dimensional models

A distance constraint approach is applied to two-dimensional models of proteins in order to visualize the nature of protein folding and to examine the relative roles of different ranges of interaction. Three different native structures (I, II, and III) are considered; they have two different kinds of residues, viz., hydrophobic and hydrophilic, and different sequences of these residues. We examine how the distance constraint approach functions in the prediction of protein folding when we know the sequence of the residues, the (fixed) bond lengths, the mean distances between residues i and i + 2, and i and i + 3, and the mean distances for hydrophobic–hydrophobic, hydrophobic–hydrophilic, and hydrophilic–hydrophilic contacts between residues i and i + j, where j ≥ 4. This approach involves optimization of an object function with respect to 98 variables and is not free of the multiple-minimum problem. The optimization is always terminated if the chain is entangled and/or the segments (residues) are packed too compactly to move. In order to escape from such situations and to take the excluded-volume effect into account, a Monte Carlo method is used after the optimization is trapped in local minima. Success in the prediction of folding is found to depend on the starting conformations and on the native conformations. Fair success is obtained in predicting the helix-like structure in protein I and the overall structure of protein III, but not the β-like structures of proteins I and II. Insofar as the prediction of the structure of protein III is reasonable, it appears that some sequences of residues produce greater constraints on their conformations than others, if one considers only the hydrophobic and hydrophilic nature of the residues. These results imply that, in the folding of real proteins in three dimensions, the competition for hydrophobic (and hydrophilic) residues for inside (outside) positions in the molecule probably constitutes a necessary but not a sufficient condition to form and stabilize the native structure. The failure to predict the structure of protein II, and part of that of protein I, suggests that there are two types of long-range interactions. One (which we considered here) is nonspecific (i.e., is defined only in terms of contacts between residues of the same or different polarity) and acts at any stage of protein folding; the other (which we did not consider here) is a specific interaction between residues in pairs and contributes only when the residues in the specific pair take on the native conformation. Presumably, incorporation of such specific long-range interactions, together with the nonspecific ones, is necessary for successful protein folding, using the distance constraint approach.     

Long- and short-range interactions in native protein structures are consistent/minimally frustrated in sequence space

We show that long- and short-range interactions in almost all protein native structures are actually consistent with each other for coarse-grained energy scales; specifically we mean the long-range inter-residue contact energies and the short-range secondary structure energies based on peptide dihedral angles, which are potentials of mean force evaluated from residue distributions observed in protein native structures. This consistency is observed at equilibrium in sequence space rather than in conformational space. Statistical ensembles of sequences are generated by exchanging residues for each of 797 protein native structures with the Metropolis method. It is shown that adding the other category of interaction to either the short- or long-range interactions decreases the means and variances of those energies for essentially all protein native structures, indicating that both interactions consistently work by more-or-less restricting sequence spaces available to one of the interactions. In addition to this consistency, independence by these interaction classes is also indicated by the fact that there are almost no correlations between them when equilibrated using both interactions and significant but small, positive correlations at equilibrium using only one of the interactions. Evidence is provided that protein native sequences can be regarded approximately as samples from the statistical ensembles of sequences with these energy scales and that all proteins have the same effective conformational temperature. Designing protein structures and sequences to be consistent and minimally frustrated among the various interactions is a most effective way to increase protein stability and foldability.     

Concordant exploration of the kinetics of RNA folding from global and local perspectives

Time-resolved small-angle X-ray scattering (SAXS) with millisecond time-resolution reveals two discrete phases of global compaction upon Mg2+-mediated folding of the Tetrahymena thermophila ribozyme. Electrostatic relaxation of the RNA occurs rapidly and dominates the first phase of compaction during which the observed radius of gyration (R(g)) decreases from 75 angstroms to 55 angstroms. A further decrease in R(g) to 45 angstroms occurs in a well-defined second phase. An analysis of mutant ribozymes shows that the latter phase depends upon the formation of long-range tertiary contacts within the P4-P6 domain of the ribozyme; disruption of the three remaining long-range contacts linking the peripheral helices has no effect on the 55-45 angstroms compaction transition. A better understanding of the role of specific tertiary contacts in compaction was obtained by concordant time-resolved hydroxyl radical (OH) analyses that report local changes in the solvent accessibility of the RNA backbone. Comparison of the global and local measures of folding shows that formation of a subset of native tertiary contacts (i.e. those defining the ribozyme core) can occur within a highly compact ensemble whose R(g) is close to that of the fully folded ribozyme. Analyses of additional ribozyme mutants and reaction conditions establish the generality of the rapid formation of a partially collapsed state with little to no detectable tertiary structure. These studies directly link global RNA compaction with formation of tertiary structure as the molecule acquires its biologically active structure, and underscore the strong dependence on salt of both local and global measures of folding kinetics.     

CONFOLD: Residue‐residue contact‐guided ab initio protein folding

Predicted protein residue–residue contacts can be used to build three‐dimensional models and consequently to predict protein folds from scratch. A considerable amount of effort is currently being spent to improve contact prediction accuracy, whereas few methods are available to construct protein tertiary structures from predicted contacts. Here, we present an ab initio protein folding method to build three‐dimensional models using predicted contacts and secondary structures. Our method first translates contacts and secondary structures into distance, dihedral angle, and hydrogen bond restraints according to a set of new conversion rules, and then provides these restraints as input for a distance geometry algorithm to build tertiary structure models. The initially reconstructed models are used to regenerate a set of physically realistic contact restraints and detect secondary structure patterns, which are then used to reconstruct final structural models. This unique two‐stage modeling approach of integrating contacts and secondary structures improves the quality and accuracy of structural models and in particular generates better β‐sheets than other algorithms. We validate our method on two standard benchmark datasets using true contacts and secondary structures. Our method improves TM‐score of reconstructed protein models by 45% and 42% over the existing method on the two datasets, respectively. On the dataset for benchmarking reconstructions methods with predicted contacts and secondary structures, the average TM‐score of best models reconstructed by our method is 0.59, 5.5% higher than the existing method. The CONFOLD web server is available at http://protein.rnet.missouri.edu/confold/ . Proteins 2015; 83:1436–1449. © 2015 Wiley Periodicals, Inc.     

Strategy for supplementing structure calculations using limited data with hydrophobic distance restraints

Introductory biochemistry texts often note that the fold of a protein is completely defined when the dihedral angles phi and psi are known for each amino acid. This assertion was examined with torsion angle dynamics and simulated annealing (TAD/SA) calculations of protein G using only dihedral angle restraints. When all dihedral angles were restrained to within 1 degrees of the values of the X-ray structure, the TAD/SA structures gave a backbone root mean square deviation to the target of 4 A. Factors that contributed to divergence from the correct solution include deviations of peptide bonds from planarity, internal conflicts resulting from the nonuniform energies of different phi, psi combinations, and relaxation to extended conformations in the absence of long-range constraints. Simulations including hydrogen-bond restraints showed that even a few long-range contacts constrain the fold better than a complete set of accurate dihedral restraints. A procedure is described for TAD/SA calculations using hydrogen-bond restraints, idealized dihedral restraints for residues in regular secondary structures, and "hydrophobic distance restraints" derived from the positions of hydrophobic residues in the amino acid sequence. The hydrogen-bond restraints are treated as inviolable, whereas violated hydrophobic restraints are removed following reduction of restraint upper bounds from 2 to 1 times the predicted radius of gyration. The strategy was tested with simulated restraints from X-ray structures of proteins from different fold classes and NMR data for cold shock protein A that included only backbone chemical shifts and hydrogen bonds obtained from a long-range HNCO experiment.     

Mechanism of protein folding: I. General considerations and refolding of myoglobin

To explain the rapidity of the process of protein folding, we cite two aspects of hydrophobic interaction: its long-range nature and the specificity of pairing after the formation of secondary structures. These two factors, when incorporated with the growth-type mechanism, can determine the folding pathway of proteins. This mechanism is applied to myoglobin. Appropriate introduction of side chains of amino acid residues and the heme group attached to His 93 yield a refolded tertiary structure that is in good agreement with the native structure.     

Influence of long-range contacts and surrounding residues on the transition state structures of proteins

Understanding the parameters influencing the formation of transition state structures in proteins is an important problem in protein folding and kinetics. In this work, we have analyzed the structure-based parameters, surrounding hydrophobicity, secondary structure, solvent accessibility, number of medium- and long-range contacts, and surrounding residues for understanding the transition state structures of 15 proteins. The analysis of Φ-values shows that 29% of the studied 378 mutants have a Φ-value of more than 0.5. The combination of different structure-based parameters could discriminate the residues that have a Φ-value cutoff of more than 0.5 with a 5-fold cross-validation accuracy of 68%, which indicates that the surrounding residues and contacts play important roles in the formation of transition state structures. Systematic analysis on different proteins reveals that the proteins azurin, cold shock protein, and C-terminal domain of ribosomal protein L9 are influenced by the number of medium- and long-range proteins, whereas barnase, FK506 binding protein, and IM9 are influenced by surrounding residues. The discrimination accuracy lies in the ranges of 81–95% and 74–85% for these respective classes of protein. Furthermore, the combination of surrounding residues and contacts improved the accuracy up to 24% in other considered proteins. We suggest that the structure-based parameters along with noncovalent interactions and conservation of residues may aid in identifying the potential residues in the formation of transition state structures in proteins.     

X-ray evidence of a native state with increased compactness populated by tryptophan-less B. licheniformis β-lactamase

β‐lactamases confer antibiotic resistance, one of the most serious world‐wide health problems, and are an excellent theoretical and experimental model in the study of protein structure, dynamics and evolution. Bacillus licheniformis exo‐small penicillinase (ESP) is a Class‐A β‐lactamase with three tryptophan residues located in the protein core. Here, we report the 1.7‐Å resolution X‐ray structure, catalytic parameters, and thermodynamic stability of ESP^ΔW, an engineered mutant of ESP in which phenylalanine replaces the wild‐type tryptophan residues. The structure revealed no qualitative conformational changes compared with thirteen previously reported structures of B. licheniformis β‐lactamases (RMSD = 0.4–1.2 Å). However, a closer scrutiny showed that the mutations result in an overall more compact structure, with most atoms shifted toward the geometric center of the molecule. Thus, ESP^ΔW has a significantly smaller radius of gyration (R_g) than the other B. licheniformis β‐lactamases characterized so far. Indeed, ESP^ΔW has the smallest R_g among 126 Class‐A β‐lactamases in the Protein Data Bank (PDB). Other measures of compactness, like the number of atoms in fixed volumes and the number and average of noncovalent distances, confirmed the effect. ESP^ΔW proves that the compactness of the native state can be enhanced by protein engineering and establishes a new lower limit to the compactness of the Class‐A β‐lactamase fold. As the condensation achieved by the native state is a paramount notion in protein folding, this result may contribute to a better understanding of how the sequence determines the conformational variability and thermodynamic stability of a given fold.     

Distance matrix-based approach to protein structure prediction

Much structural information is encoded in the internal distances; a distance matrix-based approach can be used to predict protein structure and dynamics, and for structural refinement. Our approach is based on the square distance matrix D = [r _ij ² ] containing all square distances between residues in proteins. This distance matrix contains more information than the contact matrix C, that has elements of either 0 or 1 depending on whether the distance r _ij is greater or less than a cutoff value r _cutoff. We have performed spectral decomposition of the distance matrices $ {\mathbf{D}} = \sum {\lambda_{k} {\mathbf{v}}_{k} {\mathbf{v}}_{k}^{T} } Much structural information is encoded in the internal distances; a distance matrix-based approach can be used to predict protein structure and dynamics, and for structural refinement. Our approach is based on the square distance matrix D = [r _ij²] containing all square distances between residues in proteins. This distance matrix contains more information than the contact matrix C, that has elements of either 0 or 1 depending on whether the distance r _ij is greater or less than a cutoff value r _cutoff. We have performed spectral decomposition of the distance matrices , in terms of eigenvalues and the corresponding eigenvectors and found that it contains at most five nonzero terms. A dominant eigenvector is proportional to r ²—the square distance of points from the center of mass, with the next three being the principal components of the system of points. By predicting r ² from the sequence we can approximate a distance matrix of a protein with an expected RMSD value of about 7.3 ?, and by combining it with the prediction of the first principal component we can improve this approximation to 4.0 ?. We can also explain the role of hydrophobic interactions for the protein structure, because r is highly correlated with the hydrophobic profile of the sequence. Moreover, r is highly correlated with several sequence profiles which are useful in protein structure prediction, such as contact number, the residue-wise contact order (RWCO) or mean square fluctuations (i.e. crystallographic temperature factors). We have also shown that the next three components are related to spatial directionality of the secondary structure elements, and they may be also predicted from the sequence, improving overall structure prediction. We have also shown that the large number of available HIV-1 protease structures provides a remarkable sampling of conformations, which can be viewed as direct structural information about the dynamics. After structure matching, we apply principal component analysis (PCA) to obtain the important apparent motions for both bound and unbound structures. There are significant similarities between the first few key motions and the first few low-frequency normal modes calculated from a static representative structure with an elastic network model (ENM) that is based on the contact matrix C (related to D), strongly suggesting that the variations among the observed structures and the corresponding conformational changes are facilitated by the low-frequency, global motions intrinsic to the structure. Similarities are also found when the approach is applied to an NMR ensemble, as well as to atomic molecular dynamics (MD) trajectories. Thus, a sufficiently large number of experimental structures can directly provide important information about protein dynamics, but ENM can also provide a similar sampling of conformations. Finally, we use distance constraints from databases of known protein structures for structure refinement. We use the distributions of distances of various types in known protein structures to obtain the most probable ranges or the mean-force potentials for the distances. We then impose these constraints on structures to be refined or include the mean-force potentials directly in the energy minimization so that more plausible structural models can be built. This approach has been successfully used by us in 2006 in the CASPR structure refinement ().     

The difference between protein structures obtained by x-ray analysis and nuclear magnetic resonance

We have analyzed the pairs of protein structures obtained by X-ray diffraction analysis and nuclear magnetic resonance (X-ray and NMR structures) that display no major differences when superimposed on one another (61 pairs). Analyzing atom-to-atom contacts (contact distances 2–8 Å), it has been found that the NMR structures (compared to the X-ray structures) have more contacts at distances below 3.5 Å and above 5.5 Å. In the case of residue-to-residue contacts, the NMR structures have more contacts at distances below 3 Å and between 4.5 and 6.5 Å. At other distances analyzed, the X-ray structures have more contacts. The difference in the numbers of atom-to-atom and residue-to-residue contacts is greater for buried residues inaccessible to water than for surface residues. Another important difference is related to the number of hydrogen bonds in the main chain: this number is greater in the X-ray structures. The coefficient of correlation between the numbers of hydrogen bonds identified in the structures obtained by both methods is only 32%. If a complete set of NMR models of protein structure is considered, the total number of hydrogen bonds proves to be 1.2 times greater than in the X-ray structures, whereas the correlation coefficient increases to only 65%. We have also demon-strated that -helices in the NMR structures are more distorted (compared to the ideal -helix) than those in the X-ray structures.Translated from Molekulyarnaya Biologiya, Vol. 39, No. 1, 2005, pp. 129–138.Original Russian Text Copyright © 2005 by Melnik, Garbuzynskiy, Lobanov, Galzitskaya.     

A global machine learning based scoring function for protein structure prediction

We present a knowledge‐based function to score protein decoys based on their similarity to native structure. A set of features is constructed to describe the structure and sequence of the entire protein chain. Furthermore, a qualitative relationship is established between the calculated features and the underlying electromagnetic interaction that dominates this scale. The features we use are associated with residue–residue distances, residue–solvent distances, pairwise knowledge‐based potentials and a four‐body potential. In addition, we introduce a new target to be predicted, the fitness score, which measures the similarity of a model to the native structure. This new approach enables us to obtain information both from decoys and from native structures. It is also devoid of previous problems associated with knowledge‐based potentials. These features were obtained for a large set of native and decoy structures and a back‐propagating neural network was trained to predict the fitness score. Overall this new scoring potential proved to be superior to the knowledge‐based scoring functions used as its inputs. In particular, in the latest CASP (CASP10) experiment our method was ranked third for all targets, and second for freely modeled hard targets among about 200 groups for top model prediction. Ours was the only method ranked in the top three for all targets and for hard targets. This shows that initial results from the novel approach are able to capture details that were missed by a broad spectrum of protein structure prediction approaches. Source codes and executable from this work are freely available at http://mathmed.org /#Software and http://mamiris.com/ . Proteins 2014; 82:752–759. © 2013 Wiley Periodicals, Inc.     

Native secondary structure topology has near minimum contact energy among all possible geometrically constrained topologies

Secondary structure topology in this article refers to the order and the direction of the secondary structures, such as helices and strands, with respect to the protein sequence. Even when the locations of the secondary structure Cα atoms are known, there are still (N!2^N)(M!2^M) different possible topologies for a protein with N helices and M strands. This work explored the question if the native topology is likely to be identified among a large set of all possible geometrically constrained topologies through an evaluation of the residue contact energy formed by the secondary structures, instead of the entire chain. We developed a contact pair specific and distance specific multiwell function based on the statistical characterization of the side chain distances of 413 proteins in the Protein Data Bank. The multiwell function has specific parameters to each of the 210 pairs of residue contacts. We illustrated a general mathematical method to extend a single well function to a multiwell function to represent the statistical data. We have performed a mutation analysis using 50 proteins to generate all the possible geometrically constrained topologies of the secondary structures. The result shows that the native topology is within the top 25% of the list ranked by the effective contact energies of the secondary structures for all the 50 proteins, and is within the top 5% for 34 proteins. As an application, the method was used to derive the structure of the skeletons from a low resolution density map that can be obtained through electron cryomicroscopy. Proteins 2009. © 2009 Wiley‐Liss, Inc.     

Rebuilding flavodoxin from C alpha coordinates: a test study

The tertiary structure of flavodoxin has been model built from only the X-ray crystallographic alpha-carbon coordinates. Main-chain atoms were generated from a dictionary of backbone structures. Side-chain conformations were initially set according to observed statistical distributions, clashes were resolved with reference to other knowledge-based parameters, and finally, energy minimization was applied. The RMSD of the model was 1.7 A across all atoms to the native structure. Regular secondary structural elements were modeled more accurately than other regions. About 40% of the chi 1 torsional angles were modeled correctly. Packing of side chains in the core was energetically stable but diverged significantly from the native structure in some regions. The modeling of protein structures is increasing in popularity but relatively few checks have been applied to determine the accuracy of the approach. In this work a variety of parameters have been examined. It was found that close contacts, and hydrogen-bonding patterns could identify poorly packed residues. These tests, however, did not indicate which residues had a conformation different from the native structure or how to move such residues to bring them into agreement. To assist in the modeling of interacting side chains a database of known interactions has been prepared.     

The UAA/GAN internal loop motif: a new RNA structural element that forms a cross-strand AAA stack and long-range tertiary interactions

Analysis of aligned RNA sequences and high-resolution crystal structures has revealed a new RNA structural element, termed the UAA/GAN motif. Found in internal loops of the 23 S rRNA, as well as in RNase P RNA and group I and II introns, this six-nucleotide motif adopts a distinctive local structure that includes two base-pairs with non-canonical conformations and three conserved adenine bases, which form a cross-strand AAA stack in the minor groove. Most importantly, the motif invariably forms long-range tertiary contacts, as the AAA stack typically forms A-minor interactions and the flipped-out N nucleotide forms additional contacts that are specific to the structural context of each loop. The widespread presence of this motif and its propensity to form long-range contacts suggest that it plays a critical role in defining the architectures of structured RNAs.     

A novel parameterization scheme for energy equations and its use to calculate the structure of protein molecules

A novel scheme for the parameterization of a type of “potential energy” function for protein molecules is introduced. The function is parameterized based on the known conformations of previously determined protein structures and their sequence similarity to a molecule whose conformation is to be calculated. Once parameterized, minima of the potential energy function can be located using a version of simulated annealing which has been previously shown to locate global and near-global minima with the given functional form. As a test problem, the potential was parameterized based on the known structures of the rubredoxins from Desulfovibrio vulgaris, Desulfovibrio desulfuricans, and Clostridium pasteurianum, which vary from 45 to 54 amino acids in length, and the sequence alignments of these molecules with the rubredoxin sequence from Desulfovibrio gigas. Since the Desulfovibrio gigas rubredeoxin conformation has also been determined, it is possible to check the accuracy of the results. Ten simulated-annealing runs from random starting conformations were performed. Seven of the 10 resultant conformations have an all-C_α rms deviation from the crystallographically determined conformation of less than 1.7 Å. For five of the structures, the rms deviation is less than 0.8 Å. Four of the structures have conformations which are virtually identical to each other except for the position of the carboxy-terminal residue. This is also the conformation which is achieved if the determined crystal structure is minimized with the same potential. The all-C_α rms difference between the crystal and minimized crystal structures is 0.6 Å. It is further observed that the “energies” of the structures according to the potential function exhibit a strong correlation with rms deviation from the native structure. The conformations of the individual model structures and the computational aspects of the modeling procedure are discussed. © 1993 Wiley-Liss, Inc.     

Structure-based design of model proteins

A structure-based, sequence-design procedure is proposed in which one considers a set of decoy structures that compete significantly with the target structure in being low energy conformations. The decoy structures are chosen to have strong overlaps in contacts with the putative native state. The procedure allows the design of sequences with large and small stability gaps in a random-bond heteropolymer model in both two and three dimensions by an appropriate assignment of the contact energies to both the native and nonnative contacts. The design procedure is also successfully applied to the two-dimensional HP model. Proteins 31:10–20, 1998. © 1998 Wiley-Liss, Inc.