In Search of Functional Advantages of Knots in Proteins

We analysed the structure of deeply knotted proteins representing three unrelated families of knotted proteins. We looked at the correlation between positions of knotted cores in these proteins and such local structural characteristics as the number of intra-chain contacts, structural stability and solvent accessibility. We observed that the knotted cores and especially their borders showed strong enrichment in the number of contacts. These regions showed also increased thermal stability, whereas their solvent accessibility was decreased. Interestingly, the active sites within these knotted proteins preferentially located in the regions with increased number of contacts that also have increased thermal stability and decreased solvent accessibility. Our results suggest that knotting of polypeptide chains provides a favourable environment for the active sites observed in knotted proteins. Some knotted proteins have homologues without a knot. Interestingly, these unknotted homologues form local entanglements that retain structural characteristics of the knotted cores.     

BCL::Fold - De Novo Prediction of Complex and Large Protein Topologies by Assembly of Secondary Structure Elements

Computational de novo protein structure prediction is limited to small proteins of simple topology. The present work explores an approach to extend beyond the current limitations through assembling protein topologies from idealized α-helices and β-strands. The algorithm performs a Monte Carlo Metropolis simulated annealing folding simulation. It optimizes a knowledge-based potential that analyzes radius of gyration, β-strand pairing, secondary structure element (SSE) packing, amino acid pair distance, amino acid environment, contact order, secondary structure prediction agreement and loop closure. Discontinuation of the protein chain favors sampling of non-local contacts and thereby creation of complex protein topologies. The folding simulation is accelerated through exclusion of flexible loop regions further reducing the size of the conformational search space. The algorithm is benchmarked on 66 proteins with lengths between 83 and 293 amino acids. For 61 out of these proteins, the best SSE-only models obtained have an RMSD100 below 8.0 Å and recover more than 20% of the native contacts. The algorithm assembles protein topologies with up to 215 residues and a relative contact order of 0.46. The method is tailored to be used in conjunction with low-resolution or sparse experimental data sets which often provide restraints for regions of defined secondary structure.     

Exploring the effects of sparse restraints on protein structure prediction

One of the main barriers to accurate computational protein structure prediction is searching the vast space of protein conformations. Distance restraints or inter‐residue contacts have been used to reduce this search space, easing the discovery of the correct folded state. It has been suggested that about 1 contact for every 12 residues may be sufficient to predict structure at fold level accuracy. Here, we use coarse‐grained structure‐based models in conjunction with molecular dynamics simulations to examine this empirical prediction. We generate sparse contact maps for 15 proteins of varying sequence lengths and topologies and find that given perfect secondary‐structural information, a small fraction of the native contact map (5%‐10%) suffices to fold proteins to their correct native states. We also find that different sparse maps are not equivalent and we make several observations about the type of maps that are successful at such structure prediction. Long range contacts are found to encode more information than shorter range ones, especially for α and αβ‐proteins. However, this distinction reduces for β‐proteins. Choosing contacts that are a consensus from successful maps gives predictive sparse maps as does choosing contacts that are well spread out over the protein structure. Additionally, the folding of proteins can also be used to choose predictive sparse maps. Overall, we conclude that structure‐based models can be used to understand the efficacy of structure‐prediction restraints and could, in future, be tuned to include specific force‐field interactions, secondary structure errors and noise in the sparse maps.     

Intramolecular interactions in pancreatic ribonucleases.

A detailed analysis of the composition and properties of hydrophobic nuclei and microclusters in pancreatic ribonuclease A (RNase A) has been carried out. Distance calculations for all noncovalently bonded atoms revealed that the average number of nonpolar contacts between a side chain of an amino acid and its neighbors is substantially larger if it involves hydrophobic residues rather than nonhydrophobic ones. However, the difference decreased when the number of contacts per nonpolar group and/or atom were calculated. Three main nuclei and five microclusters were identified, and their quantitative parameters were calculated. These nuclei include hydrophobic residues with a substantial number of nonpolar contacts with the environment (Phe 8, Phe 120, Phe 46, Tyr 25, Tyr 97, Ile 107, Leu 35, Ile 81, Val 54, Val 108, Met 29, Met 30). Hydrophobic nuclei of RNase A differ in shape and in composition, in the number of intranuclear contacts and of associated residues, as well as in their internal mobility. All eight cysteine residues are involved in nonpolar interactions with amino acid residues of hydrophobic nuclei. Active site amino acid residues of RNase A form a noncovalent contact network comprised of themselves, as well as of many conserved residues from hydrophobic nuclei. Sequence alignment with some other members of the RNase A family of proteins shows remarkable similarity in positions and in conservation of the main nonpolar residues, comprising cores of two (out of three) hydrophobic nuclei. A correlation was shown to exist between the average density of contacts for side-chain atoms and the number of amino acids to be found in the appropriate positions in the sequences of related mammalian ribonucleases. However, there are certain amino acid positions in the third, smaller nucleus, which are highly variable within the family. Taking into account that this nucleus is composed of residues belonging to different elements of the secondary structure, it is likely that the mutual orientation of these elements can be somehow different for these proteins.     

Identifying sequence-structure pairs undetected by sequence alignments

We examine how effectively simple potential functions previously developed can identify compatibilities between sequences and structures of proteins for database searches. The potential function consists of pairwise contact energies, repulsive packing potentials of residues for overly dense arrangement and short-range potentials for secondary structures, all of which were estimated from statistical preferences observed in known protein structures. Each potential energy term was modified to represent compatibilities between sequences and structures for globular proteins. Pairwise contact interactions in a sequence-structure alignment are evaluated in a mean field approximation on the basis of probabilities of site pairs to be aligned. Gap penalties are assumed to be proportional to the number of contacts at each residue position, and as a result gaps will be more frequently placed on protein surfaces than in cores. In addition to minimum energy alignments, we use probability alignments made by successively aligning site pairs in order by pairwise alignment probabilities. The results show that the present energy function and alignment method can detect well both folds compatible with a given sequence and, inversely, sequences compatible with a given fold, and yield mostly similar alignments for these two types of sequence and structure pairs. Probability alignments consisting of most reliable site pairs only can yield extremely small root mean square deviations, and including less reliable pairs increases the deviations. Also, it is observed that secondary structure potentials are usefully complementary to yield improved alignments with this method. Remarkably, by this method some individual sequence-structure pairs are detected having only 5-20% sequence identity.     

Information on the secondary structure improves the quality of protein sequence alignment

The most popular algorithms employed in the pairwise alignment of protein primary structures (Smith-Watermann (SW) algorithm, FASTA, BLAST, etc.) only analyze the amino acid sequence. The SW algorithm is the most accurate, yielding alignments that agree best with superimpositions of the corresponding spatial structures of proteins. However, even the SW algorithm fails to reproduce the spatial structure alignment when the sequence identity is lower than 30%. The objective of this work was to develop a new and more accurate algorithm taking the secondary structure of proteins into account. The alignments generated by this algorithm and having the maximal weight with the secondary structure considered proved to be more accurate than SW alignments. With sequences having less than 30% identity, the accuracy (i.e., the portion of reproduced positions of a reference alignment obtained by superimposing the protein spatial structures) of the new algorithm is 58 vs. 35% of the SW algorithm. The accuracy of the new algorithm is much the same with secondary structures established experimentally or predicted theoretically. Hence, the algorithm is applicable to proteins with unknown spatial structures. The program is available at ftp://194.149.64.196/STRUSWER/.     

To be folded or to be unfolded?

The lack of ordered structure in “natively unfolded” proteins raises a general question: Are there intrinsic properties of amino acid residues that are responsible for the absence of fixed structure at physiological conditions? In this article, we demonstrate that the competence of a protein to be folded or to be unfolded may be determined by the property of amino acid residues to form a sufficient number of contacts in a globular state. The expected average number of contacts per residue calculated from the amino acid sequence alone (using the average number of contacts for 20 amino acid residues in globular proteins) can be used as one of the simple indicators of natively unfolded proteins. The prediction accuracy for the sets of 80 folded and 90 natively unfolded proteins reaches 89% if the expected average number of contacts is used as a parameter and 83% in the case of hydrophobicity. An optimal set of artificial parameters for 20 amino acid residues obtained by Monte Carlo algorithm to maximally separate the sets of 90 natively unfolded and 80 folded proteins demonstrates the upper limit for prediction accuracy, which is 95%.     

A new protein folding algorithm based on hydrophobic compactness: Rigid Unconnected Secondary Structure Iterative Assembly (RUSSIA). II: Applications

The RUSSIA procedure (Rigid Unconnected Secondary Structure Iterative Assembly) produces structural models of cores of small- and medium-sized proteins. Loops are omitted from this treatment and regular secondary structures are reduced to points, the centers of their hydrophobic faces. This methodology relies on the maximum compactness of the hydrophobic residues, as described in detail in Part I. Starting data are the sequence and the predicted limits and natures of regular secondary structures (alpha or beta). Helices are treated as rigid cylinders, whereas beta-strands are collectively taken into account within beta-sheets modeled by helicoid surfaces. Strands are allowed to shift along their mean axis to allow some flexibility and the alpha-helices can be placed on either side of beta-sheets. Numerous initial conformations are produced by discrete rotations of the helices and sheets around the direction going from the center of their hydrophobic face to the global center of the protein. Selection of proposed models is based upon a criterion lying on the minimization of distances separating hydrophobic residues belonging to different regular secondary structures. The procedure is rapid and appears to be robust relative to the quality of starting data (nature and length of regular secondary structures). This dependence of the quality of the model on secondary structure prediction and in particular the beta-sheet topology, is one of the limits of the present algorithm. We present here some results for a set of 12 proteins (alpha, beta and alpha/beta classes) of lengths 40-166 amino acids. The r.m.s. deviations for core models with respect to the native proteins are in the range 1.4-3.7 A.     

Molecular basis of co-operativity in protein folding. III. Structural identification of cooperative folding units and folding intermediates.

The hierarchical partition function formalism for protein folding developed earlier has been extended through the use of three-dimensional polar and apolar contact plots. For each amino acid residue in the protein, these plots indicate the apolar and polar surfaces that are buried from the solvent, the identity of all amino acid residues that contribute to this shielding, and the magnitude of their contributions. These contact plots are then used to examine the distribution of the free energy of stabilization throughout the protein molecule. Analysis of these data allows identification of co-operative folding units and their hierarchical levels, and the identification of partially folded intermediates with a significant probability of being populated. The overall folding/unfolding thermodynamics of 12 globular proteins, for which crystallographic and experimental thermodynamics are available, is predicted within error. An energetic classification of partially folded intermediates is presented and the results compared to those cases for which structural and thermodynamic experimental information is available. Four different types of partially folded states and their structural energies are considered. (1) Local intermediates, in which only a local region of the protein loses secondary and tertiary interactions, while the rest of the protein remains intact. (2) Global intermediates, corresponding to the standard molten globule definition, in which significant secondary structure is maintained but native-like tertiary structure contacts are disrupted. (3) Extended intermediates characterized by the existence of secondary structure elements (e.g. alpha-helices) exposed to solvent. (4) Folding intermediates in proteins with two structural domains. The structure and energetics of folding intermediates of apo-myoglobin, alpha-lactalbumin, phosphoglycerate kinase and arabinose-binding protein are considered in detail.     

Direct-Coupling Analysis of nucleotide coevolution facilitates RNA secondary and tertiary structure prediction

Despite the biological importance of non-coding RNA, their structural characterization remains challenging. Making use of the rapidly growing sequence databases, we analyze nucleotide coevolution across homologous sequences via Direct-Coupling Analysis to detect nucleotide-nucleotide contacts. For a representative set of riboswitches, we show that the results of Direct-Coupling Analysis in combination with a generalized Nussinov algorithm systematically improve the results of RNA secondary structure prediction beyond traditional covariance approaches based on mutual information. Even more importantly, we show that the results of Direct-Coupling Analysis are enriched in tertiary structure contacts. By integrating these predictions into molecular modeling tools, systematically improved tertiary structure predictions can be obtained, as compared to using secondary structure information alone.     

Influence of medium and long range interactions in protein folding.

Protein structures are stabilized by both local and long range interactions. In this work, we analyze the residue-residue contacts and the role of medium- and long-range interactions in globular proteins belonging to different structural classes. The results show that while medium range interactions predominate in all-alpha class proteins, long-range interactions predominate in all-beta class. Based on this, we analyze the performance of several structure prediction methods in different structural classes of globular proteins and found that all the methods predict the secondary structures of all-alpha proteins more accurately than other classes. Also, we observed that the residues occurring in the range of 21-30 residues apart contributes more towards long-range contacts and about 85% of residues are involved in long-range contacts. Further, the preference of residue pairs to the folding and stability of globular proteins is discussed.     

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.     

The folding of an enzyme. VI. The folding pathway of barnase: comparison with theoretical models.

The sequence of events in the refolding pathway of barnase has been analysed to search for general principles in protein folding. There appears to be a correlation between burying hydrophobic surface area and early folding events. All the regions that fold early interact extensively with the beta-sheet. These interactions involve predominantly hydrophobic interactions and the burial of very extensive hydrophobic areas in which multiple, close, hydrophobic-hydrophobic contacts are established around a central group of aliphatic residues. There is no burial of hydrophilic residues in these regions; those that are partly screened from the solvent make hydrogen bonds. All the regions or interactions that are made late in the folding pathway do not make extensive contacts with the beta-sheet. Their buried hydrophobic regions lack a central hydrophobic residue or residues around which other hydrophobic residues pack. Further, in some of these regions there is an extensive burial of hydrophilic residues. The results are consistent with one of the earlier events in protein folding being the local formation of native-like secondary structure elements driven by local hydrophobic surface burial. A possible candidate for an initiation site is a beta-hairpin between beta-strands 3 and 4 that is conserved in the microbial ribonuclease family. A comparison of structures in this family shows that those regions that can be superimposed, or have sequence homology, correspond to elements of structure that are formed and interact with each other early in the folding pathway, suggesting that some of these residues could be involved in directing the folding process. The data on barnase combined with results from other laboratories suggest the following tentative conclusions for the refolding of small monomeric proteins. (1) The refolding pathway is, at least in part, sequential and of compulsory order. (2) Secondary structure formation is driven by local hydrophobic surface burial and precedes the formation of most tertiary interactions. These elements are then stabilized and sometimes elongated by tertiary interactions. It is plausible that there are stop signals encoded in the linear sequence that prevent the elongation of isolated secondary structure elements in solution to a larger extent than is found in the folded protein. (3) Many tertiary interactions are not very constrained in the intermediate but become more and more defined as the hydrophobic cores consolidate, loop structures form and the configuration of surface residues takes place. The interactions between different elements of secondary structure are the last ones to be consolidated while the interactions within the secondary structure elements are consolidated earlier.(ABSTRACT TRUNCATED AT 400 WORDS)     

SCORE: predicting the core of protein models

MOTIVATION: The prediction of the regions of homology models that can be 'restrained by' or 'copied from' the basis structures is a vital step in correct model generation, because these regions are the models most accurate part. However, there is no ideal method for the identification of their limits. In most algorithms their length depends on the number of family members and definitions of secondary structure. RESULTS: The algorithm SCORE steps away from the conventional definitions of the core to identify from large numbers of basis structures those regions that can be considered structurally related to a target sequence. The use of phi, psi constraints to accurately pinpoint the regions that are conserved across a family and environmentally constrained substitution tables to extend these regions allows SCORE to rapidly (generally in under 1 s, an order of magnitude faster than methods such as MODELLER) identify and build the core of homology models from the alignments of the target sequence to the basis structures. The SCORE algorithm was used to build 114 model cores. In only two cases was the core size less than 50% of the structure and all the cores built had an RMSD of 3.7 A or less to the target 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.     

Swapping core residues in homologous proteins swaps folding mechanism

Rat intestinal fatty acid binding protein (IFABP) displays an intermediate with little if any secondary structure during unfolding, while the structurally homologous rat ileal lipid binding protein (ILBP) displays an intermediate during unfolding with nativelike secondary structure. Double-jump experiments indicate that these intermediates are on the folding path for each protein. To test the hypothesis that differences in the number of buried hydrophobic atoms in a folding initiating site are responsible for the different types of intermediates observed for these proteins, two mutations (F68C-IFABP and C69F-ILBP) were made that swapped a more hydrophobic residue for a more hydrophilic residue in the respective cores of these two proteins. F68C-IFABP followed an unfolding path identical to that of WT-ILBP with an intermediate that showed nativelike secondary structure, whereas C69F-ILBP followed an unfolding path that was identical to that of WT-IFABP with an intermediate that lacked secondary structure. Further, a hydrophilic residue was introduced at an identical hydrophobic structural position in both proteins (F93S-IFABP and F94S-ILBP). Replacement of phenylalanine with serine at this site led to the appearance of an intermediate during refolding that lacked secondary structure for both proteins that was not detected for either parental protein. Altering the chemical characteristics and/or size of residues within an initiating core of hydrophobic interactions is critical to the types of intermediates that are observed during the folding of these proteins.     

Protein secondary structure assignment through Voronoï tessellation

We present a new automatic algorithm, named VoTAP (Vo ronoï T essellation A ssignment P rocedure), which assigns secondary structures of a polypeptide chain using the list of α‐carbon coordinates. This program uses three‐dimensional Voronoï tessellation. This geometrical tool associates with each amino acid a Voronoï polyhedron, the faces of which unambiguously define contacts between residues. Thanks to the face area, for the contacts close together along the primary structure (low‐order contacts) a distinction is made between strong and normal ones. This new definition yields new contact matrices, which are analyzed and used to assign secondary structures. This assignment is performed in two stages. The first one uses contacts between residues close together along the primary structure and is based on data collected on a bank of 282 well‐refined nonredundant structures. In this bank, associations were made between the prints defined by these low‐order contacts and the assignments performed by different automatic methods. The second step focuses on the strand assignment and uses contacts between distant residues. Comparison with several other automatic assignment methods are presented, and the influence of resolution on the assignment is investigated. Proteins 2004. © 2004 Wiley‐Liss, Inc.     

Regulation of AMPA receptor gating by ligand binding core dimers

Ionotropic glutamate receptors are tetramers, the isolated ligand binding cores of which assemble as dimers. Previous work on nondesensitizing AMPA receptor mutants, which combined crystallography, ultracentrifugation, and patch-clamp recording, showed that dimer formation by the ligand binding cores is required for activation of ion channel gating by agonists. To define the mechanisms responsible for stabilization of dimer assembly in native AMPA receptors, contacts between the adjacent ligand binding cores were individually targeted by amino acid substitutions, using the GluR2 crystal structure as a guide to design mutants. We show that disruption of a salt bridge, hydrogen bond network, and intermolecular van der Waals contacts between helices D and J in adjacent ligand binding cores greatly accelerates desensitization. Conservation of these contacts in AMPA and kainate receptors indicates that they are important determinants of dimer stability and that the dimer interface is a key structural element in the gating mechanism of these glutamate receptor families.     

Prediction of contact numbers of amino acid residues using a neural network regression algorithm

The profile of contact numbers of amino acid residues in proteins contains important information about the protein structure and is connected with the accessibility of residues to solvent. Here we propose a method for predicting the profile of contact numbers of residues in protein from its amino acid sequence. The method is based on regression using a neural network algorithm. The algorithm predicts two types of profiles, namely, the total number of contacts and the number of close contacts with the neighbors in the chain. The Pearson coefficient of correlation between the actual and predicted values of total contact numbers amounted to 0.526–0.703. As for the number of close contacts, this coefficient was higher (0.662–0.743) for all the considered threshold contact distances (6, 8, 10, and 12 Å). The program for prediction of contact numbers CONNP is available at http://wwwmgs2.bionet.nsc.ru/reloaded.