Protein local conformations arise from a mixture of Gaussian distributions

The classical approaches for protein structure prediction rely either on homology of the protein sequence with a template structure or on ab initio calculations for energy minimization. These methods suffer from disadvantages such as the lack of availability of homologous template structures or intractably large conformational search space, respectively. The recently proposed fragment library based approaches first predict the local structures, which can be used in conjunction with the classical approaches of protein structure prediction. The accuracy of the predictions is dependent on the quality of the fragment library. In this work, we have constructed a library of local conformation classes purely based on geometric similarity. The local conformations are represented using Geometric Invariants, properties that remain unchanged under transformations such as translation and rotation, followed by dimension reduction via principal component analysis. The local conformations are then modeled as a mixture of Gaussian probability distribution functions (PDF). Each one of the Gaussian PDF’s corresponds to a conformational class with the centroid representing the average structure of that class. We find 46 classes when we use an octapeptide as a unit of local conformation. The protein 3-D structure can now be described as a sequence of local conformational classes. Further, it was of interest to see whether the local conformations can be predicted from the amino acid sequences. To that end, we have analyzed the correlation between sequence features and the conformational classes.     

Protein local conformations arise from a mixture of Gaussian distributions

The classical approaches for protein structure prediction rely either on homology of the protein sequence with a template structure or on ab initio calculations for energy minimization. These methods suffer from disadvantages such as the lack of availability of homologous template structures or intractably large conformational search space, respectively. The recently proposed fragment library based approaches first predict the local structures,which can be used in conjunction with the classical approaches of protein structure prediction. The accuracy of the predictions is dependent on the quality of the fragment library. In this work, we have constructed a library of local conformation classes purely based on geometric similarity. The local conformations are represented using Geometric Invariants, properties that remain unchanged under transformations such as translation and rotation, followed by dimension reduction via principal component analysis. The local conformations are then modeled as a mixture of Gaussian probability distribution functions (PDF). Each one of the Gaussian PDF's corresponds to a conformational class with the centroid representing the average structure of that class. We find 46 classes when we use an octapeptide as a unit of local conformation. The protein 3-D structure can now be described as a sequence of local conformational classes. Further, it was of interest to see whether the local conformations can be predicted from the amino acid sequences. To that end,we have analyzed the correlation between sequence features and the conformational classes.     

Conformational analysis and clustering of short and medium size loops connecting regular secondary structures: a database for modeling and prediction.

Loops are regions of nonrepetitive conformation connecting regular secondary structures. We identified 2,024 loops of one to eight residues in length, with acceptable main-chain bond lengths and peptide bond angles, from a database of 223 protein and protein-domain structures. Each loop is characterized by its sequence, main-chain conformation, and relative disposition of its bounding secondary structures as described by the separation between the tips of their axes and the angle between them. Loops, grouped according to their length and type of their bounding secondary structures, were superposed and clustered into 161 conformational classes, corresponding to 63% of all loops. Of these, 109 (51% of the loops) were populated by at least four nonhomologous loops or four loops sharing a low sequence identity. Another 52 classes, including 12% of the loops, were populated by at least three loops of low sequence similarity from three or fewer nonhomologous groups. Loop class suprafamilies resulting from variations in the termini of secondary structures are discussed in this article. Most previously described loop conformations were found among the classes. New classes included a 2:4 type IV hairpin, a helix-capping loop, and a loop that mediates dinucleotide-binding. The relative disposition of bounding secondary structures varies among loop classes, with some classes such as beta-hairpins being very restrictive. For each class, sequence preferences as key residues were identified; those most frequently at these conserved positions than in proteins were Gly, Asp, Pro, Phe, and Cys. Most of these residues are involved in stabilizing loop conformation, often through a positive phi conformation or secondary structure capping. Identification of helix-capping residues and beta-breakers among the highly conserved positions supported our decision to group loops according to their bounding secondary structures. Several of the identified loop classes were associated with specific functions, and all of the member loops had the same function; key residues were conserved for this purpose, as is the case for the parvalbumin-like calcium-binding loops. A significant number, but not all, of the member loops of other loop classes had the same function, as is the case for the helix-turn-helix DNA-binding loops. This article provides a systematic and coherent conformational classification of loops, covering a broad range of lengths and all four combinations of bounding secondary structure types, and supplies a useful basis for modelling of loop conformations where the bounding secondary structures are known or reliably predicted.     

Discrimination between distant homologs and structural analogs: lessons from manually constructed, reliable data sets

A natural way to study protein sequence, structure, and function is to put them in the context of evolution. Homologs inherit similarities from their common ancestor, while analogs converge to similar structures due to a limited number of energetically favorable ways to pack secondary structural elements. Using novel strategies, we previously assembled two reliable databases of homologs and analogs. In this study, we compare these two data sets and develop a support vector machine (SVM)-based classifier to discriminate between homologs and analogs. The classifier uses a number of well-known similarity scores. We observe that although both structure scores and sequence scores contribute to SVM performance, profile sequence scores computed based on structural alignments are the best discriminators between remote homologs and structural analogs. We apply our classifier to a representative set from the expert-constructed database, Structural Classification of Proteins (SCOP). The SVM classifier recovers 76% of the remote homologs defined as domains in the same SCOP superfamily but from different families. More importantly, we also detect and discuss interesting homologous relationships between SCOP domains from different superfamilies, folds, and even classes.     

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.     

Protein structural motif prediction in multidimensional phi-psi space leads to improved secondary structure prediction.

A significant step towards establishing the structure and function of a protein is the prediction of the local conformation of the polypeptide chain. In this article, we present systems for the prediction of three new alphabets of local structural motifs. The motifs are built by applying multidimensional scaling (MDS) and clustering to pair-wise angular distances for multiple phi-psi angle values collected from high-resolution protein structures. The predictive systems, based on ensembles of bidirectional recurrent neural network architectures, and trained on a large non-redundant set of protein structures, achieve 72%, 66%, and 60% correct motif prediction on an independent test set for di-peptides (six classes), tri-peptides (eight classes) and tetra-peptides (14 classes), respectively, 28-30% above baseline statistical predictors. We then build a further system, based on ensembles of two-layered bidirectional recurrent neural networks, to map structural motif predictions into a traditional 3-class (helix, strand, coil) secondary structure. This system achieves 79.5% correct prediction using the "hard" CASP 3-class assignment, and 81.4% with a more lenient assignment, outperforming a sophisticated state-of-the-art predictor (Porter) trained in the same experimental conditions. The structural motif predictor is publicly available at: http://distill.ucd.ie/porter+/.     

Stabilization of local structures by pi-CH and aromatic-backbone amide interactions involving prolyl and aromatic residues

Weakly polar interactions between the side-chain aromatic rings and hydrogens of backbone amides (Ar-HN) and CHn of aliphatic groups (pi-CH) are known to form local structures and to stabilize secondary structure in peptides and proteins. To investigate the existence of these interactions and to explore their possible role in constraining the structures of Pro-Xaa and Xaa-Pro fragments in proteins, a database search was performed in a non-redundant set of proteins from the Brookheaven Protein Data Bank for pi-CH and Ar-HN interactions in Pro-Xaa and Xaa-Pro fragments (where Xaa is either Phe, Tyr or Trp). In Xaa-Pro fragments, the percentage of pi-CH interactions and Ar-HN interactions, respectively, was 20.6 and 3.2%, in Pro-Xaa fragments 26.8, 8.6 and 4.0% of the Pro-Xaa fragments contained both interactions, while no Xaa-Pro fragments had both. The protein fragments containing Ar-HN and/or pi-CH interactions were clustered on the basis of similarity of selected torsion angles. The clustering resulted in well defined clusters. Thus, pi-CH and Ar(i)-HN(i) interactions were able to constrain individual conformations of the Pro-Xaa and Xaa-Pro fragments. These local structures were found to be independent of the secondary structure of the polypeptide chains in which the fragments were found.     

Local structure of cytochrome c from horse heart in solution. Conformational analysis using data of two-dimensional nuclear Overhauser effect spectroscopy]

Using the earlier suggested method the calculation of the backbone conformations of horse heart cytochrome c in oxidized (ferricytochrome c) and reduced (ferrocytochrome c) states has been performed by the two-dimensional nuclear Overhauser effect spectroscopy data. For both protein forms the secondary structure elements have been revealed and the conformations of the irregular polypeptide chain segments have been analysed. The similarity of the secondary structures of ferri- and ferrocytochrome c in solution was established from the comparison of their conformations. Small differences between the conformations of two molecule forms are shown to be localized within the polypeptide chain fragments situated in the spatial structure near the heme crevice. The comparison of the dihedral phi and psi angles in the calculated conformations of horse cytochrome C with the corresponding characteristics of X-ray structures of tuna ferri- and ferrocytochrome c made for the oxidized and reduced protein forms using the quantitative criteria testifies the similarity of their conformations in solution and crystal. In is shown that the conformational changes of the separate amino acid residues which take place as the result of the "solution-to-crystal" transition occur on the surface fragments of protein globule and do not lead to essential alterations of the secondary molecule structure.     

Cell signal transduction: hormones,neurotransmitters and therapeutic drugs relate to purine nucleotide structure

Purine nucleotides transduce cell membrane receptor responses and modulate ion channel activity. This is accomplished through conformational change in the structure of nucleotides and cell membrane associated proteins. The aim of this study is to enhance our understanding of nucleotide dependence in regard to signal transduction events, drug action and pharmacological promiscuity. Nucleotides and ligand structures regulating Gα protein subunits, voltage- and ligand-gated ion channels are investigated for molecular similarity using a computational program. Results differentiate agonist and antagonist structures, identify molecular similarity within nucleotide and ligand structures and demonstrate the potential of ligands to regulate nucleotide conformational change. Relative molecular similarity within nucleotides and the ligands of the major receptor classes provides insight into mechanisms of receptor and ion channel regulation. The nucleotide template model has some merit as an initial screening tool in the study and comparison of drug and hormone structures.     

The task of determining the local structure of proteins by Overhauser effect nuclear spectroscopy addressed once more]

The testing of the earlier developed theoretical method for determining the backbone protein conformations (the local structure) on the basis of the two-dimensional nuclear Overhauser effect (NOE) spectroscopy has been fulfilled. The method approval has been carried out by the calculation (based upon spectral NOE parameters) of the local plastocyanin and bovine pancreatic trypsin inhibitor structures followed by the comparison of the received conformational parameters with the X-ray data. The comparison of the molecular conformations in solution and crystal has been implemented for different fragments of the polypeptide chain (beta-structures, alpha-helices, irregular segments) using the mathematical statistics methods. The verification of the "zero" hypothesis about the similarity of phi and psi variation rows which was carried out at the reliability level of 0.99 showed that in both cases there were no systematic deviations of dihedral angles of the compared conformations and that their dispersion differences were statistically indiscernible. It has been concluded that the approved method permits to determine the local structure of the conformationally rigid proteins (or their fragments) at the level close to that which provides the high resolution X-ray analysis.     

Clustering of protein structural fragments reveals modular building block approach of nature

Structures of peptide fragments drawn from a protein can potentially occupy a vast conformational continuum. We co-ordinatize this conformational space with the help of geometric invariants and demonstrate that the peptide conformations of the currently available protein structures are heavily biased in favor of a finite number of conformational types or structural building blocks. This is achieved by representing a peptides' backbone structure with geometric invariants and then clustering peptides based on closeness of the geometric invariants. This results in 12,903 clusters, of which 2207 are made up of peptides drawn from functionally and/or structurally related proteins. These are termed "functional" clusters and provide clues about potential functional sites. The rest of the clusters, including the largest few, are made up of peptides drawn from unrelated proteins and are termed "structural" clusters. The largest clusters are of regular secondary structures such as helices and beta strands as well as of beta hairpins. Several categories of helices and strands are discovered based on geometric differences. In addition to the known classes of loops, we discover several new classes, which will be useful in protein structure modeling. Our algorithm does not require assignment of secondary structure and, therefore, overcomes the limitations in loop classification due to ambiguity in secondary structure assignment at loop boundaries.     

Sequence variations within protein families are linearly related to structural variations

It is commonly believed that similarities between the sequences of two proteins infer similarities between their structures. Sequence alignments reliably recognize pairs of protein of similar structures provided that the percentage sequence identity between their two sequences is sufficiently high. This distinction, however, is statistically less reliable when the percentage sequence identity is lower than 30% and little is known then about the detailed relationship between the two measures of similarity. Here, we investigate the inverse correlation between structural similarity and sequence similarity on 12 protein structure families. We define the structure similarity between two proteins as the cRMS distance between their structures. The sequence similarity for a pair of proteins is measured as the mean distance between the sequences in the subsets of sequence space compatible with their structures. We obtain an approximation of the sequence space compatible with a protein by designing a collection of protein sequences both stable and specific to the structure of that protein. Using these measures of sequence and structure similarities, we find that structural changes within a protein family are linearly related to changes in sequence similarity.     

Thiol-based redox signalling: rust never sleeps

Cysteine residues in proteins are covalently modified under conditions of oxidative and nitrosative stress by oxidation, nitrosation, glutathionylation and disulfide formation. Modifications induce conformational changes in substrate proteins, effecting signal cascades that evoke a biological response. A growing number of structures with modified cysteines are allowing a piecemeal understanding of the mechanistic aspects of these signalling pathways to emerge. Conformational changes upon conjugation of nitric oxide and glutathione are generally small and often accompanied by a local increase in protein disorder. Burial of nitric oxide is also apparent, which may increase the timeframe of signalling. Conformational changes upon disulfide formation/reduction range from the small to the spectacular. They include order/disorder transitions; oxidation of disulfides following expulsion of metals such as Zn; major reorganisation or "morphing" of portions of the polypeptide backbone; and changes in quaternary structure including domain swapping.     

Combining evolutionary and structural information for local protein structure prediction

We study the effects of various factors in representing and combining evolutionary and structural information for local protein structural prediction based on fragment selection. We prepare databases of fragments from a set of non-redundant protein domains. For each fragment, evolutionary information is derived from homologous sequences and represented as estimated effective counts and frequencies of amino acids (evolutionary frequencies) at each position. Position-specific amino acid preferences called structural frequencies are derived from statistical analysis of discrete local structural environments in database structures. Our method for local structure prediction is based on ranking and selecting database fragments that are most similar to a target fragment. Using secondary structure type as a local structural property, we test our method in a number of settings. The major findings are: (1) the COMPASS-type scoring function for fragment similarity comparison gives better prediction accuracy than three other tested scoring functions for profile-profile comparison. We show that the COMPASS-type scoring function can be derived both in the probabilistic framework and in the framework of statistical potentials. (2) Using the evolutionary frequencies of database fragments gives better prediction accuracy than using structural frequencies. (3) Finer definition of local environments, such as including more side-chain solvent accessibility classes and considering the backbone conformations of neighboring residues, gives increasingly better prediction accuracy using structural frequencies. (4) Combining evolutionary and structural frequencies of database fragments, either in a linear fashion or using a pseudocount mixture formula, results in improvement of prediction accuracy. Combination at the log-odds score level is not as effective as combination at the frequency level. This suggests that there might be better ways of combining sequence and structural information than the commonly used linear combination of log-odds scores. Our method of fragment selection and frequency combination gives reasonable results of secondary structure prediction tested on 56 CASP5 targets (average SOV score 0.77), suggesting that it is a valid method for local protein structure prediction. Mixture of predicted structural frequencies and evolutionary frequencies improve the quality of local profile-to-profile alignment by COMPASS.     

Identification of native protein folds amongst a large number of incorrect models. The calculation of low energy conformations from potentials of mean force

We present an approach that is able to detect native folds amongst a large number of non-native conformations. The method is based on the compilation of potentials of mean force of the interactions of the C beta atoms of all amino acid pairs from a database of known three-dimensional protein structures. These potentials are used to calculate the conformational energy of amino acid sequences in a number of different folds. For a substantial number of proteins we find that the conformational energy of the native state is lowest amongst the alternatives. Exceptions are proteins containing large prosthetic groups, Fe-S clusters or polypeptide chains that do not adopt globular folds. We discuss briefly potential applications in various fields of protein structural research.     

Database searching by flexible protein structure alignment

We have recently developed a flexible protein structure alignment program (FATCAT) that identifies structural similarity, at the same time accounting for flexibility of protein structures. One of the most important applications of a structure alignment method is to aid in functional annotations by identifying similar structures in large structural databases. However, none of the flexible structure alignment methods were applied in this task because of a lack of significance estimation of flexible alignments. In this paper, we developed an estimate of the statistical significance of FATCAT alignment score, allowing us to use it as a database-searching tool. The results reported here show that (1) the distribution of the similarity score of FATCAT alignment between two unrelated protein structures follows the extreme value distribution (EVD), adding one more example to the current collection of EVDs of sequence and structure similarities; (2) introducing flexibility into structure comparison only slightly influences the sensitivity and specificity of identifying similar structures; and (3) the overall performance of FATCAT as a database searching tool is comparable to that of the widely used rigid-body structure comparison programs DALI and CE. Two examples illustrating the advantages of using flexible structure alignments in database searching are also presented. The conformational flexibilities that were detected in the first example may be involved with substrate specificity, and the conformational flexibilities detected in the second example may reflect the evolution of structures by block building.     

Fluorescence study of conformational transitions in the structure of myoglobin

Fluorescence studies of myoglobin and Mb-like structures, apomyoglobin and the complex of apo-Mb with protoporphyrin IX, reveal both the similarity between them, which is due to a common type of polypeptide chain folding, and the distinctions imposed by the influence of the prosthetic group. Close resemblance of structures of holomyoglobin and its metal-free analog, PPIX--apo-Mb, points to a key role of specific interactions between the protein and the protoporphyrin macrocycle rather than the Fe-protein bond in the formation of Mb-like structures. In PPIX--apo-Mb, both the hydrophobic core and the important ionic bonds between different structural elements () stabilizing the Mb structure are almost completely retained. The bond between Fe and proximal His-F8 allows additional integration of the structures of the heme cavity and the myoglobin molecule as a whole, providing its functional activity and highly cooperative conformational transitions. In all the myoglobin-like structures studied, a certain relationship is found between conformational states of the , the heme cavity, and the N-terminal part of the molecule. This is probably due to variations in the mutual orientation of the ABCDE and FGH helical domains, depending on the interactions between the protein, the prosthetic group, and the ligand in the heme crevice. The correlation between conformations of the N-terminal and heme regions found at a level of the globin tertiary structure is very important for understanding the mechanisms of homo- and heterotropic regulation in tetrameric hemoglobins.     

Necessary conditions for avoiding incorrect polypeptide folds in conformational search by energy minimization

Low energy conformations have been generated for melittin, pancreatic polypeptide, and ribonuclease S-peptide, both in the vicinity of x-ray structures by energy refinement and by an unconstrained search over the entire conformational space. Since the structural polymorphism of these medium-sized peptides in crystal and solution is moderate, comparing the calculated conformations to x-ray and nmr data provides information on local and global behavior of potential functions. Local analysis includes standardization calculations, which show that models with standard geometry can approximate good resolution x-ray data with less than 0.5 Å rms deviation (RMSD). However, the atomic coordinates are shifted up to 2 Å RMSD by local energy minimization, and thus 2 Å is generally the smallest RMSD value one can target in a conformational search using the same energy evaluation models. The unconstrained search was performed by a buildup-type method based on dynamic programming. To accelerate the generation of structures in the conformational search, we used the ECEPP potential, defined in terms of standard polypeptide geometry. A number of low energy conformations were further refined by relaxing the assumption of standard bond lengths and bond angles through the use of the CHARMM potential, and the hydrophobic folding energies of Eisenberg and McLachlan were calculated. Each conformation is described in terms of the RMSD from the native, hydrogen-bonding structure, solvent-acessible surface area, and the ratio of surfaces corresponding to nonpolar and polar residues. The unconstrained search finds conformations that are different from the native, sometimes substantially, and in addition, have lower conformational energies than the native. The origin of deviations is different for each of the three peptides, but in all examples the refined x-ray structures have lower energies than the calculated incorrect folds when (1) the assumption of standard bond lengths and bond angles is relaxed; (2) a small and constant effective dielectric permittivity (ε < 10) is used; and (3) the hydrophobic folding energy is incorporated into the potential. © 1993 John Wiley & Sons, Inc.     

A comparison of the restrained molecular dynamics and distance geometry methods for determining three-dimensional structures of proteins on the basis of interproton distances

A direct comparison of the metric matrix distance geometry and restrained molecular dynamics methods for determining three-dimensional structures of proteins on the basis of interproton distances is presented using crambin as a model system. It is shown that both methods reproduce the overall features of the secondary and tertiary structure (shape and polypeptide fold). The region of conformational space sampled by the converged structures generated by the two methods is similar in size, and in both cases the converged structures are distributed about mean structures which are closer to the X-ray structure than any of the individual structures. The restrained molecular dynamics structures are superior to those obtained from distance geometry as regards local backbone conformation, side chain positions and non-bonding energies.     

Exploring the universe of protein structures beyond the Protein Data Bank

It is currently believed that the atlas of existing protein structures is faithfully represented in the Protein Data Bank. However, whether this atlas covers the full universe of all possible protein structures is still a highly debated issue. By using a sophisticated numerical approach, we performed an exhaustive exploration of the conformational space of a 60 amino acid polypeptide chain described with an accurate all-atom interaction potential. We generated a database of around 30,000 compact folds with at least of secondary structure corresponding to local minima of the potential energy. This ensemble plausibly represents the universe of protein folds of similar length; indeed, all the known folds are represented in the set with good accuracy. However, we discover that the known folds form a rather small subset, which cannot be reproduced by choosing random structures in the database. Rather, natural and possible folds differ by the contact order, on average significantly smaller in the former. This suggests the presence of an evolutionary bias, possibly related to kinetic accessibility, towards structures with shorter loops between contacting residues. Beside their conceptual relevance, the new structures open a range of practical applications such as the development of accurate structure prediction strategies, the optimization of force fields, and the identification and design of novel folds.