Crystallographic and NMR spectroscopic protein structures: the inter-residue contacts

Inter-residue pair contacts have been analyzed in detail for the four pairs of protein structures determined both by X-ray analysis (X-ray) and nuclear magnetic resonance (NMR). At contact distances < or = 4.0 angstroms in the four NMR structures the overall number of pair contacts are less by 4-9% and pair contacts are in average shorter by 0.02-0.16 angstroms than those in corresponding X-ray structures. In each of four structure pairs 83-94% of common pair contacts are formed by the same residues in both structures and rest 6-17% ones are longer own pair contacts formed by the different residues in the NMR and X-ray structures. The amount of the longer own contacts is higher in the X-ray structure of the pair. In the each NMR structure there are three types of common pair contacts, which are shorter, longer or equal length in comparison with identical pair contacts in the X-ray structure of the same protein. The methodological different shortened common pair contacts predominate in the known distant dependence of the inter-residue contact densities of the 60-61 pair of the NMR/X-ray structure. Among four pairs analyzed the contact shortening proceeds upon the energy minimization of the crambin NMR structure and upon the resolving by the program X-PLOR with decreased atom van der Waals radius of the NMR structures of ubiquitin, hen lysozyme and monomeric hemoglobin. An extent of the NMR contact shortening decreased as the amount of NMR information upon the calculation of the NMR structures increased. Among 60-61 pairs of NMR/X-ray structures the main difference between alpha-helical and beta-structural proteins on the inter-residue distant dependence of the average contact densities arises from the strong alpha/beta difference in the local backbone geometry.     

Structure of crambin in solution, crystal and in the trajectories of molecular dynamics simulations

The mechanisms of the three-dimensional crambin structure alterations in the crystalline environments and in the trajectories of the molecular dynamics simulations in the vacuum and crystal surroundings have been analyzed. In the crystalline state and in the solution the partial regrouping of remote intramolecular packing contacts, involved in the formation and stabilization of the tertiary structure of the crambin molecule, occurs in NMR structures. In the crystalline state it is initiated by the formation of the intermolecular contacts, the conformational influence of its appearance is distributed over the structure. The changes of the conformations and positions of the residues of the loop segments, where the intermolecular contacts of the crystal surroundings are preferably concentrated, are most observable. Under the influence of these contacts the principal change of the regular secondary structure of crambin is taking place: extension of the two-strand β structure to the three-strand structure with the participation of the single last residue N46 of the C-terminal loop. In comparison with the C-terminal loop the more profound changes are observed in the conformation and the atomic positions of the backbone atoms and in the solvent accessibility of the residues of the interhelical loop. In the solution of the ensemble of the 8 NMR structures relative accessibility to the solvent differs more noticeably also in the region of the loop segments and rather markedly in the interhelical loop. In the crambin cryogenic crystal structures the positions of the atoms of the backbone and/or side chain of 14–18 of 46 residues are discretely disordered. The disorganizations of at least 8 of 14 residues occur directly in the regions of the intermolecular contacts and another 5 residues are disordered indirectly through the intramolecular contacts with the residues of the intermolecular contacts. Upon the molecular dynamics simulation in the vacuum surrounding as in the solution of the crystalline structure of crambin the essential changes of the backbone conformation are caused by the intermolecular contacts absence, but partly masked by the structure changes owing to the nonpolar H atoms absence on the simulated structure. The intermolecular contact absence is partly manifested upon the molecular dynamics simulation of the crambin crystal with one protein molecule. Compared to the crystal structure the lengths of the interpeptide hydrogen bonds and other interresidue contacts in an average solution NMR structure are somewhat shorter and accordingly the energy of the interpeptide hydrogen bonds is better. This length shortening can occur at the stage of the refinement of the NMR structures of the crambin and other proteins by its energy minimizations in the vacuum surroundings and not exist in the solution protein structures.     

Comparison of X‐ray and NMR structures: Is there a systematic difference in residue contacts between X‐ray‐ and NMR‐resolved protein structures?

We have compared structures of 78 proteins determined by both NMR and X-ray methods. It is shown that X-ray and NMR structures of the same protein have more differences than various X-ray structures obtained for the protein, and even more than various NMR structures of the protein. X-ray and NMR structures of 18 of these 78 proteins have obvious large-scale structural differences that seem to reflect a difference of crystal and solution structures. The other 60 pairs of structures have only small-scale differences comparable with differences between various X-ray or various NMR structures of a protein; we have analyzed these structures more attentively. One of the main differences between NMR and X-ray structures concerns the number of contacts per residue: (1) NMR structures presented in PDB have more contacts than X-ray structures at distances below 3.0 A and 4.5-6.5 A, and fewer contacts at distances of 3.0-4.5 A and 6.5-8.0 A; (2) this difference in the number of contacts is greater for internal residues than for external ones, and it is larger for beta-containing proteins than for all-alpha proteins. Another significant difference is that the main-chain hydrogen bonds identified in X-ray and NMR structures often differ. Their correlation is 69% only. However, analogous difference is found for refined and rerefined NMR structures, allowing us to suggest that the observed difference in interresidue contacts of X-ray and NMR structures of the same proteins is due mainly to a difference in mathematical treatment of experimental results.     

The difference between protein structures that are obtained by X-ray analysis and magnetic resonance spectroscopy

We have analyzed the proteins whose structures were determined both by X-ray analysis (X-ray) and nuclear magnetic resonance (NMR) on condition that these structures do not differ greatly when spatially superimposed on each other (61 pairs of protein structures). Atom-atomic contacts (contact distances varied from 2 to 8 A) have been analyzed and it has been found that NMR structures (in comparison with X-ray ones) have more contacts in the range below 3.5 A and above 5.5 A. In the case of residue-residue contacts NMR structures have more contacts below 3 A and between 4.5 and 6.5 A. At all the other contact distances analyzed the X-ray structures have more contacts. The difference in the number of atom-atomic and residue-residue contacts is greater for internal residues, that are concealed from water, as compared to the surface residues. The other, not less important difference deals with the number of hydrogen bonds in the main chain: it is larger for the X-ray structures. The correlation between the hydrogen bonds identified in the structures obtained by both methods is no more than 32%. The consideration of a complete set of protein structures obtained by NMR results in the fact that the number of hydrogen bonds grows 1.2 times as compared to those obtained with the X-ray analysis, whereas the correlation increases only by 65%. We have also demonstrated that alpha-helices in the NMR structures are more distorted in comparison with the ideal alpha-helix, than alpha-helices in the X-ray structures.     

Comparison of solution and crystal structures of maize nonspecific lipid transfer protein: A model for a potential in vivo lipid carrier protein

The three-dimensional solution structure of maize nonspecific lipid transfer protein (nsLTP) obtained by nuclear magnetic resonance (NMR) is compared to the X-ray structure. Although both structures are very similar, some local structural differences are observed in the first and the fourth helices and in several side-chain conformations. These discrepancies arise partly from intermolecular contacts in the crystal lattice. The main characteristic of nsLTP structures is the presence of an internal hydrophobic cavity whose volume was found to vary from 237 to 513 ų without major variations in the 15 solution structures. Comparison of crystal and NMR structures shows the existence of another small hollow at the periphery of the protein containing a water molecule in the X-ray structure, which could play an important structural role. A model of the complexed form of maize nsLTP by α-lysopalmitoylphosphatidylcholine was built by docking the lipid inside the protein cavity of the NMR structure. The main structural feature is a hydrogen bond found also in the X-ray structure of the complex maize nsLTP/palmitate between the hydroxyl of Tyr81 and the carbonyl of the lipid. Comparison of 12 primary sequences of nsLTPs emphasizes that all residues delineating the cavities calculated on solution and X-ray structures are conserved, which suggests that this large cavity is a common feature of all compared plant nsLTPs. Furthermore several conserved basic residues seem to be involved in the stabilization of the protein architecture. Proteins 31:160–171, 1998. © 1998 Wiley-Liss, Inc.     

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.     

Taking advantage of local structure descriptors to analyze interresidue contacts in protein structures and protein complexes

Interresidue protein contacts in proteins structures and at protein-protein interface are classically described by the amino acid types of interacting residues and the local structural context of the contact, if any, is described using secondary structures. In this study, we present an alternate analysis of interresidue contact using local structures defined by the structural alphabet introduced by Camproux et al. This structural alphabet allows to describe a 3D structure as a sequence of prototype fragments called structural letters, of 27 different types. Each residue can then be assigned to a particular local structure, even in loop regions. The analysis of interresidue contacts within protein structures defined using Vorono? tessellations reveals that pairwise contact specificity is greater in terms of structural letters than amino acids. Using a simple heuristic based on specificity score comparison, we find that 74% of the long-range contacts within protein structures are better described using structural letters than amino acid types. The investigation is extended to a set of protein-protein complexes, showing that the similar global rules apply as for intraprotein contacts, with 64% of the interprotein contacts best described by local structures. We then present an evaluation of pairing functions integrating structural letters to decoy scoring and show that some complexes could benefit from the use of structural letter-based pairing functions.     

Measurements of protein sequence-structure correlations

Correlations between protein structures and amino acid sequences are widely used for protein structure prediction. For example, secondary structure predictors generally use correlations between a secondary structure sequence and corresponding primary structure sequence, whereas threading algorithms and similar tertiary structure predictors typically incorporate interresidue contact potentials. To investigate the relative importance of these sequence-structure interactions, we measured the mutual information among the primary structure, secondary structure and side-chain surface exposure, both for adjacent residues along the amino acid sequence and for tertiary structure contacts between residues distantly separated along the backbone. We found that local interactions along the amino acid chain are far more important than non-local contacts and that correlations between proximate amino acids are essentially uninformative. This suggests that knowledge-based contact potentials may be less important for structure predication than is generally believed.     

A Systematic Search Method for the Identification of Tightly Packed Transmembrane Parallel α-Helices

Abstract

Membrane proteins play a major role in number of biological processes such as signaling pathways. The determination of the three-dimensional structure of these proteins is increasingly important for our understanding of their structure-function relationships. Due to the difficulty in isolating membrane proteins for X-ray diffraction studies, computational techniques are being developed to generate the 3D structures of TM domains. Here, we present a systematic search method for the identification of energetically favorable and tightly packed transmembrane parallel α-helices. The first step in our systematic search method is the generation of 3D models for pairs of parallel helix bundles with all possible orientations followed by an energy-based filter to eliminate structures with severe non-bonded contacts. Then, a RMS-based filter was used to cluster these structures into families. Furthermore, these dimers were energy minimized using molecular mechanics force field. Finally, we identified the tightly packed parallel α-helices by using an interface surface area. To validate our search method, we compared our predicted GlycophorinA dimer structures with the reported NMR structures. With our search method, we are able to reproduce NMR structures of GPA with 0.9Å RMSD. In addition, by considering the reported mutational data on GxxxG motif interactions, twenty percent of our predicted dimers are within in the 2.0Å RMSD. The dimers obtained from our method were used to generate parallel trimeric and tetramer TM structures of GPA and found that the structure of GPA might exist only in a dimer form as reported earlier.     

Hydrophobicity and residue-residue contacts in globular proteins

A comprehensive statistical analysis of residue-residue contacts and residue environment in protein 3-D structures is presented. In the present work the range of interresidue interactions (effective radius of influence) in tertiary structures of proteins is examined and found to be 10 Å. This result is obtained by correlating the average number of residues within a spherical volume of different radii (contact numbers) with hydrophobicity. Best correlations are obtained with a radius of 10 Å. The same result is obtained when (i) only long-range interactions are considered and (ii) representative side chain atoms are used to indicate the tertiary structure instead of the usual representation of C^α atoms. Residue environment has been investigated using similar methods. Environmental hydrophobicity varies within only a small range of all residue types. Other physicochemical properties also exhibit similar trends of variation, and only five hydrophobic residues (Leu, Val, Met, Phe and Ile) produce a decrement of around 10% from the expected mean of the physicochemical distance between a residue type and its average environment. An information theory approach is proposed to compare domains, which takes into account the effective radius of influence of residues and sequence similarity.     

An automated assignment-free Bayesian approach for accurately identifying proton contacts from NOESY data

The identification of proton contacts from NOE spectra remains the major bottleneck in NMR protein structure calculations. We describe an automated assignment-free system for deriving proton contact probabilities from NOESY peak lists that can be viewed as a quantitative extension of manual assignment techniques. Rather than assigning contacts to NOESY crosspeaks, a rigorous Bayesian methodology is used to transform initial proton contact probabilities derived from a set of 2992 protein structures into posterior probabilities using the observed crosspeaks as evidence. Given a target protein, the Bayesian approach is used to derive probabilities for all possible proton contacts. We evaluated the accuracy of this approach at predicting proton contacts on 60 ¹⁵N separated NOESY and ¹³C separated NOESY datasets simulated from experimentally determined NMR structures and compared it to CYANA, an established method for proton constraint assignment. On average, at the highest confidence level, our method accurately identifies 3.16/3.17 long range contacts per residue and 12.11/12.18 interresidue proton contacts per residue. These accuracies represent a significant increase over the performance of CYANA on the same data set. On a difficult real dataset that is publicly available, the coverage is lower but our method retains its advantage in accuracy over CANDID/CYANA. The algorithm is publicly available via the Protinfo NMR webserver .     

Toward an accurate prediction of inter-residue distances in proteins using 2D recursive neural networks

Background

Protein inter-residue contact maps provide a translation and rotation invariant topological representation of a protein. They can be used as an intermediary step in protein structure predictions. However, the prediction of contact maps represents an unbalanced problem as far fewer examples of contacts than non-contacts exist in a protein structure. In this study we explore the possibility of completely eliminating the unbalanced nature of the contact map prediction problem by predicting real-value distances between residues. Predicting full inter-residue distance maps and applying them in protein structure predictions has been relatively unexplored in the past.

Results

We initially demonstrate that the use of native-like distance maps is able to reproduce 3D structures almost identical to the targets, giving an average RMSD of 0.5Å. In addition, the corrupted physical maps with an introduced random error of ±6Å are able to reconstruct the targets within an average RMSD of 2Å. After demonstrating the reconstruction potential of distance maps, we develop two classes of predictors using two-dimensional recursive neural networks: an ab initio predictor that relies only on the protein sequence and evolutionary information, and a template-based predictor in which additional structural homology information is provided. We find that the ab initio predictor is able to reproduce distances with an RMSD of 6Å, regardless of the evolutionary content provided. Furthermore, we show that the template-based predictor exploits both sequence and structure information even in cases of dubious homology and outperforms the best template hit with a clear margin of up to 3.7Å. Lastly, we demonstrate the ability of the two predictors to reconstruct the CASP9 targets shorter than 200 residues producing the results similar to the state of the machine learning art approach implemented in the Distill server.

Conclusions

The methodology presented here, if complemented by more complex reconstruction protocols, can represent a possible path to improve machine learning algorithms for 3D protein structure prediction. Moreover, it can be used as an intermediary step in protein structure predictions either on its own or complemented by NMR restraints.     

Comprehensive statistical analysis of residues interaction specificity at protein-protein interfaces

We calculated interchain contacts on the atomic level for nonredundant set of 4602 protein-protein interfaces using an unbiased Voronoi-Delaune tessellation method, and made 20x20 residue contact matrixes both for homodimers and heterocomplexes. The area of contacts and the distance distribution for these contacts were calculated on both the residue and the atomic levels. We analyzed residue area distribution and showed the existence of two types of interresidue contacts: stochastic and specific. We also derived formulas describing the distribution of contact area for stochastic and specific interactions in parametric form. Maximum pairing preference index was found for Cys-Cys contacts and for oppositely charged interactions. A significant difference in residue contacts was observed between homodimers and heterocomplexes. Interfaces in homodimers were enriched with contacts between residues of the same type due to the effects of structure symmetry.     

A geometrical constraint approach for reproducing the native backbone conformation of a protein

It is known that the backbone conformation of a protein can be reproduced with precision once a correct contact map (two-dimensional representation showing residue pairs in contact) is given as geometrical constraints. There is, however, no way to infer the correct contact map for a protein of unknown structure. We started with one-dimensional constraints using the quantity N14 (the number of neighboring residues within the radius of 14 Å). Since the plot of N14 along a chain shows a good correlation with the corresponding amino acid sequence, the N14 profile obtained from the X-ray structure is predictable from the sequence. Construction of backbone conformations under a given N14 profile was carried out in the following two steps: (1) a contact map from the N14 profile was produced by taking the product of N14 values of every two residues; (2) backbone conformations were generated by applying the distance geometry technique to distance constraints given by the contact map. If present, disulfide bonds in a protein, as well as the secondary structure, were treated as additional constraints, and both cases with or without the additional information were examined. The method was tested for 11 proteins of known structure, and the results indicated that the reproduced conformation was fairly good, using an X-ray structure for comparison, for small proteins of less than 80 residues long. The basic assumption and effectiveness of the present method were compared with those of previous studies employing the geometrical constraint approach. It has become clear that the specific, one-dimensional information (e.g., N14 profile) is more effective than nonspecific, two-dimensional constraints, such as average interresidue distances between particular types of amino acids. © 1993 Wiley-Liss, Inc.     

Contact prediction for beta and alpha‐beta proteins using integer linear optimization and its impact on the first principles 3D structure prediction method ASTRO‐FOLD

An integer linear optimization model is presented to predict residue contacts in β, α + β, and α/β proteins. The total energy of a protein is expressed as sum of a C^α? C^α distance dependent contact energy contribution and a hydrophobic contribution. The model selects contact that assign lowest energy to the protein structure as satisfying a set of constraints that are included to enforce certain physically observed topological information. A new method based on hydrophobicity is proposed to find the β‐sheet alignments. These β‐sheet alignments are used as constraints for contacts between residues of β‐sheets. This model was tested on three independent protein test sets and CASP8 test proteins consisting of β, α + β, α/β proteins and it was found to perform very well. The average accuracy of the predictions (separated by at least six residues) was ～61%. The average true positive and false positive distances were also calculated for each of the test sets and they are 7.58 Å and 15.88 Å, respectively. Residue contact prediction can be directly used to facilitate the protein tertiary structure prediction. This proposed residue contact prediction model is incorporated into the first principles protein tertiary structure prediction approach, ASTRO‐FOLD. The effectiveness of the contact prediction model was further demonstrated by the improvement in the quality of the protein structure ensemble generated using the predicted residue contacts for a test set of 10 proteins. Proteins 2010. © 2010 Wiley‐Liss, Inc.     

Disentangling Direct from Indirect Co-Evolution of Residues in Protein Alignments

Predicting protein structure from primary sequence is one of the ultimate challenges in computational biology. Given the large amount of available sequence data, the analysis of co-evolution, i.e., statistical dependency, between columns in multiple alignments of protein domain sequences remains one of the most promising avenues for predicting residues that are contacting in the structure. A key impediment to this approach is that strong statistical dependencies are also observed for many residue pairs that are distal in the structure. Using a comprehensive analysis of protein domains with available three-dimensional structures we show that co-evolving contacts very commonly form chains that percolate through the protein structure, inducing indirect statistical dependencies between many distal pairs of residues. We characterize the distributions of length and spatial distance traveled by these co-evolving contact chains and show that they explain a large fraction of observed statistical dependencies between structurally distal pairs. We adapt a recently developed Bayesian network model into a rigorous procedure for disentangling direct from indirect statistical dependencies, and we demonstrate that this method not only successfully accomplishes this task, but also allows contacts with weak statistical dependency to be detected. To illustrate how additional information can be incorporated into our method, we incorporate a phylogenetic correction, and we develop an informative prior that takes into account that the probability for a pair of residues to contact depends strongly on their primary-sequence distance and the amount of conservation that the corresponding columns in the multiple alignment exhibit. We show that our model including these extensions dramatically improves the accuracy of contact prediction from multiple sequence alignments.     

A contact scoring matrix for qualitative prediction of change in folding of α-helices in globular proteins caused by a mutation

The atomic pairs in contact for atoms from pairs of amino-acid residues on pairs of helices in a protein database consisting of 48 proteins of known tertiary structure from the Brookhaven Protein Data Bank are searched and counted to construct a primary scoring system. Each score in the primary scoring system is weighted further with the possibility of occurrence of each residue pair in the protein database to give a final scoring matrix. Scores for predicting change in folding of α-helices in a mutant protein are calculated by assuming that every pair of helices in the protein can closely interact with each other. It is shown that the change in folding of α-helices in several mutant proteins are reflected in both the change of the contact scores and the helix geometry calculated.     

An assignment of intrinsically disordered regions of proteins based on NMR structures

Intrinsically disordered proteins (IDPs) do not adopt stable three-dimensional structures in physiological conditions, yet these proteins play crucial roles in biological phenomena. In most cases, intrinsic disorder manifests itself in segments or domains of an IDP, called intrinsically disordered regions (IDRs), but fully disordered IDPs also exist. Although IDRs can be detected as missing residues in protein structures determined by X-ray crystallography, no protocol has been developed to identify IDRs from structures obtained by Nuclear Magnetic Resonance (NMR). Here, we propose a computational method to assign IDRs based on NMR structures. We compared missing residues of X-ray structures with residue-wise deviations of NMR structures for identical proteins, and derived a threshold deviation that gives the best correlation of ordered and disordered regions of both structures. The obtained threshold of 3.2 Å was applied to proteins whose structures were only determined by NMR, and the resulting IDRs were analyzed and compared to those of X-ray structures with no NMR counterpart in terms of sequence length, IDR fraction, protein function, cellular location, and amino acid composition, all of which suggest distinct characteristics. The structural knowledge of IDPs is still inadequate compared with that of structured proteins. Our method can collect and utilize IDRs from structures determined by NMR, potentially enhancing the understanding of IDPs.     

Exploring a DNA Sequence for the Three-Dimensional Structure Determination of a Silver(I)-Mediated C-C Base Pair in a DNA Duplex By 1H NMR Spectroscopy

Recently, we discovered novel silver(I)-mediated cytosine–cytosine base pair (C–Ag^I–C) in DNA duplexes. To understand the properties of these base pairs, we searched for a DNA sequence that can be used in NMR structure determination. After extensive sequence optimizations, a non-symmetric 15-base-paired DNA duplex with a single C–Ag^I–C base pair flanked by 14 A–T base pairs was selected. In spite of its challenging length for NMR measurements (30 independent residues) with small sequence variation, we could assign most non-exchangeable protons (254 out of 270) and imino protons for structure determination.