Sampling of the native conformational ensemble of myoglobin via structures in different crystalline environments

Proteins sample multiple conformational substates in their native environment, but the process of crystallization selects the conformers that allow for close packing. The population of conformers can be shifted by varying the environment through a range of crystallization conditions, often resulting in different space groups and changes in the packing arrangements. Three high resolution structures of myoglobin (Mb) in different crystal space groups are presented, including one in a new space group P6(1)22 and two structures in space groups P2(1)2(1)2(1) and P6. We compare coordinates and anisotropic displacement parameters (ADPs) from these three structures plus an existing structure in space group P2(1). While the overall changes are small, there is substantial variation in several external regions with varying patterns of crystal contacts across the space group packing arrangements. The structural ensemble containing four different crystal forms displays greater conformational variance (Calpha rmsd of 0.54-0.79 A) in comparison to a collection of four Mb structures with different ligands and mutations in the same crystal form (Calpha rmsd values of 0.28-0.37 A). The high resolution of the data enables comparison of both the magnitudes and directions of ADPs, which are found to be suppressed by crystal contacts. A composite dynamic profile of Mb structural variation from the four structures was compared with an independent structural ensemble developed from NMR refinement. Despite the limitations and biases of each method, the ADPs of the crystallographic ensemble closely match the positional variance from the solution NMR ensemble with linear correlation of 0.8. This suggests that crystal packing selects conformers representative of the solution ensemble, and several different crystal forms give a more complete view of the plasticity of a protein structure.     

Predicting Evolutionary Site Variability from Structure in Viral Proteins: Buriedness,Packing, Flexibility,and Design

Several recent works have shown that protein structure can predict site-specific evolutionary sequence variation. In particular, sites that are buried and/or have many contacts with other sites in a structure have been shown to evolve more slowly, on average, than surface sites with few contacts. Here, we present a comprehensive study of the extent to which numerous structural properties can predict sequence variation. The quantities we considered include buriedness (as measured by relative solvent accessibility), packing density (as measured by contact number), structural flexibility (as measured by B factors, root-mean-square fluctuations, and variation in dihedral angles), and variability in designed structures. We obtained structural flexibility measures both from molecular dynamics simulations performed on nine non-homologous viral protein structures and from variation in homologous variants of those proteins, where they were available. We obtained measures of variability in designed structures from flexible-backbone design in the Rosetta software. We found that most of the structural properties correlate with site variation in the majority of structures, though the correlations are generally weak (correlation coefficients of 0.1–0.4). Moreover, we found that buriedness and packing density were better predictors of evolutionary variation than structural flexibility. Finally, variability in designed structures was a weaker predictor of evolutionary variability than buriedness or packing density, but it was comparable in its predictive power to the best structural flexibility measures. We conclude that simple measures of buriedness and packing density are better predictors of evolutionary variation than the more complicated predictors obtained from dynamic simulations, ensembles of homologous structures, or computational protein design.     

Participation of protein sequence termini in crystal contacts

The analysis of the crystal packing interactions, in a nonredundant set of high resolution and monomeric globular protein crystal structures, shows that the residues located at the N- and C-termini of the sequence tend to participate in packing interaction more often than expected and that often they interact with each other. Since the sequence termini are, in general, conformationally very flexible and since they host electrical charges of opposite sign, it can be hypothesized that they play a crucial role in the early formation of the nonphysiological contacts that bring to protein crystallization. It is thus not surprising that modest lengthening/shortening of the sequence termini have often a dramatic effect on protein crystallogenesis.     

Characterizing conserved structural contacts by pair-wise relative contacts and relative packing groups

To adequately deal with the inherent complexity of interactions between protein side-chains, we develop and describe here a novel method for characterizing protein packing within a fold family. Instead of approaching side-chain interactions absolutely from one residue to another, we instead consider the relative interactions of contacting residue pairs. The basic element, the pair-wise relative contact, is constructed from a sequence alignment and contact analysis of a set of structures and consists of a cluster of similarly oriented, interacting, side-chain pairs. To demonstrate this construct's usefulness in analyzing protein structure, we used the pair-wise relative contacts to analyze two sets of protein structures as defined by SCOP: the diverse globin-like superfamily (126 structures) and the more uniform heme binding globin family (a 94 structure subset of the globin-like superfamily). The superfamily structure set produced 1266 unique pair-wise relative contacts, whereas the family structure subset gave 1001 unique pair-wise relative contacts. For both sets, we show that these constructs can be used to accurately and automatically differentiate between fold classes. Furthermore, these pair-wise relative contacts correlate well with sequence identity and thus provide a direct relationship between changes in sequence and changes in structure. To capture the complexity of protein packing, these pair-wise relative contacts can be superimposed around a single residue to create a multi-body construct called a relative packing group. Construction of convex hulls around the individual packing groups provides a measure of the variation in packing around a residue and defines an approximate volume of space occupied by the groups interacting with a residue. We find that these relative packing groups are useful in understanding the structural quality of sequence or structure alignments. Moreover, they provide context to calculate a value for structural randomness, which is important in properly assessing the quality of a structural alignment. The results of this study provide the framework for future analysis for correlating sequence changes to specific structure changes.     

Calculation of standard atomic volumes for RNA and comparison with proteins: RNA is packed more tightly

Traditionally, for biomolecular packing calculations research has focused on proteins. Besides proteins, RNA is the other large biomolecule that has tertiary structure interactions and complex packing. No one has yet quantitatively investigated RNA packing or compared its packing to that of proteins because, until recently, there were no large RNA structures. Here we address this question in detail, using Voronoi volume calculations on a set of high-resolution RNA crystal structures. We do a careful parameterization, taking into account many factors such as atomic radii, crystal packing, structural complexity, solvent, and associated protein to obtain a self-consistent, universal set of volumes that can be applied to both RNA and protein. We report this set of volumes, which we call the NucProt parameter set. Our measured values are consistent across the many different RNA structures and packing environments. When common atom types are compared between proteins and RNA, nine of 12 types show that RNA has a smaller volume and packs more tightly than protein, suggesting that close-packing may be as important for the folding of RNAs as it is for proteins. Moreover, calculated partial specific volumes show that RNA bases pack more densely than corresponding aromatic residues from proteins. Finally, we find that RNA bases have similar packing volumes to DNA bases, despite the absence of tertiary contacts in DNA. Programs, parameter sets and raw data are available online at.     

Cover Image,Volume 88, Issue 9

There have been several studies suggesting that protein structures solved by NMR spectroscopy and X-ray crystallography show significant differences. To understand the origin of these differences, we assembled a database of high-quality protein structures solved by both methods. We also find significant differences between NMR and crystal structures—in the root-mean-square deviations of the C _α atomic positions, identities of core amino acids, backbone, and side-chain dihedral angles, and packing fraction of core residues. In contrast to prior studies, we identify the physical basis for these differences by modeling protein cores as jammed packings of amino acid-shaped particles. We find that we can tune the jammed packing fraction by varying the degree of thermalization used to generate the packings. For an athermal protocol, we find that the average jammed packing fraction is identical to that observed in the cores of protein structures solved by X-ray crystallography. In contrast, highly thermalized packing-generation protocols yield jammed packing fractions that are even higher than those observed in NMR structures. These results indicate that thermalized systems can pack more densely than athermal systems, which suggests a physical basis for the structural differences between protein structures solved by NMR and X-ray crystallography.     

Variability of conformations at crystal contacts in BPTI represent true low-energy structures: correspondence among lattice packing and molecular dynamics structures.

The structures of five basic pancreatic trypsin inhibitor (BPTI) molecules are compared to establish the extent and nature of the conformational variability resulting from crystal packing effects. BPTI is an ideal system to evaluate such factors because of the availability of high resolution X-ray models of five different BPTI structures, each in a different crystal packing environment. Differences observed among the structures are found to be distributed throughout the molecule, although the regions that display most variability are associated with the loop structures (residues 14-17 and 24-29). The regions of structure that show the largest rms deviations from the mean of the five packing motifs correlate well with the presence of intermolecular contacts in the crystal lattice. For most of the molecules there is also a correspondence between a larger number of intermolecular contacts and systematically higher B-factors, although it is not apparent whether this is induced by the crystal contact or results from the fact that the contacts are made predominantly through surface loops. The conformational differences seen among the X-ray models constitute more than local shifts at the lattice contact surfaces, and in fact involve in some cases the making and breaking of intramolecular H-bonds. The magnitudes of the differences among packing models are significantly larger than those usually associated with changes induced by mutagenesis; for instance; the structural differences at the site of mutation observed on removing an internal disulfide from the molecule are significantly less than those associated with lattice contact effects. The crystal packing conformations are compared to representative structures of BPTI generated during a 96-psec molecular dynamics (MD) simulation. This comparison shows a high level of correspondence between the protein flexibility indicated by the X-ray and MD analyses, and specifically between those regions that are most variable. This suggests that the regions that show most variability among the crystal packing models are not artifacts of crystallization, but rather represent true low-energy conformers that have been preferentially selected by crystallization factors.     

Novel method for the rapid evaluation of packing in protein structures

There has been considerable effort to predict the structure of proteins from their amino acid sequences. A major problem in all prediction efforts has been that, short of a direct comparison with crystallographic co-ordinates, it is often difficult to evaluate the merit of a model, or "proposed" protein structure. Here, we present a method for evaluating proposed protein structures that does not require a structural model of complete atomic detail. Our method evaluates residue-residue packing density using a simplified model of the polypeptide chain where amino acids are represented as one, two (histidine, tyrosine and phenylalanine), or three (tryptophan) spheres. This method also gives a measure of the appropriateness of residue-residue contacts, thus giving a measure of the amino acid distribution throughout the protein. Amino acid packing and amino acid distribution, as evaluated by this technique, are consistent with the accuracy of model-built structures. We have been able to select the best structures from a set of combinatorially generated models using this method, and we anticipate that it will be useful as a general tool for model-building.     

Protein-protein crystal-packing contacts.

Protein-protein contacts in monomeric protein crystal structures have been analyzed and compared to the physiological protein-protein contacts in oligomerization. A number of features differentiate the crystal-packing contacts from the natural contacts occurring in multimeric proteins. The area of the protein surface patches involved in packing contacts is generally smaller and its amino acid composition is indistinguishable from that of the protein surface accessible to the solvent. The fraction of protein surface in crystal contacts is very variable and independent of the number of packing contacts. The thermal motion at the crystal packing interface and that of the protein core, even for large packing interfaces, though the tendency is to be closer to that of the core. These results suggest that protein crystallization depends on random protein-protein interactions, which have little in common with physiological protein-protein recognition processes, and that the possibility of engineering macromolecular crystallization to improve crystal quality could be widened.     

An all-atom structure-based potential for proteins: bridging minimal models with all-atom empirical forcefields

Protein dynamics take place on many time and length scales. Coarse-grained structure-based (Go) models utilize the funneled energy landscape theory of protein folding to provide an understanding of both long time and long length scale dynamics. All-atom empirical forcefields with explicit solvent can elucidate our understanding of short time dynamics with high energetic and structural resolution. Thus, structure-based models with atomic details included can be used to bridge our understanding between these two approaches. We report on the robustness of folding mechanisms in one such all-atom model. Results for the B domain of Protein A, the SH3 domain of C-Src Kinase, and Chymotrypsin Inhibitor 2 are reported. The interplay between side chain packing and backbone folding is explored. We also compare this model to a C(alpha) structure-based model and an all-atom empirical forcefield. Key findings include: (1) backbone collapse is accompanied by partial side chain packing in a cooperative transition and residual side chain packing occurs gradually with decreasing temperature, (2) folding mechanisms are robust to variations of the energetic parameters, (3) protein folding free-energy barriers can be manipulated through parametric modifications, (4) the global folding mechanisms in a C(alpha) model and the all-atom model agree, although differences can be attributed to energetic heterogeneity in the all-atom model, and (5) proline residues have significant effects on folding mechanisms, independent of isomerization effects. Because this structure-based model has atomic resolution, this work lays the foundation for future studies to probe the contributions of specific energetic factors on protein folding and function.     

Effective discrimination between biologically relevant contacts and crystal packing contacts using new determinants

In the structural models determined by X‐ray crystallography, contacts between molecules can be divided into two categories: biologically relevant contacts and crystal packing contacts. With the growth in the number and quality of available large crystal packing contacts structures, distinguishing crystal packing contacts from biologically relevant contacts remains a difficult task, which can lead to wrong interpretation of structural models. In this study, we performed a systematic analysis on the biologically relevant contacts and crystal packing contacts. The analysis results reveal that biologically contacts are more tightly packed than crystal packing contacts. This property of biologically contacts may contribute to the formation of their interfacial core region. Meanwhile, the differences between the core and surface region of biologically contacts in amino acid composition and evolutionary measure are more dramatic than crystal packing contacts and these differences appear to be useful in distinguishing these two categories of contacts. On the basis of the features derived from our analysis, we developed a random forest model to classify biological relevant contacts and crystal packing contacts. Our method can achieve a high receiver operating curve of 0.923 in the 5‐fold cross‐validation and accuracies of 91.4% and 91.7% for two different test sets. Moreover, in a comparison study, our model outperforms other existing methods, such as DiMoVo, Pita, Pisa, and Eppic. We believe that this study will provide useful help in the validation of oligomeric proteins and protein complexes. The model and all data used in this paper are freely available at http://cic.scu.edu.cn/bioinformatics/bio‐cry.zip . Proteins 2014; 82:3090–3100. © 2014 Wiley Periodicals, Inc.     

Evaluating the quality of NMR structures by local density of protons

Evaluating the quality of experimentally determined protein structural models is an essential step toward identifying potential errors and guiding further structural refinement. Herein, we report the use of proton local density as a sensitive measure to assess the quality of nuclear magnetic resonance (NMR) structures. Using 256 high-resolution crystal structures with protons added and optimized, we show that the local density of different proton types display distinct distributions. These distributions can be characterized by statistical moments and are used to establish local density Z-scores for evaluating both global and local packing for individual protons. Analysis of 546 crystal structures at various resolutions shows that the local density Z-scores increase as the structural resolution decreases and correlate well with the ClashScore (Word et al. J Mol Biol 1999;285(4):1711-1733) generated by all atom contact analysis. Local density Z-scores for NMR structures exhibit a significantly wider range of values than for X-ray structures and demonstrate a combination of potentially problematic inflation and compression. Water-refined NMR structures show improved packing quality. Our analysis of a high-quality structural ensemble of ubiquitin refined against order parameters shows proton density distributions that correlate nearly perfectly with our standards derived from crystal structures, further validating our approach. We present an automated analysis and visualization tool for proton packing to evaluate the quality of NMR structures.     

Prediction of protein residue contacts with a PDB-derived likelihood matrix

Proteins with similar folds often display common patterns of residue variability. A widely discussed question is how these patterns can be identified and deconvoluted to predict protein structure. In this respect, correlated mutation analysis (CMA) has shown considerable promise. CMA compares multiple members of a protein family and detects residues that remain constant or mutate in tandem. Often this behavior points to structural or functional interdependence between residues. CMA has been used to predict pairs of amino acids that are distant in the primary sequence but likely to form close contacts in the native three-dimensional structure. Until now these methods have used evolutionary or biophysical models to score the fit between residues. We wished to test whether empirical methods, derived from known protein structures, would provide useful predictive power for CMA. We analyzed 672 known protein structures, derived contact likelihood scores for all possible amino acid pairs, and used these scores to predict contacts. We then tested the method on 118 different protein families for which structures have been solved to atomic resolution. The mean performance was almost seven times better than random prediction. Used in concert with secondary structure prediction, the new CMA method could supply restraints for predicting still undetermined structures.     

An atomic environment potential for use in protein structure prediction

We describe the derivation and testing of a knowledge-based atomic environment potential for the modeling of protein structural energetics. An analysis of the probabilities of atomic interactions in a dataset of high-resolution protein structures shows that the probabilities of non-bonded inter-atomic contacts are not statistically independent events, and that the multi-body contact frequencies are poorly predicted from pairwise contact potentials. A pseudo-energy function is defined that measures the preferences for protein atoms to be in a given microenvironment defined by the number of contacting atoms in the environment and its atomic composition. This functional form is tested for its ability to recognize native protein structures amongst an ensemble of decoy structures and a detailed relative performance comparison is made with a number of common functions used in protein structure prediction.     

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.     

Crystal structures of the Arabidopsis thaliana proliferating cell nuclear antigen 1 and 2 proteins complexed with the human p21 C‐terminal segment

The proliferating cell nuclear antigen (PCNA) is well recognized as one of the essential cellular components of the DNA replication machinery in all eukaryotic organisms. Despite their prominent importance, very little biochemical and structural information about plant PCNAs is available, in comparison with that obtained from other eukaryotic organisms. We have determined the atomic resolution crystal structures of the two distinct Arabidopsis thaliana PCNAs (AtPCNA), both complexed with the C‐terminal segment of human p21. Both AtPCNAs form homotrimeric ring structures, which are essentially identical to each other, including the major contacts with the p21 peptide. The structure of the amino‐terminal half of the p21 peptide, containing the typical PIP box sequence, is remarkably similar to those observed in the previously reported crystal structures of the human and archaeal PCNA‐PIP box complexes. Meanwhile, the carboxy‐terminal halves of the p21 peptide in the plant PCNA complexes are bound to the protein in a unique manner, most probably because of crystal packing effects. A surface plasmon resonance analysis revealed high affinity between each AtPCNA and the C‐terminal fragment of human p21. This result strongly suggests that the interaction is functionally significant, although no plant homologs of p21 have been identified yet. We also discovered that AtPCNA1 and AtPCNA2 form heterotrimers, implying that hetero‐PCNA rings may play critical roles in cellular signal transduction, particularly in DNA repair.     

Atomic size packing defects in proteins

The three-dimensional refined high resolution structures of 20 proteins were examined for the presence of packing defects of atomic size or larger. Of the proteins examined, 12 had no such packing defects, 6 proteins had just 1 packing defect, and 2 proteins had 2 or 3 packing defects. These results confirm earlier studies on smaller samples of proteins which demonstrated that proteins are well packed. The atoms that surround the packing defects are almost always hydrophobic (carbon or sulfur). This study also tabulated the number of internal waters in each protein, which varied from 0 to 28.     

Nicotine and carbamylcholine binding to nicotinic acetylcholine receptors as studied in AChBP crystal structures

Nicotinic acetylcholine receptors are prototypes for the pharmaceutically important family of pentameric ligand-gated ion channels. Here we present atomic resolution structures of nicotine and carbamylcholine binding to AChBP, a water-soluble homolog of the ligand binding domain of nicotinic receptors and their family members, GABAA, GABAC, 5HT3 serotonin, and glycine receptors. Ligand binding is driven by enthalpy and is accompanied by conformational changes in the ligand binding site. Residues in the binding site contract around the ligand, with the largest movement in the C loop. As expected, the binding is characterized by substantial aromatic and hydrophobic contributions, but additionally there are close contacts between protein oxygens and positively charged groups in the ligands. The higher affinity of nicotine is due to a main chain hydrogen bond with the B loop and a closer packing of the aromatic groups. These structures will be useful tools for the development of new drugs involving nicotinic acetylcholine receptor-associated diseases.     

Protein packing: dependence on protein size, secondary structure and amino acid composition

We have used the occluded surface algorithm to estimate the packing of both buried and exposed amino acid residues in protein structures. This method works equally well for buried residues and solvent-exposed residues in contrast to the commonly used Voronoi method that works directly only on buried residues. The atomic packing of individual globular proteins may vary significantly from the average packing of a large data set of globular proteins. Here, we demonstrate that these variations in protein packing are due to a complex combination of protein size, secondary structure composition and amino acid composition. Differences in protein packing are conserved in protein families of similar structure despite significant sequence differences. This conclusion indicates that quality assessments of packing in protein structures should include a consideration of various parameters including the packing of known homologous proteins. Also, modeling of protein structures based on homologous templates should take into account the packing of the template protein structure.     

Protein folding: a problem with multiple solutions

There is continued interest in predicting the structure of proteins either at the simplest level of identifying their fold class or persevering all the way to an atomic resolution structure. Protein folding methods have become very sophisticated and many successes have been recorded with claims to have solved the native structure of the protein. But for any given protein, there may be more than one solution. Many proteins can exist in one of the other two (or more) different forms and some populate multiple metastable states. Here, the two-state case is considered and the key structural changes that take place when the protein switches from one state to the other are identified. Analysis of these results show that hydrogen bonding patterns and hydrophobic contacts vary considerably between different conformers. Contrary to what has often been assumed previously, these two types of interaction operate essentially independently of one another. Core packing is critical for proper protein structure and function and it is shown that there are considerable changes in internal cavity volumes in many cases. The way in which these switches are made is fold dependent. Considerations such as these need to be taken into account in protein structure prediction.