Optimized Null Model for Protein Structure Networks

Much attention has recently been given to the statistical significance of topological features observed in biological networks. Here, we consider residue interaction graphs (RIGs) as network representations of protein structures with residues as nodes and inter-residue interactions as edges. Degree-preserving randomized models have been widely used for this purpose in biomolecular networks. However, such a single summary statistic of a network may not be detailed enough to capture the complex topological characteristics of protein structures and their network counterparts. Here, we investigate a variety of topological properties of RIGs to find a well fitting network null model for them. The RIGs are derived from a structurally diverse protein data set at various distance cut-offs and for different groups of interacting atoms. We compare the network structure of RIGs to several random graph models. We show that 3-dimensional geometric random graphs, that model spatial relationships between objects, provide the best fit to RIGs. We investigate the relationship between the strength of the fit and various protein structural features. We show that the fit depends on protein size, structural class, and thermostability, but not on quaternary structure. We apply our model to the identification of significantly over-represented structural building blocks, i.e., network motifs, in protein structure networks. As expected, choosing geometric graphs as a null model results in the most specific identification of motifs. Our geometric random graph model may facilitate further graph-based studies of protein conformation space and have important implications for protein structure comparison and prediction. The choice of a well-fitting null model is crucial for finding structural motifs that play an important role in protein folding, stability and function. To our knowledge, this is the first study that addresses the challenge of finding an optimized null model for RIGs, by comparing various RIG definitions against a series of network models.     

Assessing the reconstruction of macromolecular assemblies with toleranced models

We introduce toleranced models (TOMs), a generic and versatile framework meant to handle models of macromolecular assemblies featuring uncertainties on the shapes and the positions of proteins. A TOM being a continuum of nested shapes, the inner (resp. outer) ones representing high (low) confidence regions, we present topological and geometric statistics assessing features of this continuum at multiple scales. While the topological statistics qualify contacts between instances of protein types and complexes involving prescribed protein types, the geometric statistics scale the geometric accuracy of these complexes. We validate the TOM framework on recent average models of the entire nuclear pore complex (NPC) obtained from reconstruction by data integration, and confront our quantitative analysis against experimental findings related to complexes of the NPC, namely the Y-complex, the T-complex, and the Nsp1-Nup82-Nup159 complex. In the three cases, our analysis bridges the gap between global qualitative models of the entire NPC, and atomic resolution models or putative models of the aforementioned complexes. In a broader perspective, the quantitative assessments provided by the TOM framework should prove instrumental to implement a virtuous loop "model reconstruction-model selection", in the context of reconstruction by data integration.     

NMR of hydrogen bonding in cold-shock protein A and an analysis of the influence of crystallographic resolution on comparisons of hydrogen bond lengths

Hydrogen bonding in cold-shock protein A of Escherichia coli has been investigated using long-range HNCO spectroscopy. Nearly half of the amide protons involved in hydrogen bonds in solution show no measurable protection from exchange in water, cautioning against a direct correspondence between hydrogen bonding and hydrogen exchange protection. The N to O atom distance across a hydrogen bond, R(NO), is related to the size of the (3h)J(NC') trans hydrogen bond coupling constant and the amide proton chemical shift. Both NMR parameters show poorer agreement with the 2.0-A resolution X-ray structure of the cold-shock protein studied by NMR than with a 1.2-A resolution X-ray structure of a homologous cold-shock protein from the thermophile B. caldolyticus. The influence of crystallographic resolution on comparisons of hydrogen bond lengths was further investigated using a database of 33 X-ray structures of ribonuclease A. For highly similar structures, both hydrogen bond R(NO) distance and Calpha coordinate root mean square deviations (RMSD) show systematic increases as the resolution of the X-ray structure used for comparison decreases. As structures diverge, the effects of coordinate errors on R(NO) distance and Calpha coordinate root mean square deviations become progressively smaller. The results of this study are discussed with regard to the influence of data precision on establishing structure similarity relationships between proteins.     

Folding in lipid membranes (FILM): a novel method for the prediction of small membrane protein 3D structures

We present the results of applying a novel knowledge-based method (FILM) to the prediction of small membrane protein structures. The basis of the method is the addition of a membrane potential to the energy terms (pairwise, solvation, steric, and hydrogen bonding) of a previously developed ab initio technique for the prediction of tertiary structure of globular proteins (FRAGFOLD). The method is based on the assembly of supersecondary structural fragments taken from a library of highly resolved protein structures using a standard simulated annealing algorithm. The membrane potential has been derived by the statistical analysis of a data set made of 640 transmembrane helices with experimentally defined topology and belonging to 133 proteins extracted from the SWISS-PROT database. Results obtained by applying the method to small membrane proteins of known 3D structure show that the method is able to predict, at a reasonable accuracy level, both the helix topology and the conformations of these proteins.     

New Insights into the Interdependence between Amino Acid Stereochemistry and Protein Structure

To successfully design new proteins and understand the effects of mutations in natural proteins, we must understand the geometric and physicochemical principles underlying protein structure. The side chains of amino acids in peptides and proteins adopt specific dihedral angle combinations; however, we still do not have a fundamental quantitative understanding of why some side-chain dihedral angle combinations are highly populated and others are not. Here we employ a hard-sphere plus stereochemical constraint model of dipeptide mimetics to enumerate the side-chain dihedral angles of leucine (Leu) and isoleucine (Ile), and identify those conformations that are sterically allowed versus those that are not as a function of the backbone dihedral angles ? and ψ. We compare our results with the observed distributions of side-chain dihedral angles in proteins of known structure. With the hard-sphere plus stereochemical constraint model, we obtain agreement between the model predictions and the observed side-chain dihedral angle distributions for Leu and Ile. These results quantify the extent to which local, geometrical constraints determine protein side-chain conformations.     

New Insights into the Interdependence between Amino Acid Stereochemistry and Protein Structure

To successfully design new proteins and understand the effects of mutations in natural proteins, we must understand the geometric and physicochemical principles underlying protein structure. The side chains of amino acids in peptides and proteins adopt specific dihedral angle combinations; however, we still do not have a fundamental quantitative understanding of why some side-chain dihedral angle combinations are highly populated and others are not. Here we employ a hard-sphere plus stereochemical constraint model of dipeptide mimetics to enumerate the side-chain dihedral angles of leucine (Leu) and isoleucine (Ile), and identify those conformations that are sterically allowed versus those that are not as a function of the backbone dihedral angles ϕ and ψ. We compare our results with the observed distributions of side-chain dihedral angles in proteins of known structure. With the hard-sphere plus stereochemical constraint model, we obtain agreement between the model predictions and the observed side-chain dihedral angle distributions for Leu and Ile. These results quantify the extent to which local, geometrical constraints determine protein side-chain conformations.     

Application of FTTP to alpha-helix or beta-strand motifs

Information concerning protein structure is widely dispersed and cannot easily and rapidly be processed by the biological community. We present a database of tendentious factors of three states of tripeptide units from PDB database, called a bank of tendentious factors of three states of three-peptide units (FTTP). The FTTP database was constructed based on conformational dihedral angle (varphi,psi) library of 20(3) peptide triplets by exhaustively searching through PDB databases. We introduce the FTTP database for the analysis of characteristics common to relative conformational biases of all peptide triplets, especially finding some motifs apt to alpha-helix and beta-strand. Our results show that this will provide a platform for studies of short peptide motifs, folding codons, secondary structure and three-dimensional (3D) structure of proteins. Moreover, FTTP is a unique resource that will allow a comprehensive characterization of peptide triplets and thus improve our understanding of sequence-structure relationship, refined domains, 3D structures, and their associated function. We believe the FTTP database will help biologists in increasing the efficiency of finding useful and relevant information regarding structure-function relationship of proteins. Therefore, this approach will play an important role in protein folding, protein engineering, molecular design, and proteomics.     

Revisiting the Ramachandran plot based on statistical analysis of static and dynamic characteristics of protein structures

Ramachandran plots, which describe protein structures by plotting the dihedral angle pairs of the backbone on a two-dimensional plane, have played an important role in structural biology over the past few decades. However, despite continued discovery of new protein structures to date, the Ramachandran plot is still constructed by only a small number of data points, and further it cannot reflect the steric information of proteins. Here, we investigated the secondary structure of proteins in terms of static and dynamic characteristics. As for static feature, the Ramachandran plot was revisited for the dataset consisting of 9,148 non-redundant high-resolution protein structures released in the protein data bank until April 1, 2022. By calculating amino acid propensities, it was found that the proportion of secondary structures with respect to residue depth is directly related to their hydrophobicity. As for dynamic feature, normal mode analysis (NMA) based on an elastic network model (ENM) was carried out for the dataset using our KOSMOS web server (http://bioengineering.skku.ac.kr/kosmos/). All ENM-based NMA results were stored in the KOSMOS database, allowing researchers to use them in various ways. In this process, it was commonly found that high B-factors appeared at the edge of the alpha helix region, which was elucidated by introducing residue depth. In addition, by investigating the change in dihedral angle, it was possible to quantitatively survey the contribution of structural change of protein on the Ramachandran plot. In conclusion, our statistical analysis of protein characteristics will provide insight into a range of protein structural studies.     

Protein--protein recognition: juxtaposition of domain and interface cores in immunoglobulins and other sandwich-like proteins

Structural analysis of a non-redundant data set of 47 immunoglobulin (Ig) proteins was carried out using a combination of criteria: atom--atom contact compatibility, position occupancy rate, conservation of residue type and positional conservation in 3D space. Our analysis shows that roughly half of the interface positions between the light and heavy chains are specific to individual structures while the other half are conserved across the database. The tendency for conservation of a primary subset of positions holds true for the intra-domain faces as well. These subsets, with an average of 12 conserved positions and a contact surface of 630 A(2), delineate the inter- and intra-domain core, a refined instrument with a reduced target for analysis of sheet--sheet interactions in sandwich-like proteins. Employing this instrument, we find that a majority of Ig interface core positions are adjoined in sequence to domain core positions. This was derived independent of geometric considerations, however beta-sheet side-chain geometry clearly dictates it. The geometric wedding of the domain and interface cores supports the concept of a rigid-like substructure on the protein surface involved in complex formation and indicates a close relationship between surface determinants and those involved in protein folding of Ig domains. The definitions developed for the Ig interface and domain cores proved satisfactory to extract first-approximation cores for a group of 24 non-Ig sandwich-like proteins, treated as individual structures due to their diverse strand topologies. We show that the same rule of positional connectivity between the rigid domain core and interface core extends generally to sandwich-like proteins interacting in a sheet--sheet fashion. The non-Ig structures were used as templates to analyze sandwich-like interfaces of unresolved homologous proteins using a database merging structure and sequence conservation.     

An alternative topological model for Escherichia coli OmpA.

The current topological model for the Escherichia coli outer membrane protein OmpA predicts eight N-terminal transmembrane segments followed by a long periplasmic tail. Several recent reports have raised serious doubts about the accuracy of this prediction. An alternative OmpA model has been constructed using (1) computer-aided predictions developed specifically to predict topology of bacterial outer membrane porins, (2) the results of two reports that identified sequence homologies between OmpA and other peptidoglycan-associated proteins, and (3) biochemical, immunochemical, and genetic topological data on proteins of the OmpA family provided by numerous previous studies. The new model not only agrees with the varied experimental data concerning OmpA but also provides an improved understanding of the relationship between the structure and the multifunctional role of OmpA in the bacterial outer membrane.     

Protein structure comparison: implications for the nature of 'fold space', and structure and function prediction

The identification of geometric relationships between protein structures offers a powerful approach to predicting the structure and function of proteins. Methods to detect such relationships range from human pattern recognition to a variety of mathematical algorithms. A number of schemes for the classification of protein structure have found widespread use and these implicitly assume the organization of protein structure space into discrete categories. Recently, an alternative view has emerged in which protein fold space is seen as continuous and multidimensional. Significant relationships have been observed between proteins that belong to what have been termed different 'folds'. There has been progress in the use of these relationships in the prediction of protein structure and function.     

Donut-shaped fingerprint in homologous polypeptide relationships—A topological feature related to pathogenic structural changes in conformational disease

Features of homologous relationship of proteins can provide us a general picture of protein universe, assist protein design and analysis, and further our comprehension of the evolution of organisms. Here we carried out a study of the evolution of protein molecules by investigating homologous relationships among residue segments. The motive was to identify detailed topological features of homologous relationships for short residue segments in the whole protein universe. Based on the data of a large number of non-redundant proteins, the universe of non-membrane polypeptide was analyzed by considering both residue mutations and structural conservation. By connecting homologous segments with edges, we obtained a homologous relationship network of the whole universe of short residue segments, which we named the graph of polypeptide relationships (GPR). Since the network is extremely complicated for topological transitions, to obtain an in-depth understanding, only subgraphs composed of vital nodes of the GPR were analyzed. Such analysis of vital subgraphs of the GPR revealed a donut-shaped fingerprint. Utilization of this topological feature revealed the switch sites (where the beginning of exposure of previously hidden “hot spots” of fibril-forming happens, in consequence a further opportunity for protein aggregation is provided; 188-202) of the conformational conversion of the normal α-helix-rich prion protein PrP^C to the β-sheet-rich PrP^Sc that is thought to be responsible for a group of fatal neurodegenerative diseases, transmissible spongiform encephalopathies. Efforts in analyzing other proteins related to various conformational diseases are also introduced.     

Physicochemical evolution and molecular adaptation of the cetacean and artiodactyl cytochrome b proteins

Cetaceans have most likely experienced metabolic shifts since evolutionarily diverging from their terrestrial ancestors, shifts that may be reflected in the proteins such as cytochrome b that are responsible for metabolic efficiency. However, accepted statistical methods for detecting molecular adaptation are largely biased against even moderately conservative proteins because the primary criterion involves a comparison of nonsynonymous and synonymous substitution rates (dN/dS); they do not allow for the possibility that adaptation may come in the form of very few amino acid changes. We apply the MM01 model to the possible molecular adaptation of cytochrome b among cetaceans because it does not rely on a dN/dS ratio, instead evaluating positive selection in terms of the amino acid properties that comprise protein phenotypes that selection at the molecular level may act upon. We also apply the codon-degeneracy model (CDM), which focuses on evaluating overall patterns of nucleotide substitution in terms of base exchange, codon position, and synonymy to estimate the overall effect of selection. Using these relatively new models, we characterize the molecular adaptation that has occurred in the cetacean cytochrome b protein by comparing revealed amino acid replacement patterns to those found among artiodactyls, the modern terrestrial mammals found to be most closely related to cetaceans. Our findings suggest that several regions of the cetacean cytochrome b protein have experienced molecular adaptation. Also, these adaptations are spatially associated with domain structure, protein function, and the structure and function of the cytochrome bc(1) complex and its constituents. We also have found a general correlation between the results of the analytical software programs TreeSAAP (which implements the MM01 model) and CDM (which implements the codon-degeneracy model).     

Informatics and multiplexing of intact protein identification in bacteria and the archaea

Although direct fragmentation of protein ions in a mass spectrometer is far more efficient than exhaustive mapping of 1-3 kDa peptides for complete characterization of primary structures predicted from sequenced genomes, the development of this approach is still in its infancy. Here we describe a statistical model (good to within approximately 5%) that shows that the database search specificity of this method requires only three of four fragment ions to match (at +/-0.1 Da) for a 99.8% probability of being correct in a database of 5,000 protein forms. Software developed for automated processing of protein ion fragmentation data and for probability-based retrieval of whole proteins is illustrated by identification of 18 archaeal and bacterial proteins with simultaneous mass-spectrometric (MS) mapping of their entire primary structures. Dissociation of two or three proteins at once for such identifications in parallel is also demonstrated, along with retention and exact localization of a phosphorylated serine residue through the fragmentation process. These conceptual and technical advances should assist future processing of whole proteins in a higher throughput format for more robust detection of co- and post-translational modifications.     

Prospects for realizing a structure of the spiral-turn-spiral type in a "zinc finger"

The realization of two models for Zn-finger structure--DNA-binding domain was estimated by taking into account the geometric and energetic requirements of polypeptide chain folding. The following structures were taken as models: antiparallel beta-structure and helix-turn-helix motif. The latter hasn't been considered earlier as the possible structure for Zn-finger. The preference was given to the above-mentioned models on the base of the available experimental data. It was shown that the helix-turn-helix motif for which the angle between axes of alpha-helices doesn't exceed 40 degrees cannot be excluded from the list of the assumed models for Zn-finger. There is a suggestion that the helix-turn-helix motif is likely to be characteristic for the majority of DNA-binding domains in proteins.