Structural diversity of protein segments follows a power-law distribution

Secondary structure analysis of proteins within the same topology group

The native conformation of a protein plays a decisive role in ensuring its functionality. It is established that the spatial structure of proteins may exhibit a greater degree of conservation than the corresponding amino acid sequences. This study aims to clarify structural distinctions between homologous and non-homologous proteins with identical topology. The analysis focuses on secondary structures with special emphasis on their fraction, distribution along the polypeptide chain, and chirality. Three different groups of proteins with identical topology were considered according to the CATH database: a homologous group of Globins, a group of Phycocyanins, which is often considered as a potential relative of globins, and a diverse assembly of other globin-like proteins. Some structural patterns in the distribution of secondary structure have been identified within Globins. A similar profile was observed in Phycocyanins, in contrast to the third group. In addition, a distinguishable structural motif, including structures such as 310-helix and irregular structure, has been found in both Globins and Phycocyanins, which can be proposed as an evolutionary imprint.

Porous protein crystals: synthesis and applications

Large-pore protein crystals (LPCs) are an emerging class of biomaterials. The inherent diversity of proteins translates to a diversity of crystal lattice structures, many of which display large pores and solvent channels. These pores can, in turn, be functionalized via directed evolution and rational redesign based on the known crystal structures. LPCs possess extremely high solvent content, as well as extremely high surface area to volume ratios. Because of these characteristics, LPCs continue to be explored in diverse applications including catalysis, targeted therapeutic delivery, templating of nanostructures, structural biology. This Feature review article will describe several of the existing platforms in detail, with particular focus on LPC synthesis approaches and reported applications.

Complex evolutionary footprints revealed in an analysis of reused protein segments of diverse lengths

We question a central paradigm: namely, that the protein domain is the “atomic unit” of evolution. In conflict with the current textbook view, our results unequivocally show that duplication of protein segments happens both above and below the domain level among amino acid segments of diverse lengths. Indeed, we show that significant evolutionary information is lost when the protein is approached as a string of domains. Our finer-grained approach reveals a far more complicated picture, where reused segments often intertwine and overlap with each other. Our results are consistent with a recursive model of evolution, in which segments of various lengths, typically smaller than domains, “hop” between environments. The fit segments remain, leaving traces that can still be detected.

Proteins share similar segments with one another. Such “reused parts”—which have been successfully incorporated into other proteins—are likely to offer an evolutionary advantage over de novo evolved segments, as most of the latter will not even have the capacity to fold. To systematically explore the evolutionary traces of segment “reuse” across proteins, we developed an automated methodology that identifies reused segments from protein alignments. We search for “themes”—segments of at least 35 residues of similar sequence and structure—reused within representative sets of 15,016 domains [Evolutionary Classification of Protein Domains (ECOD) database] or 20,398 chains [Protein Data Bank (PDB)]. We observe that theme reuse is highly prevalent and that reuse is more extensive when the length threshold for identifying a theme is lower. Structural domains, the best characterized form of reuse in proteins, are just one of many complex and intertwined evolutionary traces. Others include long themes shared among a few proteins, which encompass and overlap with shorter themes that recur in numerous proteins. The observed complexity is consistent with evolution by duplication and divergence, and some of the themes might include descendants of ancestral segments. The observed recursive footprints, where the same amino acid can simultaneously participate in several intertwined themes, could be a useful concept for protein design. Data are available at http://trachel-srv.cs.haifa.ac.il/rachel/ppi/themes/.

Word decoding of protein amino Acid sequences with availability analysis: a linguistic approach

The amino acid sequences of proteins determine their three-dimensional structures and functions. However, how sequence information is related to structures and functions is still enigmatic. In this study, we show that at least a part of the sequence information can be extracted by treating amino acid sequences of proteins as a collection of English words, based on a working hypothesis that amino acid sequences of proteins are composed of short constituent amino acid sequences (SCSs) or "words". We first confirmed that the English language highly likely follows Zipf's law, a special case of power law. We found that the rank-frequency plot of SCSs in proteins exhibits a similar distribution when low-rank tails are excluded. In comparison with natural English and "compressed" English without spaces between words, amino acid sequences of proteins show larger linear ranges and smaller exponents with heavier low-rank tails, demonstrating that the SCS distribution in proteins is largely scale-free. A distribution pattern of SCSs in proteins is similar among species, but species-specific features are also present. Based on the availability scores of SCSs, we found that sequence motifs are enriched in high-availability sites (i.e., "key words") and vice versa. In fact, the highest availability peak within a given protein sequence often directly corresponds to a sequence motif. The amino acid composition of high-availability sites within motifs is different from that of entire motifs and all protein sequences, suggesting the possible functional importance of specific SCSs and their compositional amino acids within motifs. We anticipate that our availability-based word decoding approach is complementary to sequence alignment approaches in predicting functionally important sites of unknown proteins from their amino acid sequences.

Scale-free behaviour of amino acid pair interactions in folded proteins

The protein structure is a cumulative result of interactions between amino acid residues interacting with each other through space and/or chemical bonds. Despite the large number of high resolution protein structures, the "protein structure code" has not been fully identified. Our manuscript presents a novel approach to protein structure analysis in order to identify rules for spatial packing of amino acid pairs in proteins. We have investigated 8706 high resolution non-redundant protein chains and quantified amino acid pair interactions in terms of solvent accessibility, spatial and sequence distance, secondary structure, and sequence length. The number of pairs found in a particular environment is stored in a cell in an 8 dimensional data tensor. When plotting the cell population against the number of cells that have the same population size, a scale free organization is found. When analyzing which amino acid paired residues contributed to the cells with a population above 50, pairs of Ala, Ile, Leu and Val dominate the results. This result is statistically highly significant. We postulate that such pairs form "structural stability points" in the protein structure. Our data shows that they are in buried α-helices or β-strands, in a spatial distance of 3.8-4.3Å and in a sequence distance >4 residues. We speculate that the scale free organization of the amino acid pair interactions in the 8D protein structure combined with the clear dominance of pairs of Ala, Ile, Leu and Val is important for understanding the very nature of the protein structure formation. Our observations suggest that protein structures should be considered as having a higher dimensional organization.

Convergent evolution in structural elements of proteins investigated using cross profile analysis

Background

Evolutionary relations of similar segments shared by different protein folds remain controversial, even though many examples of such segments have been found. To date, several methods such as those based on the results of structure comparisons, sequence-based classifications, and sequence-based profile-profile comparisons have been applied to identify such protein segments that possess local similarities in both sequence and structure across protein folds. However, to capture more precise sequence-structure relations, no method reported to date combines structure-based profiles, and sequence-based profiles based on evolutionary information. The former are generally regarded as representing the amino acid preferences at each position of a specific conformation of protein segment. They might reflect the nature of ancient short peptide ancestors, using the results of structural classifications of protein segments.

Results

This report describes the development and use of "Cross Profile Analysis" to compare sequence-based profiles and structure-based profiles based on amino acid occurrences at each position within a protein segment cluster. Using systematic cross profile analysis, we found structural clusters of 9-residue and 15-residue segments showing remarkably strong correlation with particular sequence profiles. These correlations reflect structural similarities among constituent segments of both sequence-based and structure-based profiles. We also report previously undetectable sequence-structure patterns that transcend protein family and fold boundaries, and present results of the conformational analysis of the deduced peptide of a segment cluster. These results suggest the existence of ancient short-peptide ancestors.

Conclusions

Cross profile analysis reveals the polyphyletic and convergent evolution of β-hairpin-like structures, which were verified both experimentally and computationally. The results presented here give us new insights into the evolution of short protein segments.

Universal partitioning of the hierarchical fold network of 50-residue segments in proteins

Background

Several studies have demonstrated that protein fold space is structured hierarchically and that power-law statistics are satisfied in relation between the numbers of protein families and protein folds (or superfamilies). We examined the internal structure and statistics in the fold space of 50 amino-acid residue segments taken from various protein folds. We used inter-residue contact patterns to measure the tertiary structural similarity among segments. Using this similarity measure, the segments were classified into a number (K_c) of clusters. We examined various K_c values for the clustering. The special resolution to differentiate the segment tertiary structures increases with increasing K_c. Furthermore, we constructed networks by linking structurally similar clusters.

Results

The network was partitioned persistently into four regions for K_c ≥ 1000. This main partitioning is consistent with results of earlier studies, where similar partitioning was reported in classifying protein domain structures. Furthermore, the network was partitioned naturally into several dozens of sub-networks (i.e., communities). Therefore, intra-sub-network clusters were mutually connected with numerous links, although inter-sub-network ones were rarely done with few links. For K_c ≥ 1000, the major sub-networks were about 40; the contents of the major sub-networks were conserved. This sub-partitioning is a novel finding, suggesting that the network is structured hierarchically: Segments construct a cluster, clusters form a sub-network, and sub-networks constitute a region. Additionally, the network was characterized by non-power-law statistics, which is also a novel finding.

Conclusion

Main findings are: (1) The universe of 50 residue segments found here was characterized by non-power-law statistics. Therefore, the universe differs from those ever reported for the protein domains. (2) The 50-residue segments were partitioned persistently and universally into some dozens (ca. 40) of major sub-networks, irrespective of the number of clusters. (3) These major sub-networks encompassed 90% of all segments. Consequently, the protein tertiary structure is constructed using the dozens of elements (sub-networks).

Emergence of scale-free distribution in protein-protein interaction networks based on random selection of interacting domain pairs

Recent analyses of biological and artificial networks have revealed a common network architecture, called scale-free topology. The origin of the scale-free topology has been explained by using growth and preferential attachment mechanisms. In a cell, proteins are the most important carriers of function, and are composed of domains as elemental units responsible for the physical interaction between protein pairs. Here, we propose a model for protein-protein interaction networks that reveals the emergence of two possible topologies. We show that depending on the number of randomly selected interacting domain pairs, the connectivity distribution follows either a scale-free distribution, even in the absence of the preferential attachment, or a normal distribution. This new approach only requires an evolutionary model of proteins (nodes) but not for the interactions (edges). The edges are added by means of random interaction of domain pairs. As a result, this model offers a new mechanistic explanation for understanding complex networks with a direct biological interpretation because only protein structures and their functions evolved through genetic modifications of amino acid sequences. These findings are supported by numerical simulations as well as experimental data.

Crystal structure of a ten-amino acid protein

What is the smallest protein? This is actually not such a simple question to answer, because there is no established consensus among scientists as to the definition of a protein. We describe here a designed molecule consisting of only 10 amino acids. Despite its small size, its essential characteristics, revealed by its crystal structure, solution structure, thermal stability, free energy surface, and folding pathway network, are consistent with the properties of natural proteins. The existence of this kind of molecule deepens our understanding of proteins and impels us to define an "ideal protein" without inquiring whether the molecule actually occurs in nature.

Protein-segment universe exhibiting transitions at intermediate segment length in conformational subspaces

Background

Many studies have examined rules governing two aspects of protein structures: short segments and proteins' structural domains. Nevertheless, the organization and nature of the conformational space of segments with intermediate length between short segments and domains remain unclear. Conformational spaces of intermediate length segments probably differ from those of short segments. We investigated the identification and characterization of the boundary(s) between peptide-like (short segment) and protein-like (long segment) distributions. We generated ensembles embedded in globular proteins comprising segments 10–50 residues long. We explored the relationships between the conformational distribution of segments and their lengths, and also protein structural classes using principal component analysis based on the intra-segment C_α-C_α atomic distances.

Results

Our statistical analyses of segment conformations and length revealed critical dual transitions in their conformational distribution with segments derived from all four structural classes. Dual transitions were identified with the intermediate phase between the short segments and domains. Consequently, protein segment universes were categorized. i) Short segments (10–22 residues) showed a distribution with a high frequency of secondary structure clusters. ii) Medium segments (23–26 residues) showed a distribution corresponding to an intermediate state of transitions. iii) Long segments (27–50 residues) showed a distribution converging on one huge cluster containing compact conformations with a smaller radius of gyration. This distribution reflects the protein structures' organization and protein domains' origin. Three major conformational components (radius of gyration, structural symmetry with respect to the N-terminal and C-terminal halves, and single-turn/two-turn structure) well define most of the segment universes. Furthermore, we identified several conformational components that were unique to each structural class. Those characteristics suggest that protein segment conformation is described by compositions of the three common structural variables with large contributions and specific structural variables with small contributions.

Conclusion

The present results of the analyses of four protein structural classes show the universal role of three major components as segment conformational descriptors. The obtained perspectives of distribution changes related to the segment lengths using the three key components suggest both the adequacy and the possibility of further progress on the prediction strategies used in the recent de novo structure-prediction methods.

Functionally important segments in proteins dissected using Gene Ontology and geometric clustering of peptide fragments

A geometric clustering algorithm has been developed to dissect protein fragments based on their relevance to function.

We have developed a geometric clustering algorithm using backbone φ,ψ angles to group conformationally similar peptide fragments of any length. By labeling each fragment in the cluster with the level-specific Gene Ontology 'molecular function' term of its protein, we are able to compute statistics for molecular function-propensity and p-value of individual fragments in the cluster. Clustering-cum-statistical analysis for peptide fragments 8 residues in length and with only trans peptide bonds shows that molecular function propensities ≥20 and p-values ≤0.05 can dissect fragments within a protein linked to the molecular function.