Implications from a network-based topological analysis of ubiquitin unfolding simulations

Background

The architectural organization of protein structures has been the focus of intense research since it can hopefully lead to an understanding of how proteins fold. In earlier works we had attempted to identify the inherent structural organization in proteins through a study of protein topology. We obtained a modular partitioning of protein structures with the modules correlating well with experimental evidence of early folding units or “foldons”. Residues that connect different modules were shown to be those that were protected during the transition phase of folding.

Methodology/Principal Findings

In this work, we follow the topological path of ubiquitin through molecular dynamics unfolding simulations. We observed that the use of recurrence quantification analysis (RQA) could lead to the identification of the transition state during unfolding. Additionally, our earlier contention that the modules uncovered through our graph partitioning approach correlated well with early folding units was vindicated through our simulations. Moreover, residues identified from native structure as connector hubs and which had been shown to be those that were protected during the transition phase of folding were indeed more stable (less flexible) well beyond the transition state. Further analysis of the topological pathway suggests that the all pairs shortest path in a protein is minimized during folding.

Conclusions

We observed that treating a protein native structure as a network by having amino acid residues as nodes and the non-covalent interactions among them as links allows for the rationalization of many aspects of the folding process. The possibility to derive this information directly from 3D structure opens the way to the prediction of important residues in proteins, while the confirmation of the minimization of APSP for folding allows for the establishment of a potentially useful proxy for kinetic optimality in the validation of sequence-structure predictions.     

Transition states for protein folding have native topologies despite high structural variability

We present a structural analysis of the folding transition states of three SH3 domains. Our results reveal that the secondary structure is not yet fully formed at this stage of folding and that the solvent is only partially excluded from the interior of the protein. Comparison of the members of the transition state ensemble with a database of native folds shows that, despite substantial local variability, the transition state structures can all be classified as having the topology characteristic of an SH3 domain. Our results suggest a mechanism for folding in which the formation of a network of interactions among a subset of hydrophobic residues ensures that the native topology is generated. Such a mechanism enables high fidelity in folding while minimizing the need to establish a large number of specific interactions in the conformational search.     

RAG-3D: a search tool for RNA 3D substructures

To address many challenges in RNA structure/function prediction, the characterization of RNA''s modular architectural units is required. Using the RNA-As-Graphs (RAG) database, we have previously explored the existence of secondary structure (2D) submotifs within larger RNA structures. Here we present RAG-3D—a dataset of RNA tertiary (3D) structures and substructures plus a web-based search tool—designed to exploit graph representations of RNAs for the goal of searching for similar 3D structural fragments. The objects in RAG-3D consist of 3D structures translated into 3D graphs, cataloged based on the connectivity between their secondary structure elements. Each graph is additionally described in terms of its subgraph building blocks. The RAG-3D search tool then compares a query RNA 3D structure to those in the database to obtain structurally similar structures and substructures. This comparison reveals conserved 3D RNA features and thus may suggest functional connections. Though RNA search programs based on similarity in sequence, 2D, and/or 3D structural elements are available, our graph-based search tool may be advantageous for illuminating similarities that are not obvious; using motifs rather than sequence space also reduces search times considerably. Ultimately, such substructuring could be useful for RNA 3D structure prediction, structure/function inference and inverse folding.     

Structural search and retrieval using a tableau representation of protein folding patterns

Comparison and classification of folding patterns from a database of protein structures is crucial to understand the principles of protein architecture, evolution and function. Current search methods for proteins with similar folding patterns are slow and computationally intensive. The sharp growth in the number of known protein structures poses severe challenges for methods of structural comparison. There is a need for methods that can search the database of structures accurately and rapidly. We provide several methods to search for similar folding patterns using a concise tableau representation of proteins that encodes the relative geometry of secondary structural elements. Our first approach allows the extraction of identical and very closely-related protein folding patterns in constant-time (per hit). Next, we address the hard computational problem of extraction of maximally-similar subtableaux, when comparing two tableaux. We solve the problem using Quadratic and Linear integer programming formulations and demonstrate their power to identify subtle structural similarities, especially when protein structures significantly diverge. Finally, we describe a rapid and accurate method for comparing a query structure against a database of protein domains, TableauSearch. TableauSearch is rapid enough to search the entire structural database in seconds on a standard desktop computer. Our analysis of TableauSearch on many queries shows that the method is very accurate in identifying similarities of folding patterns, even between distantly related proteins. AVAILABILITY: A web server implementing the TableauSearch is available from http://hollywood.bx.psu.edu/TabSearch.     

Routes are trees: the parsing perspective on protein folding

An important puzzle in structural biology is the question of how proteins are able to fold so quickly into their unique native structures. There is much evidence that protein folding is hierarchic. In that case, folding routes are not linear, but have a tree structure. Trees are commonly used to represent the grammatical structure of natural language sentences, and chart parsing algorithms efficiently search the space of all possible trees for a given input string. Here we show that one such method, the CKY algorithm, can be useful both for providing novel insight into the physical protein folding process, and for computational protein structure prediction. As proof of concept, we apply this algorithm to the HP lattice model of proteins. Our algorithm identifies all direct folding route trees to the native state and allows us to construct a simple model of the folding process. Despite its simplicity, our model provides an account for the fact that folding rates depend only on the topology of the native state but not on sequence composition.     

Ab initio protein structure assembly using continuous structure fragments and optimized knowledge-based force field

Ab initio protein folding is one of the major unsolved problems in computational biology owing to the difficulties in force field design and conformational search. We developed a novel program, QUARK, for template-free protein structure prediction. Query sequences are first broken into fragments of 1-20 residues where multiple fragment structures are retrieved at each position from unrelated experimental structures. Full-length structure models are then assembled from fragments using replica-exchange Monte Carlo simulations, which are guided by a composite knowledge-based force field. A number of novel energy terms and Monte Carlo movements are introduced and the particular contributions to enhancing the efficiency of both force field and search engine are analyzed in detail. QUARK prediction procedure is depicted and tested on the structure modeling of 145 nonhomologous proteins. Although no global templates are used and all fragments from experimental structures with template modeling score >0.5 are excluded, QUARK can successfully construct 3D models of correct folds in one-third cases of short proteins up to 100 residues. In the ninth community-wide Critical Assessment of protein Structure Prediction experiment, QUARK server outperformed the second and third best servers by 18 and 47% based on the cumulative Z-score of global distance test-total scores in the FM category. Although ab initio protein folding remains a significant challenge, these data demonstrate new progress toward the solution of the most important problem in the field.     

The adaptive nature of protein residue networks

Protein residue networks PRNs are used to describe proteins. These networks are usually based on an average structure for the protein. However, proteins are dynamic entities that are affected by their surroundings. In this work, we study the effect of temperatures above and below the protein dynamical transition temperature(≈200 K), on three important network parameters gleaned from weighted PRNs for the solvated β‐lactamase inhibitory protein BLIP: the betweenness centrality B, the closeness centrality C, and the clustering coefficient CC. The B and C values will be extracted for each node from PRNs at six different temperatures: 150 K, 180 K, 200 K, 220 K, 250 K, and 310 K respectively. The average value for the CC for each PRN will also be calculated at each temperature, respectively. We find that at temperatures ≤200 K, the network nodes with the most significant B and C values tend to have lower relative solvent accessibility RSA values, and to fall within the protein secondary structure elements (α helices and β sheets). At temperatures >200 K, the significant nodes in terms of B and C tend to have larger RSA values, and to fall on the connecting loops in the protein. The average CC decreases in value for the PRNs up to 200 K, and then remains basically constant above 200 K. This clearly shows that any conclusions based on static PRNs should be handled with care. The dynamic nature of proteins and its coupling to the surrounding environment should be taken into consideration when using the PRN paradigm. Proteins 2017; 85:917–923. © 2016 Wiley Periodicals, Inc.     

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.     

Enhanced hybrid search algorithm for protein structure prediction using the 3D-HP lattice model

The problem of protein structure prediction in the hydrophobic-polar (HP) lattice model is the prediction of protein tertiary structure. This problem is usually referred to as the protein folding problem. This paper presents a method for the application of an enhanced hybrid search algorithm to the problem of protein folding prediction, using the three dimensional (3D) HP lattice model. The enhanced hybrid search algorithm is a combination of the particle swarm optimizer (PSO) and tabu search (TS) algorithms. Since the PSO algorithm entraps local minimum in later evolution extremely easily, we combined PSO with the TS algorithm, which has properties of global optimization. Since the technologies of crossover and mutation are applied many times to PSO and TS algorithms, so enhanced hybrid search algorithm is called the MCMPSO-TS (multiple crossover and mutation PSO-TS) algorithm. Experimental results show that the MCMPSO-TS algorithm can find the best solutions so far for the listed benchmarks, which will help comparison with any future paper approach. Moreover, real protein sequences and Fibonacci sequences are verified in the 3D HP lattice model for the first time. Compared with the previous evolutionary algorithms, the new hybrid search algorithm is novel, and can be used effectively to predict 3D protein folding structure. With continuous development and changes in amino acids sequences, the new algorithm will also make a contribution to the study of new protein sequences.     

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.     

LB3D: a protein three-dimensional substructure search program based on the lower bound of a root mean square deviation value

Searching for protein structure-function relationships using three-dimensional (3D) structural coordinates represents a fundamental approach for determining the function of proteins with unknown functions. Since protein structure databases are rapidly growing in size, the development of a fast search method to find similar protein substructures by comparison of protein 3D structures is essential. In this article, we present a novel protein 3D structure search method to find all substructures with root mean square deviations (RMSDs) to the query structure that are lower than a given threshold value. Our new algorithm runs in O(m + N/m(0.5)) time, after O(N log N) preprocessing, where N is the database size and m is the query length. The new method is 1.8-41.6 times faster than the practically best known O(N) algorithm, according to computational experiments using a huge database (i.e., >20,000,000 C-alpha coordinates).     

Network scaling invariants help to elucidate basic topological principles of proteins

The structural architecture of proteins continues to be an area of active research. Despite the difference in models dealing with the way proteins fold into their tertiary structures, it is recognized that small regions of proteins tend to fold independently and are then stabilized by interactions between these distinct subunits. However, there are a number of different definitions of what comprises an independent subunit. In the belief that an unequivocal definition of a domain must be based on the most fundamental property of protein 3D structure, namely, the adjacency matrix of inter-residues contact, we adopt a network representation of the protein. In this work, we used a well-established, global method for identifying modules in networks, without any specific reference to the kind of network being analyzed. The algorithm converges toward the maximization of the modularity of the given protein network and, in doing so, allows the representation of the residues of the protein in terms of their intramodule degree, z, and participation coefficient, P. We demonstrate that the labeling of residues in terms of these invariants allows for information-rich representations of the studied proteins as well as to sketch a new way to link sequence, structure, and the dynamical properties of proteins. We discovered a strong invariant character of protein molecules in terms of P/z characterization, pointing to a common topological design of all protein structures. This invariant representation, applied to different protein systems, enabled us to identify the possible functional role of high P/z residues during the folding process. Additionally, we observe a hierarchical behavior of protein structural organization that provides a sequence-secondary-tertiary structure link. The discovery of similar and repeatable scaling laws at different level of definitions going from hydrophobicity patterning along the sequence up to the size of an autonomous folding unit (AFU) and general contact distribution of the entire molecule suggest a hierarchical-like behavior of protein architecture. This implies the possibility to select different privileged scales of observation for deriving useful information on protein systems.     

Incorporating Secondary Features into the General form of Chou's PseAAC for Predicting Protein Structural Class

Protein structure information is very useful for the confirmation of protein function. The protein structural class can provide information for protein 3D structure analysis, causing the conformation of the protein overall folding type plays a significant part in molecular biology. In this paper, we focus on the prediction of protein structural class which was based on new feature representation. We extract features from the Chou-Fasman parameter, amino acid compositions, amino acids hydrophobicity features, polarity information and pair-coupled amino acid composition. The prediction result by the Support vector machine (SVM) classifier shows that our method is better than some others.     

Structural classification of thioredoxin-like fold proteins

Protein structure classification is necessary to comprehend the rapidly growing structural data for better understanding of protein evolution and sequence-structure-function relationships. Thioredoxins are important proteins that ubiquitously regulate cellular redox status and various other crucial functions. We define the thioredoxin-like fold using the structure consensus of thioredoxin homologs and consider all circular permutations of the fold. The search for thioredoxin-like fold proteins in the PDB database identified 723 protein domains. These domains are grouped into eleven evolutionary families based on combined sequence, structural, and functional evidence. Analysis of the protein-ligand structure complexes reveals two major active site locations for the thioredoxin-like proteins. Comparison to existing structure classifications reveals that our thioredoxin-like fold group is broader and more inclusive, unifying proteins from five SCOP folds, five CATH topologies and seven DALI domain dictionary globular folding topologies. Considering these structurally similar domains together sheds new light on the relationships between sequence, structure, function and evolution of thioredoxins.     

A segment alignment approach to protein comparison

MOTIVATION: Local structure segments (LSSs) are small structural units shared by unrelated proteins. They are extensively used in protein structure comparison, and predicted LSSs (PLSSs) are used very successfully in ab initio folding simulations. However, predicted or real LSSs are rarely exploited by protein sequence comparison programs that are based on position-by-position alignments. RESULTS: We developed a SEgment Alignment algorithm (SEA) to compare proteins described as a collection of predicted local structure segments (PLSSs), which is equivalent to an unweighted graph (network). Any specific structure, real or predicted corresponds to a specific path in this network. SEA then uses a network matching approach to find two most similar paths in networks representing two proteins. SEA explores the uncertainty and diversity of predicted local structure information to search for a globally optimal solution. It simultaneously solves two related problems: the alignment of two proteins and the local structure prediction for each of them. On a benchmark of protein pairs with low sequence similarity, we show that application of the SEA algorithm improves alignment quality as compared to FFAS profile-profile alignment, and in some cases SEA alignments can match the structural alignments, a feat previously impossible for any sequence based alignment methods.     

Folding studies of immunoglobulin-like beta-sandwich proteins suggest that they share a common folding pathway.

BACKGROUND: Are folding pathways conserved in protein families? To test this explicitly and ask to what extent structure specifies folding pathways requires comparison of proteins with a common fold. Our strategy is to choose members of a highly diverse protein family with no conservation of function and little or no sequence identity, but with structures that are essentially the same. The immunoglobulin-like fold is one of the most common structural families, and is subdivided into superfamilies with no detectable evolutionary or functional relationship. RESULTS: We compared the folding of a number of immunoglobulin-like proteins that have a common structural core and found a strong correlation between folding rate and stability. The results suggest that the folding pathways of these immunoglobulin-like proteins share common features. CONCLUSIONS: This study is the first to compare the folding of structurally related proteins that are members of different superfamilies. The most likely explanation for the results is that interactions that are important in defining the structure of immunoglobulin-like proteins are also used to guide folding.     

Molecular basis of co-operativity in protein folding. III. Structural identification of cooperative folding units and folding intermediates.

The hierarchical partition function formalism for protein folding developed earlier has been extended through the use of three-dimensional polar and apolar contact plots. For each amino acid residue in the protein, these plots indicate the apolar and polar surfaces that are buried from the solvent, the identity of all amino acid residues that contribute to this shielding, and the magnitude of their contributions. These contact plots are then used to examine the distribution of the free energy of stabilization throughout the protein molecule. Analysis of these data allows identification of co-operative folding units and their hierarchical levels, and the identification of partially folded intermediates with a significant probability of being populated. The overall folding/unfolding thermodynamics of 12 globular proteins, for which crystallographic and experimental thermodynamics are available, is predicted within error. An energetic classification of partially folded intermediates is presented and the results compared to those cases for which structural and thermodynamic experimental information is available. Four different types of partially folded states and their structural energies are considered. (1) Local intermediates, in which only a local region of the protein loses secondary and tertiary interactions, while the rest of the protein remains intact. (2) Global intermediates, corresponding to the standard molten globule definition, in which significant secondary structure is maintained but native-like tertiary structure contacts are disrupted. (3) Extended intermediates characterized by the existence of secondary structure elements (e.g. alpha-helices) exposed to solvent. (4) Folding intermediates in proteins with two structural domains. The structure and energetics of folding intermediates of apo-myoglobin, alpha-lactalbumin, phosphoglycerate kinase and arabinose-binding protein are considered in detail.