1001 optimal PDB structure alignments: integer programming methods for finding the maximum contact map overlap

Alignments of biomolecular contact maps

Alignments of discrete objects can be constructed in a very general setting as super-objects from which the constituent objects are recovered by means of projections. Here, we focus on contact maps, i.e. undirected graphs with an ordered set of vertices. These serve as natural discretizations of RNA and protein structures. In the general case, the alignment problem for vertex-ordered graphs is NP-complete. In the special case of RNA secondary structures, i.e. crossing-free matchings, however, the alignments have a recursive structure. The alignment problem then can be solved by a variant of the Sankoff algorithm in polynomial time. Moreover, the tree or forest alignments of RNA secondary structure can be understood as the alignments of ordered edge sets.

Efficient Multicriteria Protein Structure Comparison on Modern Processor Architectures

Fast increasing computational demand for all-to-all protein structures comparison (PSC) is a result of three confounding factors: rapidly expanding structural proteomics databases, high computational complexity of pairwise protein comparison algorithms, and the trend in the domain towards using multiple criteria for protein structures comparison (MCPSC) and combining results. We have developed a software framework that exploits many-core and multicore CPUs to implement efficient parallel MCPSC in modern processors based on three popular PSC methods, namely, TMalign, CE, and USM. We evaluate and compare the performance and efficiency of the two parallel MCPSC implementations using Intel's experimental many-core Single-Chip Cloud Computer (SCC) as well as Intel's Core i7 multicore processor. We show that the 48-core SCC is more efficient than the latest generation Core i7, achieving a speedup factor of 42 (efficiency of 0.9), making many-core processors an exciting emerging technology for large-scale structural proteomics. We compare and contrast the performance of the two processors on several datasets and also show that MCPSC outperforms its component methods in grouping related domains, achieving a high F-measure of 0.91 on the benchmark CK34 dataset. The software implementation for protein structure comparison using the three methods and combined MCPSC, along with the developed underlying rckskel algorithmic skeletons library, is available via GitHub.

Homology modeling of larger proteins guided by chemical shifts

We describe an approach to the structure determination of large proteins that relies on experimental NMR chemical shifts, plus sparse nuclear Overhauser effect (NOE) data if available. Our alignment method, POMONA (protein alignments obtained by matching of NMR assignments), directly exploits pre-existing bioinformatics algorithms to match experimental chemical shifts to values predicted for the crystallographic database. Protein templates generated by POMONA are subsequently used as input for chemical shift-based Rosetta comparative modeling (CS-RosettaCM) to generate reliable full-atom models.

Divide and Conquer Approach to Contact Map Overlap Problem Using 2D-Pattern Mining of Protein Contact Networks

A novel approach to Contact Map Overlap (CMO) problem is proposed using the two dimensional clusters present in the contact maps. Each protein is represented as a set of the non-trivial clusters of contacts extracted from its contact map. The approach involves finding matching regions between the two contact maps using approximate 2D-pattern matching algorithm and dynamic programming technique. These matched pairs of small contact maps are submitted in parallel to a fast heuristic CMO algorithm. The approach facilitates parallelization at this level since all the pairs of contact maps can be submitted to the algorithm in parallel. Then, a merge algorithm is used in order to obtain the overall alignment. As a proof of concept, MSVNS, a heuristic CMO algorithm is used for global as well as local alignment. The divide and conquer approach is evaluated for two benchmark data sets that of Skolnick and Ding et al. It is interesting to note that along with achieving saving of time, better overlap is also obtained for certain protein folds.

Simultaneous alignment and folding of protein sequences

Accurate comparative analysis tools for low-homology proteins remains a difficult challenge in computational biology, especially sequence alignment and consensus folding problems. We present partiFold-Align, the first algorithm for simultaneous alignment and consensus folding of unaligned protein sequences; the algorithm's complexity is polynomial in time and space. Algorithmically, partiFold-Align exploits sparsity in the set of super-secondary structure pairings and alignment candidates to achieve an effectively cubic running time for simultaneous pairwise alignment and folding. We demonstrate the efficacy of these techniques on transmembrane β-barrel proteins, an important yet difficult class of proteins with few known three-dimensional structures. Testing against structurally derived sequence alignments, partiFold-Align significantly outperforms state-of-the-art pairwise and multiple sequence alignment tools in the most difficult low-sequence homology case. It also improves secondary structure prediction where current approaches fail. Importantly, partiFold-Align requires no prior training. These general techniques are widely applicable to many more protein families (partiFold-Align is available at http://partifold.csail.mit.edu/ ).

GR-Align: fast and flexible alignment of protein 3D structures using graphlet degree similarity

MOTIVATION

Protein structure alignment is key for transferring information from well-studied proteins to less studied ones. Structural alignment identifies the most precise mapping of equivalent residues, as structures are more conserved during evolution than sequences. Among the methods for aligning protein structures, maximum Contact Map Overlap (CMO) has received sustained attention during the past decade. Yet, known algorithms exhibit modest performance and are not applicable for large-scale comparison.

RESULTS

Graphlets are small induced subgraphs that are used to design sensitive topological similarity measures between nodes and networks. By generalizing graphlets to ordered graphs, we introduce GR-Align, a CMO heuristic that is suited for database searches. On the Proteus_300 set (44 850 protein domain pairs), GR-Align is several orders of magnitude faster than the state-of-the-art CMO solvers Apurva, MSVNS and AlEigen7, and its similarity score is in better agreement with the structural classification of proteins. On a large-scale experiment on the Gold-standard benchmark dataset (3 207 270 protein domain pairs), GR-Align is several orders of magnitude faster than the state-of-the-art protein structure comparison tools TM-Align, DaliLite, MATT and Yakusa, while achieving similar classification performances. Finally, we illustrate the difference between GR-Align's flexible alignments and the traditional ones by querying a flexible protein in the Astral-40 database (11 154 protein domains). In this experiment, GR-Align's top scoring alignments are not only in better agreement with structural classification of proteins, but also that they allow transferring more information across proteins.

Predicting protein contact map using evolutionary and physical constraints by integer programming

Motivation: Protein contact map describes the pairwise spatial and functional relationship of residues in a protein and contains key information for protein 3D structure prediction. Although studied extensively, it remains challenging to predict contact map using only sequence information. Most existing methods predict the contact map matrix element-by-element, ignoring correlation among contacts and physical feasibility of the whole-contact map. A couple of recent methods predict contact map by using mutual information, taking into consideration contact correlation and enforcing a sparsity restraint, but these methods demand for a very large number of sequence homologs for the protein under consideration and the resultant contact map may be still physically infeasible.

Results: This article presents a novel method PhyCMAP for contact map prediction, integrating both evolutionary and physical restraints by machine learning and integer linear programming. The evolutionary restraints are much more informative than mutual information, and the physical restraints specify more concrete relationship among contacts than the sparsity restraint. As such, our method greatly reduces the solution space of the contact map matrix and, thus, significantly improves prediction accuracy. Experimental results confirm that PhyCMAP outperforms currently popular methods no matter how many sequence homologs are available for the protein under consideration.

Availability:http://raptorx.uchicago.edu.

Contact:jinboxu@gmail.com

DALIX: optimal DALI protein structure alignment

We present a mathematical model and exact algorithm for optimally aligning protein structures using the DALI scoring model. This scoring model is based on comparing the interresidue distance matrices of proteins and is used in the popular DALI software tool, a heuristic method for protein structure alignment. Our model and algorithm extend an integer linear programming approach that has been previously applied for the related, but simpler, contact map overlap problem. To this end, we introduce a novel type of constraint that handles negative score values and relax it in a Lagrangian fashion. The new algorithm, which we call DALIX, is applicable to any distance matrix-based scoring scheme. We also review options that allow to consider fewer pairs of interresidue distances explicitly because their large number hinders the optimization process. Using four known data sets of varying structural similarity, we compute many provably score-optimal DALI alignments. This allowed, for the first time, to evaluate the DALI heuristic in sound mathematical terms. The results indicate that DALI usually computes optimal or close to optimal alignments. However, we detect a subset of small proteins for which DALI fails to generate any significant alignment, although such alignments do exist.

On the difference in quality between current heuristic and optimal solutions to the protein structure alignment problem

The importance of pairwise protein structural comparison in biomedical research is fueling the search for algorithms capable of finding more accurate structural match of two input proteins in a timely manner. In recent years, we have witnessed rapid advances in the development of methods for approximate and optimal solutions to the protein structure matching problem. Albeit slow, these methods can be extremely useful in assessing the accuracy of more efficient, heuristic algorithms. We utilize a recently developed approximation algorithm for protein structure matching to demonstrate that a deep search of the protein superposition space leads to increased alignment accuracy with respect to many well-established measures of alignment quality. The results of our study suggest that a large and important part of the protein superposition space remains unexplored by current techniques for protein structure alignment.

LNA: fast protein structural comparison using a Laplacian characterization of tertiary structure

Abstract—In the last two decades, a lot of protein 3D shapes have been discovered, characterized, and made available thanks to the Protein Data Bank (PDB), that is nevertheless growing very quickly. New scalable methods are thus urgently required to search through the PDB efficiently. This paper presents an approach entitled LNA (Laplacian Norm Alignment) that performs a structural comparison of two proteins with dynamic programming algorithms. This is achieved by characterizing each residue in the protein with scalar features. The feature values are calculated using a Laplacian operator applied on the graph corresponding to the adjacency matrix of the residues. The weighted Laplacian operator we use estimates, at various scales, local deformations of the topology where each residue is located. On some benchmarks, which are widely shared by the community, we obtain qualitatively similar results compared to other competing approaches, but with an algorithm one or two order of magnitudes faster. 180,000 protein comparisons can be done within 1 second with a single recent Graphical Processing Unit (GPU), which makes our algorithm very scalable and suitable for real-time database querying across the web.

xPyder: a PyMOL plugin to analyze coupled residues and their networks in protein structures

A versatile method to directly identify and analyze short- or long-range coupled or communicating residues in a protein conformational ensemble is of extreme relevance to achieve a complete understanding of protein dynamics and structural communication routes. Here, we present xPyder, an interface between one of the most employed molecular graphics systems, PyMOL, and the analysis of dynamical cross-correlation matrices (DCCM). The approach can also be extended, in principle, to matrices including other indexes of communication propensity or intensity between protein residues, as well as the persistence of intra- or intermolecular interactions, such as those underlying protein dynamics. The xPyder plugin for PyMOL 1.4 and 1.5 is offered as Open Source software via the GPL v2 license, and it can be found, along with the installation package, the user guide, and examples, at http://linux.btbs.unimib.it/xpyder/.

SAS-Pro: simultaneous residue assignment and structure superposition for protein structure alignment

Protein structure alignment is the problem of determining an assignment between the amino-acid residues of two given proteins in a way that maximizes a measure of similarity between the two superimposed protein structures. By identifying geometric similarities, structure alignment algorithms provide critical insights into protein functional similarities. Existing structure alignment tools adopt a two-stage approach to structure alignment by decoupling and iterating between the assignment evaluation and structure superposition problems. We introduce a novel approach, SAS-Pro, which addresses the assignment evaluation and structure superposition simultaneously by formulating the alignment problem as a single bilevel optimization problem. The new formulation does not require the sequentiality constraints, thus generalizing the scope of the alignment methodology to include non-sequential protein alignments. We employ derivative-free optimization methodologies for searching for the global optimum of the highly nonlinear and non-differentiable RMSD function encountered in the proposed model. Alignments obtained with SAS-Pro have better RMSD values and larger lengths than those obtained from other alignment tools. For non-sequential alignment problems, SAS-Pro leads to alignments with high degree of similarity with known reference alignments. The source code of SAS-Pro is available for download at http://eudoxus.cheme.cmu.edu/saspro/SAS-Pro.html.

OPTIMAL PAIRWISE ALIGNMENT OF FIXED PROTEIN STRUCTURES IN SUBQUADRATIC TIME

The problem of finding an optimal structural alignment for a pair of superimposed proteins is often amenable to the Smith–Waterman dynamic programming algorithm, which runs in time proportional to the product of lengths of the sequences being aligned. While the quadratic running time is acceptable for computing a single alignment of two fixed protein structures, the time complexity becomes a bottleneck when running the Smith–Waterman routine multiple times in order to find a globally optimal superposition and alignment of the input proteins. We present a subquadratic running time algorithm capable of computing an alignment that optimizes one of the most widely used measures of protein structure similarity, defined as the number of pairs of residues in two proteins that can be superimposed under a predefined distance cutoff. The algorithm presented in this article can be used to significantly improve the speed–accuracy tradeoff in a number of popular protein structure alignment methods.

deepBlockAlign: a tool for aligning RNA-seq profiles of read block patterns

MOTIVATION

High-throughput sequencing methods allow whole transcriptomes to be sequenced fast and cost-effectively. Short RNA sequencing provides not only quantitative expression data but also an opportunity to identify novel coding and non-coding RNAs. Many long transcripts undergo post-transcriptional processing that generates short RNA sequence fragments. Mapped back to a reference genome, they form distinctive patterns that convey information on both the structure of the parent transcript and the modalities of its processing. The miR-miR* pattern from microRNA precursors is the best-known, but by no means singular, example.

RESULTS

deepBlockAlign introduces a two-step approach to align RNA-seq read patterns with the aim of quickly identifying RNAs that share similar processing footprints. Overlapping mapped reads are first merged to blocks and then closely spaced blocks are combined to block groups, each representing a locus of expression. In order to compare block groups, the constituent blocks are first compared using a modified sequence alignment algorithm to determine similarity scores for pairs of blocks. In the second stage, block patterns are compared by means of a modified Sankoff algorithm that takes both block similarities and similarities of pattern of distances within the block groups into account. Hierarchical clustering of block groups clearly separates most miRNA and tRNA, and also identifies about a dozen tRNAs clustering together with miRNA. Most of these putative Dicer-processed tRNAs, including eight cases reported to generate products with miRNA-like features in literature, exhibit read blocks distinguished by precise start position of reads.

AVAILABILITY

The program deepBlockAlign is available as source code from http://rth.dk/resources/dba/.

CONTACT

gorodkin@rth.dk; studla@bioinf.uni-leipzig.de

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Optimizing a widely used protein structure alignment measure in expected polynomial time

Protein structure alignment is an important tool in many biological applications, such as protein evolution studies, protein structure modeling, and structure-based, computer-aided drug design. Protein structure alignment is also one of the most challenging problems in computational molecular biology, due to an infinite number of possible spatial orientations of any two protein structures. We study one of the most commonly used measures of pairwise protein structure similarity, defined as the number of pairs of atoms in two proteins that can be superimposed under a predefined distance cutoff. We prove that the expected running time of a recently published algorithm for optimizing this (and some other, derived measures of protein structure similarity) is polynomial.

On complexity of protein structure alignment problem under distance constraint

We study the well known LCP (Largest Common Point-Set) under Bottleneck Distance Problem. Given two proteins a and b (as sequences of points in 3D space) and a distance cutoff σ, the goal is to find a spatial superposition and an alignment that maximizes the number of pairs of points from a and b that can be fit under the distance σ from each other. The best to date algorithms for approximate and exact solution to this problem run in time O(n^8) and O(n^32), respectively, where n represents the protein length. This work improves the runtime of the approximation algorithm and the algorithm for absolute optimum for both order-dependent and order-independent alignments. More specifically, our algorithms for near-optimal and optimal sequential alignments run in time O(^7 log n) and O(n^14 log n), respectively. For non-sequential alignments, corresponding running times are O(n^7.5) and O(n^14.5).

A spectral approach to protein structure alignment

A new intrinsic geometry based on a spectral analysis is used to motivate methods for aligning protein folds. The geometry is induced by the fact that a distance matrix can be scaled so that its eigenvalues are positive. We provide a mathematically rigorous development of the intrinsic geometry underlying our spectral approach and use it to motivate two alignment algorithms. The first uses eigenvalues alone and dynamic programming to quickly compute a fold alignment. Family identification results are reported for the Skolnick40 and Proteus300 data sets. The second algorithm extends our spectral method by iterating between our intrinsic geometry and the 3D geometry of a fold to make high-quality alignments. Results and comparisons are reported for several difficult fold alignments. The second algorithm's ability to correctly identify fold families in the Skolnick40 and Proteus300 data sets is also established.

Maximum contact map overlap revisited

Among the measures for quantifying the similarity between three-dimensional (3D) protein structures, maximum contact map overlap (CMO) received sustained attention during the past decade. Despite this, the known algorithms exhibit modest performance and are not applicable for large-scale comparison. This article offers a clear advance in this respect. We present a new integer programming model for CMO and propose an exact branch-and-bound algorithm with bounds obtained by a novel Lagrangian relaxation. The efficiency of the approach is demonstrated on a popular small benchmark (Skolnick set, 40 domains). On this set, our algorithm significantly outperforms the best existing exact algorithms. Many hard CMO instances have been solved for the first time. To further assess our approach, we constructed a large-scale set of 300 protein domains. Computing the similarity measure for any of the 44850 pairs, we obtained a classification in excellent agreement with SCOP. Supplementary Material is available at www.liebertonline.com/cmb.

Antilope--a Lagrangian relaxation approach to the de novo peptide sequencing problem

Peptide sequencing from mass spectrometry data is a key step in proteome research. Especially de novo sequencing, the identification of a peptide from its spectrum alone, is still a challenge even for state-of-the-art algorithmic approaches. In this paper, we present ANTILOPE, a new fast and flexible approach based on mathematical programming. It builds on the spectrum graph model and works with a variety of scoring schemes. ANTILOPE combines Lagrangian relaxation for solving an integer linear programming formulation with an adaptation of Yen’s k shortest paths algorithm. It shows a significant improvement in running time compared to mixed integer optimization and performs at the same speed like other state-of-the-art tools. We also implemented a generic probabilistic scoring scheme that can be trained automatically for a data set of annotated spectra and is independent of the mass spectrometer type. Evaluations on benchmark data show that ANTILOPE is competitive to the popular state-of-the-art programs PepNovo and NovoHMM both in terms of runtime and accuracy. Furthermore, it offers increased flexibility in the number of considered ion types. ANTILOPE will be freely available as part of the open source proteomics library OpenMS.

Fast and accurate protein substructure searching with simulated annealing and GPUs

BACKGROUND

Searching a database of protein structures for matches to a query structure, or occurrences of a structural motif, is an important task in structural biology and bioinformatics. While there are many existing methods for structural similarity searching, faster and more accurate approaches are still required, and few current methods are capable of substructure (motif) searching.

RESULTS

We developed an improved heuristic for tableau-based protein structure and substructure searching using simulated annealing, that is as fast or faster and comparable in accuracy, with some widely used existing methods. Furthermore, we created a parallel implementation on a modern graphics processing unit (GPU).

CONCLUSIONS

The GPU implementation achieves up to 34 times speedup over the CPU implementation of tableau-based structure search with simulated annealing, making it one of the fastest available methods. To the best of our knowledge, this is the first application of a GPU to the protein structural search problem.

Fast overlapping of protein contact maps by alignment of eigenvectors

MOTIVATION

Searching for structural similarity is a key issue of protein functional annotation. The maximum contact map overlap (CMO) is one of the possible measures of protein structure similarity. Exact and approximate methods known to optimize the CMO are computationally expensive and this hampers their applicability to large-scale comparison of protein structures.

RESULTS

In this article, we describe a heuristic algorithm (Al-Eigen) for finding a solution to the CMO problem. Our approach relies on the approximation of contact maps by eigendecomposition. We obtain good overlaps of two contact maps by computing the optimal global alignment of few principal eigenvectors. Our algorithm is simple, fast and its running time is independent of the amount of contacts in the map. Experimental testing indicates that the algorithm is comparable to exact CMO methods in terms of the overlap quality, to structural alignment methods in terms of structure similarity detection and it is fast enough to be suited for large-scale comparison of protein structures. Furthermore, our preliminary tests indicates that it is quite robust to noise, which makes it suitable for structural similarity detection also for noisy and incomplete contact maps.

AVAILABILITY

Available at http://bioinformatics.cs.unibo.it/Al-Eigen.

A fast mathematical programming procedure for simultaneous fitting of assembly components into cryoEM density maps

MOTIVATION

Single-particle cryo electron microscopy (cryoEM) typically produces density maps of macromolecular assemblies at intermediate to low resolution (approximately 5-30 A). By fitting high-resolution structures of assembly components into these maps, pseudo-atomic models can be obtained. Optimizing the quality-of-fit of all components simultaneously is challenging due to the large search space that makes the exhaustive search over all possible component configurations computationally unfeasible.

RESULTS

We developed an efficient mathematical programming algorithm that simultaneously fits all component structures into an assembly density map. The fitting is formulated as a point set matching problem involving several point sets that represent component and assembly densities at a reduced complexity level. In contrast to other point matching algorithms, our algorithm is able to match multiple point sets simultaneously and not only based on their geometrical equivalence, but also based on the similarity of the density in the immediate point neighborhood. In addition, we present an efficient refinement method based on the Iterative Closest Point registration algorithm. The integer quadratic programming method generates an assembly configuration in a few seconds. This efficiency allows the generation of an ensemble of candidate solutions that can be assessed by an independent scoring function. We benchmarked the method using simulated density maps of 11 protein assemblies at 20 A, and an experimental cryoEM map at 23.5 A resolution. Our method was able to generate assembly structures with root-mean-square errors <6.5 A, which have been further reduced to <1.8 A by the local refinement procedure.

AVAILABILITY

The program is available upon request as a Matlab code package.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics Online.

Optimal contact definition for reconstruction of contact maps

Background

Contact maps have been extensively used as a simplified representation of protein structures. They capture most important features of a protein's fold, being preferred by a number of researchers for the description and study of protein structures. Inspired by the model's simplicity many groups have dedicated a considerable amount of effort towards contact prediction as a proxy for protein structure prediction. However a contact map's biological interest is subject to the availability of reliable methods for the 3-dimensional reconstruction of the structure.

Results

We use an implementation of the well-known distance geometry protocol to build realistic protein 3-dimensional models from contact maps, performing an extensive exploration of many of the parameters involved in the reconstruction process. We try to address the questions: a) to what accuracy does a contact map represent its corresponding 3D structure, b) what is the best contact map representation with regard to reconstructability and c) what is the effect of partial or inaccurate contact information on the 3D structure recovery. Our results suggest that contact maps derived from the application of a distance cutoff of 9 to 11Å around the C_β atoms constitute the most accurate representation of the 3D structure. The reconstruction process does not provide a single solution to the problem but rather an ensemble of conformations that are within 2Å RMSD of the crystal structure and with lower values for the pairwise average ensemble RMSD. Interestingly it is still possible to recover a structure with partial contact information, although wrong contacts can lead to dramatic loss in reconstruction fidelity.

Conclusions

Thus contact maps represent a valid approximation to the structures with an accuracy comparable to that of experimental methods. The optimal contact definitions constitute key guidelines for methods based on contact maps such as structure prediction through contacts and structural alignments based on maximum contact map overlap.

Optimization techniques in molecular structure and function elucidation

This paper discusses recent optimization approaches to the protein side-chain prediction problem, protein structural alignment, and molecular structure determination from X-ray diffraction measurements. The machinery employed to solve these problems has included algorithms from linear programming, dynamic programming, combinatorial optimization, and mixed-integer nonlinear programming. Many of these problems are purely continuous in nature. Yet, to this date, they have been approached mostly via combinatorial optimization algorithms that are applied to discrete approximations. The main purpose of the paper is to offer an introduction and motivate further systems approaches to these problems.

Evaluating protein similarity from coarse structures

To unscramble the relationship between protein function and protein structure, it is essential to assess the protein similarity from different aspects. Although many methods have been proposed for protein structure alignment or comparison, alternative similarity measures are still strongly demanded due to the requirement of fast screening and query in large-scale structure databases. In this paper, we first formulate a novel representation of a protein structure, i.e., Feature Sequence of Surface (FSS). Then, a new score scheme is developed to measure the similarity between two representations. To verify the proposed method, numerical experiments are conducted in four different protein data sets. We also classify SARS coronavirus to verify the effectiveness of the new method. Furthermore, preliminary results of fast classification of the whole CATH v2.5.1 database based on the new macrostructure similarity are given as a pilot study. We demonstrate that the proposed approach to measure the similarities between protein structures is simple to implement, computationally efficient, and surprisingly fast. In addition, the method itself provides a new and quantitative tool to view a protein structure.

Algorithms for optimal protein structure alignment

MOTIVATION

Structural alignment is an important tool for understanding the evolutionary relationships between proteins. However, finding the best pairwise structural alignment is difficult, due to the infinite number of possible superpositions of two structures. Unlike the sequence alignment problem, which has a polynomial time solution, the structural alignment problem has not been even classified as solvable.

RESULTS

We study one of the most widely used measures of protein structural similarity, defined as the number of pairs of residues in two proteins that can be superimposed under a predefined distance cutoff. We prove that, for any two proteins, this measure can be optimized for all but finitely many distance cutoffs. Our method leads to a series of algorithms for optimizing other structure similarity measures, including the measures commonly used in protein structure prediction experiments. We also present a polynomial time algorithm for finding a near-optimal superposition of two proteins. Aside from having a relatively low cost, the algorithm for near-optimal solution returns a superposition of provable quality. In other words, the difference between the score of the returned superposition and the score of an optimal superposition can be explicitly computed and used to determine whether the returned superposition is, in fact, the best superposition.

CONTACT

poleksic@cs.uni.edu

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

A parsimony approach to biological pathway reconstruction/inference for genomes and metagenomes

A common biological pathway reconstruction approach -- as implemented by many automatic biological pathway services (such as the KAAS and RAST servers) and the functional annotation of metagenomic sequences -- starts with the identification of protein functions or families (e.g., KO families for the KEGG database and the FIG families for the SEED database) in the query sequences, followed by a direct mapping of the identified protein families onto pathways. Given a predicted patchwork of individual biochemical steps, some metric must be applied in deciding what pathways actually exist in the genome or metagenome represented by the sequences. Commonly, and straightforwardly, a complete biological pathway can be identified in a dataset if at least one of the steps associated with the pathway is found. We report, however, that this naïve mapping approach leads to an inflated estimate of biological pathways, and thus overestimates the functional diversity of the sample from which the DNA sequences are derived. We developed a parsimony approach, called MinPath (Minimal set of Pathways), for biological pathway reconstructions using protein family predictions, which yields a more conservative, yet more faithful, estimation of the biological pathways for a query dataset. MinPath identified far fewer pathways for the genomes collected in the KEGG database -- as compared to the naïve mapping approach -- eliminating some obviously spurious pathway annotations. Results from applying MinPath to several metagenomes indicate that the common methods used for metagenome annotation may significantly overestimate the biological pathways encoded by microbial communities.

Tableau-based protein substructure search using quadratic programming

Background

Searching for proteins that contain similar substructures is an important task in structural biology. The exact solution of most formulations of this problem, including a recently published method based on tableaux, is too slow for practical use in scanning a large database.

Results

We developed an improved method for detecting substructural similarities in proteins using tableaux. Tableaux are compared efficiently by solving the quadratic program (QP) corresponding to the quadratic integer program (QIP) formulation of the extraction of maximally-similar tableaux. We compare the accuracy of the method in classifying protein folds with some existing techniques.

Conclusion

We find that including constraints based on the separation of secondary structure elements increases the accuracy of protein structure search using maximally-similar subtableau extraction, to a level where it has comparable or superior accuracy to existing techniques. We demonstrate that our implementation is able to search a structural database in a matter of hours on a standard PC.

A new graph-based method for pairwise global network alignment

BACKGROUND

In addition to component-based comparative approaches, network alignments provide the means to study conserved network topology such as common pathways and more complex network motifs. Yet, unlike in classical sequence alignment, the comparison of networks becomes computationally more challenging, as most meaningful assumptions instantly lead to NP-hard problems. Most previous algorithmic work on network alignments is heuristic in nature.

RESULTS

We introduce the graph-based maximum structural matching formulation for pairwise global network alignment. We relate the formulation to previous work and prove NP-hardness of the problem. Based on the new formulation we build upon recent results in computational structural biology and present a novel Lagrangian relaxation approach that, in combination with a branch-and-bound method, computes provably optimal network alignments. The Lagrangian algorithm alone is a powerful heuristic method, which produces solutions that are often near-optimal and - unlike those computed by pure heuristics - come with a quality guarantee.

CONCLUSION

Computational experiments on the alignment of protein-protein interaction networks and on the classification of metabolic subnetworks demonstrate that the new method is reasonably fast and has advantages over pure heuristics. Our software tool is freely available as part of the LISA library.

A simple and fast heuristic for protein structure comparison

Background

Protein structure comparison is a key problem in bioinformatics. There exist several methods for doing protein comparison, being the solution of the Maximum Contact Map Overlap problem (MAX-CMO) one of the alternatives available. Although this problem may be solved using exact algorithms, researchers require approximate algorithms that obtain good quality solutions using less computational resources than the formers.

Results

We propose a variable neighborhood search metaheuristic for solving MAX-CMO. We analyze this strategy in two aspects: 1) from an optimization point of view the strategy is tested on two different datasets, obtaining an error of 3.5%(over 2702 pairs) and 1.7% (over 161 pairs) with respect to optimal values; thus leading to high accurate solutions in a simpler and less expensive way than exact algorithms; 2) in terms of protein structure classification, we conduct experiments on three datasets and show that is feasible to detect structural similarities at SCOP's family and CATH's architecture levels using normalized overlap values. Some limitations and the role of normalization are outlined for doing classification at SCOP's fold level.

Conclusion

We designed, implemented and tested.a new tool for solving MAX-CMO, based on a well-known metaheuristic technique. The good balance between solution's quality and computational effort makes it a valuable tool. Moreover, to the best of our knowledge, this is the first time the MAX-CMO measure is tested at SCOP's fold and CATH's architecture levels with encouraging results.

Software is available for download at .

ProCKSI: a decision support system for Protein (structure) Comparison, Knowledge, Similarity and Information

Background

We introduce the decision support system for Protein (Structure) Comparison, Knowledge, Similarity and Information (ProCKSI). ProCKSI integrates various protein similarity measures through an easy to use interface that allows the comparison of multiple proteins simultaneously. It employs the Universal Similarity Metric (USM), the Maximum Contact Map Overlap (MaxCMO) of protein structures and other external methods such as the DaliLite and the TM-align methods, the Combinatorial Extension (CE) of the optimal path, and the FAST Align and Search Tool (FAST). Additionally, ProCKSI allows the user to upload a user-defined similarity matrix supplementing the methods mentioned, and computes a similarity consensus in order to provide a rich, integrated, multicriteria view of large datasets of protein structures.

Results

We present ProCKSI's architecture and workflow describing its intuitive user interface, and show its potential on three distinct test-cases. In the first case, ProCKSI is used to evaluate the results of a previous CASP competition, assessing the similarity of proposed models for given targets where the structures could have a large deviation from one another. To perform this type of comparison reliably, we introduce a new consensus method. The second study deals with the verification of a classification scheme for protein kinases, originally derived by sequence comparison by Hanks and Hunter, but here we use a consensus similarity measure based on structures. In the third experiment using the Rost and Sander dataset (RS126), we investigate how a combination of different sets of similarity measures influences the quality and performance of ProCKSI's new consensus measure. ProCKSI performs well with all three datasets, showing its potential for complex, simultaneous multi-method assessment of structural similarity in large protein datasets. Furthermore, combining different similarity measures is usually more robust than relying on one single, unique measure.

Conclusion

Based on a diverse set of similarity measures, ProCKSI computes a consensus similarity profile for the entire protein set. All results can be clustered, visualised, analysed and easily compared with each other through a simple and intuitive interface.

ProCKSI is publicly available at for academic and non-commercial use.

A Reduction-Based Exact Algorithm for the Contact Map Overlap Problem

Aligning proteins based on their structural similarity is a fundamental problem in molecular biology with applications in many settings, including structure classification, database search, function prediction, and assessment of folding prediction methods. Structural alignment can be done via several methods, including contact map overlap (CMO) maximization that aligns proteins in a way that maximizes the number of common residue contacts. In this paper, we develop a reduction-based exact algorithm for the CMO problem. Our approach solves CMO directly rather than after transformation to other combinatorial optimization problems. We exploit the mathematical structure of the problem in order to develop a number of efficient lower bounding, upper bounding, and reduction schemes. Computational experiments demonstrate that our algorithm runs significantly faster than existing exact algorithms and solves some hard CMO instances that were not solved in the past. In addition, the algorithm produces protein clusters that are in excellent agreement with the SCOP classification. An implementation of our algorithm is accessible as an on-line server at http://eudoxus.scs.uiuc.edu/cmos/cmos.html.

A Parameterized Algorithm for Protein Structure Alignment

This paper proposes a parameterized polynomial time approximation scheme (PTAS) for aligning two protein structures, in the case where one protein structure is represented by a contact map graph and the other by a contact map graph or a distance matrix. If the sequential order of alignment is not required, the time complexity is polynomial in the protein size and exponential with respect to two parameters D(u)/D(l) and D(c)/D(l), which usually can be treated as constants. In particular, D(u) is the distance threshold determining if two residues are in contact or not, D(c) is the maximally allowed distance between two matched residues after two proteins are superimposed, and D(l) is the minimum inter-residue distance in a typical protein. This result clearly demonstrates that the computational hardness of the contact map based protein structure alignment problem is related not to protein size but to several parameters modeling the problem. The result is achieved by decomposing the protein structure using tree decomposition and discretizing the rigid-body transformation space. Preliminary experimental results indicate that on a Linux PC, it takes from ten minutes to one hour to align two proteins with approximately 100 residues.

Projections for fast protein structure retrieval

BACKGROUND

In recent times, there has been an exponential rise in the number of protein structures in databases e.g. PDB. So, design of fast algorithms capable of querying such databases is becoming an increasingly important research issue. This paper reports an algorithm, motivated from spectral graph matching techniques, for retrieving protein structures similar to a query structure from a large protein structure database. Each protein structure is specified by the 3D coordinates of residues of the protein. The algorithm is based on a novel characterization of the residues, called projections, leading to a similarity measure between the residues of the two proteins. This measure is exploited to efficiently compute the optimal equivalences.

RESULTS

Experimental results show that, the current algorithm outperforms the state of the art on benchmark datasets in terms of speed without losing accuracy. Search results on SCOP 95% nonredundant database, for fold similarity with 5 proteins from different SCOP classes show that the current method performs competitively with the standard algorithm CE. The algorithm is also capable of detecting non-topological similarities between two proteins which is not possible with most of the state of the art tools like Dali.

Connectivity independent protein-structure alignment: a hierarchical approach

Background

Protein-structure alignment is a fundamental tool to study protein function, evolution and model building. In the last decade several methods for structure alignment were introduced, but most of them ignore that structurally similar proteins can share the same spatial arrangement of secondary structure elements (SSE) but differ in the underlying polypeptide chain connectivity (non-sequential SSE connectivity).

Results

We perform protein-structure alignment using a two-level hierarchical approach implemented in the program GANGSTA. On the first level, pair contacts and relative orientations between SSEs (i.e. α-helices and β-strands) are maximized with a genetic algorithm (GA). On the second level residue pair contacts from the best SSE alignments are optimized. We have tested the method on visually optimized structure alignments of protein pairs (pairwise mode) and for database scans. For a given protein structure, our method is able to detect significant structural similarity of functionally important folds with non-sequential SSE connectivity. The performance for structure alignments with strictly sequential SSE connectivity is comparable to that of other structure alignment methods.

Conclusion

As demonstrated for several applications, GANGSTA finds meaningful protein-structure alignments independent of the SSE connectivity. GANGSTA is able to detect structural similarity of protein folds that are assigned to different superfamilies but nevertheless possess similar structures and perform related functions, even if these proteins differ in SSE connectivity.

MUSTANG: a multiple structural alignment algorithm

Multiple structural alignment is a fundamental problem in structural genomics. In this article, we define a reliable and robust algorithm, MUSTANG (MUltiple STructural AligNment AlGorithm), for the alignment of multiple protein structures. Given a set of protein structures, the program constructs a multiple alignment using the spatial information of the C(alpha) atoms in the set. Broadly based on the progressive pairwise heuristic, this algorithm gains accuracy through novel and effective refinement phases. MUSTANG reports the multiple sequence alignment and the corresponding superposition of structures. Alignments generated by MUSTANG are compared with several handcurated alignments in the literature as well as with the benchmark alignments of 1033 alignment families from the HOMSTRAD database. The performance of MUSTANG was compared with DALI at a pairwise level, and with other multiple structural alignment tools such as POSA, CE-MC, MALECON, and MultiProt. MUSTANG performs comparably to popular pairwise and multiple structural alignment tools for closely related proteins, and performs more reliably than other multiple structural alignment methods on hard data sets containing distantly related proteins or proteins that show conformational changes.

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.

Evolution of Structural Shape in Bacterial Globin-Related Proteins

The globin family of proteins has a characteristic structural pattern of helix interactions that nonetheless exhibits some variation. A simplified model for globin structural evolution was developed in which protein shape evolved by random change of contacts between helices. A conserved globin domain of 15 bacterial proteins representing four structural families was studied. Using a parsimony approach ancestral structural states could be reconstructed. The distribution of number of contact changes per site for a fixed topology tree fit a gamma distribution. Homoplasy was high, with multiple changes per site and no support for an invariant class of residue-residue contacts. Contacts changed more slowly than sequence. A phylogenetic reconstruction using a distance measure based on the proportion of shared contacts was generally consistent with a sequence-based phylogeny but not highly resolved. Contact pattern convergence between members of different globin family proteins could not be detected. Simulation studies indicated the convergence test was sensitive enough to have detected convergence involving only 10% of the contacts, suggesting a limit on the extent of selection for a specific contact pattern. Contact site methods may provide additional approaches to study the relationship between protein structure and sequence evolution.

Automatic 3D protein structure classification without structural alignment

In this paper, we present a new scheme named ProtClass for automatic classification of three-dimensional (3D) protein structures. It is a dedicated and unified multiclass classification scheme. Neither detailed structural alignment nor multiple binary classifications are required in this scheme. We adopt a nearest neighbor-based classification strategy. We use a filter-and-refine scheme. In the first step, we filter out the improbable answers using the precalculated parameters from the training data. In the second, we perform a relatively more detailed nearest neighbor search on the remaining answers. We use very concise and effective encoding schemes of the 3D protein structures in both steps. We compare our proposed method against two other dedicated protein structure classification schemes, namely SGM and CPMine. The experimental results show that ProtClass is slightly better in accuracy than SGM and much faster. In comparison with CPMine, ProtClass is much more accurate, while their running times are about the same. We also compare ProtClass against a structural alignment-based classification scheme named DALI, which is found to be more accurate, but extremely slow. The software is available upon request from the authors. The supplementary information on ProtClass method can be found at: http://xena1.ddns.comp.nus.edu.sg/ approximately genesis/PClass.htm.