A random graph approach to NMR sequential assignment.

Nuclear magnetic resonance (NMR) spectroscopy allows scientists to study protein structure, dynamics and interactions in solution. A necessary first step for such applications is determining the resonance assignment, mapping spectral data to atoms and residues in the primary sequence. Automated resonance assignment algorithms rely on information regarding connectivity (e.g., through-bond atomic interactions) and amino acid type, typically using the former to determine strings of connected residues and the latter to map those strings to positions in the primary sequence. Significant ambiguity exists in both connectivity and amino acid type information. This paper focuses on the information content available in connectivity alone and develops a novel random-graph theoretic framework and algorithm for connectivity-driven NMR sequential assignment. Our random graph model captures the structure of chemical shift degeneracy, a key source of connectivity ambiguity. We then give a simple and natural randomized algorithm for finding optimal assignments as sets of connected fragments in NMR graphs. The algorithm naturally and efficiently reuses substrings while exploring connectivity choices; it overcomes local ambiguity by enforcing global consistency of all choices. By analyzing our algorithm under our random graph model, we show that it can provably tolerate relatively large ambiguity while still giving expected optimal performance in polynomial time. We present results from practical applications of the algorithm to experimental datasets from a variety of proteins and experimental set-ups. We demonstrate that our approach is able to overcome significant noise and local ambiguity in identifying significant fragments of sequential assignments.     

Speed improvements of peptide-spectrum matching using single-instruction multiple-data instructions

Peptide-spectrum matching is one of the most time-consuming portion of the database search method for assignment of tandem mass spectra to peptides. In this study, we develop a parallel algorithm for peptide-spectrum matching using Single-Instruction Multiple Data (SIMD) instructions. Unlike other parallel algorithms in peptide-spectrum matching, our algorithm parallelizes the computation of matches between a single spectrum and a given peptide sequence from the database. It also significantly reduces the number of comparison operations. Extra improvements are obtained by using SIMD instructions to avoid conditional branches and unnecessary memory access within the algorithm. The implementation of the developed algorithm is based on the Streaming SIMD Extensions technology that is embedded in most Intel microprocessors. Similar technology also exists in other modern microprocessors. A simulation shows that the developed algorithm achieves an 18-fold speedup over the previous version of Real-Time Peptide-Spectrum Matching algorithm [F. X. Wu et al., Rapid Commun. Mass Sepctrom. 2006, 20, 1199-1208]. Therefore, the developed algorithm can be employed to develop real-time control methods for MS/MS.     

Efficient large-scale protein sequence comparison and gene matching to identify orthologs and co-orthologs

Broadly, computational approaches for ortholog assignment is a three steps process: (i) identify all putative homologs between the genomes, (ii) identify gene anchors and (iii) link anchors to identify best gene matches given their order and context. In this article, we engineer two methods to improve two important aspects of this pipeline [specifically steps (ii) and (iii)]. First, computing sequence similarity data [step (i)] is a computationally intensive task for large sequence sets, creating a bottleneck in the ortholog assignment pipeline. We have designed a fast and highly scalable sort-join method (afree) based on k-mer counts to rapidly compare all pairs of sequences in a large protein sequence set to identify putative homologs. Second, availability of complex genomes containing large gene families with prevalence of complex evolutionary events, such as duplications, has made the task of assigning orthologs and co-orthologs difficult. Here, we have developed an iterative graph matching strategy where at each iteration the best gene assignments are identified resulting in a set of orthologs and co-orthologs. We find that the afree algorithm is faster than existing methods and maintains high accuracy in identifying similar genes. The iterative graph matching strategy also showed high accuracy in identifying complex gene relationships. Standalone afree available from http://vbc.med.monash.edu.au/～kmahmood/afree. EGM2, complete ortholog assignment pipeline (including afree and the iterative graph matching method) available from http://vbc.med.monash.edu.au/～kmahmood/EGM2.     

Peptide sequence tag-based blind identification of post-translational modifications with point process model

An important but difficult problem in proteomics is the identification of post-translational modifications (PTMs) in a protein. In general, the process of PTM identification by aligning experimental spectra with theoretical spectra from peptides in a peptide database is very time consuming and may lead to high false positive rate. In this paper, we introduce a new approach that is both efficient and effective for blind PTM identification. Our work consists of the following phases. First, we develop a novel tree decomposition based algorithm that can efficiently generate peptide sequence tags (PSTs) from an extended spectrum graph. Sequence tags are selected from all maximum weighted antisymmetric paths in the graph and their reliabilities are evaluated with a score function. An efficient deterministic finite automaton (DFA) based model is then developed to search a peptide database for candidate peptides by using the generated sequence tags. Finally, a point process model-an efficient blind search approach for PTM identification, is applied to report the correct peptide and PTMs if there are any. Our tests on 2657 experimental tandem mass spectra and 2620 experimental spectra with one artificially added PTM show that, in addition to high efficiency, our ab-initio sequence tag selection algorithm achieves better or comparable accuracy to other approaches. Database search results show that the sequence tags of lengths 3 and 4 filter out more than 98.3% and 99.8% peptides respectively when applied to a yeast peptide database. With the dramatically reduced search space, the point process model achieves significant improvement in accuracy as well. AVAILABILITY: The software is available upon request.     

Path matching and graph matching in biological networks.

We develop algorithms for the following path matching and graph matching problems: (i) given a query path p and a graph G, find a path p' that is most similar to p in G; (ii) given a query graph G (0) and a graph G, find a graph G (0)' that is most similar to G (0) in G. In these problems, p and G (0) represent a given substructure of interest to a biologist, and G represents a large network in which the biologist desires to find a related substructure. These algorithms allow the study of common substructures in biological networks in order to understand how these networks evolve both within and between organisms. We reduce the path matching problem to finding a longest weighted path in a directed acyclic graph and show that the problem of finding top k suboptimal paths can be solved in polynomial time. This is in contrast with most previous approaches that used exponential time algorithms to find simple paths which are practical only when the paths are short. We reduce the graph matching problem to finding highest scoring subgraphs in a graph and give an exact algorithm to solve the problem when the query graph G (0) is of moderate size. This eliminates the need for less accurate heuristic or randomized algorithms.We show that our algorithms are able to extract biologically meaningful pathways from protein interaction networks in the DIP database and metabolic networks in the KEGG database. Software programs implementing these techniques (PathMatch and GraphMatch) are available at http://faculty.cs.tamu.edu/shsze/pathmatch and http://faculty.cs.tamu.edu/shsze/graphmatch.     

Computational assignment of protein backbone NMR peaks by efficient bounding and filtering

NMR resonance assignment is one of the key steps in solving an NMR protein structure. The assignment process links resonance peaks to individual residues of the target protein sequence, providing the prerequisite for establishing intra- and inter-residue spatial relationships between atoms. The assignment process is tedious and time-consuming, which could take many weeks. Though there exist a number of computer programs to assist the assignment process, many NMR labs are still doing the assignments manually to ensure quality. This paper presents a new computational method based on the combination of a suite of algorithms for automating the assignment process, particularly the process of backbone resonance peak assignment. We formulate the assignment problem as a constrained weighted bipartite matching problem. While the problem, in the most general situation, is NP-hard, we present an efficient solution based on a branch-and-bound algorithm with effective bounding techniques using two recently introduced approximation algorithms. We also devise a greedy filtering algorithm for reducing the search space. Our experimental results on 70 instances of (pseudo) real NMR data derived from 14 proteins demonstrate that the new solution runs much faster than a recently introduced (exhaustive) two-layer algorithm and recovers more correct peak assignments than the two-layer algorithm. Our result demonstrates that integrating different algorithms can achieve a good tradeoff between backbone assignment accuracy and computation time.     

An efficient randomized algorithm for contact-based NMR backbone resonance assignment

MOTIVATION: Backbone resonance assignment is a critical bottleneck in studies of protein structure, dynamics and interactions by nuclear magnetic resonance (NMR) spectroscopy. A minimalist approach to assignment, which we call 'contact-based', seeks to dramatically reduce experimental time and expense by replacing the standard suite of through-bond experiments with the through-space (nuclear Overhauser enhancement spectroscopy, NOESY) experiment. In the contact-based approach, spectral data are represented in a graph with vertices for putative residues (of unknown relation to the primary sequence) and edges for hypothesized NOESY interactions, such that observed spectral peaks could be explained if the residues were 'close enough'. Due to experimental ambiguity, several incorrect edges can be hypothesized for each spectral peak. An assignment is derived by identifying consistent patterns of edges (e.g. for alpha-helices and beta-sheets) within a graph and by mapping the vertices to the primary sequence. The key algorithmic challenge is to be able to uncover these patterns even when they are obscured by significant noise. RESULTS: This paper develops, analyzes and applies a novel algorithm for the identification of polytopes representing consistent patterns of edges in a corrupted NOESY graph. Our randomized algorithm aggregates simplices into polytopes and fixes inconsistencies with simple local modifications, called rotations, that maintain most of the structure already uncovered. In characterizing the effects of experimental noise, we employ an NMR-specific random graph model in proving that our algorithm gives optimal performance in expected polynomial time, even when the input graph is significantly corrupted. We confirm this analysis in simulation studies with graphs corrupted by up to 500% noise. Finally, we demonstrate the practical application of the algorithm on several experimental beta-sheet datasets. Our approach is able to eliminate a large majority of noise edges and to uncover large consistent sets of interactions. AVAILABILITY: Our algorithm has been implemented in the platform-independent Python code. The software can be freely obtained for academic use by request from the authors.     

Structured motifs search.

In this paper, we describe an algorithm for the localization of structured models, i.e. sequences of (simple) motifs and distance constraints. It basically combines standard pattern matching procedures with a constraint satisfaction solver, and it has the ability, not present in similar tools, to search for partial matches. A significant feature of our approach, especially in terms of efficiency for the application context, is that the (potentially) exponentially many solutions to the considered problem are represented in compact form as a graph. Moreover, the time and space necessary to build the graph are linear in the number of occurrences of the component patterns.     

Structure-based protein NMR assignments using native structural ensembles

An important step in NMR protein structure determination is the assignment of resonances and NOEs to corresponding nuclei. Structure-based assignment (SBA) uses a model structure ("template") for the target protein to expedite this process. Nuclear vector replacement (NVR) is an SBA framework that combines multiple sources of NMR data (chemical shifts, RDCs, sparse NOEs, amide exchange rates, TOCSY) and has high accuracy when the template is close to the target protein's structure (less than 2 A backbone RMSD). However, a close template may not always be available. We extend the circle of convergence of NVR for distant templates by using an ensemble of structures. This ensemble corresponds to the low-frequency perturbations of the given template and is obtained using normal mode analysis (NMA). Our algorithm assigns resonances and sparse NOEs using each of the structures in the ensemble separately, and aggregates the results using a voting scheme based on maximum bipartite matching. Experimental results on human ubiquitin, using four distant template structures show an increase in the assignment accuracy. Our algorithm also improves the robustness of NVR with respect to structural noise. We provide a confidence measure for each assignment using the percentage of the structures that agree on that assignment. We use this measure to assign a subset of the peaks with even higher accuracy. We further validate our algorithm on data for two additional proteins with NVR. We then show the general applicability of our approach by applying our NMA ensemble-based voting scheme to another SBA tool, MARS. For three test proteins with corresponding templates, including the 370-residue maltose binding protein, we increase the number of reliable assignments made by MARS. Finally, we show that our voting scheme is sound and optimal, by proving that it is a maximum likelihood estimator of the correct assignments.     

Parallel Clustering Algorithm for Large Data Sets with Applications in Bioinformatics

Large sets of bioinformatical data provide a challenge in time consumption while solving the cluster identification problem, and that is why a parallel algorithm is so needed for identifying dense clusters in a noisy background. Our algorithm works on a graph representation of the data set to be analyzed. It identifies clusters through the identification of densely intraconnected subgraphs. We have employed a minimum spanning tree (MST) representation of the graph and solve the cluster identification problem using this representation. The computational bottleneck of our algorithm is the construction of an MST of a graph, for which a parallel algorithm is employed. Our high-level strategy for the parallel MST construction algorithm is to first partition the graph, then construct MSTs for the partitioned subgraphs and auxiliary bipartite graphs based on the subgraphs, and finally merge these MSTs to derive an MST of the original graph. The computational results indicate that when running on 150 CPUs, our algorithm can solve a cluster identification problem on a data set with 1,000,000 data points almost 100 times faster than on single CPU, indicating that this program is capable of handling very large data clustering problems in an efficient manner. We have implemented the clustering algorithm as the software CLUMP.     

Distributed graph coloring: an approach based on the calling behavior of Japanese tree frogs

Graph coloring—also known as vertex coloring—considers the problem of assigning colors to the nodes of a graph such that adjacent nodes do not share the same color. The optimization version of the problem concerns the minimization of the number of colors used. In this paper we deal with the problem of finding valid graphs colorings in a distributed way, that is, by means of an algorithm that only uses local information for deciding the color of the nodes. The algorithm proposed in this paper is inspired by the calling behavior of Japanese tree frogs. Male frogs use their calls to attract females. Interestingly, groups of males that are located near each other desynchronize their calls. This is because female frogs are only able to correctly localize male frogs when their calls are not too close in time. The proposed algorithm makes use of this desynchronization behavior for the assignment of different colors to neighboring nodes. We experimentally show that our algorithm is very competitive with the current state of the art, using different sets of problem instances and comparing to one of the most competitive algorithms from the literature.     

An Efficient Algorithm for Mapping of Reads to a Genome Graph Using an Index Based on Hash Tables and Dynamic Programming

The problem of storage of the sequences of a number of closely related genomes and analysis of genome variations is considered. A genome graph with the structure of an acyclic directed graph is used to store matching sections of sequences and known variants. An algorithm for rapid mapping of reads to the genome graph is developed to align the individual nucleotide sequence fragments to the genome graph. The algorithm combines rapid searching using hash tables with the algorithm of dynamic programming and solves the problem of exponential growth in the number of paths on the graph. The implementation of the genome graph and the algorithm of the alignment of reads is developed. A comparison with the best-known programs with similar functionality is made.     

A CLIQUE algorithm using DNA computing techniques based on closed-circle DNA sequences

DNA computing has been applied in broad fields such as graph theory, finite state problems, and combinatorial problem. DNA computing approaches are more suitable used to solve many combinatorial problems because of the vast parallelism and high-density storage. The CLIQUE algorithm is one of the gird-based clustering techniques for spatial data. It is the combinatorial problem of the density cells. Therefore we utilize DNA computing using the closed-circle DNA sequences to execute the CLIQUE algorithm for the two-dimensional data. In our study, the process of clustering becomes a parallel bio-chemical reaction and the DNA sequences representing the marked cells can be combined to form a closed-circle DNA sequences. This strategy is a new application of DNA computing. Although the strategy is only for the two-dimensional data, it provides a new idea to consider the grids to be vertexes in a graph and transform the search problem into a combinatorial problem.     

Efficient and accurate construction of genetic linkage maps from the minimum spanning tree of a graph

Genetic linkage maps are cornerstones of a wide spectrum of biotechnology applications, including map-assisted breeding, association genetics, and map-assisted gene cloning. During the past several years, the adoption of high-throughput genotyping technologies has been paralleled by a substantial increase in the density and diversity of genetic markers. New genetic mapping algorithms are needed in order to efficiently process these large datasets and accurately construct high-density genetic maps. In this paper, we introduce a novel algorithm to order markers on a genetic linkage map. Our method is based on a simple yet fundamental mathematical property that we prove under rather general assumptions. The validity of this property allows one to determine efficiently the correct order of markers by computing the minimum spanning tree of an associated graph. Our empirical studies obtained on genotyping data for three mapping populations of barley (Hordeum vulgare), as well as extensive simulations on synthetic data, show that our algorithm consistently outperforms the best available methods in the literature, particularly when the input data are noisy or incomplete. The software implementing our algorithm is available in the public domain as a web tool under the name MSTmap.     

基于质粒DNA匹配问题的分子算法

给定无向图,图的最小极大匹配问题是寻找每条边都不相邻的最大集中的最小者,这个问题是著名的NP-完全问题.1994年Adleman博士首次提出用DNA计算解决NP-完全问题,以编码的DNA序列为运算对象,通过分子生物学的运算操作解决复杂的数学难题,使得NP-完全问题的求解可能得到解决.提出了基于质粒DNA的无向图的最大匹配问题的DNA分子生物算法,通过限制性内切酶的酶切和凝胶电泳完成解的产生和最终接的分离,依据分子生物学的实验手段,算法是有效并且可行的.     

Consensus genetic maps as median orders from inconsistent sources

A genetic map is an ordering of genetic markers calculated from a population of known lineage.While traditionally a map has been generated from a single population for each species, recently researchers have created maps from multiple populations. In the face of these new data, we address the need to find a consensus map--a map that combines the information from multiple partial and possibly inconsistent input maps. We model each input map as a partial order and formulate the consensus problem as finding a median partial order. Finding the median of multiple total orders (preferences or rankings)is a well studied problem in social choice. We choose to find the median using the weighted symmetric difference distance, a more general version of both the symmetric difference distance and the Kemeny distance. Finding a median order using this distance is NP-hard. We show that for our chosen weight assignment, a median order satisfies the positive responsiveness, extended Condorcet,and unanimity criteria. Our solution involves finding the maximum acyclic subgraph of a weighted directed graph.We present a method that dynamically switches between an exact branch and bound algorithm and a heuristic algorithm, and show that for real data from closely related organisms, an exact median can often be found.We present experimental results using seven populations of the crop plant Zea mays.     

An expectation/maximization nuclear vector replacement algorithm for automated NMR resonance assignments

We report an automated procedure for high-throughput NMR resonance assignment for a protein of known structure, or of an homologous structure. Our algorithm performs Nuclear Vector Replacement (NVR) by Expectation/Maximization (EM) to compute assignments. NVR correlates experimentally-measured NH residual dipolar couplings (RDCs) and chemical shifts to a given a priori whole-protein 3D structural model. The algorithm requires only uniform (15)N-labelling of the protein, and processes unassigned H(N)-(15)N HSQC spectra, H(N)-(15)N RDCs, and sparse H(N)-H(N) NOE's (d(NN)s). NVR runs in minutes and efficiently assigns the (H(N),(15)N) backbone resonances as well as the sparse d(NN)s from the 3D (15)N-NOESY spectrum, in O (n(3)) time. The algorithm is demonstrated on NMR data from a 76-residue protein, human ubiquitin, matched to four structures, including one mutant (homolog), determined either by X-ray crystallography or by different NMR experiments (without RDCs). NVR achieves an average assignment accuracy of over 99%. We further demonstrate the feasibility of our algorithm for different and larger proteins, using different combinations of real and simulated NMR data for hen lysozyme (129 residues) and streptococcal protein G (56 residues), matched to a variety of 3D structural models.     

Efficient algorithms for protein sequence design and the analysis of certain evolutionary fitness landscapes.

Protein sequence design is a natural inverse problem to protein structure prediction: given a target structure in three dimensions, we wish to design an amino acid sequence that is likely fold to it. A model of Sun, Brem, Chan, and Dill casts this problem as an optimization on a space of sequences of hydrophobic (H) and polar (P) monomers; the goal is to find a sequence that achieves a dense hydrophobic core with few solvent-exposed hydrophobic residues. Sun et al. developed a heuristic method to search the space of sequences, without a guarantee of optimality or near-optimality; Hart subsequently raised the computational tractability of constructing an optimal sequence in this model as an open question. Here we resolve this question by providing an efficient algorithm to construct optimal sequences; our algorithm has a polynomial running time, and performs very efficiently in practice. We illustrate the implementation of our method on structures drawn from the Protein Data Bank. We also consider extensions of the model to larger amino acid alphabets, as a way to overcome the limitations of the binary H/P alphabet. We show that for a natural class of arbitrarily large alphabets, it remains possible to design optimal sequences efficiently. Finally, we analyze some of the consequences of this sequence design model for the study of evolutionary fitness landscapes. A given target structure may have many sequences that are optimal in the model of Sun et al.; following a notion raised by the work of J. Maynard Smith, we can ask whether these optimal sequences are "connected" by successive point mutations. We provide a polynomial-time algorithm to decide this connectedness property, relative to a given target structure. We develop the algorithm by first solving an analogous problem expressed in terms of submodular functions, a fundamental object of study in combinatorial optimization.     

Ranking valid topologies of the secondary structure elements using a constraint graph

Electron cryo-microscopy is a fast advancing biophysical technique to derive three-dimensional structures of large protein complexes. Using this technique, many density maps have been generated at intermediate resolution such as 6-10 ? resolution. Although it is challenging to derive the backbone of the protein directly from such density maps, secondary structure elements such as helices and β-sheets can be computationally detected. Our work in this paper provides an approach to enumerate the top-ranked possible topologies instead of enumerating the entire population of the topologies. This approach is particularly practical for large proteins. We developed a directed weighted graph, the topology graph, to represent the secondary structure assignment problem. We prove that the problem of finding the valid topology with the minimum cost is NP hard. We developed an O(N(2)2(N)) dynamic programming algorithm to identify the topology with the minimum cost. The test of 15 proteins suggests that our dynamic programming approach is feasible to work with proteins of much larger size than we could before. The largest protein in the test contains 18 helical sticks detected from the density map out of 33 helices in the protein.