A fast algorithm for computing geodesic distances in tree space

Comparing and computing distances between phylogenetic trees are important biological problems, especially for models where edge lengths play an important role. The geodesic distance measure between two phylogenetic trees with edge lengths is the length of the shortest path between them in the continuous tree space introduced by Billera, Holmes, and Vogtmann. This tree space provides a powerful tool for studying and comparing phylogenetic trees, both in exhibiting a natural distance measure and in providing a euclidean-like structure for solving optimization problems on trees. An important open problem is to find a polynomial time algorithm for finding geodesics in tree space. This paper gives such an algorithm, which starts with a simple initial path and moves through a series of successively shorter paths until the geodesic is attained.     

An algorithm for efficient constrained mate selection

Background

Mate selection can be used as a framework to balance key technical, cost and logistical issues while implementing a breeding program at a tactical level. The resulting mating lists accommodate optimal contributions of parents to future generations, in conjunction with other factors such as progeny inbreeding, connection between herds, use of reproductive technologies, management of the genetic distribution of nominated traits, and management of allele/genotype frequencies for nominated QTL/markers.

Methods

This paper describes a mate selection algorithm that is widely used and presents an extension that makes it possible to apply constraints on certain matings, as dictated through a group mating permission matrix.

Results

This full algorithm leads to simpler applications, and to computing speed for the scenario tested, which is several hundred times faster than the previous strategy of penalising solutions that break constraints.

Conclusions

The much higher speed of the method presented here extends the use of mate selection and enables implementation in relatively large programs across breeding units.     

Approximate geodesic distances reveal biologically relevant structures in microarray data

MOTIVATION: Genome-wide gene expression measurements, as currently determined by the microarray technology, can be represented mathematically as points in a high-dimensional gene expression space. Genes interact with each other in regulatory networks, restricting the cellular gene expression profiles to a certain manifold, or surface, in gene expression space. To obtain knowledge about this manifold, various dimensionality reduction methods and distance metrics are used. For data points distributed on curved manifolds, a sensible distance measure would be the geodesic distance along the manifold. In this work, we examine whether an approximate geodesic distance measure captures biological similarities better than the traditionally used Euclidean distance. RESULTS: We computed approximate geodesic distances, determined by the Isomap algorithm, for one set of lymphoma and one set of lung cancer microarray samples. Compared with the ordinary Euclidean distance metric, this distance measure produced more instructive, biologically relevant, visualizations when applying multidimensional scaling. This suggests the Isomap algorithm as a promising tool for the interpretation of microarray data. Furthermore, the results demonstrate the benefit and importance of taking nonlinearities in gene expression data into account.     

An efficient algorithm for DNA fragment assembly in MapReduce

Fragment assembly is one of the most important problems of sequence assembly. Algorithms for DNA fragment assembly using de Bruijn graph have been widely used. These algorithms require a large amount of memory and running time to build the de Bruijn graph. Another drawback of the conventional de Bruijn approach is the loss of information. To overcome these shortcomings, this paper proposes a parallel strategy to construct de Bruijin graph. Its main characteristic is to avoid the division of de Bruijin graph. A novel fragment assembly algorithm based on our parallel strategy is implemented in the MapReduce framework. The experimental results show that the parallel strategy can effectively improve the computational efficiency and remove the memory limitations of the assembly algorithm based on Euler superpath. This paper provides a useful attempt to the assembly of large-scale genome sequence using Cloud Computing.     

An efficient algorithm for minimal primer set selection

SUMMARY: We have developed U-PRIMER, a primer design program, to compute a minimal primer set (MPS) for any given set of DNA sequences. The U-PRIMER algorithm, which uses automatic variable fixing and automatic redundant constraint elimination to tackle the binary integer programming problem associated with the MPS selection problem. The program has been tested successfully with 32 adipocyte development-related genes and 9 TB-specific genes to obtain their respective MPSs. AVAILABILITY: A free copy of U-PRIMER implemented in C++ programming language is available from http://www.u-vision-biotech.com     

An algorithm for efficient identification of branched metabolic pathways

This article presents a new graph-based algorithm for identifying branched metabolic pathways in multi-genome scale metabolic data. The term branched is used to refer to metabolic pathways between compounds that consist of multiple pathways that interact biochemically. A branched pathway may produce a target compound through a combination of linear pathways that split compounds into smaller ones, work in parallel with many compounds, and join compounds into larger ones. While branched metabolic pathways predominate in metabolic networks, most previous work has focused on identifying linear metabolic pathways. The ability to automatically identify branched pathways is important in applications that require a deeper understanding of metabolism, such as metabolic engineering and drug target identification. The algorithm presented in this article utilizes explicit atom tracking to identify linear metabolic pathways and then merges them together into branched metabolic pathways. We provide results on several well-characterized metabolic pathways that demonstrate that the new merging approach can efficiently find biologically relevant branched metabolic pathways.     

An efficient Z-score algorithm for assessing sequence alignments.

We describe an alternative method for scoring of the pairwise alignment of two biological sequences. Designed to overcome the bias due to the composition of the alignment, it measures the distance (in standard deviations) between the given alignment and the mean value of all other alignments that can be obtained by a permutation of either sequence. We demonstrate that the standard deviation can be calculated efficiently. By concentrating upon the ungapped case, the mean and standard deviation can be calculated exactly and in two steps, the first being O(N) time, where N is the length of the sequence, the second in a fixed number of calculations, i.e., in O(1) time. We argue that this statistic is a more consistent measure than a similarity score based upon a standard scoring matrix. Even in the ungapped case, the statistic proves in many cases to be more accurate than the commonly used (FASTA) (Pearson and Lipman, 1988) gapped Z-score in which the sequence is matched against a random sample of the database. We demonstrate the use of the POZ-score as a secondary filter which screens out several well-known types of false positive, reducing the amount of manual screening to be done by the biologist.     

An efficient algorithm for finding short approximate non-tandem repeats

We study the problem of approximate non-tandem repeat extraction. Given a long subject string S of length N over a finite alphabet Sigma and a threshold D, we would like to find all short substrings of S of length P that repeat with at most D differences, i.e., insertions, deletions, and mismatches. We give a careful theoretical characterization of the set of seeds (i.e., some maximal exact repeats) required by the algorithm, and prove a sublinear bound on their expected numbers. Using this result, we present a sub-quadratic algorithm for finding all short (i.e., of length O(log N)) approximate repeats. The running time of our algorithm is O(DN(3pow(epsilon)-1)log N), where epsilon = D/P and pow(epsilon) is an increasing, concave function that is 0 when epsilon = 0 and about 0.9 for DNA and protein sequences.     

GIGA: a simple,efficient algorithm for gene tree inference in the genomic age

Background  

Phylogenetic relationships between genes are not only of theoretical interest: they enable us to learn about human genes through the experimental work on their relatives in numerous model organisms from bacteria to fruit flies and mice. Yet the most commonly used computational algorithms for reconstructing gene trees can be inaccurate for numerous reasons, both algorithmic and biological. Additional information beyond gene sequence data has been shown to improve the accuracy of reconstructions, though at great computational cost.     

LMProt: an efficient algorithm for Monte Carlo sampling of protein conformational space

A new and efficient Monte Carlo algorithm for sampling protein configurations in the continuous space is presented; the efficiency of this algorithm, named Local Moves for Proteins (LMProt), was compared to other alternative algorithms. For this purpose, we used an intrachain interaction energy function that is proportional to the root mean square deviation (rmsd) with respect to alpha-carbons from native structures of real proteins. For phantom chains, the LMProt method is approximately 10(4) and 20 times faster than the algorithms Thrashing (no local moves) and Sevenfold Way (local moves), respectively. Additionally, the LMProt was tested for real chains (excluded-volume all-atoms model); proteins 5NLL (138 residues) and 1BFF (129 residues) were used to determine the folding success xi as a function of the number eta of residues involved in the chain movements, and as a function of the maximum amplitude of atomic displacement delta r(max). Our results indicate that multiple local moves associated with relative chain flexibility, controlled by appropriate adjustments for eta and delta r(max), are essential for configurational search efficiency.     

An efficient algorithm for optimizing whole genome alignment with noise

MOTIVATION: This paper is concerned with algorithms for aligning two whole genomes so as to identify regions that possibly contain conserved genes. Motivated by existing heuristic-based software tools, we initiate the study of an optimization problem that attempts to uncover conserved genes with a global concern. Another interesting feature in our formulation is the tolerance of noise, which also complicates the optimization problem. A brute-force approach takes time exponential in the noise level. RESULTS: We show how an insight into the optimization structure can lead to a drastic improvement in the time and space requirement [precisely, to O(k2n2) and O(k2n), respectively, where n is the size of the input and k is the noise level]. The reduced space requirement allows us to implement the new algorithm, called MaxMinCluster, on a PC. It is exciting to see that when tested with different real data sets, MaxMinCluster consistently uncovers a high percentage of conserved genes that have been published by GenBank. Its performance is indeed favorably compared to MUMmer (perhaps the most popular software tool for uncovering conserved genes in a whole-genome scale). AVAILABILITY: The source code is available from the website http://www.csis.hku.hk/~colly/maxmincluster/ detailed proof of the propositions can also be found there.     

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.     

An efficient algorithm after ungapped analysis in BLAST.

Basic Local Alignment Search Tool (BLAST) is a popular tool used for determining the patterns in genomic sequences. The algorithm of BLAST has gone for various changes from time to time. One third of the time is taken by BLAST to perform the gapped analysis on the sequences. An efficient algorithm has been presented that employs a new approach for curtailing the amount of sequences that proceed for gapped alignment. So this method will work after the ungapped alignment process is over. This works because of the fact that it is not necessary to perform gapped alignment for all the sequences that are coming from ungapped analysis. There is a significant increase in speed of the alignment process without compromising on the sensitivity of the result.     

Scatter-Gather-Merge: An efficient star-join query processing algorithm for data-parallel frameworks

A data-parallel framework is very attractive for large-scale data processing since it enables such an application to easily process a huge amount of data on commodity machines. MapReduce, a popular data-parallel framework, is used in various fields such as web search, data mining and data warehouses; it is proven to be very practical for such a data-parallel application. A star-join query is a popular query in data warehouses that are a current target domain of data-parallel frameworks. This article proposes a new algorithm that efficiently processes star-join queries in data-parallel frameworks such as MapReduce and Dryad. Our star-join algorithm for general data-parallel frameworks is called Scatter-Gather-Merge, and it processes star-join queries in a constant number of computation steps, although the number of participating dimension tables increases. By adopting bloom filters, Scatter-Gather-Merge reduces a non-trivial amount of IO. We also show that Scatter-Gather-Merge can be easily applied to MapReduce. Our experimental results in both cluster and cloud environments show that Scatter-Gather-Merge outperforms existing approaches.     

An efficient policy evaluation engine with locomotive algorithm

Cluster Computing - The evaluation performance of PDP (policy decision point), especially in large-scale policy sets, is one of the most significant challenges in XACML (eXtensible Access Control...     

An efficient algorithm for identifying matches with errors in multiple long molecular sequences

An efficient algorithm is described for finding matches, repeats and other word relations, allowing for errors, in large data sets of long molecular sequences. The algorithm entails hashing on fixed-size words in conjunction with the use of a linked list connecting all occurrences of the same word. The average memory and run time requirement both increase almost linearly with the total sequence length. Some results of the program's performance on a database of Escherichia coli DNA sequences are presented.     

An efficient algorithm for the identification of structured motifs in DNA promoter sequences

We propose a new algorithm for identifying cis-regulatory modules in genomic sequences. The proposed algorithm, named RISO, uses a new data structure, called box-link, to store the information about conserved regions that occur in a well-ordered and regularly spaced manner in the data set sequences. This type of conserved regions, called structured motifs, is extremely relevant in the research of gene regulatory mechanisms since it can effectively represent promoter models. The complexity analysis shows a time and space gain over the best known exact algorithms that is exponential in the spacings between binding sites. A full implementation of the algorithm was developed and made available online. Experimental results show that the algorithm is much faster than existing ones, sometimes by more than four orders of magnitude. The application of the method to biological data sets shows its ability to extract relevant consensi.     

An efficient grid layout algorithm for biological networks utilizing various biological attributes

Background  

Clearly visualized biopathways provide a great help in understanding biological systems. However, manual drawing of large-scale biopathways is time consuming. We proposed a grid layout algorithm that can handle gene-regulatory networks and signal transduction pathways by considering edge-edge crossing, node-edge crossing, distance measure between nodes, and subcellular localization information from Gene Ontology. Consequently, the layout algorithm succeeded in drastically reducing these crossings in the apoptosis model. However, for larger-scale networks, we encountered three problems: (i) the initial layout is often very far from any local optimum because nodes are initially placed at random, (ii) from a biological viewpoint, human layouts still exceed automatic layouts in understanding because except subcellular localization, it does not fully utilize biological information of pathways, and (iii) it employs a local search strategy in which the neighborhood is obtained by moving one node at each step, and automatic layouts suggest that simultaneous movements of multiple nodes are necessary for better layouts, while such extension may face worsening the time complexity.