BACKGROUND: Gene and protein interaction data are often represented as interaction networks, where nodes stand for genes or gene products and each edge stands for a relationship between a pair of gene nodes. Commonly, that relationship within a pair is specified by high similarity between profiles (vectors) of experimentally defined interactions of each of the two genes with all other genes in the genome; only gene pairs that interact with similar sets of genes are linked by an edge in the network. The tight groups of genes/gene products that work together in a cell can be discovered by the analysis of those complex networks. RESULTS: We show that the choice of the similarity measure between pairs of gene vectors impacts the properties of networks and of gene modules detected within them. We re-analyzed well-studied data on yeast genetic interactions, constructed four genetic networks using four different similarity measures, and detected gene modules in each network using the same algorithm. The four networks induced different numbers of putative functional gene modules, and each similarity measure induced some unique modules. In an example of a putative functional connection suggested by comparing genetic interaction vectors, we predict a link between SUN-domain proteins and protein glycosylation in the endoplasmic reticulum. CONCLUSIONS: The discovery of molecular modules in genetic networks is sensitive to the way of measuring similarity between profiles of gene interactions in a cell. In the absence of a formal way to choose the "best" measure, it is advisable to explore the measures with different mathematical properties, which may identify different sets of connections between genes.

Accurate inference of orthologous genes is a pre-requisite for most comparative genomics studies, and is also important for functional annotation of new genomes. Identification of orthologous gene sets typically involves phylogenetic tree analysis, heuristic algorithms based on sequence conservation, synteny analysis, or some combination of these approaches. The most direct tree-based methods typically rely on the comparison of an individual gene tree with a species tree. Once the two trees are accurately constructed, orthologs are straightforwardly identified by the definition of orthology as those homologs that are related by speciation, rather than gene duplication, at their most recent point of origin. Although ideal for the purpose of orthology identification in principle, phylogenetic trees are computationally expensive to construct for large numbers of genes and genomes, and they often contain errors, especially at large evolutionary distances. Moreover, in many organisms, in particular prokaryotes and viruses, evolution does not appear to have followed a simple 'tree-like' mode, which makes conventional tree reconciliation inapplicable. Other, heuristic methods identify probable orthologs as the closest homologous pairs or groups of genes in a set of organisms. These approaches are faster and easier to automate than tree-based methods, with efficient implementations provided by graph-theoretical algorithms enabling comparisons of thousands of genomes. Comparisons of these two approaches show that, despite conceptual differences, they produce similar sets of orthologs, especially at short evolutionary distances. Synteny also can aid in identification of orthologs. Often, tree-based, sequence similarity- and synteny-based approaches can be combined into flexible hybrid methods.

MOTIVATION: Identifying orthologous genes in multiple genomes is a fundamental task in comparative genomics. Construction of intergenomic symmetrical best matches (SymBets) and joining them into clusters is a popular method of ortholog definition, embodied in several software programs. Despite their wide use, the computational complexity of these programs has not been thoroughly examined. RESULTS: In this work, we show that in the standard approach of iteration through all triangles of SymBets, the memory scales with at least the number of these triangles, O(g(3)) (where g = number of genomes), and construction time scales with the iteration through each pair, i.e. O(g(6)). We propose the EdgeSearch algorithm that iterates over edges in the SymBet graph rather than triangles of SymBets, and as a result has a worst-case complexity of only O(g(3)log g). Several optimizations reduce the run-time even further in realistically sparse graphs. In two real-world datasets of genomes from bacteriophages (POGs) and Mollicutes (MOGs), an implementation of the EdgeSearch algorithm runs about an order of magnitude faster than the original algorithm and scales much better with increasing number of genomes, with only minor differences in the final results, and up to 60 times faster than the popular OrthoMCL program with a 90% overlap between the identified groups of orthologs. AVAILABILITY AND IMPLEMENTATION: C++ source code freely available for download at ftp.ncbi.nih.gov/pub/wolf/COGs/COGsoft/. SUPPLEMENTARY INFORMATION: Supplementary materials are available at Bioinformatics online.

BACKGROUND: Identification of the structural domains of proteins is important for our understanding of the organizational principles and mechanisms of protein folding, and for insights into protein function and evolution. Algorithmic methods of dissecting protein of known structure into domains developed so far are based on an examination of multiple geometrical, physical and topological features. Successful as many of these approaches are, they employ a lot of heuristics, and it is not clear whether they illuminate any deep underlying principles of protein domain organization. Other well-performing domain dissection methods rely on comparative sequence analysis. These methods are applicable to sequences with known and unknown structure alike, and their success highlights a fundamental principle of protein modularity, but this does not directly improve our understanding of protein spatial structure. RESULTS: We present a novel graph-theoretical algorithm for the identification of domains in proteins with known three-dimensional structure. We represent the protein structure as an undirected, unweighted and unlabeled graph whose nodes correspond to the secondary structure elements and edges represent physical proximity of at least one pair of alpha carbon atoms from two elements. Domains are identified as constrained partitions of the graph, corresponding to sets of vertices obtained by the maximization of the cycle distributions found in the graph. When a partition is found, the algorithm is iteratively applied to each of the resulting subgraphs. The decision to accept or reject a tentative cut position is based on a specific classifier. The algorithm is applied iteratively to each of the resulting subgraphs and terminates automatically if partitions are no longer accepted. The distribution of cycles is the only type of information on which the decision about protein dissection is based. Despite the barebone simplicity of the approach, our algorithm approaches the best heuristic algorithms in accuracy. CONCLUSION: Our graph-theoretical algorithm uses only topological information present in the protein structure itself to find the domains and does not rely on any geometrical or physical information about protein molecule. Perhaps unexpectedly, these drastic constraints on resources, which result in a seemingly approximate description of protein structures and leave only a handful of parameters available for analysis, do not lead to any significant deterioration of algorithm accuracy. It appears that protein structures can be rigorously treated as topological rather than geometrical objects and that the majority of information about protein domains can be inferred from the coarse-grained measure of pairwise proximity between elements of secondary structure elements.

MOTIVATION: Periodic patterns in time series resulting from biological experiments are of great interest. The commonly used Fast Fourier Transform (FFT) algorithm is applicable only when data are evenly spaced and when no values are missing, which is not always the case in high-throughput measurements. The choice of statistic to evaluate the significance of the periodic patterns for unevenly spaced gene expression time series has not been well substantiated. METHODS: The Lomb-Scargle periodogram approach is used to search time series of gene expression to quantify the periodic behavior of every gene represented on the DNA array. The Lomb-Scargle periodogram analysis provides a direct method to treat missing values and unevenly spaced time points. We propose the combination of a Lomb-Scargle test statistic for periodicity and a multiple hypothesis testing procedure with controlled false discovery rate to detect significant periodic gene expression patterns. RESULTS: We analyzed the Plasmodium falciparum gene expression dataset. In the Quality Control Dataset of 5080 expression patterns, we found 4112 periodic probes. In addition, we identified 243 probes with periodic expression in the Complete Dataset, which could not be examined in the original study by the FFT analysis due to an excessive number of missing values. While most periodic genes had a period of 48 h, some had a period close to 24 h. Our approach should be applicable for detection and quantification of periodic patterns in any unevenly spaced gene expression time-series data.

MOTIVATION: Many types of genomic data are naturally represented as binary vectors. Numerous tasks in computational biology can be cast as analysis of relationships between these vectors, and the first step is, frequently, to compute their pairwise distance matrix. Many distance measures have been proposed in the literature, but there is no theory justifying the choice of distance measure. RESULTS: We examine the approaches to measuring distances between binary vectors and study the characteristic properties of various distance measures and their performance in several tasks of genome analysis. Most distance measures between binary vectors turn out to belong to a single parametric family, namely generalized average-based distance with different exponents. We show that descriptive statistics of distance distribution, such as skewness and kurtosis, can guide the appropriate choice of the exponent. On the contrary, the more familiar distance properties, such as metric and additivity, appear to have much less effect on the performance of distances. AVAILABILITY: R code GADIST and Supplementary material are available at http://research.stowers-institute.org/bioinfo/

MOTIVATION: Hybridization of oligonucleotides with longer nucleotide sequences is an essential step in nucleic acid biosynthesis in vitro and in vivo, in oligonucleotide-based diagnostics, and in therapeutic applications of oligonucleotides. A major factor determining sensitivity and selectivity of hybridization is the number of base pair mismatches that occur in an ungapped alignment of the oligonucleotide (probe) and a longer sequence (target). RESULTS: The k-distance match count between the probe and the target is defined as the number of ungapped alignments between the two sequences that have exactly k mismatches, and the k-neighbor match count is defined as the sum of the j-distance match counts for j between 0 and k. We derive a novel formula for the probability of a k-distance match. This formula is based on the assumption that the target is strand-symmetric Bernoulli text (i.e. nucleotides are independently, identically distributed in the target and satisfy Chargaff's second parity rule). Our model predicts that the GC-content in both the probe and the target significantly affects the match count expectation. The ratio of k-neighbor match counts in two distinct genomes for a given probe is a measure of its specificity. We calculated such ratios for pairs of bacterial genomes with different combinations of length, GC-content and phylogenetic distance. Examination of the extreme values of these ratios indicates that probes with a high discriminative power exist for each tested pair.