Clustering biomolecular complexes by residue contacts similarity

Inaccuracies in computational molecular modeling methods are often counterweighed by brute-force generation of a plethora of putative solutions. These are then typically sieved via structural clustering based on similarity measures such as the root mean square deviation (RMSD) of atomic positions. Albeit widely used, these measures suffer from several theoretical and technical limitations (e.g., choice of regions for fitting) that impair their application in multicomponent systems (N > 2), large-scale studies (e.g., interactomes), and other time-critical scenarios. We present here a simple similarity measure for structural clustering based on atomic contacts--the fraction of common contacts--and compare it with the most used similarity measure of the protein docking community--interface backbone RMSD. We show that this method produces very compact clusters in remarkably short time when applied to a collection of binary and multicomponent protein-protein and protein-DNA complexes. Furthermore, it allows easy clustering of similar conformations of multicomponent symmetrical assemblies in which chain permutations can occur. Simple contact-based metrics should be applicable to other structural biology clustering problems, in particular for time-critical or large-scale endeavors.     

Population model-based inter-diplotype similarity measure for accurate diplotype clustering

Classification of the individuals' genotype data is important in various kinds of biomedical research. There are many sophisticated clustering algorithms, but most of them require some appropriate similarity measure between objects to be clustered. Hence, accurate inter-diplotype similarity measures are always required for classification of diplotypes. In this article, we propose a new accurate inter-diplotype similarity measure that we call the population model-based distance (PMD), so that we can cluster individuals with diplotype SNPs data (i.e., unphased-diplotypes) with higher accuracies. For unphased-diplotypes, the allele sharing distance (ASD) has been the standard to measure the genetic distance between the diplotypes of individuals. To achieve higher clustering accuracies, our new measure PMD makes good use of a given appropriate population model which has never been utilized in the ASD. As the population model, we propose to use an hidden Markov model (HMM)-based model. We call the PMD based on the model the HHD (HIT HMM-based Distance). We demonstrate the impact of the HHD on the diplotype classification through comprehensive large-scale experiments over the genome-wide 8930 data sets derived from the HapMap SNPs database. The experiments revealed that the HHD enables significantly more accurate clustering than the ASD.     

A structural similarity analysis of double-helical DNA

A database of the structural properties of all 32,896 unique DNA octamer sequences has been calculated, including information on stability, the minimum energy conformation and flexibility. The contents of the database have been analysed using a variety of Euclidean distance similarity measures. A global comparison of sequence similarity with structural similarity shows that the structural properties of DNA are much less diverse than the sequences, and that DNA sequence space is larger and more diverse than DNA structure space. Thus, there are many very different sequences that have very similar structural properties, and this may be useful for identifying DNA motifs that have similar functional properties that are not apparent from the sequences. On the other hand, there are also small numbers of almost identical sequences that have very different structural properties, and these could give rise to false-positives in methods used to identify function based on sequence alignment. A simple validation test demonstrates that structural similarity can differentiate between promoter and non-promoter DNA. Combining structural and sequence similarity improves promoter recall beyond that possible using either similarity measure alone, demonstrating that there is indeed information available in the structure of double-helical DNA that is not readily apparent from the sequence.     

Exon discovery by genomic sequence alignment

MOTIVATION: During evolution, functional regions in genomic sequences tend to be more highly conserved than randomly mutating 'junk DNA' so local sequence similarity often indicates biological functionality. This fact can be used to identify functional elements in large eukaryotic DNA sequences by cross-species sequence comparison. In recent years, several gene-prediction methods have been proposed that work by comparing anonymous genomic sequences, for example from human and mouse. The main advantage of these methods is that they are based on simple and generally applicable measures of (local) sequence similarity; unlike standard gene-finding approaches they do not depend on species-specific training data or on the presence of cognate genes in data bases. As all comparative sequence-analysis methods, the new comparative gene-finding approaches critically rely on the quality of the underlying sequence alignments. RESULTS: Herein, we describe a new implementation of the sequence-alignment program DIALIGN that has been developed for alignment of large genomic sequences. We compare our method to the alignment programs PipMaker, WABA and BLAST and we show that local similarities identified by these programs are highly correlated to protein-coding regions. In our test runs, PipMaker was the most sensitive method while DIALIGN was most specific. AVAILABILITY: The program is downloadable from the DIALIGN home page at http://bibiserv.techfak.uni-bielefeld.de/dialign/.     

Weighted relative entropy for alignment-free sequence comparison based on Markov model

In this paper, we introduce a probabilistic measure for computing the similarity between two biological sequences without alignment. The computation of the similarity measure is based on the Kullback-Leibler divergence of two constructed Markov models. We firstly validate the method on clustering nine chromosomes from three species. Secondly, we give the result of similarity search based on our new method. We lastly apply the measure to the construction of phylogenetic tree of 48 HEV genome sequences. Our results indicate that the weighted relative entropy is an efficient and powerful alignment-free measure for the analysis of sequences in the genomic scale.     

Div-BLAST: Diversification of Sequence Search Results

Sequence similarity tools, such as BLAST, seek sequences most similar to a query from a database of sequences. They return results significantly similar to the query sequence and that are typically highly similar to each other. Most sequence analysis tasks in bioinformatics require an exploratory approach, where the initial results guide the user to new searches. However, diversity has not yet been considered an integral component of sequence search tools for this discipline. Some redundancy can be avoided by introducing non-redundancy during database construction, but it is not feasible to dynamically set a level of non-redundancy tailored to a query sequence. We introduce the problem of diverse search and browsing in sequence databases that produce non-redundant results optimized for any given query. We define diversity measures for sequences and propose methods to obtain diverse results extracted from current sequence similarity search tools. We also propose a new measure to evaluate the diversity of a set of sequences that is returned as a result of a sequence similarity query. We evaluate the effectiveness of the proposed methods in post-processing BLAST and PSI-BLAST results. We also assess the functional diversity of the returned results based on available Gene Ontology annotations. Additionally, we include a comparison with a current redundancy elimination tool, CD-HIT. Our experiments show that the proposed methods are able to achieve more diverse yet significant result sets compared to static non-redundancy approaches. In both sequence-based and functional diversity evaluation, the proposed diversification methods significantly outperform original BLAST results and other baselines. A web based tool implementing the proposed methods, Div-BLAST, can be accessed at cedar.cs.bilkent.edu.tr/Div-BLAST     

A weighted measure for the similarity analysis of DNA sequences

Here we propose a weighted measure for the similarity analysis of DNA sequences. It is based on LZ complexity and (0,1) characteristic sequences of DNA sequences. This weighted measure enables biologists to extract similarity information from biological sequences according to their requirements. For example, by this weighted measure, one can obtain either the full similarity information or a similarity analysis from a given biological aspect. Moreover, the length of DNA sequence is not problematic. The application of the weighted measure to the similarity analysis of β-globin genes from nine species shows its flexibility.     

Effective similarity measures for expression profiles

It is commonly accepted that genes with similar expression profiles are functionally related. However, there are many ways one can measure the similarity of expression profiles, and it is not clear a priori what is the most effective one. Moreover, so far no clear distinction has been made as for the type of the functional link between genes as suggested by microarray data. Similarly expressed genes can be part of the same complex as interacting partners; they can participate in the same pathway without interacting directly; they can perform similar functions; or they can simply have similar regulatory sequences. Here we conduct a study of the notion of functional link as implied from expression data. We analyze different similarity measures of gene expression profiles and assess their usefulness and robustness in detecting biological relationships by comparing the similarity scores with results obtained from databases of interacting proteins, promoter signals and cellular pathways, as well as through sequence comparisons. We also introduce variations on similarity measures that are based on statistical analysis and better discriminate genes which are functionally nearby and faraway. Our tools can be used to assess other similarity measures for expression profiles, and are accessible at biozon.org/tools/expression/     

Markov model plus k-word distributions: a synergy that produces novel statistical measures for sequence comparison

MOTIVATION: Many proposed statistical measures can efficiently compare biological sequences to further infer their structures, functions and evolutionary information. They are related in spirit because all the ideas for sequence comparison try to use the information on the k-word distributions, Markov model or both. Motivated by adding k-word distributions to Markov model directly, we investigated two novel statistical measures for sequence comparison, called wre.k.r and S2.k.r. RESULTS: The proposed measures were tested by similarity search, evaluation on functionally related regulatory sequences and phylogenetic analysis. This offers the systematic and quantitative experimental assessment of our measures. Moreover, we compared our achievements with these based on alignment or alignment-free. We grouped our experiments into two sets. The first one, performed via ROC (receiver operating curve) analysis, aims at assessing the intrinsic ability of our statistical measures to search for similar sequences from a database and discriminate functionally related regulatory sequences from unrelated sequences. The second one aims at assessing how well our statistical measure is used for phylogenetic analysis. The experimental assessment demonstrates that our similarity measures intending to incorporate k-word distributions into Markov model are more efficient.     

Phylogenetic analysis based on spectral methods

Whole-genome or multiple gene phylogenetic analysis is of interest since single gene analysis often results in poorly resolved trees. Here, the use of spectral techniques for analyzing multigene data sets is explored. The protein sequences are treated as categorical time series, and a measure of similarity between a pair of sequences, the spectral covariance, is based on the common periodicity between these two sequences. Unlike the other methods, the spectral covariance method focuses on the relationship between the sites of genetic sequences. By properly scaling the dissimilarity measures derived from different genes between a pair of species, we can use the mean of these scaled dissimilarity measures as a summary statistic to measure the taxonomic distances across multiple genes. The methods are applied to three different data sets, one noncontroversial and two with some dispute over the correct placement of the taxa in the tree. Trees are constructed using two distance-based methods, BIONJ and FITCH. A variation of block bootstrap sampling method is used for inference. The methods are able to recover all major clades in the corresponding reference trees with moderate to high bootstrap support. Through simulations, we show that the covariance-based methods effectively capture phylogenetic signal even when structural information is not fully retained. Comparisons of simulation results with the bootstrap permutation results indicate that the covariance-based methods are fairly robust under perturbations in sequence similarity but more sensitive to perturbations in structural similarity.     

Genomic classification using an information-based similarity index: application to the SARS coronavirus.

Measures of genetic distance based on alignment methods are confined to studying sequences that are conserved and identifiable in all organisms under study. A number of alignment-free techniques based on either statistical linguistics or information theory have been developed to overcome the limitations of alignment methods. We present a novel alignment-free approach to measuring the similarity among genetic sequences that incorporates elements from both word rank order-frequency statistics and information theory. We first validate this method on the human influenza A viral genomes as well as on the human mitochondrial DNA database. We then apply the method to study the origin of the SARS coronavirus. We find that the majority of the SARS genome is most closely related to group 1 coronaviruses, with smaller regions of matches to sequences from groups 2 and 3. The information based similarity index provides a new tool to measure the similarity between datasets based on their information content and may have a wide range of applications in the large-scale analysis of genomic databases.     

Fuzzy measures on the Gene Ontology for gene product similarity

One of the most important objects in bioinformatics is a gene product (protein or RNA). For many gene products, functional information is summarized in a set of Gene Ontology (GO) annotations. For these genes, it is reasonable to include similarity measures based on the terms found in the GO or other taxonomy. In this paper, we introduce several novel measures for computing the similarity of two gene products annotated with GO terms. The fuzzy measure similarity (FMS) has the advantage that it takes into consideration the context of both complete sets of annotation terms when computing the similarity between two gene products. When the two gene products are not annotated by common taxonomy terms, we propose a method that avoids a zero similarity result. To account for the variations in the annotation reliability, we propose a similarity measure based on the Choquet integral. These similarity measures provide extra tools for the biologist in search of functional information for gene products. The initial testing on a group of 194 sequences representing three proteins families shows a higher correlation of the FMS and Choquet similarities to the BLAST sequence similarities than the traditional similarity measures such as pairwise average or pairwise maximum.     

A biologically inspired measure for coexpression analysis

Two genes are said to be coexpressed if their expression levels have a similar spatial or temporal pattern. Ever since the profiling of gene microarrays has been in progress, computational modeling of coexpression has acquired a major focus. As a result, several similarity/distance measures have evolved over time to quantify coexpression similarity/dissimilarity between gene pairs. Of these, correlation coefficient has been established to be a suitable quantifier of pairwise coexpression. In general, correlation coefficient is good for symbolizing linear dependence, but not for nonlinear dependence. In spite of this drawback, it outperforms many other existing measures in modeling the dependency in biological data. In this paper, for the first time, we point out a significant weakness of the existing similarity/distance measures, including the standard correlation coefficient, in modeling pairwise coexpression of genes. A novel measure, called BioSim, which assumes values between -1 and +1 corresponding to negative and positive dependency and 0 for independency, is introduced. The computation of BioSim is based on the aggregation of stepwise relative angular deviation of the expression vectors considered. The proposed measure is analytically suitable for modeling coexpression as it accounts for the features of expression similarity, expression deviation and also the relative dependence. It is demonstrated how the proposed measure is better able to capture the degree of coexpression between a pair of genes as compared to several other existing ones. The efficacy of the measure is statistically analyzed by integrating it with several module-finding algorithms based on coexpression values and then applying it on synthetic and biological data. The annotation results of the coexpressed genes as obtained from gene ontology establish the significance of the introduced measure. By further extending the BioSim measure, it has been shown that one can effectively identify the variability in the expression patterns over multiple phenotypes. We have also extended BioSim to figure out pairwise differential expression pattern and coexpression dynamics. The significance of these studies is shown based on the analysis over several real-life data sets. The computation of the measure by focusing on stepwise time points also makes it effective to identify partially coexpressed genes. On the whole, we put forward a complete framework for coexpression analysis based on the BioSim measure.     

Defining a similarity threshold for a functional protein sequence pattern: The signal peptide cleavage site

When preparing data sets of amino acid or nucleotide sequences it is necessary to exclude redundant or homologous sequences in order to avoid overestimating the predictive performance of an algorithm. For some time methods for doing this have been available in the area of protein structure prediction. We have developed a similar procedure based on pair-wise alignments for sequences with functional sites. We show how a correlation coefficient between sequence similarity and functional homology can be used to compare the efficiency of different similarity measures and choose a nonarbitrary threshold value for excluding redundant sequences. The impact of the choice of scoring matrix used in the alignments is examined. We demonstrate that the parameter determining the quality of the correlation is the relative entropy of the matrix, rather than the assumed (PAM or identity) substitution model. Results are presented for the case of prediction of cleavage sites in signal peptides. By inspection of the false positives, several errors in the database were found. The procedure presented may be used as a general outline for finding a problem-specific similarity measure and threshold value for analysis of other functional amino acid or nucleotide sequence patterns.     

Least Squares Estimation of Molecular Distance - Noise Abatement in Phylogenetic Reconstruction

Zuckerkandl and Pauling (1962, "Horizons in Biochemistry," pp. 189-225, Academic Press, New York) first noticed that the degree of sequence similarity between the proteins of different species could be used to estimate their phylogenetic relationship. Since then models have been developed to improve the accuracy of phylogenetic inferences based on amino acid or DNA sequences. Most of these models were designed to yield distance measures that are linear with time, on average. The reliability of phylogenetic reconstruction, however, depends on the variance of the distance measure in addition to its expectation. In this paper we show how the method of generalized least squares can be used to combine data types, each most informative at different points in time, into a single distance measure. This measure reconstructs phylogenies more accurately than existing non-likelihood distance measures. We illustrate the approach for a two-rate mutation model and demonstrate that its application provides more accurate phylogenetic reconstruction than do currently available analytical distance measures.     

Using Random Walks to Generate Associations between Objects

Measuring similarities between objects based on their attributes has been an important problem in many disciplines. Object-attribute associations can be depicted as links on a bipartite graph. A similarity measure can be thought as a unipartite projection of this bipartite graph. The most widely used bipartite projection techniques make assumptions that are not often fulfilled in real life systems, or have the focus on the bipartite connections more than on the unipartite connections. Here, we define a new similarity measure that utilizes a practical procedure to extract unipartite graphs without making a priori assumptions about underlying distributions. Our similarity measure captures the relatedness between two objects via the likelihood of a random walker passing through these nodes sequentially on the bipartite graph. An important aspect of the method is that it is robust to heterogeneous bipartite structures and it controls for the transitivity similarity, avoiding the creation of unrealistic homogeneous degree distributions in the resulting unipartite graphs. We test this method using real world examples and compare the obtained results with alternative similarity measures, by validating the actual and orthogonal relations between the entities.