Two Dimensional Yau-Hausdorff Distance with Applications on Comparison of DNA and Protein Sequences

Comparing DNA or protein sequences plays an important role in the functional analysis of genomes. Despite many methods available for sequences comparison, few methods retain the information content of sequences. We propose a new approach, the Yau-Hausdorff method, which considers all translations and rotations when seeking the best match of graphical curves of DNA or protein sequences. The complexity of this method is lower than that of any other two dimensional minimum Hausdorff algorithm. The Yau-Hausdorff method can be used for measuring the similarity of DNA sequences based on two important tools: the Yau-Hausdorff distance and graphical representation of DNA sequences. The graphical representations of DNA sequences conserve all sequence information and the Yau-Hausdorff distance is mathematically proved as a true metric. Therefore, the proposed distance can preciously measure the similarity of DNA sequences. The phylogenetic analyses of DNA sequences by the Yau-Hausdorff distance show the accuracy and stability of our approach in similarity comparison of DNA or protein sequences. This study demonstrates that Yau-Hausdorff distance is a natural metric for DNA and protein sequences with high level of stability. The approach can be also applied to similarity analysis of protein sequences by graphic representations, as well as general two dimensional shape matching.     

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 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.     

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.     

New method for comparing DNA primary sequences based on a discrimination measure

We introduce a new approach to compare DNA primary sequences. The core of our method is a new measure of pairwise distances among sequences. Using the primitive discrimination substrings of sequence S and Q, a discrimination measure DM(S, Q) is defined for the similarity analysis of them. The proposed method does not require multiple alignments and is fully automatic. To illustrate its utility, we construct phylogenetic trees on two independent data sets. The results indicate that the method is efficient and powerful.     

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.     

A probabilistic measure for alignment-free sequence comparison

MOTIVATION: Alignment-free sequence comparison methods are still in the early stages of development compared to those of alignment-based sequence analysis. In this paper, we introduce a probabilistic measure of similarity between two biological sequences without alignment. The method is based on the concept of comparing the similarity/dissimilarity between two constructed Markov models. RESULTS: The method was tested against six DNA sequences, which are the thrA, thrB and thrC genes of the threonine operons from Escherichia coli K-12 and from Shigella flexneri; and one random sequence having the same base composition as thrA from E.coli. These results were compared with those obtained from CLUSTAL W algorithm (alignment-based) and the chaos game representation (alignment-free). The method was further tested against a more complex set of 40 DNA sequences and compared with other existing sequence similarity measures (alignment-free). AVAILABILITY: All datasets and computer codes written in MATLAB are available upon request from the first author.     

A mathematical consideration of the word-composition vector method in comparison of biological sequences

To measure the similarity or dissimilarity between two given biological sequences, several papers proposed metrics based on the "word-composition vector". The essence of these metrics is as follows. First, we count the appearance frequencies of all the K-tuple words throughout each of two given sequences. Then, the two given sequences are transformed into their respective word-composition vectors. Next, the distance metrics, for example the angle between the two vectors, are calculated. A significant issue is to determine the optimal word size K. With a mathematical model of mutational events (including substitutions, insertions, deletions and duplications) that occur in sequences, we analyzed how the angle between the composition vectors depends on the mutational events. We also considered the optimal word size (=resolution) from our original approach. Our results were verified by computational experiments using artificially generated sequences, amino acid sequences of hemoglobin and nucleotide sequences of 16S ribosomal RNA.     

3D HUMAN MOTION RETRIEVAL BASED ON HUMAN HIERARCHICAL INDEX STRUCTURE

With the development and wide application of motion capture technology, the captured motion data sets are becoming larger and larger. For this reason, an efficient retrieval method for the motion database is very important. The retrieval method needs an appropriate indexing scheme and an effective similarity measure that can organize the existing motion data well. In this paper, we represent a human motion hierarchical index structure and adopt a nonlinear method to segment motion sequences. Based on this, we extract motion patterns and then we employ a fast similarity measure algorithm for motion pattern similarity computation to efficiently retrieve motion sequences. The experiment results show that the approach proposed in our paper is effective and efficient.     

Efficient pattern comparative method for selecting functionally important motifs in protein sequences: Application to zinc enzymes

We have developed a pattern comparative method for identifying functionally important motifs in protein sequences. The essence of most standard pattern comparative methods is a comparison of patterns occurring in different sequences using an optimized weight matrix. In contrast, our approach is based on a measure of similarity among all the candidate motifs within the same sequence. This method may prove to be particularly efficient for proteins encoding the same biochemical function, but with different primary sequences, and when tertiary structure information from one or more sequences is available. We have applied this method to a special class of zinc-binding enzymes known as endopeptidases.     

Enlarged Similarity of Nucleic Acid Sequences

The concept of nucleic acid sequence base alternations is presented.The number of base alterations for the sequences of differentlength is established. The definition of "enlarged similarity"of nucleic acids sequences on the basis of sequence base alterationsis introduced. Mutual information between sequences is usedas a quantitative measure of enlarged similarity for two comparedsequences. The method of mutual information calculation is developedconsidering the correlation of bases in compared sequences.The definitions of correlated similarity and evolution similaritybetween compared sequences are given. Results of the use ofenlarged similarity approach for DNA sequences analysis arediscussed.     

Similarity among nucleotide sequences

In this work we report a simple way to measure the similarity between two nucleotide sequences by using graph theory and information theory. This method reported allows for theoretical comparisons of naturally occurring nucleotide sequences.     

An alignment-free domain architecture similarity search (ADASS) algorithm for inferring homology between multi-domain proteins

Annotations of the genes and their products are largely guided by inferring homology. Sequence similarity is the primary measure used for annotation purpose however, the domain content and order were given less importance albeit the fact that domain insertion, deletion, positional changes can bring in functional varieties. Of late, several methods developed quantify domain architecture similarity depending on alignments of their sequences and are focused on only homologous proteins. We present an alignment-free domain architecture-similarity search (ADASS) algorithm that identifies proteins that share very poor sequence similarity yet having similar domain architectures. We introduce a “singlet matching-triplet comparison” method in ADASS, wherein triplet of domains is compared with other triplets in a pair-wise comparison of two domain architectures. Different events in the triplet comparison are scored as per a scoring scheme and an average pairwise distance score (Domain Architecture Distance score - DAD Score) is calculated between protein domains architectures. We use domain architectures of a selected domain termed as centric domain and cluster them based on DAD score. The algorithm has high Positive Prediction Value (PPV) with respect to the clustering of the sequences of selected domain architectures. A comparison of domain architecture based dendrograms using ADASS method and an existing method revealed that ADASS can classify proteins depending on the extent of domain architecture level similarity. ADASS is more relevant in cases of proteins with tiny domains having little contribution to the overall sequence similarity but contributing significantly to the overall function.     

A measure of DNA sequence dissimilarity based on free energy of nearest-neighbor interaction

We develop a novel method of asserting the similarity between two biological sequences without the need for alignment. The proposed method uses free energy of nearest-neighbor interactions as a simple measure of dissimilarity. It is used to perform a search for similarities of a query sequence against three complex datasets. The sensitivity and selectivity are computed and evaluated and the performance of the proposed distance measure is compared. Real data analysis shows that is a very efficient, sensitive and high-selective algorithm in comparing large dataset of DNA sequences.     

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.     

A graph-based clustering method applied to protein sequences

The number of amino acid sequences is increasing very rapidly in the protein databases like Swiss-Prot, Uniprot, PIR and others, but the structure of only some amino acid sequences are found in the Protein Data Bank. Thus, an important problem in genomics is automatically clustering homologous protein sequences when only sequence information is available. Here, we use graph theoretic techniques for clustering amino acid sequences. A similarity graph is defined and clusters in that graph correspond to connected subgraphs. Cluster analysis seeks grouping of amino acid sequences into subsets based on distance or similarity score between pairs of sequences. Our goal is to find disjoint subsets, called clusters, such that two criteria are satisfied: homogeneity: sequences in the same cluster are highly similar to each other; and separation: sequences in different clusters have low similarity to each other. We tested our method on several subsets of SCOP (Structural Classification of proteins) database, a gold standard for protein structure classification. The results show that for a given set of proteins the number of clusters we obtained is close to the superfamilies in that set; there are fewer singeltons; and the method correctly groups most remote homologs.     

基于DTW距离的DNA序列相似性分析

在DNA序列相似性的研究中,通常采用的动态规划算法对空位罚分函数缺乏理论依据而带有主观性,从而取得不同的结果,本文提出了一种基于DTW（Dynamic Time Warping,动态时间弯曲）距离的DNA序列相似性度量方法可以解决这一问题．通过DNA序列的图形表示把DNA序列转化为时间序列,然后计算DTW距离来度量序列相似度以表征DNA序列属性,得到能够比较DNA序列相似性度量方法,并用这个方法比较分析了七种东亚钳蝎神经毒素（Buthusmartensi Karsch neurotoxin）基因序列的相似性,验证了该度量方法的有效性和准确性．     

Prediction of common secondary structures of RNAs: a genetic algorithm approach

In this study we apply a genetic algorithm to a set of RNA sequences to find common RNA secondary structures. Our method is a three-step procedure. At the first stage of the procedure for each sequence, a genetic algorithm is used to optimize the structures in a population to a certain degree of stability. In this step, the free energy of a structure is the fitness criterion for the algorithm. Next, for each structure, we define a measure of structural conservation with respect to those in other sequences. We use this measure in a genetic algorithm to improve the structural similarity among sequences for the structures in the population of a sequence. Finally, we select those structures satisfying certain conditions of structural stability and similarity as predicted common structures for a set of RNA sequences. We have obtained satisfactory results from a set of tRNA, 5S rRNA, rev response elements (RRE) of HIV-1 and RRE of HIV-2/SIV, respectively.     

MTRAP: Pairwise sequence alignment algorithm by a new measure based on transition probability between two consecutive pairs of residues

Background  

Sequence alignment is one of the most important techniques to analyze biological systems. It is also true that the alignment is not complete and we have to develop it to look for more accurate method. In particular, an alignment for homologous sequences with low sequence similarity is not in satisfactory level. Usual methods for aligning protein sequences in recent years use a measure empirically determined. As an example, a measure is usually defined by a combination of two quantities (1) and (2) below: (1) the sum of substitutions between two residue segments, (2) the sum of gap penalties in insertion/deletion region. Such a measure is determined on the assumption that there is no an intersite correlation on the sequences. In this paper, we improve the alignment by taking the correlation of consecutive residues.