Markov models of genome segmentation

Thakur, Vivek; Azad, Rajeev K.; Ramaswamy, Ramakrishna

doi:10.1103/physreve.75.011915

Cited by 21 publications

(31 citation statements)

References 40 publications

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“…41 reduces to Lamberti and Majtey’s non-extensive generalization [6] (Eqn. 21), while in the limit q→1, we recover Thakur et al’s Markovian generalization [7]. Note that (Eqn.…”

Section: Theory and Methodssupporting

confidence: 77%

“…In addition to non-negativity and symmetricity, JSD also has a lower and upper bound, 0≤JSD≤1, and has been shown to be the square of a metric [6], [7], [9], [10]. Because of these interesting properties, this measure has been successfully applied to solving a variety of problems arising from different fields including molecular biology (e.g.…”

Section: Theory and Methodsmentioning

confidence: 99%

“…21), this generalization takes the full entropic form. Thakur et al introduced “Markov models for genomic segmentation” (MMS) [7], where they replaced the BGSE with Markovian entropy (Eqn. 27) in the expression of JSD (Eqn.…”

Section: Theory and Methodsmentioning

confidence: 99%

“…Lin introduced the JensenShannon divergence (JSD) as a generalization of a symmetrized version of KulbackLeibler divergence, assigning weights to the probability distributions involved according to their relative importance [5]. Subsequently, different generalizations of JSD were proposed, either within the framework of Tsallis statistics [6] or within Markovian statistical framework [7]. While the former exploits the non-extensivity implicit in the Tsallis generalization of BGSE, the latter is based on conditional entropy that facilitates exploiting higher order correlations within symbolic sequences.…”

Section: Introductionmentioning

confidence: 99%

“…While the former exploits the non-extensivity implicit in the Tsallis generalization of BGSE, the latter is based on conditional entropy that facilitates exploiting higher order correlations within symbolic sequences. Since the latter was obtained within the framework of Markov chain models, this generalization was named Markovian Jensen-Shannon divergence (MJSD) and was shown to significantly outperform standard JSD in its application to deciphering genomic heterogeneities [7], [8].…”

Section: Introductionmentioning

confidence: 99%

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Generalization of Entropy Based Divergence Measures for Symbolic Sequence Analysis

Ré

Azad

2014

PLoS ONE

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Entropy based measures have been frequently used in symbolic sequence analysis. A symmetrized and smoothed form of Kullback-Leibler divergence or relative entropy, the Jensen-Shannon divergence (JSD), is of particular interest because of its sharing properties with families of other divergence measures and its interpretability in different domains including statistical physics, information theory and mathematical statistics. The uniqueness and versatility of this measure arise because of a number of attributes including generalization to any number of probability distributions and association of weights to the distributions. Furthermore, its entropic formulation allows its generalization in different statistical frameworks, such as, non-extensive Tsallis statistics and higher order Markovian statistics. We revisit these generalizations and propose a new generalization of JSD in the integrated Tsallis and Markovian statistical framework. We show that this generalization can be interpreted in terms of mutual information. We also investigate the performance of different JSD generalizations in deconstructing chimeric DNA sequences assembled from bacterial genomes including that of E. coli, S. enterica typhi, Y. pestis and H. influenzae. Our results show that the JSD generalizations bring in more pronounced improvements when the sequences being compared are from phylogenetically proximal organisms, which are often difficult to distinguish because of their compositional similarity. While small but noticeable improvements were observed with the Tsallis statistical JSD generalization, relatively large improvements were observed with the Markovian generalization. In contrast, the proposed Tsallis-Markovian generalization yielded more pronounced improvements relative to the Tsallis and Markovian generalizations, specifically when the sequences being compared arose from phylogenetically proximal organisms.

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“…41 reduces to Lamberti and Majtey’s non-extensive generalization [6] (Eqn. 21), while in the limit q→1, we recover Thakur et al’s Markovian generalization [7]. Note that (Eqn.…”

Section: Theory and Methodssupporting

confidence: 77%

Section: Theory and Methodsmentioning

confidence: 99%

Section: Theory and Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Generalization of Entropy Based Divergence Measures for Symbolic Sequence Analysis

Ré

Azad

2014

PLoS ONE

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Detecting Laterally Transferred Genes

Azad

Lawrence

2012

Methods in Molecular Biology

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Deciphering evolutionary strata on plant sex chromosomes and fungal mating-type chromosomes through compositional segmentation

Pandey

Azad

2015

Plant Mol Biol

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Sex chromosomes have evolved from a pair of homologous autosomes which differentiated into sex determination systems, such as XY or ZW system, as a consequence of successive recombination suppression between the gametologous chromosomes. Identifying the regions of recombination suppression, namely, the "evolutionary strata", is central to understanding the history and dynamics of sex chromosome evolution. Evolution of sex chromosomes as a consequence of serial recombination suppressions is well-studied for mammals and birds, but not for plants, although 48 dioecious plants have already been reported. Only two plants Silene latifolia and papaya have been studied until now for the presence of evolutionary strata on their X chromosomes, made possible by the sequencing of sex-linked genes on both the X and Y chromosomes, which is a requirement of all current methods that determine stratum structure based on the comparison of gametologous sex chromosomes. To circumvent this limitation and detect strata even if only the sequence of sex chromosome in the homogametic sex (i.e. X or Z chromosome) is available, we have developed an integrated segmentation and clustering method. In application to gene sequences on the papaya X chromosome and protein-coding sequences on the S. latifolia X chromosome, our method could decipher all known evolutionary strata, as reported by previous studies. Our method, after validating on known strata on the papaya and S. latifolia X chromosome, was applied to the chromosome 19 of Populus trichocarpa, an incipient sex chromosome, deciphering two, yet unknown, evolutionary strata. In addition, we applied this approach to the recently sequenced sex chromosome V of the brown alga Ectocarpus sp. that has a haploid sex determination system (UV system) recovering the sex determining and pseudoautosomal regions, and then to the mating-type chromosomes of an anther-smut fungus Microbotryum lychnidis-dioicae predicting five strata in the non-recombining region of both the chromosomes.

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Markov models of genome segmentation

Cited by 21 publications

References 40 publications

Generalization of Entropy Based Divergence Measures for Symbolic Sequence Analysis

Generalization of Entropy Based Divergence Measures for Symbolic Sequence Analysis

Detecting Laterally Transferred Genes

Deciphering evolutionary strata on plant sex chromosomes and fungal mating-type chromosomes through compositional segmentation

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