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Generalization of entropy based divergence measures for symbolic sequence analysis.

Miguel A Ré1, Rajeev K Azad2

  • 1Departamento de Ciencias Básicas, CIII - Facultad Regional Córdoba, Universidad Tecnológica Nacional, Córdoba, Argentina; Facultad de Matemática, Astronomía y Física, Universidad Nacional de Córdoba, Córdoba, Argentina.

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Jensen-Shannon divergence (JSD) generalizations improve DNA sequence analysis, especially for closely related organisms. A novel Tsallis-Markovian JSD offers superior performance in deconstructing chimeric bacterial genomes.

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Area of Science:

  • Information theory and statistical physics
  • Symbolic sequence analysis
  • Genomic data deconstruction

Background:

  • Jensen-Shannon divergence (JSD) is a versatile measure for symbolic sequence analysis, rooted in information theory and statistical physics.
  • JSD's entropic formulation allows generalization within frameworks like non-extensive Tsallis statistics and higher-order Markovian statistics.
  • Existing JSD generalizations have shown utility in analyzing complex biological sequences.

Purpose of the Study:

  • To propose a novel generalization of JSD within an integrated Tsallis and Markovian statistical framework.
  • To demonstrate the interpretation of this new JSD generalization in terms of mutual information.
  • To evaluate the performance of various JSD generalizations in deconstructing chimeric bacterial DNA sequences.

Main Methods:

  • Revisiting and extending existing generalizations of Jensen-Shannon divergence.
  • Developing a new JSD generalization combining Tsallis and Markovian statistical concepts.
  • Applying different JSD generalizations to analyze chimeric DNA sequences from bacterial genomes (E. coli, S. enterica typhi, Y. pestis, H. influenzae).

Main Results:

  • JSD generalizations show improved performance in distinguishing phylogenetically proximal bacterial sequences.
  • The Tsallis statistical JSD generalization provided noticeable improvements.
  • The Markovian generalization yielded larger improvements, while the proposed Tsallis-Markovian generalization demonstrated the most pronounced enhancements, particularly for closely related organisms.

Conclusions:

  • The novel Tsallis-Markovian JSD generalization effectively enhances the deconstruction of chimeric DNA sequences.
  • This approach offers significant advantages for distinguishing between phylogenetically similar bacterial genomes.
  • The integrated statistical framework provides a powerful tool for advanced sequence analysis in bioinformatics.