Journal of Statistical Physics

, Volume 146, Issue 2, pp 408–422 | Cite as

A Gibbs Approach to Chargaff’s Second Parity Rule

Article

Abstract

Chargaff’s second parity rule (CSPR) asserts that the frequencies of short polynucleotide chains are the same as those of the complementary reversed chains. Up to now, this hypothesis has only been observed empirically and there is currently no explanation for its presence in DNA strands. Here we argue that CSPR is a probabilistic consequence of the reverse complementarity between paired strands, because the Gibbs distribution associated with the chemical energy between the bonds satisfies CSPR. We develop a statistical test to study the validity of CSPR under the Gibbsian assumption and we apply it to a large set of bacterial genomes taken from the GenBank repository.

Keywords

Reverse complementary relation Chargaff’s parity rules Gibbs measure Central Limit Theorem 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Albrecht-Buehler, G.: Asymptotically increasing compliance of genomes with Chargaff’s second parity rules through inversions and inverted transpositions. Proc. Natl. Acad. Sci. USA 103(47), 17828–17833 (2006) CrossRefADSGoogle Scholar
  2. 2.
    Bell, S.J., Forsdyke, R.: Deviations from Chargaff’s second parity rule correlate with direction of transcription. J. Theor. Biol. 197, 63–76 (1999) CrossRefGoogle Scholar
  3. 3.
    Bowen, R.: Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms. Lecture Notes in Mathematics, vol. 470, revised edn. Springer, Berlin (2008). With a preface by David Ruelle, Edited by Jean-René Chazottes Google Scholar
  4. 4.
    Chargaff, E.: Chemical specificity of nucleic acids and mechanism of their enzymatic degradation. Experientia 6(6), 201–209 (1950) CrossRefGoogle Scholar
  5. 5.
    Coelho, Z., Parry, W.: Central limit asymptotics for shifts of finite type. Isr. J. Math. 69(2), 235–249 (1990). doi: 10.1007/BF02937307. http://www.springerlink.com/content/g415tk6310717655/ CrossRefMATHMathSciNetGoogle Scholar
  6. 6.
    Forsdyke, R., Bell, S.J.: Purine loading, stem-loops and Chargaff’s second parity rule: a discussion of the application of elementary principles to early chemical observations. Appl. Bioinformatics 3(3), 3–8 (2004) CrossRefGoogle Scholar
  7. 7.
    Hart, A., Martínez, S.: Statistical testing of Chargaff’s second parity rule in bacterial genome sequences. Stoch. Models 27(2), 1–46 (2011) CrossRefMathSciNetGoogle Scholar
  8. 8.
    Kong, S.-G., Fan, W.-L., Chen, H.-D., Hsu, Z.-T., Zhou, N., Zheng, B., Lee, H.-C.: Inverse symmetry in complete genomes and whole-genome inverse duplication. PLoS ONE 4(11), e7553 (2009) CrossRefGoogle Scholar
  9. 9.
    Lobry, J.: Properties of a general model of DNA evolution under no-strand-bias conditions. J. Mol. Evol. 40(3), 326–330 (1995) CrossRefGoogle Scholar
  10. 10.
    Mitchell, D., Bridge, R.: A test of Chargaff’s second rule. Biochem. Biophys. Res. Commun. 340(1), 90–94 (2006) CrossRefGoogle Scholar
  11. 11.
    Powdel, B., Satapathy, S., Kumar, A., Jha, P., Buragohain, A., Borah, M., Ray, S.: A study in entire chromosomes of violation of the intra-strand parity of complementary nucleotides. DNA Res. 16, 325–343 (2009) CrossRefGoogle Scholar
  12. 12.
    Prabhu, V.: Symmetry observations in long nucleotide sequences. Nucleic Acids Res. 21(12), 2797–2800 (1993) CrossRefGoogle Scholar
  13. 13.
    Rudner, R., Karkas, J., Chargaff, E.: Separation of B. subtilis DNA into complementary strands. III. Direct analysis. Proc. Natl. Acad. Sci. USA 60, 921–922 (1968) CrossRefADSGoogle Scholar
  14. 14.
    Sueoka, N.: Intrastrand parity rules of DNA base composition and usage biases of synonymous codons. J. Mol. Evol. 40(3), 18–325 (1995) CrossRefGoogle Scholar
  15. 15.
    Zhang, S., Huang, Y.: Limited contribution of stem-loop potential to symmetry of single-stranded genomic DNA. Bioinformatics 26(4), 478–485 (2010) CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Departamento Ingeniería Matemática and Centro Modelamiento Matemático, UMI 2071 CNRS-UCHILE, Facultad de Ciencias Físicas y MatemáticasUniversidad de ChileSantiagoChile

Personalised recommendations