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Random Fields Approach to the Study of DNA Chains

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Abstract

We apply the random field theory tothe study of DNA chains which we assume tobe trajectories of a stochastic process. Weconstruct statistical potential betweennucleotides corresponding to theprobabilities of those trajectories thatcan be obtained from the DNA data basecontaining millions of sequences. It turnsout that this potential has aninterpretation in terms of quantitiesnaturally arrived at during the study ofevolution of species i.e. probabilities ofmutations of codons. Making use of recentlyperformed statistical investigations of DNAwe show that this potential has differentqualitative properties in coding andnoncoding parts of genes. We apply ourmodel to data for various organisms andobtain a good agreement with the resultsjust presented in the literature. We alsoargue that the coding/noncoding boundariescan corresponds to jumps of the potential.

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References

  • Arneodo, A., d'Aubenton-Carafa, Y., Audit, B., Bacry, E., Muzy, J.F. and Thermes, C.: What Can We Learn With Wavelets about DNA Sequences, Physica A 249(Feb.1) (1998), 439-448.

    Google Scholar 

  • Arneodo, A., Bacry, E., Graves, P.V. and Muzy, J.F.: Characterizing Long-Range Correlations in DNA Sequences from Wavelet Analysis, Phys. Rev. Lett. 74(16) (1995), 3293-3296.

    Google Scholar 

  • Audit, B., Vaillant, C., Arneodo, A., d'Aubenton-Carafa, Y. and Thermes, C.: Long-Range Correlations between DNA Bending Sites: Relation to the Structure and Dynamics of Nucleosomes, J. Mol. Biol. 316(4, Mar. 1) (2002), 903-918.

    Google Scholar 

  • Barral, J.P., Hasmy, A., Jimenez, J. and Marcano, A.: Nonlinear Modeling Technique for the Analysis of DNA Chains, Phys. Rev. E. 61(2, Feb.) (2000), 1812-1815.

    Google Scholar 

  • Buldyrev, S.V., Goldberger, A.L., Havlin, S., Mantegna, R.N., Matsa, M.E., Peng, C.K., Simons, M. and Stanley, H.E.: Long-Range Correlation Properties of Coding and Noncoding DNA Sequences: GenBank Analysis, Phys. Rev. E 51 (1995), 5084-5091.

    Google Scholar 

  • Buldyrev, S.V., Dokholyan, N.V., Goldberger, A.L., Havlin, S., Peng, C.K., Stanley, H.E. and Viswanathan, G.M.: Analysis of DNA Sequences Using Methods of Statistical Physics, Physica A 249 (1998), 430-438.

    Google Scholar 

  • Calladine, C.R. and Drew, H.R.: Understanding DNA, Academic Press, New York, 1992.

    Google Scholar 

  • Chen, Y.Z., Mohan, V. and Griffey, R.H.: Base Opening in RNA and DNA Duplexes: Implication for RNA Stability, Phys. Rev. E 61(5, May) (2000), 5640-5645.

    Google Scholar 

  • Cover, T.M. and Thomas, J.A.: Elements of Information Theory, J. Wiley & Sons, New York, 1991.

    Google Scholar 

  • Coward, E.: Equivalence of two Fourier Methods for Biological Sequences, J. Math. Biol. 36 (1997), 64-70.

    Google Scholar 

  • Dreismann, A.C. and Larhammer, D.: Long-Range Correlations in DNA, Nature 361 (1993), 212-213.

    Google Scholar 

  • Farach, M., Noordewier, M., Savari, S., Shepp, L., Wyner, A. and Ziv, J.: On the Entropy of DNA: Algorithms and Measurements based on Memory and Rapid Convergence, Symposium on Discrete Algorithms (SODA) 1995.

  • Grosse, I., Herzel, H., Buldyrev, S.V. and Stanley, H.E.: Species Independence ofMutual Information in Coding and Noncoding DNA, Physical Review E 61(5, May) (2000), 5624-5629.

    Google Scholar 

  • Herzel, H., Trifonov, E.N., Weiss, O. and Grosse, I.: Interpreting Correlations in Biosequences, Physica A 249 (1998), 449-459.

    Google Scholar 

  • Huang, K.: Statistical Mechanics, John Wiley and Sons, Inc., New York, 1963.

    Google Scholar 

  • Kemeny, J., Snell, J.L. and Kanpp, A.W.: Denumerable Markov Chains, New York-Heidelberg-Berlin, Springer Verlag, 1976.

    Google Scholar 

  • Kreitman, M. and Cameron, J.M.: Coding Sequence Evolution, Curr. Opinion Genet. Devel. 9 (1999), 637-641.

    Google Scholar 

  • Li, W.-H., Marr, T.G. and Kaneko, K.: Understanding Long-Range Correlations in DNA Sequences, Physica D 75 (1994), 392-416.

    Google Scholar 

  • Lipniacki, T.: Chemically Driven Travelling Waves in DNA, Phys. Rev. E 60(6, December) (1999), 7253-7261.

    Google Scholar 

  • Luo, L., Lee, W., Jia, L., Ji, F. and Tsai, L.: Statistical Correlation of Nucleotides in a DNA Sequence, Phys. Rev. E 58(1, July) (1998), 861-871.

    Google Scholar 

  • Peng, C.K., Buldyrev, S.V., Goldberger, A.L., Havlin, S., Sciortino, F., Simons, M. and Stanley, H.E.: Long-Range Correlations in Nucleotide Sequences, Nature 356 (1992), 168-170.

    Google Scholar 

  • Roman-Roldan, R., Bernaola-Galvan, P. and Oliver, J.L.: Sequence Complexity of DNA through an Entropic Segmentation Method, Phys. Rev. Lett. 80 (1998), 1344-1347.

    Google Scholar 

  • Voss, R.F.: Evolution of Long-Range Fractal Correlations and 1/f Noise in DNA Base Sequences, Phys. Rev. Lett. 68 (1992), 3805-3808.

    Google Scholar 

  • Wyner, A.D., Ziv, J. and Wyner, A.J.: On the Role of Pattern Matching in Information Theory, IEEE Trans. on Inform. Theory 44(6, October) (1998), 2045-2056.

    Google Scholar 

  • Yockey, H.P.: Information Theory and Molecular Biology, Cambridge University Press, 1992.

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Szczepański, J., Michałek, T. Random Fields Approach to the Study of DNA Chains. Journal of Biological Physics 29, 39–54 (2003). https://doi.org/10.1023/A:1022508206826

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