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Gibbs field approach for evolutionary analysis of regulatory signal of gene expression. (English. Russian original) Zbl 1172.92351
Probl. Inf. Transm. 44, No. 4, 333-351 (2008); translation from Probl. Peredachi Inf. 44, No. 4, 52-71 (2008).
Summary: We propose a new approach to modeling a nucleotide sequence evolution subject to constraints on the secondary structure. The approach is based on the problem of optimizing a functional that involves both standard evolution of the primary structure and a condition of secondary structure conservation. We discuss simulation results in the example of evolution in the case of classical attenuation regulation.
92C40 Biochemistry, molecular biology
92D15 Problems related to evolution
60J22 Computational methods in Markov chains
92-08 Computational methods for problems pertaining to biology
92D10 Genetics and epigenetics
Full Text: DOI
[1] Ewens, W. and Grant, G., Statistical Methods in Bioinformatics: An Introduction, New York: Springer, 2001. · Zbl 0965.92001
[2] Mathematics of Evolution and Phylogeny, Gascuel, O., Ed., New York: Oxford Univ. Press, 2005. · Zbl 1104.92332
[3] Lyubetsky, V., Gorbunov, K., Rusin, L., and V’yugin, V., Algorithms to Reconstruct Evolutionary Events at Molecular Level and Infer Species Phylogeny, Bioinformatics of Genome Regulation and Structure II, Kolchanov, N., Hofest√§dt, R., and Milanesi, L., Eds., New York: Springer, 2006, pp. 189–204.
[4] Singer, M., and Berg, P., Genes & Genomes: A Changing Perspective, Mill Valley: Univ. Science Book, 1991. Translated under the title Geny i genomy, Moscow: Mir, 1998.
[5] Lyubetsky, V.A., Pirogov, S.A., Rubanov, L.I., and Seliverstov, A.V., Modeling Classic Attenuation Regulation of Gene Expression in Bacteria, J. Bioinform. Comput. Biol., 2007, vol. 5, no. 1, pp. 155–180. · Zbl 05427806 · doi:10.1142/S0219720007002576
[6] Lee, F. and Yanofsky, C., Transcription Termination at the trp Operon Attenuators of Escherichia coli and Salmonella typhimurium: RNA Secondary Structure and Regulation of Termination, Proc. Natl. Acad. Sci. USA, 1977, vol. 74, no. 10, pp. 4365–4369. · doi:10.1073/pnas.74.10.4365
[7] Mironov, A.A. and Kister, A.E., Theoretical Analysis of RNA Secondary Structure Formation Kinetics during Transcription and Translation. Accounting for Imperfect Helices, Mol. Biol. (Moscow), 1985, vol. 19, no. 5, pp. 1350–1357.
[8] Bleher, P.M., Ruiz, J., and Zagrebnov, V.A., On the Purity of Limiting Gibbs State for the Ising Model on the Bethe Lattice, J. Stat. Phys., 1995, vol. 79, nos. 1–2, pp. 473–482. · Zbl 1081.82515 · doi:10.1007/BF02179399
[9] Evans, W., Kenyon, C., Peres, Y., and Schulman, L.J., Broadcasting on Trees and the Ising Model, Ann. Appl. Probab., 2000, vol. 10, no. 2, pp. 410–433. · Zbl 1052.60076 · doi:10.1214/aoap/1019487349
[10] Martinelli, F., Sinclair, A., and Weitz, D., Glauber Dynamics on Trees. Boundary Conditions and Mixing Time, Comm. Math. Phys., 2004, vol. 250, no. 2, pp. 301–334. · Zbl 1076.82010 · doi:10.1007/s00220-004-1147-y
[11] Durbin, R., Eddy, S., Krogh, A., and Mitchison, G., Biological Sequence Analysis: Probabilistic Models of Proteins and Nucleic Acids, Cambridge: Cambridge Univ. Press, 1998. Translated under the title Analiz biologicheskikh posledovatel’nostei, Moscow-Izhevsk: Regulyarnaya i haoticheskaya dinamika, 2006.
[12] Muse, S.V., Evolutionary Analyses of DNA Sequences subject to Constraints on Secondary Structure, Genetics, 1995, vol. 139, pp. 1429–1439.
[13] Savill, N.J., Hoyle, D.C., and Higgs, P.G., RNA Sequence Evolution with Secondary Structure Constraints: Comparison of Substitution Rate Models Using Maximum-Likelihood Methods, Genetics, 2001, vol. 157, no. 1, pp. 399–411.
[14] Telford, M.J., Wise, M.J., and Gowri-Shankar, V., Consideration of RNA Secondary Structure Significantly Improves Likelihood-based Estimates of Phylogeny: Examples from the Bilateria, Mol. Biol. Evol., 2005, vol. 22, no. 4, pp. 1129–1136. · doi:10.1093/molbev/msi099
[15] Kosakovsky Pond, S.L., Mannino, F.V., Gravenor, M.B., Muse, S.V., and Frost, S.D., Evolutionary Model Selection with a Genetic Algorithm: A Case Study Using Stem RNA, Mol. Biol. Evol., 2007, vol. 24, no. 1, pp. 159–170. · doi:10.1093/molbev/msl144
[16] Mathematical Methods for DNA Sequences, Waterman, M.S., Ed., Boca Raton: CRC Press, 1989. Translated under the title Matematicheskie metody dlya analiza posledovatel’nostei DNK, Moscow: Mir, 1999.
[17] Lyubetsky, V.A., Zhizhina, E.A., Gorbunov, K.Yu., and Seliverstov, A.V., Model of Evolution of Nucleotide Sequence, in Proc. 13th All-Russia Conf. on Mathematical Methods of Pattern Recognition, Zelenogorsk, Russia, 2007, Moscow: MAKS Press, 2007, pp. 605–609.
[18] Geman, S. and Geman, D., Stochastic Relaxation, Gibbs Distribution, and the Bayesian Restoration of Images, IEEE Trans. Pattern Anal. Machine Intelligence, 1984, vol. 6, pp. 721–741. · Zbl 0573.62030 · doi:10.1109/TPAMI.1984.4767596
[19] Kirkpatrick, S., Gelatt, C.D., and Vecchi, M.P., Optimization by Simulated Annealing, Science, 1983, vol. 220, no. 4598, pp. 671–680. · Zbl 1225.90162 · doi:10.1126/science.220.4598.671
[20] Vitreschak, A.G., Lyubetskaya, E.V., Shirshin, M.A., Gelfand, M.S., and Lyubetsky, V.A., Attenuation Regulation of Amino Acid Biosynthetic Operons in Proteobacteria: Comparative Genomics Analysis, FEMS Microbiol. Lett., 2004, vol. 234, no. 2, pp. 357–370. · doi:10.1111/j.1574-6968.2004.tb09555.x
[21] Gorbunov, K.Yu. and Lyubetsky, V.A., Model of Evolution of Nucleotide Sequence Considering Its Secondary Structure, in Proc. Int. Sci. Conf. on Computational Phylogenomics and Genosystematics, Moscow, 2007, Moscow: Mosk. Gos. Univ., 2007, pp. 68–71.
[22] Gorbunov, K. and Lyubetsky, V., Reconstruction of Ancestral Regulatory Signals along a Transcription Factor Tree, Mol. Biol. (Moscow), 2007, vol. 41, no. 5, pp. 836–842. · doi:10.1134/S0026893307050172
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