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Gene expression from polynomial dynamics in the 2-adic information space

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  • Khrennikov, Andrei Yu.

Abstract

We perform geometrization of genetics by representing genetic information by points of the 4-adic information space. By well known theorem of number theory this space can also be represented as the 2-adic space. The process of DNA-reproduction is described by the action of a 4-adic (or equivalently 2-adic) dynamical system. As we know, the genes contain information for production of proteins. The genetic code is a degenerate map of codons to proteins. We model this map as functioning of a polynomial dynamical system. The purely mathematical problem under consideration is to find a dynamical system reproducing the degenerate structure of the genetic code. We present one of possible solutions of this problem.

Suggested Citation

  • Khrennikov, Andrei Yu., 2009. "Gene expression from polynomial dynamics in the 2-adic information space," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 341-347.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:1:p:341-347
    DOI: 10.1016/j.chaos.2008.12.012
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    References listed on IDEAS

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    1. Andrie Khrennikov, 2000. "p -Adic discrete dynamical systems and collective behaviour of information states in cognitive models," Discrete Dynamics in Nature and Society, Hindawi, vol. 5, pages 1-11, January.
    2. Khrennikov, A.Yu. & Kozyrev, S.V., 2007. "Genetic code on the diadic plane," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 381(C), pages 265-272.
    3. El Naschie, M.S., 2007. "Feigenbaum scenario for turbulence and Cantorian E-infinity theory of high energy particle physics," Chaos, Solitons & Fractals, Elsevier, vol. 32(3), pages 911-915.
    4. Khrennikov, A.Yu. & Kozyrev, S.V., 2006. "Replica symmetry breaking related to a general ultrametric space—II: RSB solutions and the n→0 limit," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 359(C), pages 241-266.
    5. El Naschie, M.S., 2006. "Fuzzy Dodecahedron topology and E-infinity spacetime as a model for quantum physics," Chaos, Solitons & Fractals, Elsevier, vol. 30(5), pages 1025-1033.
    6. El Naschie, M.S., 2007. "On the topological ground state of E-infinity spacetime and the super string connection," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 468-470.
    7. Khrennikov, A.Yu. & Kozyrev, S.V., 2006. "Replica symmetry breaking related to a general ultrametric space I: Replica matrices and functionals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 359(C), pages 222-240.
    8. El Naschie, M.S., 2006. "Topics in the mathematical physics of E-infinity theory," Chaos, Solitons & Fractals, Elsevier, vol. 30(3), pages 656-663.
    9. He, Ji-Huan, 2006. "Application of E-infinity theory to turbulence," Chaos, Solitons & Fractals, Elsevier, vol. 30(2), pages 506-511.
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