Geodesic
Gene Expression from 2-adic Dynamical Systems
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Selected topics of mathematical physics and $p$-adic analysis, Tome 265 (2009), pp. 142-150.

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We perform geometrization of genetics by representing genetic information by points of the 4-adic information space. By a 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 the 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. 
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A. Yu. Khrennikov. Gene Expression from 2-adic Dynamical Systems. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Selected topics of mathematical physics and $p$-adic analysis, Tome 265 (2009), pp. 142-150. http://geodesic.mathdoc.fr/item/TM_2009_265_a10/

[1] Vladimirov V. S., Volovich I. V., Zelenov E. I., $p$-Adicheskii analiz i matematicheskaya fizika, Nauka, M., 1994 | MR

[2] Volovich I. V., “$p$-Adic string”, Class. and Quantum Grav., 4 (1987), L83–L87 | DOI | MR

[3] Khrennikov A. Yu., $p$-Adic valued distributions in mathematical physics, Kluwer, Dordrecht, 1994 | MR | Zbl

[4] Khrennikov A. Yu., Non-Archimedean analysis: Quantum paradoxes, dynamical systems and biological models, Kluwer, Dordrecht, 1997 | MR | Zbl

[5] Parisi G., Sourlas N., “$p$-Adic numbers and replica symmetry breaking”, Eur. Phys. J. B, 14 (2000), 535–542 | DOI | MR

[6] Avetisov V. A., Bikulov A. Kh., Kozyrev S. V., “Opisanie logarifmicheskoi relaksatsii modelyu ierarkhicheskogo sluchainogo bluzhdaniya”, DAN, 368:2 (1999), 164–167 | MR | Zbl

[7] Khrennikov A. Yu., Kozyrev S. V., “Replica symmetry breaking related to a general ultrametric space. I: Replica matrices and functionals”, Physica A, 359 (2006), 222–240 | DOI | MR

[8] Khrennikov A. Yu., Kozyrev S. V., “Replica symmetry breaking related to a general ultrametric space. II: RSB solutions and the $n\to0$ limit”, Physica A, 359 (2006), 241–266 | DOI | MR

[9] Khrennikov A. Yu., “Human subconscious as a $p$-adic dynamical system”, J. Theor. Biol., 193 (1998), 179–196 | DOI

[10] Khrennikov A. Yu., “$p$-Adicheskie dinamicheskie sistemy: opisanie konkurentnoi borby v biologicheskoi populyatsii s ogranichennym rostom naseleniya”, DAN, 361:6 (1998), 752–754 | MR | Zbl

[11] Khrennikov A. Yu., “Opisanie raboty chelovecheskogo podsoznaniya s pomoschyu $p$-adicheskikh dinamicheskikh sistem”, DAN, 365:4 (1999), 458–460 | MR | Zbl

[12] Dubischar D., Gundlach V. M., Steinkamp O., Khrennikov A., “A $p$-adic model for the process of thinking disturbed by physiological and information noise”, J. Theor. Biol., 197 (1999), 451–467 | DOI

[13] Khrennikov A., “$p$-Adic discrete dynamical systems and collective behaviour of information states in cognitive models”, Discr. Dyn. Nat. and Soc., 5 (2000), 59–69 | DOI | Zbl

[14] Khrennikov A., “Classical and quantum dynamics on $p$-adic trees of ideas”, Biosystems, 56 (2000), 95–120 | DOI

[15] Khrennikov A., Information dynamics in cognitive, psychological, social and anomalous phenomena, Kluwer, Dordrecht, 2004 | MR | Zbl

[16] Khrennikov A., “Probabilistic pathway representation of cognitive information”, J. Theor. Biol., 231 (2004), 597–613 | DOI

[17] Khrennikov A. Yu., “Ultrametric thinking and Freud's theory of the unconscious mind”, New research on consciousness, ed. J. T. Locks, Nova Sci. Publ., Hauppauge, NY, 2006, 119–187 | MR

[18] Khrennikov A. Yu., Nilsson M., $p$-Adic deterministic and random dynamics, Kluwer, Dordrecht, 2004 | MR | Zbl

[19] Pitkänen M., TGD inspired theory of consciousness with applications to biosystems, E-print , 2006 http://tgd.wippiespace.com/public_html/cbookI.html

[20] Khrennikov A. Yu., “$p$-Adic information space and gene expression”, Integrative approaches to brain complexity, eds. S. Grant, N. Heintz, J. Noebels, Wellcome Trust, Cambridge, 2006, 14

[21] Dragovich B., Dragovich A., A $p$-adic model of DNA sequence and genetic code, E-print , 2006 arXiv: q-bio/0607018

[22] Khrennikov A. Yu., Kozyrev S. V., “Genetic code on the diadic plane”, Physica A: Stat. Mech. and Appl., 381 (2007), 265–272 ; E-print arXiv: q-bio/0701007 | DOI

[23] Human genome collection, Nature, Suppl., 2006, June 1

[24] Genetic code, Wikipedia, the free encyclopedia , 1 May 2009, 01:48 http://en.wikipedia.org/w/index.php?title=Genetic_code&oldid=287167098