Gene expression from polynomial dynamics in the 2-adic information space. (English) Zbl 1198.37144
Summary: 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.
Editorial remark: There are doubts about a proper peer-reviewing procedure of this journal. The editor-in-chief has retired, but, according to a statement of the publisher, articles accepted under his guidance are published without additional control.
Editorial remark: There are doubts about a proper peer-reviewing procedure of this journal. The editor-in-chief has retired, but, according to a statement of the publisher, articles accepted under his guidance are published without additional control.
References:
| [1] | Vladimirov, V. S.; Volovich, I. V.; Zelenov, E. I., \(p\)-Adic analysis and mathematical physics (1994), World Scientific Publ.: World Scientific Publ. Singapore · Zbl 0812.46076 |
| [2] | Volovich, I. V., \(p\)-Adic string, Class Quant Gravity, 4, 83-87 (1987) · Zbl 0636.12015 |
| [3] | Khrennikov, A. Yu., \(p\)-Adic valued distributions in mathematical physics (1994), Kluwer Academic Publishers: Kluwer Academic Publishers Dordrecht · Zbl 0833.46061 |
| [4] | Khrennikov, A. Yu., Non-archimedean analysis: quantum paradoxes, dynamical systems and biological models (1997), Kluwer Academic Publishers: Kluwer Academic Publishers Dordrecht · Zbl 0920.11087 |
| [5] | Parisi, G.; Sourlas, N., \(p\)-Adic numbers and replica symmetry breaking, Eur Phys J, 14B, 535-542 (2000) |
| [6] | Avetisov, V. A.; Bikulov, A. H.; Kozyrev, S. V., Description of logarithmic relaxation by a hierarchical random walk model, Dokl Math, 60, 2, 271-274 (1999) · Zbl 0957.82034 |
| [7] | Khrennikov, A. Yu.; Kozyrev, S. V., Replica symmetry breaking related to a general ultrametric space I: replica matrices and functionals, Physica A, 359, 222-240 (2006) |
| [8] | Khrennikov, A. Yu.; Kozyrev, S. V., Replica symmetry breaking related to a general ultrametric space II: RSB solutions and the \(n \to 0\) limit, Physica A, 359, 241-266 (2006) |
| [9] | El Naschie, M. S., A review of E infinity theory and the mass spectrum of high energy particle physics, Chaos, Solitons and Fractals, 19, 209-236 (2004) · Zbl 1071.81501 |
| [10] | El Naschie, M. S., Fuzzy Dodecahedron topology and E-infinity spacetime as a model for quantum physics, Chaos, Solitons and Fractals, 30, 1025-1033 (2006) |
| [11] | El Naschie, M. S., Topics in the mathematical physics of E-infinity theory, Chaos, Solitons and Fractals, 30, 656-663 (2006) |
| [12] | El Naschie, M. S., On the topological ground state of E-infinity spacetime and the super string connection, Chaos, Solitons and Fractals, 30, 1025-1033 (2007) |
| [13] | El Naschie, M. S., Feigenbaum scenario for turbulence and Cantorian E-infinity theory of high energy particle physics, Chaos, Solitons and Fractals, 32, 911-915 (2007) |
| [14] | Ji-Huan, He., Application of E-infinity theory to turbulence, Chaos, Solitons and Fractals, 30, 506-511 (2006) |
| [15] | Khrennikov, A. Yu., Human subconscious as the \(p\)-adic dynamical system, J Theor Biol, 193, 179-196 (1998) |
| [16] | Khrennikov, A. Yu., \(p\)-Adic dynamical systems: description of concurrent struggle in biological population with limited growth, Dokl Akad Nauk, 361, 752-756 (1998) · Zbl 0955.92028 |
| [17] | Khrennikov, A. Yu., Description of the operation of the human subconscious by means of \(p\)-adic dynamical systems, Dokl Akad Nauk, 365, 458-460 (1999) · Zbl 0964.91045 |
| [18] | Dubischar, D.; Gundlach, M.; Steinkamp, O.; Khrennikov, A. Yu., A \(p\)-adic model for the process of thinking disturbed by physiological and information noise, J Theor Biol, 197, 451-467 (1999) |
| [19] | Khrennikov, A. Yu., \(p\)-Adic discrete dynamical systems and collective behaviour of information states in cognitive models, Discrete Dyn Nat Soc, 5, 59-69 (2000) · Zbl 1229.37128 |
| [20] | Khrennikov, A. Yu., Classical and quantum mechanics on \(p\)-adic trees of ideas, BioSystems, 56, 95-120 (2000) |
| [21] | Khrennikov, A. Yu., Information dynamics in cognitive, psychological, social, and anomalous phenomena (2004), Kluwer Academic Publishers: Kluwer Academic Publishers Dordrecht · Zbl 1175.91151 |
| [22] | Khrennikov, A. Yu., Probabilistic pathway representation of cognitive information, J Theor Biol., 231, 597-613 (2004) · Zbl 1465.92004 |
| [23] | Khrennikov, A. Yu., Ultrametric thinking and Freud’s theory of unconscious mind, (Locks, J. T., New research on consciousness (2006), Nova Science Publ. Inc.), 117-185 |
| [24] | Khrennikov, A. Yu.; Nilsson, M., \(p\)-Adic deterministic and random dynamical systems (2004), Kluwer Academic Publishers: Kluwer Academic Publishers Dordrecht · Zbl 1135.37003 |
| [25] | Pitkänen M. TGD inspired theory of consiousness with applications to biosystems. Electronic book: http://www.physics.helsinki.fi/matpitka/cbookI.html; Pitkänen M. TGD inspired theory of consiousness with applications to biosystems. Electronic book: http://www.physics.helsinki.fi/matpitka/cbookI.html |
| [26] | Khrennikov, A. Yu., P-adic information space and gene expression, (Grant, S.; Heintz, N.; Noebels, J., Integrative approaches to brain complexity (2006), Wellcome Trust Publ.), 14 |
| [27] | Dragovich B, Dragovich A. A p-Adic model of DNA sequence and genetic code. q-bio.GN/0607018; 2006.; Dragovich B, Dragovich A. A p-Adic model of DNA sequence and genetic code. q-bio.GN/0607018; 2006. · Zbl 1187.92039 |
| [28] | Khrennikov, A. Yu.; Kozyrev, S. V., Genetic code on the dyadic plane, Phys A Stat Mech Appl, 381, 265-272 (2007), q-bio/0701007 |
| [29] | Human genom, Nature Collection, 1 June; 2006.; Human genom, Nature Collection, 1 June; 2006. |
| [30] | Wikipedia, 2006, Genetic code, http://en.wikipedia.org; Wikipedia, 2006, Genetic code, http://en.wikipedia.org |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
