Abstract
The well-known golden ratio and knowledge about genetic coding systems are useful for artificial intelligence systems, engineering, and education. The golden ratio has been recently suggested for an expansion to the field of probabilistic and artificial intelligence in Tanackov et al. (Tehni ki vjesnikč 18:641–647, 2011) [1], in brain research (Conte et al. in Chaos, Solitons Fractals 41:2790–2800, 2009; Pletzer et al. in Brain Res. 1335:91–102) [2, 3], and in human facial proportion (Mizumoto et al. in Am. J. Orthod. Dentofac. Orthop. 136:168–74; Petoukhov in Binary sub-alphabets of genetic language and problem of unification bases of biological languages. Dubna, Russia, p. 191, 2002) [4, 5]. In this paper, we consider the number of hydrogen bonds of genetic code matrix and establish a relation with golden ratio matrix. We construct three-dimensional cubes from two-dimensional matrices. Furthermore, we revealed some numerical patterns of golden ratios under basic addition operation. The relationship data about the genetic stochastic matrices/cubes associated with the genetic codes play important roles on our new understanding of genetic code systems and can lead to new effective algorithms of information processing for modeling mutual communication among different parts of the genetic ensemble.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Tanackov, I., Jovan, T., Kostelacepi’c, M.: The golden ratio in probabilistic and artificial intelligence. Tehni ki vjesnikč 18(4), 641–647 (2011)
Conte, E., Khrennikov, A., Federici, A., Zbilut, J. P.: Fractal fluctuations and quantum-like chaos in the brain by analysis of variability of brain waves: a new method based on a fractal variance function and random matrix theory: a link with El Naschie fractal Cantorian space–time and V. Weiss and H. Weiss golden ratio in brain. Chaos, Solitons Fractals 41, 2790–2800 (2009)
Pletzer, B., Kerschbaum, H., Klimesch, W.: When frequencies never synchronize: the golden mean and the resting EEG. Brain Res. 1335, 91–102 (2010)
Mizumoto, Y., Deguchi, T., Kelvin, W.C.F.: Assessment of facial golden proportions among young Japanese women. Am. J. Orthod. Dentofac. Orthop. 136, 168–174 (2009)
Petoukhov, S. V.: Binary sub-alphabets of genetic language and problem of unification bases of biological languages. In: IX International Conference on Mathematics, Computer, Education, p. 191. Russia, Dubna, 28–31 Jan 2002 (in Russian)
Knight, R.D., Freeland, S.J., Landweber, L.F.: Selection, history and chemistry: the three faces of the genetic code. TIBS 24, 241–247 (1999)
Swanson, R.: A unifying concept for the amino acid code. Bull. Math. Biol. 46(2), 187–203 (1984)
Jimenéz-Montaño, M.A., Mora-Basáñez, C.R., Pöschel, T.: On the hypercube structure of the genetic code. In: Lim, H.A., Cantor, C.A. (eds.) Proceedings of 3rd International Conference on Bioinformatics and Genome Research, p. 445. World Scientific (1994)
Yang, C.M.: The naturally designed spherical symmetry in the genetic code (2003). http://arxiv.org/abs/q-bio.BM/0309014
Štambuk, N.: Universal metric properties of the genetic code. Croat. Chem. Acta 73(4), 1123–1139 (2000)
Petoukhov, S.V.: The Bi-periodic Table of Genetic Code and Number of Protons, Foreword of K. V. Frolov, p. 258. Moscow (in Russian) (2001)
Petoukhov, S.V.: Genetic code and the ancient chinese book of changes. Symmetry: Cult. Sci. 10(3–4), 211–226 (1999)
He, M.: Double helical sequences and doubly stochastic matrices. In: Symmetry: Culture and Science, Symmetries in Genetic Information, International Symmetry Foundation, Budapest, 2004, pp. 307–330 (2003a)
He, M.: Symmetry in structure of genetic code. In: Proceedings of the Third All-Russian Interdisciplinary Scientific Conference on Ethics and the Science of Future. Unity in Diversity, Moscow, 12–14 Feb 2003b
He, M.: Genetic code, attributive mappings and stochastic matrices. Bull. Math. Biol. 66(5), 965–973 (2004)
He, M., Petoukhov, S.V.: Mathematics of Bioinformatics: Theory, Practice, and Applications, Wiley (2011)
He, M., Petoukhov, S.V., Ricci, P.E.: Genetic code, Hamming distance and stochastic matrices. Bull. Math. Biol. 66, 1405–1421 (2004)
Perez, J.C.: Codon populations in single-stranded whole human genome DNA are fractal and fine-tuned by the Golden ratio 1.618. Interdiscip. Sci. 2(3), 228–240 (2010)
Watson, J.: The Double Helix. Atheneum, New York (1968)
Higgins, D., Taylor, W.: Bioinformatics. Oxford University Press, Oxford (2000)
Percus, J.: Mathematics of Genome Analysis. Cambridge University Press Press, New York (2002)
Pevzner, P.: Computational Molecular Biology. MIT Press, Cambridge (2000)
Kay, L.: Who Wrote the Book of Life? A History of the Genetic Code. Stanford University Press, Stanford (2000)
Mousa, H.M.: DNA-genetic encryption technique. Int. J. Comput. Netw. Inf. Secur. (IJCNIS) 8(7): 1–9 (2016). https://doi.org/10.5815/ijcnis.2016.07.01
Ma, J., Li, J., Dong, Y.: DNA 3D self-assembly algorithmic model to solve maximum Clique problem. Int. J. Image, Graph. Sign. Process. (IJIGSP) 3(3), 41–48 (2011). https://doi.org/10.5815/ijigsp.2011.03.06
Hossein, S.M., Roy, S.: A compression & encryption algorithm on dna sequences using dynamic look up table and modified huffman techniques. Int. J. Inf. Technol. Comput. Sci. (IJITCS) 5(10), 39–61 (2013). https://doi.org/10.5815/ijitcs.2013.10.05
Schmid, K., Marx, D., Samal, A.: Computation of a face attractiveness index based on neoclassical canons, symmetry, and golden ratios. Pattern Recogn. 41, 2710–2717 (2008)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
He, M., Hu, Z.B., Petoukhov, S.V. (2020). Standard Genetic Code and Golden Ratio Cubes. In: Hu, Z., Petoukhov, S., He, M. (eds) Advances in Artificial Systems for Medicine and Education II. AIMEE2018 2018. Advances in Intelligent Systems and Computing, vol 902. Springer, Cham. https://doi.org/10.1007/978-3-030-12082-5_3
Download citation
DOI: https://doi.org/10.1007/978-3-030-12082-5_3
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-12081-8
Online ISBN: 978-3-030-12082-5
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)