Analogies of Coding Systems of DNA and Elementary Particles
DOI:
https://doi.org/10.26713/jims.v17i3.3250Abstract
We suggest that physical reality can be described in the language of division algebras, which dictates that their symmetries must be manifested in the coding systems of different structures of nature. We compare the structures of DNA and fundamental fermions. In both cases we observe (3+4)-element divisions which may arise from the symmetries of the 8-dimensional normed split-algebra. The analogies between the genetic code (given by codons that contain three nucleotide bases) and the properties of the structures of all possible baryons (quark triplets) are discussed. In the genetic code we have the degeneracy of codons built by four standard nucleotides that specify 21 amino acids in humans. Similarly, there are 21 major types of baryons built by four lightest quarks with the degeneration of their spin values. These analogies can help to address some unsolved problems in genetics and physics, like the origin of codon degeneracy, the fermion generation problem and structure of atomic nuclei.
Downloads
References
S. Alexander and T. Manton, Pure gauge theory for the gravitational spin connection, Physical Review D 107 (2023), 064065, DOI: 10.1103/PhysRevD.107.064065.
F. Antoneli and M. Forger, Symmetry breaking in the genetic code: Finite groups, Physical Review Letters 53(7-8) (2011), 1469 – 1488, DOI: 10.1016/j.mcm.2010.03.050.
N. Arkani-Hamed and M. Schmaltz, Hierarchies without symmetries from extra dimensions, Physical Review D 61 (2000), 033005, DOI: 10.1103/PhysRevD.61.033005.
J. C. Baez, The octonions, Bulletin of the American Mathematical Society 39 (2002), 145 – 205, DOI: 10.1090/S0273-0979-01-00934-X, [Erratum: Bulletin of the American Mathematical Society 42 (2005), 213 – 213, DOI: 10.1090/S0273-0979-05-01052-9].
R. Barbieri, L. J. Hall, S. Raby and A. Romanino, Unified theories with U(2) flavor symmetry, Nuclear Physics B 493(1-3) (1997), 3 – 26, DOI: 10.1016/S0550-3213(97)00134-X.
C. Becchi, A. Rouet and R. Stora, Renormalization of gauge theories, Annals of Physics 98(2) (1976), 287 – 321, DOI: 10.1016/0003-4916(76)90156-1.
K. Cahill and S. Özenli, Unitary gauge theories of noncompact groups, Physical Review D 27 (1983), 1396, DOI: 10.1103/PhysRevD.27.1396.
K. Cahill, General internal gauge symmetry, Physical Review D 18 (1978), 2930, DOI: 10.1103/PhysRevD.18.2930.
K. Cahill, Soluble gauge theory of a noncompact group, Physical Review D 20 (1979), 2636, DOI: 10.1103/PhysRevD.20.2636.
N. L. Craig, R. R. Green, C. C. Greider, G. G. Storz and C. Wolberger, Molecular Biology: Principles of Genome Function, Oxford University Press, New York, 983 pages (2021).
R. P. Feynman, R. B. Leighton and M. Sands, The Feynman Lectures on Physics, Vol. 1, Basic Books, NY (2015).
C. D. Froggatt and H. B. Nielsen, Hierarchy of quark masses, cabibbo angles and CP violation, Nuclear Physics B 147(3-4) (1979), 277 – 298, DOI: 10.1016/0550-3213(79)90316-X.
M. Günaydin and F. Gürsey, Quark structure and octonions, Journal of Mathematical Physics 14 (1973), 1651 – 1667, DOI: 10.1063/1.1666240.
M. D. Giulio, The origin of the genetic code: Theories and their relationships, a review, Biosystems 80(2) (2005), 175 – 184, DOI: 10.1016/j.biosystems.2004.11.005.
M. Gogberashvili and A. Gurchumelia, Geometry of the non-compact G(2), Journal of Geometry and Physics 144 (2019), 308 – 313, DOI: 10.1016/j.geomphys.2019.06.015.
M. Gogberashvili and O. Sakhelashvili, Geometrical applications of the split octonions, Advances in Mathematical Physics 2015(1) (2015), 196708, DOI: 10.1155/2015/196708.
D. L. Gonzalez, S. Giannerini and R. Rosa, On the origin of degeneracy in the genetic code, Interface Focus 9 (2019), 20190038, DOI: 10.1098/rsfs.2019.0038.
D. Griffiths, Introduction to Elementary Particles, John Wiley & Sons, Inc., New York (1987).
W. Grimus and P. O. Ludl, Finite flavour groups of fermions, Journal of Physics A: Mathematical and Theoretical 45 (2012), 233001, DOI: 10.1088/1751-8113/45/23/233001.
V. J. Hill and P. Rowlands, Nature’s code, AIP Conference Proceedings 1051 (2008), 117 – 126, DOI: 10.1063/1.3020651.
J. E. M. Hornos and Y. M. Hornos, Algebraic model for the evolution of the genetic code, Physical Review Letters 71 (1993), 4401, DOI: 10.1103/PhysRevLett.71.4401.
J. E. M. Hornos, Y. M. M. Hornos and M. Forger, Symmetry and symmetry breaking: An algebraic approach to the genetic code, International Journal of Modern Physics B 13(23) (1999), 2795 – 2885, DOI: 10.1142/S021797929900268X.
K. Inoue, Generations of quarks and leptons from noncompact horizontal symmetry, Progress of Theoretical Physics 93(2) (1995), 403 – 416, DOI: 10.1143/PTP.93.403.
S. Ito, L. Shen, Q. Dai, S. C. Wu, L. B. Collins, J. A. Swenberg, C. He and Y. Zhang, Tet proteins can convert 5-methylcytosine to 5-formylcytosine and 5-carboxylcytosine, Science 333(6047) (2011), 1300 – 1303, DOI: 10.1126/science.1210597.
B. Julia and J. F. Luciani, Nonlinear realizations of compact and noncompact gauge groups, Physics Letters B 90(3) (1980), 270 – 274, DOI: 10.1016/0370-2693(80)90739-X.
S. F. King and C. Luhn, Neutrino mass and mixing with discrete symmetry, Reports on Progress in Physics 76 (2013), 056201, DOI: 10.1088/0034-4885/76/5/056201.
S. F. King and G. G. Ross, Fermion masses and mixing angles from SU(3) family symmetry, Physics Letters B 520(3-4) (2001), 243 – 253, DOI: 10.1016/S0370-2693(01)01139-X.
E. V. Koonin and A. S. Novozhilov, Origin and evolution of the genetic code: The universal enigma, IUBMB Life 61(2) (2009), 99 – 111, DOI: 10.1002/iub.146.
I. Kwon, K. Kirshenbaum and D. A. Tirrell, Breaking the degeneracy of the genetic code, Journal of the American Chemical Society 125(25) (2003), 7512 – 7513, DOI: 10.1021/ja0350076.
J. Lehmann and A. Libchaber, Degeneracy of the genetic code and stability of the base pair at the second position of the anticodon, RNA 14 (2008), 1264 – 1249, DOI: 10.1261/rna.1029808.
R. Lenstra, Evolution of the genetic code through progressive symmetry breaking, Journal of Theoretical Biology 347 (2014), 95 – 108, DOI: 10.1016/j.jtbi.2014.01.002.
X. Lin, A. C. S. Yu and T. F. Chan, Efforts and challenges in engineering the genetic code, Life 7(1) (2017), 12, DOI: 10.3390/life7010012.
A. E. Margolin and V. I. Strazhev, Quantum non-compact sigma models, Physics Letters B 249(3-4) (1990), 438 – 440, DOI: 10.1016/0370-2693(90)91012-Z.
A. E. Margolin and V. I. Strazhev, Yang-Mills field quantization with non-compact gauge group, Modern Physics Letters A 07(29) (1992), 2747 – 2752, DOI: 10.1142/S0217732392002214.
W. G. McKay and J. Patera, Tables of Dimensions, Indices and Branching Rules for Representations of Simple Lie Algebras, Marcel Dekker, New York, 334 pages (1981).
T. Negadi, The multipletstructure of the genetic code, from one and small number, NeuroQuantology 9(4) (2011), 767 – 771.
Particle Data Group, R. L. Workman, V. D. Burkert, V. Crede, E. Klempt, U. Thoma, L. Tiator, K. Agashe, G. Aielli, B. C. Allanach, C. Amsler, M. Antonelli, E. C. Aschenauer, D. M. Asner, H. Baer, Sw. Banerjee, R. M. Barnett, L. Baudis, C. W. Bauer, J. J. Beatty, V. I. Belousov, J. Beringer, A. Bettini, O. Biebel, K. M. Black, E. Blucher, R. Bonventre, V. V. Bryzgalov, O. Buchmuller, M. A. Bychkov, R. N. Cahn, M. Carena, A. Ceccucci, A. Cerri, R. Sekhar. Chivukula, G. Cowan, K. Cranmer, O. Cremonesi, G. D’Ambrosio, T. Damour, D. de Florian, A. de Gouvêa, T. DeGrand, P. de Jong, S. Demers, B. A. Dobrescu, M. D’Onofrio, M. Doser, H. K. Dreiner, P. Eerola, U. Egede, S. Eidelman, A. X. El-Khadra, J. Ellis, S. C. Eno, J. Erler, V. V. Ezhela, W. Fetscher, B. D. Fields, A. Freitas, H. Gallagher, Y. Gershtein, T. Gherghetta, M. C. GonzalezGarcia, M. Goodman, C. Grab, A. V. Gritsan, C. Grojean, D. E. Groom, M. Grünewald, A. Gurtu, T. Gutsche, H. E. Haber, Matthieu. Hamel, C. Hanhart, S. Hashimoto, Y. Hayato, A. Hebecker, S. Heinemeyer, J. J. Hernández-Rey, K. Hikasa, J. Hisano, A. Höcker, J. Holder, L. Hsu, J. Huston, T. Hyodo, Al. Ianni, M. Kado, M. Karliner, U. F. Katz, M. Kenzie, V. A. Khoze, S. R. Klein, F. Krauss, M. Kreps, P. Križan, B. Krusche, Y. Kwon, O. Lahav, J. Laiho, L. P. Lellouch, J. Lesgourgues, A. R. Liddle, Z. Ligeti, C.-J. Lin, C. Lippmann, T. M. Liss, L. Littenberg, C. Lourenço, K. S. Lugovsky, S. B. Lugovsky, A. Lusiani, Y. Makida, F. Maltoni, T. Mannel, A. V. Manohar, W. J. Marciano, A. Masoni, J. Matthews, U.-G. Meißner, I.-A. Melzer-Pellmann, M. Mikhasenko, D. J. Miller, D. Milstead, R. E. Mitchell, K. Mönig, P. Molaro, F. Moortgat, M. Moskovic, K. Nakamura, M. Narain, P. Nason, S. Navas, A. Nelles, M. Neubert, P. Nevski, Y. Nir, K. A. Olive, C. Patrignani, J. A. Peacock, V. A. Petrov, E. Pianori, A. Pich, A. Piepke, F. Pietropaolo, A. Pomarol, S. Pordes, S. Profumo, A. Quadt, K. Rabbertz, J. Rademacker, G. Raffelt, M. Ramsey-Musolf, B. N. Ratcliff, P. Richardson, A. Ringwald, D. J. Robinson, S. Roesler, S. Rolli, A. Romaniouk, L. J. Rosenberg, J. L. Rosner, G. Rybka, M. G. Ryskin, R. A. Ryutin, Y. Sakai, S. Sarkar, F. Sauli, O. Schneider, S. Schönert, K. Scholberg, A. J. Schwartz, J. Schwiening, D. Scott, F. Sefkow, U. Seljak, V. Sharma, S. R. Sharpe, V. Shiltsev, G. Signorelli, M. Silari, F. Simon, T. Sjöstrand, P. Skands, T. Skwarnicki, G. F. Smoot, A. Soffer, M. S. Sozzi, S. Spanier, C. Spiering, A. Stahl, S. L. Stone, Y. Sumino, M. J. Syphers, F. Takahashi, M. Tanabashi, J. Tanaka, M. Taševský, K. Terao, K. Terashi, J. Terning, R. S. Thorne, M. Titov, N. P. Tkachenko, D. R. Tovey, K. Trabelsi, P. Urquijo, G. Valencia, R. Van. de Water, N. Varelas, G. Venanzoni, L. Verde, I. Vivarelli, P. Vogel, W. Vogelsang, V. Vorobyev, S. P. Wakely, W. Walkowiak, C. W. Walter, D. Wands, D. H. Weinberg, E. J. Weinberg, N. Wermes, M. White, L. R. Wiencke, S. Willocq, C. G. Wohl, C. L. Woody, W.-M. Yao, M. Yokoyama, R. Yoshida, G. Zanderighi, G. P. Zeller, O. V. Zenin, R.-Y. Zhu, S.-L. Zhu, F. Zimmermann, P. A. Zyla, Review of particle physics, Progress of Theoretical and Experimental Physics 2022(8) (2022), 083C01, DOI: 10.1093/ptep/ptac097.
J. A. Piccirilli, S. A. Benner, T. Krauch and S. E. Moroney, Enzymatic incorporation of a new base pair into DNA and RNA extends the genetic alphabet, Nature 343 (1990), 33 – 37, DOI: 10.1038/343033a0.
A. Piovesan, F. Antonaros, L. Vitale, P. Strippoli, M. C. Pelleri and M. Caracausi, Human protein-coding genes and gene feature statistics in 2019, BMC Research Notes 12 (2019), Article number: 315, DOI: 10.1186/s13104-019-4343-8.
D. J. Pons, A. D. Pons and A. J. Pons, Nuclear polymer explains the stability, instability, and nonexistence of nuclides, Physics Research International 2015(1) (2015), 651361, DOI: 10.1155/2015/651361.
K. Popper, Realism and the Aim of Science: From the Postscript to the Logic of Scientific Discovery, 1st edition, edited by W. W. Bartley III, Routledge, London, 464 pages (2013), DOI: 10.4324/9780203713969.
L. Pray, Discovery of DNA structure and function: Watson and Crick, Nature Education 1(1) (2008) 100.
E. A. Rietman, R. L. Karp and J. A. Tuszynski, Review and application of group theory to molecular systems biology, Theoretical Biology and Medical Modelling 8 (2011), Article number: 21, DOI: 10.1186/1742-4682-8-21.
R. Schafer, Introduction to Non-Associative Algebras, Dover, NY (1995).
S. Sengupta and P. G. Higgs, A unified model of codon reassignment in alternative genetic codes, Genetics 170(2) (2005), 831 – 840, DOI: 10.1534/genetics.104.037887.
O. Sorlin and M. G. Porquet, Nuclear magic numbers: New features far from stability, Progress in Particle and Nuclear Physics 61(2) (2008), 602 – 673, DOI: 10.1016/j.ppnp.2008.05.001.
T. A. Springer and F. D. Veldkamp, Octonions, Jordan Algebras and Exceptional Groups, 1st edition, Springer Monographs in Mathematics, Springer, Berlin (2000), DOI: 10.1007/978-3-662-12622-6.
C. Switzer, S. E. Moroney and S. A. Benner, Enzymatic incorporation of a new base pair into DNA and RNA, Journal of the American Chemical Society 111(21) (1989), 8322 – 8323, DOI: 10.1021/ja00203a067.
R. A. Wilson, Finite symmetry groups in physics, arXiv 2102.02817 [math.GR], DOI: 10.48550/arXiv.2102.02817.
Y. Zhang, P. V. Baranov, J. F. Atkins and V. N. Gladyshev, Pyrrolysine and selenocysteine use dissimilar decoding strategies, Journal of Biological Chemistry 280(21) (2005), 20740 – 20751, DOI: 10.1074/jbc.M501458200.
L. Zhang, Z. Yang, K. Sefah, K. M. Bradley, S. Hoshika, M.-J. Kim, H.-J. Kim, G. Zhu, E. Jiménez, S. Cansiz, I.-T. Teng, C. Champanhac, C. McLendon, C. Liu, W. Zhang, D. L. Gerloff, Z. Huang, W. Tan and S. A. Benner, Evolution of functional six-nucleotide DNA, Journal of the American Chemical Society 137(21) (2015), 6734 – 6737, DOI: 10.1021/jacs.5b02251.
J. Zupan, Introduction to flavour physics, CERN Yellow Reports: School Proceedings 6 (2019), 181 – 212, DOI: 10.23730/CYRSP-2019-006.181.
Downloads
Published
How to Cite
Issue
Section
License
Authors who publish with this journal agree to the following terms:- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a CCAL that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.
