Skip to main content
SpringerLink
Log in

On the 28-gon symmetry inherent in the genetic code intertwined with aminoacyl-tRNA synthetases—The Lucas series

  • Published:
Bulletin of Mathematical Biology Aims and scope Submit manuscript

Abstract

Despite considerable efforts it has remained unclear what principle governs the selection of the 20 canonical amino acids in the genetic code. Based on a previous study of the 28-gonal and rotational symmetric arrangement of the 20 amino acids in the genetic code, new analyses of the organization of the genetic code system together with their intrinsic relation to the two classes of aminoacyl-tRNA synthetases are reported in this work. A close inspection revealed how the enzymes and the 20 gene-encoded amino acids are intertwined on the polyhedron model. Complementary and cooperative symmetries between class I and class II aminoacyl-tRNA synthetases displayed by a 28-gon organization are discussed, and we found that the two previously suggested evolutionary axes within the genetic code overlap the symmetry axes within the two classes of aminoacyl-tRNA synthetases. Moreover, it has been shown that the side-chain carbon-atom numbers (2, 1, 3, 4 and 7) in the overwhelming majority of the amino acids recognized by each of the two classes of aminoacyl-tRNA synthetases are determined by a mathematical relationship, the Lucas series. A stepwise co-evolutionary selection logic of the amino acids is manifested by the amino acid side-chain carbon-atom number balance at ‘17’, when grouping the genetic code doublets in the 28-gon organization. The number ‘17’ equals the sum of the initial five numbers in the Lucas series, which are 2, 1, 3, 4 and 7.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Arnez, J. G. and D. Moras (1997). Structural and functional considerations of the amino-acylation reaction. Trends Biochem. Sci. 22, 211–216.

    Article  Google Scholar 

  • Bertman, M. O. and J. R. Jungck (1979). Group graph of the genetic code. J. Hered. 70, 379–384.

    Google Scholar 

  • Burbaum, J. J. and P. Schimmel (1991). Structural relationships and the classification of aminoacyl-tRNA synthetases. J. Biol. Chem. 266, 16965–16968.

    Google Scholar 

  • Casper, D. L. D. and A. Klug (1962). Physical principles in the construction of regular viruses. Cold Spring Harb. Symp. Quant. Biol. 27, 1–24.

    Google Scholar 

  • Cavalcanti, A. R., B. D. Neto and R. Ferreira (2000). On the classes of aminoacyl-tRNA synthetases and the error minimization in the genetic code. J. Theor. Biol. 204, 15–20.

    Article  Google Scholar 

  • Cusack, S. (1997). Aminoacyl-tRNA synthetases. Curr. Opin. Struct. Biol. 7, 881–889.

    Article  Google Scholar 

  • Davydov, O. V. (1998). Amino acid contribution to the genetic code structure: end-atom chemical rules of doublet composition. J. Theor. Biol. 193, 679–690.

    Article  Google Scholar 

  • Di Giulio, M. (1992). The evolution of aminoacyl-tRNA synthetases, the biosynthetic pathways of amino acids and the genetic code. Orig. Life Evol. Biosph. 22, 309–319.

    Article  Google Scholar 

  • Dufton, M. J. (1997). Genetic synonym quotas and amino acid complexity: cutting the cost of proteins? J. Theor. Biol. 187, 165–173.

    Article  Google Scholar 

  • Eriani, G., M. Delarue, O. Poch, J. Gangloff and D. Moras (1990). Partition of tRNA synthetases into two classes based on mutually exclusive sets of sequence motifs. Nature 347, 203–206.

    Article  Google Scholar 

  • Hartlein, M. and S. Cusack (1995). Structure, function and evolution of seryl-tRNA synthetases: implications for the evolution of aminoacyl-tRNA synthetases and the genetic code. J. Mol. Evol. 40, 519–530.

    Google Scholar 

  • Hartman, H. (1995). Speculations on the evolution of the genetic code IV. The evolution of the aminoacyl-tRNA synthetases. Orig. Life Evol. Biosph. 25, 265–269.

    Article  Google Scholar 

  • Jiménez-Montaño, M. A., R. de la Mora-Basañez and T. Pöschel (1996). The hyperstructure of the genetic code explains conservative and non-conservative amino acid substitutions in vivo and in vitro. Biosystems 39, 117–125.

    Article  Google Scholar 

  • Kappraff, J. M. and C. Marzec (1983). Properties of maximal spacing on a circle relate to phyllotaxis and to the golden mean. J. Theor. Biol. 103, 201–226.

    Article  MathSciNet  Google Scholar 

  • Karasev, V. A. and V. E. Stefanov (2001). Topological nature of the genetic code. J. Theor. Biol. 209, 303–317.

    Article  Google Scholar 

  • Miller, S. L. (1987). Which organic compounds could have occurred on the prebiotic earth? Cold Spring Harb. Symp. Quant. Biol. 52, 17–27.

    Google Scholar 

  • Nagel, G. M. and R. F. Doolittle (1991). Evolution and relatedness in two aminoacyl-tRNA synthetase families. Proc. Natl. Acad. Sci. USA 88, 8121–8125.

    Article  Google Scholar 

  • Racaniello, V. R. (1996). Early events in poliovirus infection: virus-receptor interactions. Proc. Natl. Acad. Sci. USA 21, 11378–11381.

    Google Scholar 

  • Rakočević, M. M. (1998). The genetic code as a golden mean determined system. BioSystem 46, 283–291.

    Article  Google Scholar 

  • Rakočević, M. and A. Jokic (1996). Four stereochemical types of protein amino acids: synchronic determination with chemical characteristics, atom and nucleon number. J. Theor. Biol. 183, 345–349.

    Article  Google Scholar 

  • Ribas de Pouplana, L. and P. Schimmel (2001). Aminoacyl-tRNA synthetases: potential markers of genetic code development. Trends Biochem. Sci. 26, 591–596.

    Article  Google Scholar 

  • Shcherbak, V. I. (1989). Rumer’s rule and transformation in the context of the co-operative symmetry of the genetic code. J. Theor. Biol. 139, 271–276.

    Google Scholar 

  • Shcherbak, V. I. (1993). Twenty canonical amino acids of the genetic code: the arithmetical regularity. J. Theor. Biol. 162, 399–401.

    Article  Google Scholar 

  • Shcherbak, V. I. (2003). Arithmetic inside the universal genetic code. Biosystems 70, 187–209.

    Article  Google Scholar 

  • Swanson, R. A. (1984). A unifying concept for the amino acid code. Bull. Math. Biol. 46, 187–203.

    Article  MATH  MathSciNet  Google Scholar 

  • Szathmary, E. (1999). The origin of the genetic code—amino acids as cofactors in an RNA world. Trends Genet. 15, 223–229.

    Article  Google Scholar 

  • Trifonov, E. N. (2000). Consensus temporal order of amino acids and evolution of the triplet code. Gene 261, 139–151.

    Article  Google Scholar 

  • Trifonov, E. N. and T. Bettecken (1997). Sequence fossils, triplet expansion, and reconstruction of earliest codons. Gene 205, 1–6.

    Article  Google Scholar 

  • Verkhovod, A. B. (1994). Alphanumerical divisions of the universal genetic code: new divisions reveal new balances. J. Theor. Biol. 170, 327–330.

    Article  Google Scholar 

  • Weber, A. L. and S. L. Miller (1981). Reasons for the occurrence of the twenty coded protein amino acids. J. Mol. Evol. 17, 273–284.

    Article  Google Scholar 

  • Woese, C. R., D. H. Dugre, W. C. Saxinger and S. A. Dugre (1966). The molecular basis for the genetic code. Proc. Natl. Acad. Sci. USA 55, 966–974.

    Article  Google Scholar 

  • Woese, C. R., G. J. Olsen, M. Ibba and D. Söll (2000). Aminoacyl-tRNA synthetases, the genetic code, and the evolutionary process. Microbiol. Mol. Biol. Rev. 64, 202–236.

    Article  Google Scholar 

  • Yang, C. M. (2003a). Nitrogen atom hybrid in nucleobases suggests a primordial “core” in the genetic code? (submitted for publication).

  • Yang, C. M. (2003b). On the quasi-icosikaioctagon (quasi-28-gon) symmetry and a presumed evolutionary axes of the genetic code (submitted for publication).

  • Yang, C. M. (2003c). On the chemistry and three-dimensional display of the genetic code (submitted for publication).

  • Yarus, M. (1998). Amino acids as RNA ligands: a direct-RNA-template theory for the code’s origin. J. Mol. Evol. 47, 109–117.

    Article  Google Scholar 

  • Zhang, C. T. (1997). A symmetrical theory of DNA sequences and its applications. J. Theor. Biol. 187, 297–306.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Physical Organic Chemistry and Chemical Biology, Neurochemistry and System Chemical Biology Program, Nankai University, Tian Jin, 300071, China

    Chi Ming Yang

Authors
  1. Chi Ming Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Chi Ming Yang.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Yang, C.M. On the 28-gon symmetry inherent in the genetic code intertwined with aminoacyl-tRNA synthetases—The Lucas series. Bull. Math. Biol. 66, 1241–1257 (2004). https://doi.org/10.1016/j.bulm.2003.12.006

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1016/j.bulm.2003.12.006

Keywords

Search

Navigation