Rumer's transformation: a symmetry puzzle standing for half a century.

In 1966, only a few months after the complete elucidation of the standard nuclear genetic code (Kay, 2000), the Russian theoretical physicist Yury Borisovich Rumer uncovered the existence of a particular symmetry (Rumer, 1966): when the keto-amino transformation (also known as Rumer's transformation) is applied to the bases of a codon then the degeneracy of the transformed codon was changed. In particular, if the amino acid associated to the starting codon has degeneracy 4, then the amino acid associated to the transformed codon has degeneracy 1, 2 or 3 (and vice versa). After half a century from this discovery and despite the universality of Rumer's symmetry, little is known about its origin and its possible biological significance. In this article we show that the Rumer's symmetry could have originated in an ancestral version of the genetic code, i.e., the pre-early code, and is a natural consequence of the stereo-chemical symmetries of the ancestral synthesis machinery working around such code (Gonzalez et al., 2019). Moreover, the conservation of Rumer's symmetry through evolutionary periods suggests a connection with key biological features. In this respect, intriguing possibilities include those of error detection/correction, control over the synthesis of proteins, and frame maintenance. To a certain extent, such ideas have been explored in the framework of a mathematical model of the genetic code (the non-power model of the genetic code (Gonzalez, 2004; Gonzalez, 2008; Gonzalez et al., 2016), whose definition of dichotomic classes naturally includes Rumer's symmetry (Gonzalez, 2008; Gonzalez et al., 2006, 2008) and the theory of circular codes (Arquès and Michel, 1996; Gonzalez et al., 2011; Fimmel et al., 2015).