Hypothesis Paper Symmetry Preservation in the Evolution of the Genetic Code Jose´ Eduardo M. Hornos 1 , Lı´gia Braggion 1 , Marcio Magini 2 and Michael Forger 3 1 Instituto de Fı´sica de Sa˜o Carlos, Universidade de Sa˜o Paulo, Caixa Postal 369, BR-13560-970 Sa˜o Carlos, SP, Brazil 2 InstitutodePesquisa e Desenvolvimento,UniversidadedoVale doParaı´ba, Av. Shishima Hifumi, 2911, BR-12244-000 Sa˜oJose´ dos Campos, SP, Brazil 3 Instituto de Matema´tica e Estatı´stica, Universidade de Sa˜o Paulo, Caixa Postal 66281, BR-05315-970 Sa˜o Paulo, SP, Brazil Summary The standard genetic code is found to exhibit an exact symmetry under a finite group of order 4 known in mathematics as the Klein group. The same symmetry is also present in almost all non-standard codes, mitochondrial as well as nuclear. Analysis of the phylogenetic tree for the evolution of the mitochondrial codes reveals that all changes along the main line of evolution preserve this symmetry, with a tendency towards symmetry enhancement. In the side branches of the evolutionary tree, the majority of changes also respect the symmetry. The few exceptional cases where it is broken correspond to reassignments that appear to be unstable or incomplete. Since the Klein group emerges naturally from the symplectic model for the prebiotic evolution that has led to the standard code, we interpret these results as lending support to the hypothesis that this symmetry has been selected during the evolution of the genetic code, not only before but also after establishment of the standard code. IUBMB Life, 56: 125–130, 2004 Keywords Evolution; genetic code; symmetry. The significance of the regularities observed in the standard genetic code and in non-standard codes has been a long- standing problem. In particular, the degeneracies in the codon to amino-acid assignments, as well as the changes that appear to have occurred in these assignments during evolution, have been the subject of much discussion. The most important deviations from the standard code, first found in 1979 in studies of the human cytochrome oxidase subunit II gene, are UGA and AUA coding for Trp and Met, rather than for Stop and Ile, respectively. Since then, many other examples of non- standard codes have been identified, burying definitively the hypothesis of a universal code and triggering an extensive debate about the evolution of the genetic code. A large amount of experimental data relevant to this question, together with phenomenological and theoretical considera- tions, has been assembled by Osawa, Jukes and collaborators (1, 2). In recent years, the number of articles on the problem has steadily increased and the pertinent literature has become so extensive that it has become almost impossible to compile a reasonably complete bibliography. As an illustration of the great variety of approaches to the subject, we may quote the discussion on the chronological order in which the twenty aminoacids have been incorporated into the code: there are presently about 40 models referring to various aspects of the early evolution of life on Earth that lead to predictions about this order and based on very different approaches; see Ref. (3) for an overview. Among them is the algebraic model for the evolution of the genetic code first proposed in 1993 (4) and further developed in subsequent years (5–8). The present paper is devoted to the further development of the algebraic model. Our main goal is to lay the ground for making closer contact between the predictions of this model and experimentally accessible facts from evolutionary biology. The basic idea underlying the algebraic model for the evolution of the genetic code is the concept of symmetry, viewed as the ‘raison d’eˆ tre’ of the degeneracies observed in the genetic code. In order to avoid misunderstandings, we would like to emphasize from the very beginning that symmetry arguments are not intended nor able to replace biochemical considerations. Rather, their role in understanding the evolution of the genetic code is to postulate constraints on the possible pathways of evolution – constraints whose validity must be checked independently. For example, the by now generally accepted picture of a primordial evolution of the genetic code, accompanied and characterized by a stepwise inclusion of more and more amino acids into the machinery of protein synthesis, is completely consistent with the picture of stepwise symmetry breaking, starting out from a large Received 21 July 2003; accepted 12 January 2004 Address correspondence to: Jose´ Eduardo Hornos, Instituto de Fı´sica de Sa˜o Carlos, Universidade de Sa˜o Paulo, Caixa Postal 369, BR-13560-970 Sa˜o Carlos, SP, Brazil. E-mail: hornos@if.sc.usp.br IUBMB Life, 56(3): 125–130, March 2004 ISSN 1521-6543 print/ISSN 1521-6551 online # 2004 IUBMB DOI: 10.1080/15216540410001687838