Study of equivariants maps under octahedral group action: a dynamic system for the evolution of the genetic code.

Author(s)

Marcio Magini

• Document type: Doctoral Thesis
• Press: São Carlos.
• Institution: Universidade de São Paulo (USP). Instituto de Física de São Carlos (IFSC/BT)
• Defense date: 2002-06-10

Examining board members

Jose Eduardo Martinho Hornos; Junior Barrera; Esmerindo de Sousa Bernardes; Francisco Gorgonio da Nobrega; Maisa de Oliveira Terra

• Advisor: Jose Eduardo Martinho Hornos

Abstract

The study of natural symmetry breaking processes have attracted interest in many physics areas including energy atoms studies in quantum physics as well elementary particles in high energy physics. These processes were related with microscpics physic systems, in 1993 appears one propose to use the ideas of symmetry breaking in one macroscopic system the genetic code. The basic idea is that the differentiation of the codons wich are components of the code was done in a process of symmetry breaking preserving the degeneracy properties given to us one picture of how this process occour resulting in 20 aminoacids and termination sign known in the present days. With this model for example, we can predict how many aminoacids were primordial\'s. Our interest is in verify this symmetry breaking and study the codon temporal relations for this we use a dynamical system. The preservation of the starting symmetry proposed by the model is the main caracteristic of our system and through of the symmetry breaking we will study what relations between the symmetry breaking proposed by the model and the dynamical symmetry breaking. As a first step we will study the group Sp(6) in its tridimensional representation which is the starting point in the symmetry breaking process in the mode!. This representation in known as Weyl group of Sp(6). It is possible construct this dynamical system or map, which is one function in the R3 with the same symmetry properties of the Weyl group of Sp(6). The construction of this map and its mathematical study is our second step of this work. The map depends on parameter\'s which are changed in a correct way to produce some symmetry breaking chain. The symmetry breaking studies is our third step. At the end we look at the action of our map in the codons, in other words, how this action change the codons labelling proposed by the model Moreover, what kind of biological information can be extract from this action. As a result the symmetry breaking and the labelling of codons proposed by the model are isomophics, with little restrictions, when compared with the dynamical systems. (AU)

• FAPESP's process: 98/14909-9 - Symmetry analysis in genetic code using dynamic systems concepts
• Grantee: Marcio Magini
• Support Opportunities: Scholarships in Brazil - Doctorate