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Life 2014, 4(3), 341-373; doi:10.3390/life4030341

Three-Dimensional Algebraic Models of the tRNA Code and 12 Graphs for Representing the Amino Acids

1
Theoretical Biology Group, Instituto de Investigaciones Biomédicas, Universidad Nacional Autónoma de México, México D.F. 04510, Mexico
2
Facultad de Matemática, Física y Computación, Universidad Central "Marta Abreu" de Las Villas, Santa Clara, Cuba
3
Laboratório de Biodiversidade e Evolução Molecular, Departamento de Biologia Geral, Instituto de Ciências Biológicas, Universidade Federal de Minas Gerais, 31270.901 Belo Horizonte, MG, Brazil
4
Centro de Ciencias Exactas y Naturales, Universidade Federal da Paraíba, João Pessoa, Brazil
*
Author to whom correspondence should be addressed.
Received: 29 April 2014 / Revised: 23 July 2014 / Accepted: 25 July 2014 / Published: 11 August 2014
(This article belongs to the Special Issue The Origins and Early Evolution of RNA)
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Abstract

Three-dimensional algebraic models, also called Genetic Hotels, are developed to represent the Standard Genetic Code, the Standard tRNA Code (S-tRNA-C), and the Human tRNA code (H-tRNA-C). New algebraic concepts are introduced to be able to describe these models, to wit, the generalization of the 2n-Klein Group and the concept of a subgroup coset with a tail. We found that the H-tRNA-C displayed broken symmetries in regard to the S-tRNA-C, which is highly symmetric. We also show that there are only 12 ways to represent each of the corresponding phenotypic graphs of amino acids. The averages of statistical centrality measures of the 12 graphs for each of the three codes are carried out and they are statistically compared. The phenotypic graphs of the S-tRNA-C display a common triangular prism of amino acids in 10 out of the 12 graphs, whilst the corresponding graphs for the H-tRNA-C display only two triangular prisms. The graphs exhibit disjoint clusters of amino acids when their polar requirement values are used. We contend that the S-tRNA-C is in a frozen-like state, whereas the H-tRNA-C may be in an evolving state. View Full-Text
Keywords: standard tRNA code; human tRNA code; graphs of amino acids; algebraic models; symmetry; evolution genetic code; polar requirement standard tRNA code; human tRNA code; graphs of amino acids; algebraic models; symmetry; evolution genetic code; polar requirement
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This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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MDPI and ACS Style

José, M.V.; Morgado, E.R.; Guimarães, R.C.; Zamudio, G.S.; de Farías, S.T.; Bobadilla, J.R.; Sosa, D. Three-Dimensional Algebraic Models of the tRNA Code and 12 Graphs for Representing the Amino Acids. Life 2014, 4, 341-373.

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