title: Three-Dimensional Algebraic Models of the tRNA Code and 12 Graphs for Representing the Amino Acids.
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.
authors.affiliation: Theoretical Biology Group, Instituto de Investigaciones Biomédicas, Universidad Nacional Autónoma de México, México D.F. 04510, Mexico. marcojose@biomedicas.unam.mx.
authors.forename: Marco V
authors.initials: MV
authors.lastname: José
authors.affiliation: Facultad de Matemática, Física y Computación, Universidad Central "Marta Abreu" de Las Villas, Santa Clara, Cuba. morgado@uclv.edu.cu.
authors.forename: Eberto R
authors.initials: ER
authors.lastname: Morgado
authors.affiliation: 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. romeucardosoguimaraes@gmail.com.
authors.forename: Romeu Cardoso
authors.initials: RC
authors.lastname: Guimarães
authors.affiliation: Theoretical Biology Group, Instituto de Investigaciones Biomédicas, Universidad Nacional Autónoma de México, México D.F. 04510, Mexico. gazaso92@gmail.com.
authors.forename: Gabriel S
authors.initials: GS
authors.lastname: Zamudio
authors.affiliation: Centro de Ciencias Exactas y Naturales, Universidade Federal da Paraíba, João Pessoa, Brazil. stfarias@yahoo.com.br.
authors.forename: Sávio Torres
authors.initials: ST
authors.lastname: de Farías
authors.affiliation: Theoretical Biology Group, Instituto de Investigaciones Biomédicas, Universidad Nacional Autónoma de México, México D.F. 04510, Mexico. jromanb@unam.mx.
authors.forename: Juan R
authors.initials: JR
authors.lastname: Bobadilla
authors.affiliation: Theoretical Biology Group, Instituto de Investigaciones Biomédicas, Universidad Nacional Autónoma de México, México D.F. 04510, Mexico. dani.dansp16@gmail.com.
authors.forename: Daniela
authors.initials: D
authors.lastname: Sosa