Symmetrical Properties of Graph Representations of Genetic Codes: From Genotype to Phenotype

José, Marco V.; Zamudio, Gabriel S.

doi:10.3390/sym10090388

Cited by 3 publications

(1 citation statement)

References 41 publications

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“…Symmetric graphs have many real-life applications as vehicle routing, warehouse logistics, planning circuit boards, virtual networking [1][2][3][4]. The goal of the base Symmetric Traveling Salesman Problem (sTSP) is to find the shortest Hamiltonian cycle in a graph.…”

Section: Introductionmentioning

confidence: 99%

IntraClusTSP—An Incremental Intra-Cluster Refinement Heuristic Algorithm for Symmetric Travelling Salesman Problem

2018

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The Symmetric Traveling Salesman Problem (sTSP) is an intensively studied NP-hard problem. It has many important real-life applications such as logistics, planning, manufacturing of microchips and DNA sequencing. In this paper we propose a cluster level incremental tour construction method called Intra-cluster Refinement Heuristic (IntraClusTSP). The proposed method can be used both to extend the tour with a new node and to improve the existing tour. The refinement step generates a local optimal tour for a cluster of neighbouring nodes and this local optimal tour is then merged into the global optimal tour. Based on the performed evaluation tests the proposed IntraClusTSP method provides an efficient incremental tour generation and it can improve the tour efficiency for every tested state-of-the-art methods including the most efficient Chained Lin-Kernighan refinement algorithm. As an application example, we apply IntraClusTSP to automatically determine the optimal number of clusters in a cluster analysis problem. The standard methods like Silhouette index, Elbow method or Gap statistic method, to estimate the number of clusters support only partitional (single level) clustering, while in many application areas, the hierarchical (multi-level) clustering provides a better clustering model. Our proposed method can discover hierarchical clustering structure and provides an outstanding performance both in accuracy and execution time.

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Section: Introductionmentioning

confidence: 99%

IntraClusTSP—An Incremental Intra-Cluster Refinement Heuristic Algorithm for Symmetric Travelling Salesman Problem

2018

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The Evolution of Life Is a Road Paved with the DNA Quadruplet Symmetry and the Supersymmetry Genetic Code

Rosandić

Paar

2023

IJMS

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Symmetries have not been completely determined and explained from the discovery of the DNA structure in 1953 and the genetic code in 1961. We show, during 10 years of investigation and research, our discovery of the Supersymmetry Genetic Code table in the form of 2 × 8 codon boxes, quadruplet DNA symmetries, and the classification of trinucleotides/codons, all built with the same physiochemical double mirror symmetry and Watson–Crick pairing. We also show that single-stranded RNA had the complete code of life in the form of the Supersymmetry Genetic Code table simultaneously with instructions of codons’ relationship as to how to develop the DNA molecule on the principle of Watson–Crick pairing. We show that the same symmetries between the genetic code and DNA quadruplet are highly conserved during the whole evolution even between phylogenetically distant organisms. In this way, decreasing disorder and entropy enabled the evolution of living beings up to sophisticated species with cognitive features. Our hypothesis that all twenty amino acids are necessary for the origin of life on the Earth, which entirely changes our view on evolution, confirms the evidence of organic natural amino acids from the extra-terrestrial asteroid Ryugu, which is nearly as old as our solar system.

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On the Importance of Asymmetry in the Phenotypic Expression of the Genetic Code upon the Molecular Evolution of Proteins

José

Zamudio

2020

Symmetry

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The standard genetic code (SGC) is a mapping between the 64 possible arrangements of the four RNA nucleotides (C, A, U, G) into triplets or codons, where 61 codons are assigned to a specific amino acid and the other three are stop codons for terminating protein synthesis. Aminoacyl-tRNA synthetases (aaRSs) are responsible for implementing the SGC by specifically amino-acylating only its cognate transfer RNA (tRNA), thereby linking an amino acid with its corresponding anticodon triplets. tRNAs molecules bind each codon with its anticodon. To understand the meaning of symmetrical/asymmetrical properties of the SGC, we designed synthetic genetic codes with known symmetries and with the same degeneracy of the SGC. We determined their impact on the substitution rates for each amino acid under a neutral model of protein evolution. We prove that the phenotypic graphs of the SGC for codons and anticodons for all the possible arrangements of nucleotides are asymmetric and the amino acids do not form orbits. In the symmetrical synthetic codes, the amino acids are grouped according to their codonicity, this is the number of triplets encoding a given amino acid. Both the SGC and symmetrical synthetic codes exhibit a probability of occurrence of the amino acids proportional to their degeneracy. Unlike the SGC, the synthetic codes display a constant probability of occurrence of the amino acid according to their codonicity. The asymmetry of the phenotypic graphs of codons and anticodons of the SGC, has important implications on the evolutionary processes of proteins.

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Symmetrical Properties of Graph Representations of Genetic Codes: From Genotype to Phenotype

Cited by 3 publications

References 41 publications

IntraClusTSP—An Incremental Intra-Cluster Refinement Heuristic Algorithm for Symmetric Travelling Salesman Problem

IntraClusTSP—An Incremental Intra-Cluster Refinement Heuristic Algorithm for Symmetric Travelling Salesman Problem

The Evolution of Life Is a Road Paved with the DNA Quadruplet Symmetry and the Supersymmetry Genetic Code

On the Importance of Asymmetry in the Phenotypic Expression of the Genetic Code upon the Molecular Evolution of Proteins

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