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Quaternionic representation of the genetic code.

C Manuel Carlevaro1, Ramiro M Irastorza2, Fernando Vericat3

  • 1Instituto de Física de Líquidos y Sistemas Biológicos, 59 Nro. 789, 1900 La Plata, Argentina; Universidad Tecnológica Nacional, Facultad Regional Buenos Aires, Mozart Nro. 2300, C14071VT Buenos Aires, Argentina.

Bio Systems
|January 12, 2016
PubMed
Summary
This summary is machine-generated.

This study presents a novel mathematical model for the genetic code using Hamilton quaternions, reflecting its evolutionary history and protein folding.

Keywords:
Broken symmetryGenetic code evolutionHamilton quaternionsProtein folding

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Area of Science:

  • Biophysics
  • Theoretical Biology
  • Bioinformatics

Background:

  • The standard genetic code's evolution remains incompletely understood.
  • Existing models do not fully integrate evolutionary history with mathematical representations.
  • The physical principles underlying the genetic code's structure are actively researched.

Purpose of the Study:

  • To present a heuristic diagram illustrating the evolution of the standard genetic code.
  • To propose a mathematical representation of the current genetic code using Hamilton quaternions.
  • To explore the application of this quaternionic representation in protein structure prediction.

Main Methods:

  • Development of a heuristic evolutionary diagram incorporating broken symmetry.
  • Formulation of a codon function assigning integer quaternions to amino acids.
  • Proposal of an algorithm for protein 3D structure prediction from quaternionic sequences.

Main Results:

  • The proposed diagram aligns with established theories on genetic code evolution and amino acid appearance.
  • The quaternionic representation successfully preserves the observed degeneracy of the genetic code.
  • A novel algorithm is presented for predicting protein structures from quaternionic representations.

Conclusions:

  • The Hamilton quaternions-based mathematical representation offers a comprehensive description of the genetic code.
  • This approach captures known properties and opens new avenues for research, particularly in protein folding.
  • The link between quaternions, rotations, and biological structures suggests deeper connections.