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Potential automata. Application to the genetic code III.

Jacques Demongeot1, Adrien Elena, Georges Weil

  • 1TIMC-IMAG UMR CNRS 5525, Faculté de Médecine, Université Joseph-Fourier, Grenoble, 38700 La Tronche, France. Jacques.Demongeot@imag.fr

Comptes Rendus Biologies
|November 28, 2006
PubMed
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This study introduces potential automata, demonstrating a discrete Hopfield-like system as a candidate. Physicochemical properties of amino acids suffice to construct a potential that decreases on genetic code synonymy classes, supporting the stereochemical hypothesis.

Area of Science:

  • * Computational Biology and Bioinformatics
  • * Theoretical Computer Science
  • * Biophysics

Background:

  • * Previous work established mathematical properties of continuous differential systems (potential and potential-Hamiltonian) and their biological applications, particularly concerning primitive cyclic RNAs and the genetic code.
  • * The Hopfield-like system, a discrete dynamical system, has been previously introduced by Goles et al.

Purpose of the Study:

  • * To define a general concept of a potential automaton.
  • * To demonstrate that a discrete Hopfield-like system functions as a potential automaton with a decreasing Lyapunov functional.
  • * To apply the potential automaton framework to the genetic code, utilizing physicochemical properties of amino acids.

Main Methods:

  • * Definition of a general potential automaton.

Related Experiment Videos

  • * Analysis of a discrete Hopfield-like system, verifying its properties as a potential automaton (decreasing Lyapunov functional).
  • * Application of the potential automaton concept to the genetic code by considering amino acid physicochemical properties (molecular weight, hydrophobicity, hydrogen bond ability).

    • Main Results:

    • * A discrete Hopfield-like system was identified as a potential automaton, exhibiting a Lyapunov functional that decreases along its trajectories.
    • * Physicochemical properties of amino acids alone are sufficient to construct a potential that decreases on trajectories corresponding to the genetic code's synonymy classes.
    • * This construction supports the stereochemical hypothesis for the origin of the genetic code.

    Conclusions:

    • * The potential automaton framework provides a novel approach to studying discrete systems, including biological ones.
    • * The findings reinforce the classical stereochemical hypothesis by showing that fundamental amino acid properties can explain aspects of the genetic code's structure.
    • * The study opens new perspectives on the optimality of genetic code synonymy classes.