On the Hypercube Structure of the Genetic Code

TL;DR

This paper models the genetic code as a six-dimensional Boolean hypercube, revealing a balance between conservation and innovation, and showing how the code's structure facilitates evolution through well-defined codon regions.

Contribution

It introduces a hypercube representation of the genetic code based on hierarchical interaction energies, providing new insights into its structure and evolutionary dynamics.

Findings

Genetic code modeled as a 6D hypercube based on interaction energies.

Identifies two behaviors at homologous sites: attractor nodes and closed hypercube paths.

Code structure supports evolution through defined hypercube regions.

Abstract

A representation of the genetic code as a six-dimensional Boolean hypercube is proposed. It is assumed here that this structure is the result of the hierarchical order of the interaction energies of the bases in codon-anticodon recognition. The proposed structure demonstrates that in the genetic code there is a balance between conservatism and innovation. Comparing aligned positions in homologous protein sequences two different behaviors are found: a) There are sites in which the different amino acids present may be explained by one or two "attractor nodes" (coding for the dominating amino acid(s)) and their one-bit neighbors in the codon hypercube, and b) There are sites in which the amino acids present correspond to codons located in closed paths in the hypercube. The structure of the code facilitates evolution: the variation found at the variable positions of proteins do not corresponds to random jumps at the codon level, but to well defined regions of the hypercube.