Gene expression from polynomial dynamics in the 2-adic information space

TL;DR

This paper models genetic information and DNA reproduction using polynomial dynamical systems in 2-adic space, providing a mathematical framework to reproduce the degenerate genetic code structure.

Contribution

It introduces a novel polynomial dynamical system in 2-adic space that models the genetic code's degeneracy and DNA reproduction process.

Findings

Representation of genetic information in 2-adic space.

Modeling DNA reproduction as a 2-adic dynamical system.

A proposed polynomial system reproduces genetic code degeneracy.

Abstract

We perform geometrization of genetics by representing genetic information by points of the 4-adic {\it information space.} By well known theorem of number theory this space can also be represented as the 2-adic space. The process of DNA-reproduction is described by the action of a 4-adic (or equivalently 2-adic) dynamical system. As we know, the genes contain information for production of proteins. The genetic code is a degenerate map of codons to proteins. We model this map as functioning of a polynomial dynamical system. The purely mathematical problem under consideration is to find a dynamical system reproducing the degenerate structure of the genetic code. We present one of possible solutions of this problem.