Generation of genetic codes with 2-adic codon algebra and adaptive dynamics.

Area of Science:

• Mathematics and Biology
• Dynamical Systems Theory
• Bioinformatics

Background:

• Genetic codes translate nucleotide sequences into amino acids.
• Dynamical systems offer a framework for modeling complex biological processes.
• 2-adic numbers and their associated dynamics provide a unique mathematical structure.

Purpose of the Study:

• To model genetic codes using 2-adic dynamical systems.
• To encode amino acids as attractors of these dynamical systems.
• To explore the optimization and biological interpretation of genetic code functions.

Main Methods:

• Utilizing discrete dynamical systems, specifically iterations of functions F:Z2→Z2.
• Characterizing genetic codes by the attractors of code-generating functions.
• Minimizing the Lipschitz constant for function optimization.
• Applying the model to generate standard nuclear and vertebrate mitochondrial genetic codes.

Main Results:

• Amino acids are successfully encoded by the attractors of 2-adic dynamical systems.
• A method for reducing degeneration in dynamic representations is proposed.
• The approach is illustrated with the generation of known genetic codes.
• The study provides a framework for understanding genetic code evolution in an ultrametric information space.

Conclusions:

• 2-adic dynamical systems provide a novel mathematical framework for modeling genetic codes.
• The concept of attractors in these systems offers a new perspective on amino acid encoding.
• Further research into the biological interpretation of code-functions and their evolutionary dynamics is warranted.