Binary oppositions, algebraic holography and stochastic rules in genetic informatics.

Area of Science:

• Molecular biology
• Genomics
• Theoretical physics
• Algebraic geometry

Background:

• Understanding the organizational principles of genomic DNA is crucial for deciphering biological complexity.
• Existing models often struggle to reconcile deterministic and probabilistic aspects of genetic inheritance.
• The application of algebraic and geometric principles to biological systems is an emerging area of research.

Purpose of the Study:

• To perform an algebraic analysis of molecular genetic systems, including DNA alphabets and nucleotide sequences.
• To explore connections between DNA organization, algebraic holography, and hyperbolic geometry.
• To uncover universal rules governing the stochastic organization of genomic DNA.

Main Methods:

• Algebraic analysis of structured DNA alphabets and long nucleotide sequences.
• Application of principles from algebraic holography.
• Utilizing the Poincaré disk model of Lobachevski hyperbolic geometry.
• Analysis of long DNA sequences as parallel texts in different DNA n-plets alphabets.

Main Results:

• Established a connection between DNA n-plets alphabets and algebraic holography.
• Revealed a relationship between DNA n-plets alphabets and the Poincaré disk model of hyperbolic geometry.
• Discovered universal rules for the stochastic organization of genomic DNA.
• Demonstrated the potential of algebraic-harmonic models for understanding biological systems.

Conclusions:

• The study provides evidence for the efficacy of modeling living organisms as quantum-informational algebraic-harmonic essences.
• The findings offer a novel perspective on the interplay between probability and determinism in biological systems.
• The integration of algebraic geometry and holography offers new avenues for genomic research.