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Genetic coding and united-hypercomplex systems in the models of algebraic biology
1Mechanical Engineering Research Institute of the Russian Academy of Sciences, 101990, Moscow, Russia.
Bio Systems
|May 25, 2017
Summary
New united-hypercomplex numbers offer insights into DNA and RNA structures, revealing hidden genetic properties. This algebraic approach enhances understanding of genetic coding and noise-immunity in biological systems.
Area of Science:
- Algebraic Biology
- Bioinformatics
- Theoretical Computer Science
Background:
- DNA and RNA alphabets are fundamental to genetics.
- Complex and hypercomplex numbers are crucial in science and technology.
- Existing mathematical frameworks may not fully capture genetic code complexities.
Purpose of the Study:
- Introduce a novel system of united-hypercomplex numbers.
- Explore the application of these numbers to DNA and RNA structures.
- Investigate the potential of this system for understanding genetic coding and biological systems.
Main Methods:
- Representing DNA and RNA alphabets in matrix form.
- Connecting these representations with Walsh functions.
- Developing and applying systems of united-hypercomplex numbers.
Main Results:
- U-hypercomplex numbers reveal hidden properties of genetic alphabets under cyclic permutations.
- Demonstrated conformity between U-numerical systems and DNA alphabet properties.
- Identified potential for U-hypercomplex numbers in modeling multi-parametrical biological systems.
Conclusions:
- United-hypercomplex numbers provide a new mathematical lens for algebraic biology.
- This system may explain genetic multi-linguistic and noise-immunity in DNA.
- Genetic information processing can be modeled using U-hypercomplex numbers, aligning with "numbers rule the world".
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