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Investigating Protein Sequence-structure-dynamics Relationships with Bio3D-web
Published on: July 16, 2017
2-Adic clustering of the PAM matrix
1International Center for Mathematical Modelling in Physics and Cognitive Sciences, University of Vaxjo, Vaxjo, S-35195, Sweden. Andrei.Khrennikov@vxu.se
Journal of Theoretical Biology
|August 25, 2009
Summary
This study introduces 2-adic numbers to analyze genetic code degeneracy and PAM matrix structure in bioinformatics. This novel number-theoretic approach reveals new insights into amino acid substitutions and alignment procedures.
Area of Science:
- Bioinformatics
- Number Theory
- Genetics
Background:
- Ultrametric distances are used in bioinformatics.
- 2-adic distance is an ultrametric.
- Existing bioinformatics applications of ultrametrics are known.
Purpose of the Study:
- To provide new insights into genetic code degeneracy and PAM matrix structure using 2-adic numbers.
- To link ultrametric properties with number theoretic structures.
- To discover novel applications of ultrametrics in bioinformatics.
Main Methods:
- Application of 2-adic number system to genetic code analysis.
- Decomposition of the PAM matrix (A) into 2-adic (A((2))) and sparse (A((infinity))) components.
- Analysis of the A((infinity)) matrix in relation to amino acid side chain properties.
Main Results:
- The PAM matrix can be expressed as A = A((2)) + A((infinity)).
- A((2)) is shown to be 2-adically regular, relating to a 2-adic parametrization of the genetic code.
- A((infinity)) is a sparse matrix whose structure is linked to amino acid properties.
Conclusions:
- 2-adic numbers offer a new perspective on genetic code and PAM matrix analysis.
- The decomposition provides a framework for understanding amino acid substitution matrices.
- A family of matrices A(alpha,beta) is proposed to refine alignment procedures based on amino acid chemical and geometric properties.
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