## Genetic Phase Angle Distance (GPAD)

**Authors:** Daniel K. Pratt

It is hypothesized that a mathematical mapping of the biochemical properties of genetic nucleotides into a three dimensional vector space will yield a novel and meaningful evolutionary distance measure. The nucleotides A,T,C,G are mapped into a complex vector space according to three biochemical properties: amino/keto, purine/pyrimidine, weak/strong. This mapping is represented in Mathematica. A weighted linear combination of these base-vector triplets results in a "Tetrahedral Genetic Code" (TGC), where all 64 codons map to 64 unique vector positions in the space. Phase distance θ is measured as the angle between sequentially neighboring codon vectors, and a sequence of codons can be measured as the total path length in radians of the vector as it traverses the TGC. Angular difference Δθ is computed as the absolute value of the difference in phase θ between sequences under investigation, at homologous (aligned) genetic loci. The Genetic Phase Angle Distance (GPAD) is computed as the normalized mean Δθ over the full aligned genetic sequences for any two species. The GPAD distance measure is computed on a sample sequence matrix for 11 different species and compared side by side to the Tamura 3-parameter distance computed on that same species matrix.

**Comments:** 9 Pages. This is a powerpoint presentation of research/thesis for B.S. Biotechnology. An essay is forthcoming. contact: daniel dot k dot pratt at gmail dot com

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### Submission history

[v1] 2013-04-16 14:19:09

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