This new bioinformatics research bridges Genomics and Mathematics. We propose a universal "Fractal Genome Code Law": The frequency of each of the 64 codons across the entire human genome is controlled by the codon's position in the Universal Genetic Code table. We analyze the frequency of distribution of the 64 codons (codon usage) within single-stranded DNA sequences. Concatenating 24 Human chromosomes, we show that the entire human genome employs the well known universal genetic code table as a macro structural model. The position of each codon within this table precisely dictates its population. So the Universal Genetic Code Table not only maps codons to amino acids, but serves as a global checksum matrix. Frequencies of the 64 codons in the whole human genome scale are a self-similar fractal expansion of the universal genetic code. The original genetic code kernel governs not only the micro scale but the macro scale as well. Particularly, the 6 folding steps of codon populations modeled by the binary divisions of the "Dragon fractal paper folding curve" show evidence of 2 attractors. The numerical relationship between the attractors is derived from the Golden Ratio. We demonstrate that: (i) The whole Human Genome Structure uses the Universal Genetic Code Table as a tuning model. It predetermines global codons proportions and populations. The Universal Genetic Code Table governs both micro and macro behavior of the genome. (ii) We extend the Chargaff's second rule from the domain of single TCAG nucleotides to the larger domain of codon triplets. (iii) Codon frequencies in the human genome are clustered around 2 fractal-like attractors, strongly linked to the golden ratio 1.618.
This article proves the existence of a hyper-precise global numerical meta-architecture unifying, structuring, binding and controlling the billion triplet codons constituting the sequence of single-stranded DNA of the entire human genome. Beyond the evolution and erratic mutations like transposons within the genome, it's as if the memory of a fossil genome with multiple symmetries persists. This recalls the "intermingling" of information characterizing the fractal universe of chaos theory. The result leads to a balanced and perfect tuning between the masses of the two strands of the huge DNA molecule that constitute our genome. We show here how codon populations forming the single-stranded DNA sequences can constitute a critical approach to the understanding of junk DNA function. Then, we suggest revisiting certain methods published in our 2009 book "Codex Biogenesis". In fact, we demonstrate here how powerful a analytical filter the universal genetic code table is to characterize single-stranded DNA sequences constituting chromosomes and genomes. We can then show that any genomic DNA sequence is featured by three numbers, which characterize it and its 64 codon populations with correlations greater than 99%. The number "1" is common to all sequences, expressing the second law of Chargaff. The other 2 numbers are related to each specific DNA sequence case characterizing life species. For example, the entire human genome is characterized by three remarkable numbers 1, 2, and Phi = 1.618 the golden ratio. Associated with each of these three numbers, we can match three axes of symmetry, then "imagine" a kind of hyperspace formed by these codon populations. Then we revisit the value (3-Phi)/2 which is probably universal and common to both the scale of quarks and atomic levels, balancing and tuning the whole human genome codon population. Finally, we demonstrate a new kind of duality between "form and substance" overlapping the whole human genome: we will show that-simultaneously with the duality between genes and junk DNA-there is a second layer of embedded hidden structure overlapping all the DNA of the whole human genome, dividing it into a second type of duality information/redundancy involving golden ratio proportions.
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