The way that information is stored extremely compactly in DNA leads to the suspicion that fractality is involved. Fractal properties in plants and animals tend to crop up in space packing optimization, for example in seed pods. DNA compactly stores information in chromosomes as well as in the code’s long-range structure.
Is the Golden ratio in DNA real or fake?
Mathematical models and direct MRI imaging have both found leads to the golden ratio structuring DNA. First we have phi ratios between the pitches of magnetic resonance waveforms shown to moderate degree of accuracy. (Details below.) We have also found the frequencies of the different base pairs are less than random, but can be modeled using phi attractors in (mathematically) chaotic conditions. Lastly the newest studies have found a physical decagonal symmetry, which leads to a can of worms of phi proportions, as pentagonal symmetry is a natural pantry of phi relationships.
Many purport that the helical spiral has golden ratio proportions. While this may be true, the way it’s presented is definitely not evidence. Usually they use numbers of base pairs like 21 and 34 and being the first few terms in the Fibonacci sequence divide to make 1.8 which would not be good enough really to resonate on the scales needed. What is the actual golden ratio?
THE STUDIES
The studies correlating the golden ratio with DNA do so in the structure of an informational waveform. Groundwork was laid showing that the patterns and frequencies of base pairs follow chaos theory with golden ratio spaced attractors. Further studies found conformational links to the golden ratio in the form of decagonal symmetry, which is the same as two pentagonal symmetries overlaid. Pentagonal symmetry is indicative of golden ratio properties.
Study main findings #1: Computational Fractal Wave Models
In 1991 were the first real efforts to look at the long-range order of the genome. Researcher Jean-Claude Perez from France is the main researcher creating computational models.
Perez went through several layers with his initial 1991 investigation looking for long-range order in DNA. He established rules that would constitute a longitudinal wave, and set a computational search for the Fibonacci numbers that would represent a large unfolding of this energy form. He is only looking for large waves, with farther out terms in the Fibonacci sequence, as these are more likely to be close to phi. A 3,5,8 is no where near enough to conclude golden ratio involvement.
Perez’s work takes a nucleotide as start, creates a frame, and seeks patterns within that frame.
They looked at some artificial genes that spat and coded for the same nucleotide sequence but were not naturally generated. This was used as a comparison for the results.
The results they found were significant up to a 2% chance of this type of order generated at random. The authors propose that there is no artifacts in the code, and that the order of the natural gene as more proof that the global order of the gene has more “selectivity”, “relief”, and “roughness” (chaos theory / statistics terminology, think of as natural structured fractality) than the fake gene. Perez went on to use this to test genomes for synthetic components in other papers.
Perez tightens up his theory
In 2010, Perez came back and had a way stronger paper essentially investigating the same thing. Bioinformatics indeed came a long way between 1991 and 2010, so the results and theory and a lot more robust. Codon frequencies were found to have fractal attractors, essentially meaning generative forces within the structure. I will give the pieces of analogous structures given in the paper. The numbers of combinations of base pairs are known as “binary code constraints”. This is the options the strands can “choose” from randomness. But rather than randomness per say, they did find a “tendency force” of two attractors, 1/2phi apart. This study was firm but the magnetic resonance approach was overly complex and some next people found a simpler model with a firm significance.
Between Perez’s two papers, the Bulletin of Mathematical Biology had another author chime in with regards to single-stranded DNA. Yamagishi et al examined single strand DNA and found the nucleotide frequencies could be predicted with a high degree of accuracy using golden attractors. These were .5% from expected values.
“Everything unfolds as if the populations held concurrently by the 64 codons in the whole human genome scale are a self-similar fractal projection of the original universal genetic code primitive matrix.”
Perez 2010
Study main findings #2: Decagonal Symmetry
Now lastly I must comment on some studies from 2020 and 2021. These papers provide a mathematical conceptualization of the structure of DNA, informatically. Using the finite group modelling they at least substantiate the possibility that the golden ratio is embedded. The math is a lot more obtuse but it basically uses the symmetry properties.
Lastly, a 2021 paper follows the actually length:width ratio of the helix turning. This is a favorite on Pintrist accounts and pop sacred geometry news, often citing the 13 angstrom and 21 base pairs (Fibnacci numbers). However this approximation gives out to 1% off. This paper found “he ratio of the length of one turn of the molecule to its width is 33.750:20.978 = 1.6088 or within 0.5% of the value of Φ (1.61803…)”.
And a better image of the crossectional view
Promise this is the last figure, they’re just so pretty
Particularly, the occurrance of phi in the axial plane is a neqw feature, yet so plain. A striking feature of these studies is that convergence to phi is found in three independent processes.
“Speculatively then, could some such quasicrystal, perhaps containing phosphate and borate, have provided a Φ patterned ionic surface template (see for example [54]) on which the molecules to produce short strands of RNA, or even DNA, might have been adsorbed and arranged? The bonds holding the RNA/DNA molecule together are stronger than the Van der Waals or ionic bonds with which it would be adsorbed to the quasicrystal surface, so potentially allowing strands of RNA/DNA to form and be released. If this were possible, then it might start to explain why DNA has the Φ structure it does: it is an artefact [sic] of a particular mineral template that formed the first RNA/DNA strands.”
Larson, 2021
Conclusion
So now you see how the golden ratio appears in DNA. The best way to find the golden ratio in DNA is not through Fibonacci base pair numbers, but in the informational waveforms.
Sources:
Perez, jean-claude. (1991). J.C. Perez (1991), “Chaos DNA and Neuro-computers: A Golden Link”, in Speculations in Science and Technologyvol. 14 no. 4, ISSN 0155-7785. Speculations in Science and Technology. 14. 155-7785.
Yamagishi, M. E. B., & Shimabukuro, A. I. (2007). Nucleotide Frequencies in Human Genome and Fibonacci Numbers. Bulletin of Mathematical Biology, 70(3), 643–653. doi:10.1007/s11538-007-9261-6
Perez, J.-C. (2010). Codon populations in single-stranded whole human genome DNA Are fractal and fine-tuned by the Golden Ratio 1.618. Interdisciplinary Sciences: Computational Life Sciences, 2(3), 228–240. doi:10.1007/s12539-010-0022-0
Planat M, Aschheim R, Amaral MM, Fang F, Irwin K. Complete Quantum Information in the DNA Genetic Code. Symmetry. 2020; 12(12):1993. https://doi.org/10.3390/sym12121993
Larsen SH. DNA Structure and the Golden Ratio Revisited. Symmetry. 2021; 13(10):1949. https://doi.org/10.3390/sym13101949
Consulted
Bindi, L., Lin, C., Ma, C. et al. Collisions in outer space produced an icosahedral phase in the Khatyrka meteorite never observed previously in the laboratory. Sci Rep 6, 38117 (2016). https://doi.org/10.1038/srep38117
Phantom DNA Effect rabbit hole entrance (far more interesting phenomenon)
Further reading
Further works of Perez:
Perez, J.-claude. (2015). Deciphering hidden DNA meta-codes -the great unification & master code of biology. Journal of Glycomics & Lipidomics, 05(02). https://doi.org/10.4172/2153-0637.1000131
Flower of life projections:
Rapoport, D. L., & Pérez, J. C. (2018). Golden ratio and Klein bottle Logophysics: the Keys of the Codes of Life and Cognition. Quantum Biosystems, 9(2), 8-76.
Pingback: 11 Cultural Symbols Beautiful because of their Rotational Symmetry - Abnormal Ways
Pingback: The Golden Gnomon Triangle That Dishes Out Star Codes