The authors have declared that no competing interests exist.

DUF1220 proteins regions show the largest Homo-Sapiens lineage-specific increase in copy number of any protein-coding region in the human genome and map principally to 1q21.1. DUF1220 deletions have been associated with microcephaly and macrocephaly, respectively. DUF1220 copy number has been linked to both brain size in humans and brain evolution among primates. Remarkably, dosage variations involving DUF1220 sequences have now been linked to human brain expansion, autism severity, total IQ, and cognitive and mathematical aptitude scores. We analyzed in chromosome 1q a total of 245 DUF1220 proteins. Finally the method is extended analysing the long 1q21 region from 7 other close primates like Neanderthal, great apes : chimp, gorilla, orangutan and monkeys : macaque, marmoset, vervet. This remarkable property is confirmed by comparing these primates to other mammals such as mice, rabbit, cow, dolphin and Elephant. We then show four classes of multi-periodic fractal structures for all 19 DUF1220 regions and 19 NBPF genes studied cases. The analysis of these spectra of fractal periods

The exact function of the DUF1220 protein is not known. DUF1220 proteins regions show the largest Homo-Sapiens lineage-specific increase in copy number of any protein-coding region in the human genome and map principally to 1q21.1, and partially also in 1p. DUF1220 deletions have been associated with microcephaly and macrocephaly, respectively. In Colorado University Dr Sikela team established that human genome sequences encoding DUF1220, show a dramatically elevated copy number in the human lineage and variation in DUF1220 copy number has been linked to both brain size in humans and brain evolution among primates

There are many more copies of DUF1220 encoded in the human genome compared to the genome of any other species (

Dr Sikela Lab. demonstrates the hypothesis that increasing copy number of sequences encoding DUF1220 protein domains is a major contributor to the evolutionary increase in brain size, neuron number, and cognitive capacity that is associated with the primate order. They propose that this relationship is restricted to the anthropoid sub-order of primates

Dim x Dim y | 0 | d1 1 | d2 | 2 | 3 | …/... d100 4 | 5 | |

5 | 318499 | 377103 | 401874 | 416629 | 424005 | |||

6 | 369260 | 440557 | 364717 | 405943 | 357653 | |||

7 | 389780 | 351783 | 332589 | 318646 | 310074 | |||

8 | 253290 | 289225 | 304361 | 258865 | 273966 | |||

9 | 275885 | 243343 | 226178 | 259486 | 245390 | |||

10 | 188558 | 208306 | 214670 | 218930 | 222246 | |||

11 | 208279 | 180867 | 204098 | 187607 | 203513 | |||

12 | 220206 | 203013 | 194628 | 190435 | 187589 | |||

…/... 377 |

NBPF genes | Resonance | Periods | Fibonacci/Lucas Periods | Shifted sequences | Hyper-reson ance class | ||||||||||||

Test1 | NBPF1 | 7 | 9 | 16 | 25 | 41 | 5 | 8 | 13 | 21 | 34 | 2 | 1 | 3 | 4 | 7 | B |

Test2 | NBPF14 | 7 | 9 | 16 | 25 | 41 | 5 | 8 | 13 | 21 | 34 | 2 | 1 | 3 | 4 | 7 | B |

Test3 | NBPF12 | 7 | 9 | 16 | 25 | 41 | 5 | 8 | 13 | 21 | 34 | 2 | 1 | 3 | 4 | 7 | B |

Test4NBPF20 | 7 9 16 25 41 | 5 8 13 21 34 | 2 1 3 4 7 | B | |||||||||||||

Test5NBPF4 | 9 11 20 31 51 | 8 8 16 24 40 = 8x(1 1 2 3 5) | 1 3 47 11 | C | |||||||||||||

Neanderthal NBPF4 | 9 11 20 31 51 | 8 8 16 24 40 = 8x(1 1 2 3 5) | 1 3 47 11 | C | |||||||||||||

Test6NBPF10 | 7 9 16 25 41 | 5 8 13 21 34 | 2 1 3 4 7 | B | |||||||||||||

Test7NBPF6 | 9 11 20 31 51 | 8 8 16 24 40 = 8x(1 1 2 3 5) | 1 3 47 11 | C | |||||||||||||

Test8NBPF9 | 9 11 20 31 51 | 8 8 16 24 40 = 8x(1 1 2 3 5) | 1 3 47 11 | C | |||||||||||||

Neanderthal NBPF9 | 9 11 20 31 51 | 8 8 16 24 40 = 8x(1 1 2 3 5) | 1 3 47 11 | C | |||||||||||||

Test9NBPF9 | 7 9 16 25 41 | 5 8 13 21 34 | 2 1 3 4 7 | B | |||||||||||||

Test10NBPF9 | 7 9 16 25 41 | 5 8 13 21 34 | 2 1 3 4 7 | B | |||||||||||||

Test11NBPF6 | 9 11 20 31 51 | 8 8 16 24 40 = 8x(1 1 2 3 5) | 1 3 47 11 | C | |||||||||||||

Test12NBPF15 | 5 7 12 19 31 | 8 13 21 34 | 1 1 2 3 | A | |||||||||||||

Neanderthal NBPF15 | 5 7 12 19 31 | 8 13 21 34 | 1 1 2 3 | A | |||||||||||||

Test13NBPF15 | 5 7 12 19 31 | 8 13 21 34 | 1 1 2 3 | A | |||||||||||||

Test14NBPF3 | 7 9 16 25 41 | 5 8 13 21 34 | 2 1 3 4 7 | B | |||||||||||||

Test15NBPF3 | 7 9 16 25 41 | 5 8 13 21 34 | 2 1 3 4 7 | B | |||||||||||||

Test16NBPF3 | 7 9 16 25 41 | 5 8 13 21 34 | 2 1 3 4 7 | B |

Indeed, thanks to the CRISPR technology, it is now possible to modify locally the genomes, and more particularly the human genome

Especially since it has been established that this region is extremely fragile, difficult to sequence, and often causes severe cerebral disorders.

On the other hand, the fractal and global structures of the human genome were demonstrated

For more than 25 years, we have been looking for possible global, even digital, structures that would organize DNA, genes, chromosomes, and even whole genomes

We will analyze here several major sequences containing these proteins DUF1220 according to an original approach highlighting kinds of "fractal periodicities".

We have completely and systematically analyzed the DUF1220 protein rich regions in many genomes and more specifically in each of the following 2 reference genomes:

Neanderthal reference genome :-Neanderthalgenome(2014)ref

Sapiens HG38 (2013) human reference genome ref

- Sapiens HG38 (2013) genomehttps:/ www.ncbi.nlm.nih.gov/grc/human

Analysed DUF1220 regions in Sapiens HG38 chromosome1 :

The main links to regions of DUF1220 are available by this link : http://genome.ucsc.edu/cgi-bin/hgTracks?

hggroup_map_close=0&hgtgroup_genes_close=0&hgtgroup_phenDis_close=0&hgtgroup_rna_close=0&hgt group_expression_close=0&hgtgroup_regulation_close=0&hgtgroup_compGeno_close=0&hgtgroup_varRep

_close=0&hgtgroup_rep_close=0&hgsid=573629553_vMKvaa3cdohKVHtDV1yCaoEhuia9&position=DUF12 20&hgt.positionInput=DUF1220&hgt.jump=go&hgt.suggestTrack=knownGene&db=hg38&c=chr4&l=0&r=190 214555&pix=800&dinkL=2.0&dinkR=2.0

For more details, please visit complementary materials (part I).

We introduce here a method of global analysis of the roughness or fractal texture of the DNA sequences at the chromosome scale. To do this, we generalize the method of numerical analysis of the "Master Code of Biology"

The discrete interferences fields resulting from the analysis of an entire chromosome are therefore a three- dimensional space:

Dim y (vertical) restructuring in meta codons of lengths 17 to 377 nucleotides Dim x (horizontal) derived mobile1 such that 1/2 1/3 1/4 ... 1 / n

Dim z cumulated populations from the "Master code" operators

The + 1 / -1 derivatives will be of type increase, ie +1 if derivative increasing and will be of type decrease, ie

-1 if derived decreasing.

In this context we will explore these 3d spaces in 2 forms:

-Horizontal, meta codons dimension: curves for a given meta codon dimension, see in the example "resonances" below (see

-Vertically, spectral differentiation: discrete series d2-d1 is +1 if increase and -1 if decrease (see

We represent in top the +1 and in low the -1, (see the examples below).

Example of three-dimensional interference fields (Neanderthal chromosome 1q21.1 DUF1220 rich region6).

Horizontal scan example : 5318499 377103 401874 416639 424005 …/...

(see

Vertical scan example : 1 if d2>d1 and -1 if d2<d1 then : 1 1 -1 1 -1 1 -1 -1 …/...

(see

These two independent methods lead in all the cases analyzed to the same period value: here, for example, the main period "horizontal scan" is a resonance of 12bp (

The study of the long region6 of more than 5 million base pairs and containing 218 DUF1220 will reveal the spectrum of the following periods:

First remark: there are various possible interferences between Fibonacci/Lucas sub-spectrums : Main resonances periods:

5 7 12 19 31 50 81 DUF1220 resonances and periods

5 8 13 21 34 55 89 Fibonacci

0 1 1 2 3 5 8 Fibonacci

5 7 12 19 31 50 81 DUF1220 resonances and periods

2 1 3 4 7 11 18 29 47 Lucas

3 6 9 15 24 39 63... = 3 x ( 1 2 3 5 8 13..) = 3 times Fibonacci

5 7 12 19 31 50 81

3 4 7 11 Lucas

4 4 8 12 20 = 4 x (1 1 2 3 5...) = 4 times Fibonacci

5 7 12 19 31 50 81

3 4 7 11 18 Lucas

3 5 8 13 Fibonacci etc...

Second remark : There are main resonances periods like 5 7 12 19 31 50... but also secondary resonances

periods like : 17 (5+12), 24 (5+19), 26 (7+19), 57 (7+50), 69 (50+19), etc...

Main resonances :

5 7 12 19 31 50 81 …/...

Harmonic resonances :

17 24 26 36 38 43 48 55 62 74 91 93 98 …/...

Finally, we could propose the following rule :

The rule is :

"The distance between the waves flow periods sequence from DUF1220 region (5 7 12 19 31 50...) and a

Fibonacci similar sequence (5 8 13 21 34 55...) is ALSO another shifted Fibonacci sequence (0 1 1 2 3 5...) !"

A corollary is:

The waves spectrum associated with DUF1220 region (5 7 12 19... ) is analog with the INTERFERENCE substraction between TWO Fibonacci waves spectrum shifted (then 5 8 13 21 34... and 0 1 1 2 3 5 8 13 ...)

We now study the 16 cases of NBPF genes containing DUF1220 proteins in Homo-Sapiens (HG38), which we will then complete with 3 other representative analogues in Neanderthal.

Recall:

Lucas: 2 1 3 7 11 18 29 47 ...

Fibonacci: 0 1 1 2 3 5 8 13 21 34 …

Finally, we study the 19 cases of DUF1220 regions, including: the six regions from chromosome1 in Homo-Sapiens, then we concentrate on the long region6 of 1q21.1 in Neanderthal, then in the large apes primates, then in Other primates, and finally in other mammals of which the very small number of DUF1220 is known (see

Recall :

Lucas 2 1 3 7 11 18 29 47

Fibonacci 0 1 1 2 3 5 8 13 21 34

Here are the details of the periods, resonances and dissonances for the 2 long regions6 of 218 DUF1220 in Sapiens (HG38) and in Neanderthal.

REGION6 sapiens HG38 vs Neanderthal Recall Resonances :

Main resonances : 5 7 12 19 31 50 81 …/...

Harmonic resonances : 17 24 26 36 38 43 48 55 62 69 74 91 93 98 100…/.

In

Although Sapiens

Illustrated by

The fourfold correlation between different mammalian species, brain evolution, populations of DUF1220 and our numerical classification.

The study of the protein DUF1220.

Dynamic analysis of the long region of 218 DUF1220.

-2- Convergence, hierarchization and unification around the numbers of Fibonacci and Lucas of the 4 classes of digital spectra of DUF1220 regions and NBPF genes.

The study of 19 cases of NBPF genes on the one hand and of 19 regions DUF1220 on the other hand, 38 distinct analyzes appear to us UNIFIED around a single common generic law that can be stated thus:

A / The analysis of each of the regions containing DUF1220 proteins is characterized by a spectrum of numerical periods consisting of a sequence of integers.

B / These numerical spectra are grouped in only 4 characteristic classes.

C / each of these numerical classes can always be written in the form of a simple linear combination between 2 sequences of Fibonacci or Lucas.

D / It emerges a hierarchy allowing to classify these 4 classes among themselves.

Consequently, we can affirm that all the regions containing DUF1220 proteins can be CLASSIFIED, HIERARCHISEE and UNIFIED around a single law linking the numerical spectra of these regions DUF1220 and the sequences of Fibonacci and Lucas.

Let us now go over the rules outlined above.

The table below summarizes the properties of each of these 4 classes.

Let us recall the values of the two suites of Fibonacci and Lucas:

Fibonacci: 0 1 1 2 3 5 8 13 21 34 ...

Lucas: 2 1 3 4 7 11 18 29 47 …

About the HIERARCHY of the 4 classes:

First, we note this remarkable fact: each of the 4 digital spectra always starts with a sequence of 2 consecutive odd numbers (example 5 7).

In the second place, these 4 sequences of odd numbers can be hierarchized with respect to the ratio Phi (where Phi is the number of gold = 1.618033 ...).

5 ÷ 3 = 1.666666667 7 ÷ 5 = 1.4 9 ÷ 7 = 1.285714286 11 ÷ 9 = 1.222222222 13 ÷ 11 = 1.181818182

It will be noted that the best ratio would be the ratio 3/5, where 3 and 5 are numbers of Fibonacci. Although we have not met this ratio among the 38 cases studied, we will specify that the analysis of the large hybrid region fusing the 2 region1 and region2 in 1p has indeed led to a Fibonacci type spectrum, 5 8 13 ... See the figures below.

5 7 12 19 31 50 81 DUF1220 resonances and periods interference between :

2 1 3 4 7 11 18 29 47 Lucas

3 6 9 15 24 39 63... = 3 x ( 1 2 3 5 8 13...) = 3 times Fibonacci

5 7 12 19 31 50 81 DUF1220 resonances and periods interference between :

1 3 4 7 11 Lucas

4 8 12 20 = 2 x 1 1 2 3 5 = 2 times Fibonacci

7 12 19 31 50 81 DUF1220 resonances and periods interference between :
3 4 7 11 18 = Lucas
2 3 5 8 13 = Fibonacci
…/..

Weighting of the 4 classes A B C D: (please see

The distance of the successive ratios 7/5 9/7 11/9 and 13/11 is calculated to the ideal ratio of 1 / Phi = 0.6180339887. We thus obtain: 0.7142857143 0.7777777778 0.8181818182 0.8461538462

Then:

0.09625172555 0.1597437891 0.2001478295 0.2281198575

Of which we calculate the inverse: 1 / 0.09625172555 0.1597437891 0.2001478295 0.2281198575

= 10.38942413 6.26002429 4.996306992 4.383660462

Which we relativize in order to compare these values to the order of magnitude of the numbers of DUF1220 and the numbers of NBTF.

Finally, by weighting by a coefficient = 10:

10 × 10.38942413 6.26002429 4.996306992 4.383660462 = 103.8942413 62.6002429 49.96306992 43.83660462

Are finally: A: 104 B: 63 C: 50 D: 44

In

http://genome.ucsc.edu/cgi-bin/hgTracks? db=hg38&lastVirtModeType=default&lastVirtModeExtraState=&virtModeType=default&virtMode=0&nonVirtP osition=&position=chr1%3A144423094-144423901&hgsid=573629553_vMKvaa3cdohKVHtDV1yCaoEhuia9

>hg38_dna range=chr1:144423094-144423901 5'pad=0 3'pad=0 strand=+ repeatMasking=none

AAGGGCGAAGCTGATATGCTCTTCCTCAAATGAGTAAAACACACTTCTGT

AGTGCTGGAATGAGTCAGGTTGTTCAAAGTACATTGACGGAGTCGAATAA

CATCTATCCAGTGAGTCCTGTAAGACTTCAGGCTCTTCCACTTCCATCAG

CACGCCGTAGAGCCTGGAAAAGGAGACAAAACTAAAGAAGCAGCCAGGGA

AAATCAGACACCACAGAGCCCCACTAGATTTCAGAAGTAATATAAGGAAG

TGGTTAGAAAAGAAAAAGGATAGATTCATTAATGAGGTAAAAAAAAAAAA

TTTATTGCCTTTATGTTGGGATAGAACAGGGCCAGGTAGAAAACAATGAA

AGAGAAAGACAGAGAGAGAGAGACAGAGACAGAGACAGAGAGAAAGTGAG

CTAGTGAATTGCCCAGGTGACATACTGGTAAGGGAGTAAAAGGACACTCT

GAGTTAGTGCCCTCATGACACACAGCAAACTGTGATCACAAAAAGAGTGA

GCTCAATAGTTTTCCATAAAATATGCTCAAAATTTGATGCAGTGGCCATC

AGAGTACAGCTTTTGAAGTATGGTCAACCTATGGTACGTTAGTAAATGAT

AAGGGGAGGAAGAAATGGAAACCTAAACATCTACTGCAATGAAAACCAAC

AGCAATGACAGTAGGAGTAATTCAGCCTTCGTTGAAAACATGACATCAAA

CACACTCTGGTTTCCCTGAATCTGTTGCCTCCAGGTGTTAACACAGAATT

AAGCATCCACAATTGCTGAAAGTTACCTGGGGCATGGTGGGTTGTCATCT

TCCCCTTC

We analyzed this DNA sequence using the "Master Code of DNA" method described in (15). Here is a summary of the main results:

================== Strand2 =========================================== ANALYSING GLOBAL GENOMICS/PROTEOMICS COUPLING RATIO PERCENTAGE...

UNIVERSALIS GENETIC CODE (Global Unified Genetic Code)
GENONOMICS/PROTEOMICS Global Coupling percentage:

=== Strand 2 ===================================================================

MAJOR GENOMICS SITES…

15 FIRST + Major sites: 59 60 61 58 62 63 64 51 56 57 65 69 43 55 67<==== (b)

15 LAST - Minorsites: 218 220 243 219 215 222 214 225 221 217 209 201 244 216 208

MAJOR PROTEOMICS SITES...

15 FIRST Major sites: 38 39 40 34 35 36 37 33 44 58 59 41 42 43 32<==== (c)

15 LAST Minor sites: 201 200 199 203 202 240 239 219 218 89 236 235 185 180 87

================= VECTPIM2…

GENOMICS teeth of saw PERCENT CODE...

INCREASE /.\ DECREASE:

INCREASE /.\ DECREASE:

======================================================================

PERIODS ANALYSER SUMMARY:

TOPS. PERIODS: 3 7 11 15 19 23 27 31 35 43 47 51 55 59 63 67 71 74 79 83 85 95 …/...<==== €

PERIODS: 4 4 4 4 4 4 4 4 8 4 4 4 4 4 4 4 3 5 4 2 10 5 3 4 4 5 4 3 <==== (f)

AVERAGE PERIODS: 4.285714286

GAUSS PERIODS: VALUE / NB TIMES <==== (g)

Suggested PERIOD: 4

The three figures below and remarks (a) to (d) will enable the reader to grasp the potential of this method whose two strong points are unification between the genomics and proteomics images and On the other hand, a characterization of the fractal texture of the sequence and the demonstration of PERIODS. It is these periods which constitute the elementary brick of our spectral analysis, the object of this article.

a) As shown in the figure above, one observes that - for one of the 3 codon reading frames and for one of the reading directions of the sequence - there is a very strong correlation (> 90%) Between the master code image of the double-stranded DNA sequence and the master code of the virtual (or potential) amino acid translation of this same double strand. Here it may seem natural since it is a protein (DUF1220) but the same phenomena are universal throughout the genome, even for non-coding regions! This means that the master code produces a UNIFICATION between the 2 languages of the living being DNA and amino acids. In

b) c) It can be seen here that the extreme sites (lowest and highest in the figure) most often have local couplings on the scale of their address of triplets codons. For proteins, we have established that this corresponds to "active sites". For chromosomes, we have established that this corresponds to the points of fragility (breakpoints) of the chromosomes.

d) The "sawtooth" textures (see visual example in

e) f) g) These numerical values illustrate the periodic phenomena of fractal roughness of the textures of the genomics images of the master code. Here we see the sawtooth peaks (e), the corresponding periods (f), and the Gaussian distribution of these periods (g). The probable period is here = 4. Let 4 triplets codons, or ... 3x4 = 12 nucleotides ...

We then wanted to analyze in the same way the "gap" separating 2 consecutive proteins DUF1220.

For example, DUF1220 is the first protein of 218 DUF1220 and INTERDUF1220, the gap separating this first DUF1220 from the second DUF1220:

DUF1220 at chr1:144423094-144423901 start

DUF1220 at chr1:144424700-144425551

INTERDUF1220 in : chr1 : 144423902-144424699

chr1:144,423,094-144,423,901 808 bp.

>hg38_dna range=chr1:144423094-144423901 5'pad=0 3'pad=0 strand=+ repeatMasking=none

DUF1220

chr1:144423094-144423901 INTERDUF1220

chr1 : 144423902-144424699

Here their respective compositions in bases T C A G: DUF1220: 179 T, 292 A, 149 T, 188 A.

INTERDUF1220: 179 T, 292 A, 149 T, 188 A.

A detailed analysis will then make us discover this strange fact: the gap separating the first 2 proteins DUF1220 of the sequence region6 of 218 DUF1220 is, itself, a new protein DUF1220! Or, more precisely, the exact sequence capable of coding for a protein DUF1220, because, in fact, just in front of the gene of a protein is most often found a so-called "promoter" sequence ...

The consequence is that a more exhaustive analysis of this region of 218 DUF1220 may expose - perhaps - a number even greater than 218 proteins DUF1220! At the start of the long region6, there are therefore 3 occurrences of the protein DUF1220 attached and consecutive. This long region6 would therefore include not 218, but at least 219 DUF1220 proteins. The entirety of this region must be studied in more detail6. It will also be necessary and above all to carry out this same type of analyses on individual genomes!

Incidentally, the ratios TA and CG at DUF1220 and INTERDUF1220 also show that:

Accumulation DUF1220 = TA = 471

Cumulative DUF1220 = CG = 337

That is, 337 ÷ 471 = 0.7154989384 = 2 - "e".

Where "e" is the Euler constant (

Indeed, the error is very low: 0.7154989384 ÷ 0.71828 = 0.9961281651

We then carried out the same analyzes on the following 2 gaps. It appears then that they are, on the one hand different from DUF1220 and, on the other hand different from each other.

INTER2DUF1220 second gap

PERIOD......... | 4 | 19 |

PERIOD......... | 3 | 3 |

PERIOD......... | 5 | 3 |

PERIOD......... | 2 | 1 |

PERIOD......... | 8 | 1 |

PERIOD......... | 10 | 1 |

144425552-144426287

>hg38_dna range=chr1:144425552-144426287 5'pad=0 3'pad=0 strand=+ repeatMasking=none

INTER3DUF1220

DUF1220 at chr1:144426288-144427081

DUF1220 at chr1:144427831-144428634

144427080-144427830

>hg38_dna range=chr1:144424701-144425552 5'pad=0 3'pad=0 strand=+ repeatMasking=none

In this figure the reader observes the "saw teeth" typical of the phenomenon of fractal roughness, at the origin of the periods and resonances.

In

Of the first 5 DUF1220,

Of the first 10 DUF1220,

Of the first 20 DUF1220,

-of the first 50 DUF1220,

Here is an overview of these results, the reader will find the complete study in complementary materials (Part IV). Reminder of the sequence of 218 DUF1220:

Chr1q

Case2 : Analyse des 10 premiers DUF1220 :

1: 144423094-145297173

DUF1220by10

Chromosome 1: 144,423,094-145,297,173

As illustrated by

Main resonances periods:

5 7 12 19 31 50 81

DUF1220 resonances and periods

+ 0 1 1 2 3 5 8 Fibonacci

= 5 8 13 21 34 55 89 Fibonacci

5 7 12 19 31 50 81

DUF1220 resonances and periods

- 2 1 3 4 7 11 18 29 47 Lucas

= 3 6 9 15 24 39 63... = 3 x ( 1 2 3 5 8 13..) = 3 times Fibonacci

This means, according to our intuition, that this region of spectrum (5 7 12 19 31 50 81) represents the first part of a kind of potential "resonator".

Then, "interference" with an external spectrum of Fibonacci in addition (+ 0 1 1 2 3 5 8) or with a Lucas spectrum in subtraction (-2 1 3 4 7 11 18 29 47) will produce a "resonance "Of type Fibonacci (= 5 8 13 21 34 55 89) or else (3 x 1 2 3 5 8 13 ..) ...

Certainly, this second part of the resonator coming from an external source would remain to be determined ... Thus, in a kind of "key-lock" system, this 1q21.1 region would then act as a kind of "receiver", the "lock"!

But a receiver of what type "transmitter", the "key"?

The profoundly bipolar character of this phenomenon remains indivisible.

Can one imagine how the perception of the image of a nautilus or the musical resonance of Bach or the subtle aesthetic of a mathematical equation could constitute the beginning of the process constituting this "key"?

Certainly the genome when studied as a mathematical object with the tools of mathematical topology can offer a medium of resonance via the subtle topologies of the ribbon of Moebius or the bottle of Klein as demonstrated by the studies of Diego Lucio Rapoport

Indeed, as demonstrated by Volkmar Weiss

During our Artificial Intelligence research at IBM, based on our model "Fractal Chaos"

The fractal architecture

The reality that we have discovered for more than 25 years of biomathematics exploration of DNA is much more subtle:

Phi the Golden ratio

In 1991

In 1997

Finally, from 2010

This multi-level diversity of Phi is as astonishing as it is radiant ...

For example, in front of the cluster formed by the four discoveries presented in this article on the one hand, in

In this paper, we show that there is a sort of HGO (human genome optimum) unifying the entire human genome. This HGO will then allow the discovery of a universal law guiding all the LOH deletions implied in the cancers.

In "Humans and Primates Chromosomes4 Fractal CODES: periodic stationary waveforms characterizing and differentiating Neanderthal and Sapiens whole chromosomes DNA sequences"

Finally, in this article we discover more strange still: Phi and the numbers of Fibonacci and Lucas no longer appear explicitly. They hide behind a subtle interference, hiding behind a spectrum of numerical periods in the appearance of any numbers.

Our intuition is that there exists a link, "dialogues" between these three heterogeneous but subtle mechanisms ...

We suggest in this scenario Key lock or transmitter receiver, a probable link between the chromosome4 of which

And this famous region 1p21.1 with more than 200 DUF1220 would then behave like a kind of "resonance box", the resonator.

Finally, in "Global and long range fractal differences between sapiens and Neanderthal genomes"

If this article had been an article of “pure mathematics” we could have discussed the convergence properties of the respective sequences discovered here:

1 3 4 ... (Lucas)

3 5 8 ... (Fibonacci)

5 7 12 ...

7 9 16 ...

9 11 20 ...

11 13 24 ...

... / ...

But this article concerns genetics and human genomics ... The genetics of the densest protein region within the whole human genome: DUF1220 protein region.

The genomics of the longest of our chromosomes, the chromosome 1.

How can we explain that these sequences of DUF1220 are organized in periodic structures obeying these numerical sequences ALL constructed from 2 consecutive odd numbers?

How to explain this total correlation between the levels of evolution of the 4 classes of sequences observed (

DUF1220 regions | Number of DUF1220 | Resonance Periods | Fibonacci/Lucas Periods | Shifted sequences | Hyper - resonance class | |

Anthropoids Primates | ||||||

Region11:16564024 16587759 | 7 | 9 11 20 31 51 | 8 8 16 24 40 = 8x(1 1 2 3 5) | 1 3 47 11 | C | |

Region21:21472881 21483305 | 5 | 7 9 16 25 41 | 5 8 13 21 34 | 2 1 3 4 7 | B | |

Region31:108232266 108239862 | 4 | 7 9 16 25 41 | 5 8 13 21 34 | 2 1 3 4 7 | B | |

Region4108454483 108462078 | 4 | 7 9 16 25 41 | 5 8 13 21 34 | 2 1 3 4 7 | B | |

Region51:120809849 120840512 | 7 | 7 9 16 25 41 | 5 8 13 21 34 | 2 1 3 4 7 | B | |

Region61:144423094- 149554657 | 218 | 5 7 12 19 31 50 81 | 5 8 13 21 34 55 89 | 0 1 1 2 3 5 8 | A | |

Region6 | 5 7 12 19 31 50 81 | 5 8 13 21 34 55 89 | 0 1 1 2 3 5 8 | A | ||

NEANDERTHAL1:141527445-146659008 | ||||||

Chimp region61:111091664-116223227 | 5 7 12 19 31 50 81 | 5 8 13 21 34 55 89 | 0 1 1 2 3 5 8 | A | ||

Gorilla region61:124329600-129461163 | 5 7 12 19 31 50 81 | 5 8 13 21 34 55 89 | 0 1 1 2 3 5 8 | A | ||

Orangutan region61:102601348-107732911 | 5 7 12 19 31 50 81 | 5 8 13 21 34 55 89 | 0 1 1 2 3 5 8 | A | ||

Olive Baboon Region61:119609055-124740618 | 5 7 12 19 31 | 8 13 21 34 | 1 1 2 3 | A | ||

Macaque region61:120005413-125136976 | 5 7 12 19 31 50 81 | 5 8 13 21 34 55 89 | 0 1 1 2 3 5 8 | A | ||

Marmoset region618:1-5131564 | 9 11 20 31 51 | 8 8 16 24 40 = 8x(1 1 2 3 5) | 1 3 47 11 | C | ||

Vervet Region61:1-1280666 | 7 9 16 25 41 | 5 8 13 21 34 | 2 1 3 4 7 | B | ||

Prosimians | ||||||

Mice Region63:94635287-99766850 | 7 9 16 25 41 | 5 8 13 21 34 | 2 1 3 4 7 | B | ||

Rabbit Region613:40672536-45804099 | 11 13 24 37 | 2 1 3 4 | 9 12 21 333 x (3 4 711) | D | ||

Laurasiatheria | ||||||

Cow Region63:19523691-24655254 | 5 7 12 19 31 50 81 | 5 8 13 21 34 55 89 | 0 1 1 2 3 5 8 | A | ||

Dolphin region6GeneScaffold_2231:20869 5:327249 | 9 11 20 31 51 | 8 8 16 24 40 = 8x(1 1 2 3 5) | 1 3 47 11 | C | ||

Afrotheria | ||||||

Elephant region6scaffold_127:1-2319825 | 5 7 12 19 31 50 81 | 5 8 13 21 34 55 89 | 0 1 1 2 3 5 8 | A |

Class reference | Hierarchy | Basic initial fractal periods spectrum... ==> | ==> Interfering with Fibonacci or Lucas pattern ... ==> | ==> Result of the numerical interference... reveals another Fibonacci or Lucas pattern | Number of DUF1220cases |

A | High = 1 | 5 7 12 19 31 50 81 | + 0 1 1 2 3 5 8 | = 5 8 13 21 34 55 89 | 12 |

B | Medium = 2 | 7 9 16 25 41 | - 2 1 3 4 7 | = 5 8 13 21 34 | 16 |

C | Medium = 3 | 9 11 20 31 51 | - 1 3 47 11 | = 8 8 16 24 40 = 8x(1 1 2 3 5) | 9 |

D | Low = 4 | 11 13 24 37 | - 2 1 3 4 | = 9 12 21 33 = 3x(3 4 7 11) | 1 |

Species | Total DUF1220 | Spectra class | NBPF genes |

Neanderthal | 272 | 104 | 23 |

Sapiens | 272 | 104 | 23 |

chimp | 125 | 104 | 15 |

Gorilla | 99 | 104 | 11 |

Orangutan | 92 | 104 | 10 |

OliveBaboon | 53 | 104 | 10 |

Macaque | 35 | 104 | 10 |

Marmoset | 31 | 50 | 11 |

Vervet | 3 | 63 | 2 |

Mice | 1 | 63 | 0 |

Rabbit | 8 | 44 | 3 |

Cow | 7 | 104 | 3 |

Dolphin | 4 | 50 | 1 |

Elephant | 1 | 104 | 2 |

We especially thank Dr. Volkmar Weiss who suggested we look for possible hidden codes in these long 1q21.1 DNA sequences containing large DUF1220 proteins population. We also thank the mathematician Diego Lucio Rapoport (Buenos aires), the biologist François Gros (Pasteur Institut,co-discoverer of RNA messenger with james Watson and walter Gilbert ) and Professor Luc Montagnier, medicine Nobel prizewinner for their interest in my research of biomathematics laws of genomes.