Jean-Yves Boulay
email: jean-yvesboulay@orange.fr

NUMBERING OF THE TWENTY PROTEINOGENIC AMINO ACIDS AND NEW ALPHANUMERICAL NOMENCLATURE PROPOSAL TO THEM

Keywords: amino acids, genetic code, symmetry, number theory, molecular biology, organic chemistry, physics, quantum shells, OMH index, fractal

By proposing a numbering of the twenty proteinogenic amino acids deduced from the physicochemical properties of the four coding DNA nucleobases, it is established that this amino acid number, equal to 5x entities, is not arbitrary. Indeed, we demonstrate that many attributes of these twenty amino acids, as a whole, are also 5x in number and that by isolating, since their numbering, the 3x peripheral amino acids from the 2x internal ones, these attributes are divided into ratios of 3/2 as exact value. This is verified both as the physicochemical properties of the 20 amino acids and as the coding configurations of the nucleobases, the source of this numbering.

INTRODUCTION

Today, it is now firmly established that living matter is organized via a so-called "universal" genetic code and that this genetic code encodes only, and very precisely, twenty proteinogenic amino acids. This number is not arbitrary, it is equal to 5x. More precisely this number of 20 entities is equal to 3x + 2x entities with a value of x equal to 4.

As we will demonstrate over the different parts of this study of the genetic code, it turns out that different components that make up the set of twenty (5x) proteinogenic amino acids are also to 5x (so 3x + 2x) entities. Also, it is the same considering this time different coding characteristics (arrangement and physico-chemical properties of DNA nucleobases) linked to these twenty amino acids. We will also demonstrate that these coding characteristics, organized around values equal to 5x, are intimately related to the physico-chemical properties of the twenty encoded amino acids.

From a subtle numbering of the 64 codons of the universal genetic code, we propose a numbering (from 0 to 19) of the twenty amino acids. These two numbering systems, including the first proposed by Professor Sergey Petoukhov [START_REF] Petoukhov | Genetic Code and the Ancient Chinese Book Of Changes[END_REF], are very directly dependent on the physico-chemical properties of the four nucleobases that make up DNA. They are therefore very legitimate to be used for the study of the genetic code mechanism. By "genetic code", we consider in this paper the totality of its components, namely simultaneously the 64 codons and the twenty encoded amino acids.

When we number the twenty amino acids, which are, very importantly, 5x in number, then we classify them into two symmetrical sets of 12 (or 3x) and 8 (or 2x) entities. By doing this, then it turns out that the different attributes respective to these two groups are always also in a ratio whose value is very precisely equal to 3/2. This, both for different and numerous attributes (physico-chemical properties: number of atoms, CH2 groups, etc.) of the twenty proteinogenic amino acids and in some aspects for the characteristics of their respective codons.

Finally, according to this numbering, we propose a new nomenclature official list of these twenty proteinogenic amino acids. This nomenclature, supplementing the current one (trivial name, 3-letter and 1-letter symbols) is alphanumeric in nature and is standardized in 2 digits and 3 letters as form.

In order to be able to number the twenty proteinogenic amino acids, we must first proceed to a numbering of the 64 codons of the universal genetic code. Also, this numbering of amino acids must depend on the physico-chemical character of the nucleobases constituting the codons. To this end, we use the very original numbering devised by Professor Sergey Petoukhov, which is based on the possible deamination and depurination of the four nucleobases.

Petoukhov's numbering of the 64 genetic code codons

In his investigations of the genetic code [START_REF] Petoukhov | Genetic Code and the Ancient Chinese Book Of Changes[END_REF] Sergey Petoukhov assigns a number from 0 to 63 to each of the sixty-four codons. This Petoukhov numbering is directly dependent on the physico-chemical properties of the four DNA coding bases. Using a very sophisticated method, Sergey Petoukhov manages to classify the full sixty-four codons set using a binary language (or alphabet, we invite the reader to consult the full article by Sergei Petoukhov [START_REF] Petoukhov | Genetic Code and the Ancient Chinese Book Of Changes[END_REF]). Depending on whether each nucleobase can undergo deamination or not, Sergey Petoukhov assigns them either the value 1 or the value 0 (table Figure 1). Also, depending on whether each nucleobase can undergo depurination or not, Sergey Petoukhov assigns them either the value 0 or the value 1. This double criterion makes it possible, for each codon, to create a six-digit binary number by juxtaposition of two three-digit numbers as described in Figure 2. It is important to emphasize that, in this innovative codon arrangement, DNA triplets located on the same line all have their three bases (even though they are unique) classified in the same order according to the criterion of possible deamination and that those located on the same column all have their three bases (yet unique) classified in the same order according to the criterion of possible depurination.

Numbering of the twenty proteinogenic amino acids

From this numbering system, in order to assign a number to each of the twenty proteinogenic amino acids, the most logical procedure is therefore proposed here, which is to follow the order of appearance of the amino acids according to this numbering of the codons (from 0 to 63) of the table by Sergey Petoukhov (Figure 3).

By this process, it is thus assigned (Figure 4) number 0 to Glycine, number 1 to Valine and to Proline, the last amino acid to appear according to this order of numbering of the sixty-four genetic code codons, 19 as number.

Symmetrical break-up of the 20 AAs in 3/2 ratio

Now that we have determined a numbering of amino acids by assigning them a unique and personal number, we propose to isolate these twenty entities in two sets of unequal size. We therefore distinguish a first set of 12 entities then a second set of 8 other entities. As illustrated in Figure 5, these two sets then oppose each other in a ratio of value 3/2.

Conventional representation of amino acids numbering.

Using symmetry graphics, many arithmetic phenomena presented in this paper will be presented in the way illustrated in Figure 5. Thereby, each of the 20 amino acids is symmetrically positioned to the one of opposite numbering in relation to the numbering order of these 20 AAs*: 0Gly versus 19Pro, 1Val versus 18His, etc. Also, we therefore isolate two numbering zones:

-an area called "external" with inside the six first and six last numbered AAs an area called "internal" with inside the two times four centrally numbered AAs. This is only by this way that appears many singular arithmetic arrangements about amino acids attributes. Also, in some demonstrations, we can likewise speak of grey area (grey) and light area (white) to define these two sets respectively made up of 3x and 2x entities.

DEPICTION OF THE TWENTY PROTEINOGENIC AMINO ACIDS

Schematic graphics table

In this article, the different atoms, five in number, which make up the 20 proteinogenic amino acids, will be represented, in an unconventional way, as in the table in Figure 6.

This is inspired by proton-numerical module concept introduced by Sergey

Petoukhov [1 and 2]. According to this genetic code researcher, in organic chemistry, module is a group formed of just one non-hydrogen atom with possibly its satellite hydrogen atoms attached. Also, Sergey Petoukhov considers Sulfur as constituted in a twice module.

Not by chance, there are precisely five atoms that make up the 20 AAs. Also, as we will demonstrate in the next chapter, these five entities oppose each other in a ratio of 3/2 value. The previous table (Figure 6) lists the 20 amino acids in the order of their numbering just introduced in Chapter 2. In this study of the genetic code, it is considered the amino acids in their isolated and saturated state, therefore (important point of view) in non-ionized states.

This schematic representation of the 20 proteinogenic amino acids makes it possible to highlight several of their physicochemical characteristics studied here in this paper. This table therefore highlights for each AA (and not restrictively) :

-alphanumeric appellation, -number of atoms, -sort of atom, -number of CH2 groups -radical symmetry (or not).

Some prime amino acid attributes.

The table in Figure 7 condenses the main values relating to the twenty proteinogenic amino acids. This table lists absolute (integer) values which are therefore not suggestive and subject to debate. The criteria introduced here will be more widely illustrated throughout the various chapters presented. For each amino acid, it is so listed, its numbering, its atom number inside its radical, detail of this number with atoms at even or odd electron shells, its number of CH2 groups (methylene bridges directly connected to alpha carbon).

It is also listed, for each of twenty proteinogenic amino acids, its rank of OMH hydrophobicity index and its number of codons in its largest respective codon set with two first same DNA bases. A brief overview of this table already demonstrates the powerful tendency of the mechanism of the genetic code to organize itself into perfect arithmetic ratios of 3/2 values.

We study here from the outset, both the anatomy of amino acids (physical structure), their chemical properties (hydrophobicity) and the coding genetic structure associated with them. This voluntary approach in order to suggest the inter connectivity of the phenomena studied. Other various aspects relating to amino acids and the genetic code will complete and flesh out this first approach.

ORGANIZATION OF THE 20 AMINO ACIDS ATTRIBUTES INTO 3/2 RATIOS

Atom number

The total number of atoms contained inside the radicals of the twenty amino acids is equal to 205. This number is therefore equal to 5x entities with x = 41.

Also, as shown in Figure 8, there are 123 atoms (3x atoms → x = 41) in the 12 external AAs set as defined in Chapter 2.2 and there are 82 atoms (2x atoms → x = 41) in the 8 AAs of the internal group. Thus, these two sets are opposed in an exact ratio of 3/2 as value.

Atom number and quantum shells

The 3/2 ratio operates simultaneously within the genetic code in different aspects. Thus, the differentiation of two categories of atoms, respectively with an even number of electron shells and with a odd number of electron shells, oppose them in 3/2 ratios. Indeed, the amino acids are (only) made up of Carbon, Nitrogen and Oxygen, three atoms with two electron shells and of Hydrogen and Sulphur, two atoms with one and three electron shells. Figure 9 illustrates this prime opposition of genetic code constituents in 3/2 values ratio. Figure 11 illustrates just a few oppositions between these two sets of three and two atoms. In a previous paper [START_REF] Boulay | Genetic code, quantum physics and the 3/2 ratio[END_REF] we demonstrated that a very large number of their physico-chemical and so even quantum characteristics also oppose each other in exact ratios of value 3/2. The separate counting of these two categories of atoms, which grouped together gave (Figure 10) already an opposition of the values in a 3/2 ratio according to the numbering of the 20 amino acids, continues to generate the same exact ratios of 3/2 values.

Atom number gap

Since each of the two distributions of atoms illustrated in Figure 10 generates an opposition of the values in ratio 3/2, in relative value, it is arithmetically logical that the differences in the numbers of atoms with an even and odd number of shells of electrons also generates the same ratios. However, it is remarkable to note that these ratios, of exact value 3/2, are maintained by considering the differences of atoms in absolute values as it appears in Figure 11.

CH2 groups

Many of the twenty amino acids contains CH2 groups (methylene bridges) in their radical. All these methylene bridges are located just after the alpha carbon either directly connected to it, alone or in a chain.

There is however an exception to this in Isoleucine where the CH2 group is not connected directly to the alpha carbon. Figure 12 illustrates these two configuration types. There are therefore 26 CH2 groups in all of the twenty amino acid radicals but just 25 directly connected (alone or in a chain) to the alpha carbon. Thus, this number is equal to 5x entities. As it appears in Figure 13, it turns out that these 25 CH2 groups are distributed in an exact ratio of value 3/2 between the set of 12 external AAs and the set of 8 internal AAs with respectively 15 (3x → x = 5) and 10 (2x → x = 5) entities listed. Depending on their numbering, the twenty amino acids therefore oppose their quantity of methylene bridges in a 3/2 ratio according to their membership of the external and internal groups defined in Chapter 2. This numerical differentiation is not the only one to generate this type of arithmetic phenomenon.

CH2 groups gaps and numbering

The difference in the number of CH2 groups between two amino acids of opposite numbering (0 versus 19, 1 versus 18, etc.) also overall generates an opposition of values in an exact 3/2 ratio. This, once more between the two sets of external and internal entities as shown in Figure 14. This therefore greatly reinforces the numbering proposal introduced and studied in this paper relating to the genetic code and its physicochemical attributes (AAs, nucleobases, etc.).

CH2 groups number parity

Inside the radicals of the twenty amino acids, there are from 0 to 4 CH2 groups directly attached to the alpha carbon. It turns that the parity of the number of these CH2 groups also generates singular arithmetic phenomena in connection with the concept of numbering proposed in this paper.

As illustrated Figure 15, segregation of CH2 groups in even or odd number inside AA radicals generate also a opposition of these entities in 3/2 ratios according to the two numbering areas. Moreover, these two sets of CH2 groups oppose themselves in 3/2 ratio with 15 CH2 groups in even number versus 10 in odd number.

CH2 Groups parity and remarkable identity

As shown in Figure 15 and much more in detail in Figure 16, the distribution and number of CH2 groups according to the double criterion of parity and numbering introduced here is perfectly organized into the remarkable identity:

(a + b) 2 = a 2 + 2ab + b 2
This, with 3 and 2 as respective values for a and b. Thus, the quantity of CH2 groups in even number and in external numerated AAs corresponds to the value a 2 of the remarkable identity and the quantity of CH2 groups in even number and in internal numerated AAs corresponds to the value ab.

The quantity of CH2 groups in odd number and in external numerated AAs also corresponds to the value ab and that of CH2 groups in odd number and in internal numerated AAs corresponds to the value b 2 . These different values therefore transcend into these equal ratios:

OMH index rank

According to the exact values of the OMH scale [START_REF] Sweet | Optimized matching hydrophobicity (OMH)[END_REF], we created (f in Figure 7) an index rank scale ranging from 1 (largest index) to 20 (lowest index) for the twenty amino acids.

Full OMH index rank

The cumulative value of these ranks gives a value of 126 (3x ranks→ x = 42) for the external set of AAs and a value of 84 (2x ranks→ x = 42) for the internal one as this is illustrated Figure 17. The OMH index [START_REF] Sweet | Optimized matching hydrophobicity (OMH)[END_REF] is universally recognized in the study of the twenty proteinogenic amino acids and it is highly unlikely that this perfect arithmetic arrangement is so by pure chance. What emerges from the next demonstration will reinforce this point of view.

OMH index ranks parity

Although the distribution of the different OMH index ranks (Fig. 17 and18) seems random within the two defined AAs sets of external and internal, the even and odd isolated values continue to generate a perfect 3/2 ratio between these two sets.

Greater number of codons with the first two identical nucleobases

Due to the structural mechanics of the genetic code, i.e. the association of three out of four possible nucleobases to form a coding signal, 64 codons are necessary for the encoding of 20 amino acids. It turns out that each amino acid is associated with a seemingly random number of codons. In fact, AAs are usually encoded with codons at the same first two identical nucleobases. In this universal genetic code, each amino acid is associated with a set of codons with two identical first bases varying from 1 to 4 codons.

Three amino acids are encoded with more than one of these sets at the same first nucleobases. Arginine, Leucine and Serine encoded by these 4-codon sets are also encoded with 2-codon sets. We therefore propose, Figure 19, to consider only a reduced genetic code of these smaller sets since for these three AAs, a set of larger codons also encodes them. We therefore subtract from the initial 64 codons these three times two codons and we do not consider the three "Stop" codons either. Thus, we lighten the initial genetic code of 9 codons and therefore keep only 55 codons for the coding of the 20 amino acids.

This residual number of 55 codons is therefore equal to 5x entities. The final count of these 55 residual codons in the two predefined sets of 12 and 8 AAs respectively qualified as external and internal generates here also an exact ratio of value 3/2 with 33 versus 22 counted codons as this is illustrated Figure 20.

Synthesis of the distribution of the AAs prime attributes

Figure 21 summarizes the main attributes of the twenty amino acids. It should therefore be noted that there are always 5x in number and that they are also always divided into 3x entities in the set of 12 AAs with external numbering and into 2x entities in that of 8 AAs with internal numbering. In view of this first synthesis, and because they concern very different aspects, it seems very unlikely that all these physico-arithmetic arrangements are so by chance. The results of the next investigations will reinforce this hypothesis.

SYMMETRY AND ATOM COUNT

Here is studied anatomy of the twenty amino acids and connections between radical symmetry and atom count of complet AA.

Amino acid symmetry

From a schematic point of view, we distinguish here between amino acids with symmetric radicals and those with asymmetric radicals. This symmetry concerns the way in which the molecular chain is distributed beyond the alpha carbon. The nature of the bonds (which can be single or double) is not considered but just the distribution of the groups of atoms in the radical. As illustrated Figure 6*, just ten amino acids have a symmetrical radical. Consecutively, ten amino acids do not have a symmetric radical structure. It turns out, Figure 22, that the distribution of these two sets of ten amino acids, distinguished by their symmetry or non-symmetry, is organized in 3/2 ratios in the two predefined numbering zones.

* Figure 12, about CH2 groups, illustrate also this symmetry concept.

Atom count

We demonstrate here that the number of atoms contained in each of the twenty amino acids, in their complete version (base + radical as presented in the introduction table Figure 6) is related to the decimal system.

Indeed, it turns out that the smallest amino acid, Glycine has exactly 10 atoms. Also, the ten amino acids with the smallest number of atoms have 19 as maximum 19. The other ten have a number of atoms from 20 to 29 (27 more precisely for Tryptophan). Thus, we can say that 10 AAs have a number of atoms of ten and 10 others of two tens. These two sets of 10 AAs are distributed in perfect 3/2 ratios in accordance with the two predefined numbering zones as illustrated Figure 23.

3 Symmetry and atom count transcendence

As it is clearly visible and synthesized in Figure 24, it turns out that these two notions introduced here, that of symmetry of the radical (or not symmetry) and that of quantity of number of atoms transcend each other completely. Thus, do we identify four subsets of five amino acids:

-5 AAs at symmetrical radical and at atom number of one ten, -5 AAs at symmetrical radical and at atom number of two tens, -5 AAs at asymmetrical radical and at atom number of one ten, -5 AAs at asymmetrical radical and at atom number of two tens.

Also, systematically, in each of these four subsets, in exact 3/2 ratios, three amino acids are externally numbered and 2 AAs are internally numbered.

Amino acid fractal organization

This remarkable organization of the twenty proteinogenic amino acids turns out in reality to be fractal in nature, as illustrated by the graphic in Figure 25. This fractal representation makes better appear how we go from 20 entities to the final ratio 3/2. Indeed, from the twenty entities of the genetic code that are the proteinogenic amino acids, two sets of 10 entities can be isolated according to physico-chemical criteria. These two sets can each be split into two subsets of 5 AAs. Finally each of these subsets can be separated into sets with ultimate numbers of 3 and 2 entities.

This fractal organization also reveals a perfect symmetry of the distribution of these two times ten amino acids. indeed, as reflected in the graphics in Figure 25, each of the four final subsets of 2 or 3 entities finds its double mirror subset with two identical criteria against an opposite criterion which is precisely the criterion of radical symmetry or non-symmetry of radical.

ALPHANUMERIC SYMBOL PROPOSAL

We have therefore firmly established, in many aspects, that the various characteristics of the twenty proteinogenic amino acids are closely linked to their numbering, which itself depends on their DNA codification as proposed at the beginning of the article. This is why we suggest here, to enrich the current nomenclature applied to these twenty entities, the creation of new standardized alphanumeric symbols making it possible to identify these twenty proteinogenic amino acids.

In this paper, we have numbered these entities from 0 to 19 and have attached their respective number to their three-letter alphabetic symbol. For example, we have described Valine as 1Val and Arginine as 11Arg so by respectively four and five characters.

For the sake of standardization (and even formalization), we propose, as illustrated Figures 26 and27, to describe all the twenty AAs with five characters, two of which are numeric and three alphabetical. So we add the number symbol 0 (zero) to the first ten AAs numbered from 0 to 9. By this, for each AA, we therefore propose a unified symbol of 2 digits + 3 letters. The table in Figure 27 therefore lists all of the 20 proteinogenic amino acids involved in the mechanism of the universal genetic code. It is therefore described, from the conventional nomenclature, the trivial name, the symbol in 3 letters and the one letter symbol. To this is added, for each AA, its alphanumeric symbol of 5 characters that we propose as a new standardized and official nomenclature. We also propose, in a legitimate logic, that these twenty amino acids appear in the tables listing them in this order. Indeed, this sequence corresponds to certain real coding criteria and even, as demonstrated throughout this paper, to physical criteria both linked to the DNA triplets and to the specific characteristics of the amino acids.

Thus we propose to no longer present them in alphabetical order as practiced until now because this order does not correspond to any physico-chemical criteria. In their new alphanumeric order, the data concerning them will be more directly visible and usable. This, as the various tables presented in this paper have already demonstrated.

OTHER 3/2 RATIOS REGARDING GENETIC CODE ORGANIZATION

The numbering of the twenty proteinogenic amino acids is not the only concept to generate singular arithmetic phenomena opposing the entities of the genetic code in various ratios of value 3/2. Some of these other investigations are presented in the author's previous paper: Jean-Yves Boulay. Genetic code, quantum physics and the 3/2 ratio. 2020. hal-02902700v4 [START_REF] Boulay | Genetic code, quantum physics and the 3/2 ratio[END_REF]. Also, some other genetic code investigations are in connections with the subject of this paper especially about ratio 3/2, symmetry, listing of proteinogenic amino acids or more generally connections between number theory and the genetic code. As example, some of these investigations are listed in references [from 4 to 8].

DISCUSSIONS AND CONCLUSIONS

This study reveals that the set of 64 codons, or the coding structure, and the set of 20 proteinogenic amino acids, or the coded structure, must in fact be considered as a single and unique entity that we more formally name The Genetic Code. The universal genetic code encodes very exactly and only twenty proteinogenic amino acids, that is 5x entities. These 5x entities are made up of only 5 different atoms, including three with two quantum shells and two with 1 or 3 quantum shells, i.e. three atoms with an even number of shells and two atoms with an odd number of quantum shells. The set of twenty amino acids operating within the universal genetic code totals 205 atoms, or 5x atoms. Among these 205 atoms, 85, or 5x atoms, have an even number of quantum shells and 120, or 5x atoms have an odd number of quantum shells. Also, in all of these twenty proteinogenic amino acids, there are very precisely 25 CH2 groups (methylene bridges) linked to the alpha carbon, so again 5x entities.

Since their coding characteristics, that is to say the nature of the nucleobases which encode them, the twenty amino acids can be legitimately numbered from 0 to 19, i.e. twenty different numbers being assigned to them. Since this numbering, by operating a symmetrical distinction between the 3/5th amino acids with external numbering and the 2/5th with internal numbering, it turns out that the main components and other attributes of these twenty amino acids, considered as a whole, oppose in exact ratios of value 3/2 in these two zones of numbering made up of 3x and 2x amino acids.

Also, some criteria, as radical symmetry and atom count, transcend each other, revealing a fractal organization of the genetic code. This fractal organization, like all the other arithmetic arrangements presented in this paper, operates with the three absolute values 2, 3 and 5. These numbers are not arbitrary. They are all simply the first three prime numbers. Also the number 5 is the only prime number which is the sum of two consecutive primes: 2 and 3. And these two numbers are the only ones which are simultaneously two consecutive primes and two consecutive integers. Thus we can say that the global structure of the genetic code is directly related to the theory of numbers since it is organized with the first three and singular prime numbers that are 2, 3 and 5.

Since we have clearly demonstrated here that the structure of the twenty amino acids, in many aspects, is intimately linked to the nature of nucleobases and to the numbering of both codons and coded which emanates from them, we propose a new nomenclature official list of these twenty proteinogenic amino acids. This nomenclature, supplementing the current one (trivial name, 3-letter and 1-letter symbols) is alphanumeric in nature and is standardized in 2 digits and 3 letters as form. It is therefore strongly suggested to list the twenty amino acids according to this new nomenclature and in numerical order (from 00Gly to 19Pro) rather than as currently in alphabetical order. This new nomenclature being related to numerous and real physicochemical criteria (both coding and structure of AAs) must therefore be favoured in the study of the mechanism of the genetic code and of the twenty proteinogenic amino acids, a set of study subject which we call The Genetic Code.

Figure 1 :

 1 Figure 1: Method of assigning a double binary value to the four DNA nucleobases according to Sergey Petoukhov [1].

Figure 2 :

 2 Figure 2: Method of assigning a number to codons according to Sergey Petoukhov. See Fig. 1 and 3 also.

Figure 3 :

 3 Figure 3: Numbering of the 64 codons according to Sergey Petoukhov genetic code investigations [1] and distinction (grey areas) of the first appearance of each of the 20 coded amino acids.

Figure 4 :

 4 Figure 4: Assigning a single only one number to each of 20 proteinogenic amino acids in the table of the complete genetic code. See Fig. 3 also.

Figure 5 :

 5 Figure 5: Conventional representation of 20 proteinogenic amino acids numbering in symmetry graphics.

Figure 6 :

 6 Figure 6: Molecular description of the 20 proteinogenic AAs in the order of their numbering (in an unconventional graphic design which is inspired by S. Petoukhov papers [1-2]).

Figure 7 :

 7 Figure 7: Some prime amino acid attributes. See Figure 7 also.*Radical only and in non-ionized state.** From OMH scale [3].

Figure 8 :

 8 Figure 8: Atom counting inside radical of each proteinogenic amino acid. Distribution in 3/2 ratio regarding AA numbering areas.

Figure 9 :

 9 Figure 9: Differentiation of the 5 atoms constituting the 20 proteinogenic amino acids into 2 sets of 3 and 2 atoms according to the parity of their number of electron shells.

Figure 10 :

 10 Figure 10: Atom counting inside radical of each proteinogenic amino acid. Distribution in 3/2 ratio regarding AAs numbering and number parity of electron shells.

Figure 11 :

 11 Figure 11: In absolute values: atom gap counting regarding number parity of electron shells. * C,N and O. ** H and S. See Fig. 10 also.

Figure 12 :

 12 Figure 12: CH2 groups (methylene bridges) differentiation. Also radical symmetry differentiation as 12Met symmetrical and 13Ile not symmetrical radical, see Chapter 5.1.

Figure 13 :

 13 Figure 13: CH2 groups counting. Only methylene bridges directly connected with alpha carbon.

Figure 14 :

 14 Figure 14: CH2 groups gaps between opposed numbering amino acids. See Fig 13 also.

Figure 15 :

 15 Figure 15: Distribution of the 25 CH2 groups in various and interconnected 3/2 ratios according to the parity of their number in the radicals and of the two predefined numbering zones.

Figure 16 :

 16 Figure 16: Remarkable identity revealed in the count of CH2 groups in even number or in odd number and according to numbering areas. See Figure 15 also.

Figure 17 :

 17 Figure 17: OMH index ranks distribution in exact 3/2 ratio into two external and internal sets of AAs.

Figure 18 :

 18 Figure 18: According of the rank parities: OMH index ranks distribution in exact 3/2 ratio into two external and internal sets of AAs.

Figure 19 :

 19 Figure 19: Complete genetic code (64 codons) and lighter genetic code (55 codons) with only, for each AA, consideration of the largest codons sets with the first two identical nucleobases.

Figure 20 :

 20 Figure 20: Codon number in largest codon sets with 2 first same DNA bases.

Figure 21 :

 21 Figure 21: Depending on their numbering (external or internal): synthesis of the distribution of the prime attributes (to 5x in number) related to the 20 proteinogenic amino acids in exact 3/2 ratios.

Figure 22 :

 22 Figure 22: Distribution of the two sets of the ten symmetrical and ten asymmetrical AAs in 3/2 ratio according to internal and external numbering. See Figures 7 and 13 also.

Figure 23 :

 23 Figure 23: Distribution of the two sets of the ten AAs at one ten number of atoms and at two tens numbers in 3/2 ratios according to internal and external numbering. See Figure 6 also.

Figure 24 :

 24 Figure 24: Distribution of four AAs subsets in perfect 3/2 ratios according to their numbering, their radical symmetry state and their atom counting. See Figure 25 also.

Figure 25 :

 25 Figure 25: Fractal distribution of amino acids according to two physico-chemical criteria and to one numbering criterion (derived from the physico-chemical properties of nucleobases). Appearance of the final 3/2 ratio in this fractal configuration of the genetic code.

Figure 26 :

 26 Figure 26: Conventional nomenclature and alphanumeric symbol proposal to proteinogenic amino acids into 5 characters: 2 digits + 3 letters. Here Glycine as example. See Figure 27 also.

Figure 27 :

 27 Figure 27: Conventional nomenclature and alphanumeric symbol proposal to the twenty proteinogenic amino acids into 5 characters: 2 digits + 3 letters.