THE NUMERIC CONNECTIONS OF THE GENETIC CODE©

Shcherbak’s arithmetic and Boulay’s arithmetic: the proline hypothesis.

1. Introduction.

In this paper, the author proposes a new hypothesis on the structure of proline. This hypothesis confirms the Shcherbak’s arithmetic and feature unusual arrangements in the counting of the various entities (nucleons, atoms, etc.) which make up the amino acids.

1.1. Proline specificity.

The proline is the only amino acid which has a very particular chemical structure. The base and the radical of this amino acid are fixed two times. So, the proline has a base which is different of all other amino acids with a lost hydrogen atom.

Common structure of each AA (here SER)	Particular proline structure

Radical zone and base zone are fixed one time	Radical zone and base zone are fixed two times

In his arithmetic, Shcherbak conserves a hydrogen atom in the counting of the proline base but he removes this hydrogen from the radical. In Boulay’s arithmetic, this hydrogen atom is also conserved in the base but it’s not removed from the radical. Without these two special counting, the arithmetic of Shcherback and of Boulay would be completely destroyed! Without these two special counting, the very numerous and organized phenomena presented by Shcherback and Boulay disappear. These respectively presented phenomena are too much numerous and too much structured to be destroyed by an apparent contradiction of chemical arrangement.

1.2. “The proline hypothesis” depiction.

“The proline hypothesis”

The author, Jean-Yves Boulay, thus proposes a hypothesis in order to preserve these two arithmetic. It must occur a “singularity” with the second junction (specific junction to the proline) between the base and the radical. The author proposes a hypothesis that a neutron could behave as a proton. In this event, the counting of the particles of the carbon where is located this singularity gives 5 neutrons and 7 protons including 6 protons to be counted for the radical and 1 proton for the base. This possibility also lets suppose a new chemical (or physical) property of the nucleons which can to be interesting to study.

Depiction of the proline structure in a new proposed hypothesis:

Special particles counting of the proline (“the proline hypothesis”)

Hydrogen

Carbon

Nitrogen

Oxygen

Singularity:

one carbon

one hydrogen

Entities

Complete AA

Radical zone

Base zone

Protons

Neutrons

Nucleons

115

Atoms

This new structure of the proline is perfectly in agreement with the phenomena presented by Shcherbak and Boulay [3]. The presented following phenomena are in accord with this new counting system: the proline is constituted by 18 atoms, 115 nucleons, 63 protons and 52 neutrons.

2. Shcherbak’s arithmetic and Boulay’s rebel group.

2.1. Shcherbak’s arithmetic.

In an article [1], Shcherbak have described two sets of amino acids which have a nucleons number multiple of the prime number 37.

The two Shcherbak’s sets which have a nucleons number multiple of the prime number 37
	SET 1				SET 2
	SET 1				SET 2
	Coded (amino acids)	Nucleons in base	Nucleons in radical	Nucleons in complete AA	Coded (amino acids)	Nucleons in base	Nucleons in radical	Nucleons in complete AA
	GLY	74	1	75	SER	74	31	105
	ALA	74	15	89	CYS	74	47	121
	SER	74	31	105	LEU	74	57	131
	PRO	74	41	115	ILE	74	57	131
	VAL	74	43	117	ASN	74	58	132
	THR	74	45	119	ASP	74	59	133
	LEU	74	57	131	GLN	74	72	146
	ARG	74	100	174	LYS	74	72	146
					GLU	74	73	147
					MET	74	75	149
					HIS	74	81	155
					PHE	74	91	165
					ARG	74	100	174
					TYR	74	107	181
					TRP	74	130	204
	8	592	333	925	15	1110	1110	2220
		4 x 4 x 37	3 x 3 x 37	5 x 5 x 37		2 x 3 x 5 x 37	2 x 3 x 5 x 37	4 x 3 x 5 x 37

In the first set are included the height coded (amino acids) which are coded four times by the codons (triplets) with the two first identical DNA bases. In the second set are included the alls coded (amino acids) which are coded three, two or one times by the codons (triplets) with the two first identical DNA bases.

The nucleons numbers of these two sets are multiple of the prime number 37: 25 times 37 for the first set and 60 times 37 for the second set. These two counting are not the totality of nucleons of the 64 coded but only the sub totals of the amino acids counted one time for each set. Nevertheless the total nucleons number for the 64 coded is also multiple of 37.

2.2. Boulay’s rebel group.

Boulay observation (The numeric connections of the genetic code 2001-2005^©on the Web only) [3]:

Systematically, it seems that the coded are identical if the final base of the codon is either A or G or if this base is either T or C. This except for a named group the rebel group :

the rebel group
Codon	Coded	Nucleons number	Codon	Coded	Nucleons number
ATA	isoleucine	131	TGA	*STOP*	0
ATG	methionine	149	TGG	tryptophan	204

The rebel group set apart, codons code for the same coded if and only if their last base is either A or G or their last base is either T or C.

For the first Shcherbak’s set, the total nucleons number is, of course, multiple of 37 because the AA are all represented four times (2 times + 2 times):

925 x 4 = 3700 = 100 x 37.

For the second set, the AA are not alls represented two times but the total nucleons number is nevertheless multiple of 37. Because? Of cause to the special configuration of the rebel group! ILE is represented 3 times, MET and TRP 1 time only. The arrangement of the nucleons numbers in these three AA preserves the arithmetical phenomena of multiples of prime number 37:

Nucleons in the set 2 of AA		2220	60 x	37
All AA are represented 2 times (except…)	x 2 =	4440	120 x	37
…ILE is represented 3 times Þ (+ 1 time)	+ 131	} - 222	- 6 x	37
MET is represented 1 only time Þ (- 1 time)	- 149
TRP is represented 1 time only Þ (- 1 time)	-204
STOP is represented 3 times (+ 1 time)	+ 0
total nucleons number in set 2		4218	114 x	37

total nucleons number in the two Shcherbak’s sets
	SET 1				SET 2
	Coded (amino acids)	Nucleons in complete AA	Number of coded for the AA	Total nucleons number	Coded (amino acids)	Nucleons in complete AA	Number of coded for the AA	Total nucleons number
	GLY	75	2 + 2	300	(STOP)	-	(2 + 1)	(0)
	ALA	89	2 + 2	356	SER	105	2	210
	SER	105	2 + 2	420	CYS	121	2	242
	PRO	115	2 + 2	460	LEU	131	2	262
	VAL	117	2 + 2	468	ILE	131	2 + 1	393
	THR	119	2 + 2	476	ASN	132	2	264
	LEU	131	2 + 2	524	ASP	133	2	266
	ARG	174	2 + 2	696	GLN	146	2	292
					LYS	146	2	292
					GLU	147	2	294
					MET	149	2 – 1	149
					HIS	155	2	310
					PHE	165	2	330
					ARG	174	2	348
					TYR	181	2	362
					TRP	204	2 – 1	204
	8	925	32	3700	16	2220	32	4218
		5 x 5 x 37	4 x 8	10 x 10 x 37			(2 x 16) + 2 - 2	114 x 37

2.3. Others similarity between Shcherbak’s observations and Boulay’s observations.

The numbers of the different qualities of particles in each base of amino acid and in the totality of the 64 coded are multiple of the same prime numbers: 37 for the nucleons, 13 for the protons and 7 for the neutrons.

particles	in the base of each AA	in all amino acids
nucleons number	74 = 37 x 2	7918 = 37 x 214
protons number	39 = 13 x 3	4264 = 13 x 318
neutrons number	35 = 7 x 5	3654 = 7 x 522

With or without the rebel group, the numbers of the different qualities of nucleons are multiple of the same prime numbers: 13 for the protons and 7 for the neutrons.

protons number in all amino acids	protons number in the rebel group only	protons number in all AA without the rebel group
4264 = 13 x 328	260 = 13 x 4 x 5	4004 = 13 x 7 x 11 x 2 x 2

neutrons number in all amino acids	neutrons number in the rebel group only	neutrons number in all AA without the rebel group
3654 = 7 x 522	224 = 7 x 4 x 8	3430 = 7 x 7 x 7 x 5 x 2

The same phenomenon appears with the counting of Petoukhov’s modules* [4]:

modules number in all amino acids	modules number in the rebel group	modules number in all AA without the rebel group
544 = 17 x 32	34 = 17 x 2	510 = 17 x 30

Also:

counting of the modules liaisons in all amino acids	counting of the modules liaisons in the rebel group	counting of the modules liaisons in all AA without the rebel group
495 = 11 x 45	33 = 11 x 3	462 = 11 x 42

*The Petoukhov’s structure is a original system describing the molecular structure:

For example, atom of nitrogen will be represented by number 7. If one or several atoms of hydrogen are joined to some non-hydrogen atom, we shall add protons of hydrogen to number of protons of non-hydrogen atom always. Such group of the non-hydrogen atom with its adjoined hydrogen atoms (i.e., “protonated” non-hydrogen atom) will be denote by sum of protons of their nucleuses. For example, amino group NH₂ will be denoted by number 9 which is sum of 7 protons of nitrogen atom and 2 protons of two hydrogen atoms. In such schemes the atoms of hydrogen are not represented independently at all, and their presence at a molecule simply increases general number of protons of the atoms, connected to them directly.

*Extrait of : S.V.Petoukhov “Genetic Code and the Ancient Chinese “Book Of Changes”” , “Symmetry: Culture and Science”, 1999, vol.10, № 3-4, p. 211

For more details on the Petoukhov’s structure please consult: Petoukhov’s modules

3. Similarity between atoms numbers and nucleons numbers

The total number of atoms in the 64 coded is equal to: 1147 = 37 x 31

Without the rebel group, the total number of atoms in the 64 coded is equal to: 1078 = 7 x 7 x 22

So, the atoms number and the nucleons number are multiple of the same prime numbers in the different counting.

Similarity between atoms numbers and nucleons numbers
counting depiction	Atoms number	Nucleons number
total number in the 64 coded	1147 =	7918 =
total number in the 64 coded	31 x 37	214 x 37
total number in the 64 coded without the rebel group	1078 =	7434 =
total number in the 64 coded without the rebel group	22 x 7 x 7	1062 x 7

So, without the rebel group, the numbers of atoms, nucleons, protons and neutrons are all multiple of the prime number 7:

multiples of prime number 7 in according to different entities
entities	entities numbers
atoms	1078 =	22 x 7²
nucleons	7434 =	1062 x 7
protons	4004 =	572 x 7
neutrons	3430 =	10 x 7³

4. Tables of counting of the different entities

Counting of different entities in each amino acid. These counting are in according with the special proline depiction which is presented in the proline hypothesis:

counting of different entities in each amino acid
entities counting in the complete amino acids (base + radical which are united)	entities counting in the amino acids according to the counting system of apartheid*

*entities counting in the amino acids in according to the counting system of apartheid: this counting system is presented in the following chapter (just now)

counting of different entities in the 64 coded
entities counting in the complete amino acids (base + radical which are united)	entities counting in the amino acids according to the counting system of apartheid*

5. Study of the counting of nucleons by physical apartheid of the radical and the base of the amino acid.

5.1. Depiction of the counting of nucleons by physical apartheid.

In this counting system, the radical and the base of each amino acid are separated in two molecules and the two molecules are closed by a hydrogen atom. By this new counting system, only the protons numbers are different. This is just a theoretical (algebraic) separation bat not a real physical apartheid. So, for proline, is preserved a singular counting of neutrons number in the carbon atom which is affixed to the nitrogen atom of the base: 5 neutrons only.

Detail of apartheid system (common and special configurations)
For each amino acid: + one hydrogen in the base and + one hydrogen in the radical

For example : SER = 56 protons		New counting : SER = 58 protons
Glycine Particularity

GLY = 40	Glycine is separated also		New counting GLY = 42
Proline Particularity

PRO = 63	only + one hydrogen		New counting PRO = 64

By this new counting system, the phenomena of multiples of prime number 7 are much amplified.

5.2. Counting of nucleons by physical apartheid system.

Counting of the different particles in the genetic code table:

Counting of protons, neutrons and nucleons in the genetic code table by apartheid system counting
	A			G	T	C
A
G
T
C
Neutrons number			Protons number				Nucleons number
With the rebel group:
3654		4382						8036
7 x 522		7 x 626						7 x 7 x 164
Rebel group only:
224		266						490
7 x 32		7 x 38						7 x 7 x 10
Without the rebel group:
3430		4116						7546
7 x 7 x 7 x 10		7 x 7 x 7 x 12						7 x 7 x 7 x 22

5.3. Arithmetic results.

Counting of nucleons in this apartheid system reveals surprising results: the totals are all multiples of 7 with or without the rebel group. Also, without the rebel group, the totals are multiples of 7 x 7 x 7 (so 7³):

With or without the rebel group, the total protons number is multiple of the prime number 7:

with the rebel group:	4382 protons	= 7 x 626
the rebel group only:	266 protons	= 7 x 38
without the rebel group:	4116 protons	= 7 x 7 x 7 x 12

With or without the rebel group, the total neutrons number is multiple of the prime number 7:

with the rebel group:	3654 neutrons	= 7 x 522
the rebel group only:	224 neutrons	= 7 x 32
without the rebel group:	3430 neutrons	= 7 x 7 x 7 x 10

With or without the rebel group, the total nucleons number is multiple of the number 49 (so 7²). Without the rebel group the total protons numbers and the total neutrons numbers are multiple of the number 343 so multiple of 7³(so 7 x 7 x 7)!

with the rebel group:	4382 protons	= 7 x 626
	3654 neutrons	= 7 x 522
	8036 nucleons	= 7 x 7 x 164

the rebel group only:	266 protons	= 7 x 38
	224 neutrons	= 7 x 32
	490 nucleons	= 7 x 7 x 10

without the rebel group:	4116 protons	= 7 x 7 x 7 x 12
	3430 neutrons	= 7 x 7 x 7 x 10
	7546 nucleons	= 7 x 7 x 7 x 22

5.4. Depiction of symmetrical and identical configurations in genetic code table.

In the genetic code table appear symmetrical and identical configurations of multiples of the prime number 7 for the totality of the nucleons, for the protons only and for the neutrons only:

In the following descriptions, this genetic code table is represented in a compressed version:
A box is the total sum (nucleons number) of 4 coded with two identical first DNA bases.

Symmetrical and identical configurations (without the rebel group)
Total nucleons numbers
		2 x 11 x 7 x 7 x 7
6 x 11 x 7 x 7				8 x 11 x 7 x 7

Protons numbers only			Neutrons numbers only
12 x 7 x 7 x 7			10 x 7 x 7 x 7
6 x 6 x 7 x 7	6 x 8 x 7 x 7		6 x 5 x 7 x 7		5 x 8 x 7 x 7

Symmetrical and identical configurations (with the rebel group)
Total nucleons numbers
4 x 19 x 7 x 7				4 x 22 x 7 x 7
		4 x 41 x 7 x 7
Rebel group only: 10 x 7 x 7
Protons numbers only			Neutrons numbers only
10 x 29 x 7	6 x 8 x 7 x 7		11 x 22 x 7		5 x 8 x 7 x 7

626 x 7			522 x 7
Rebel group only: 38 x 7			Rebel group only: 32 x 7

Also, without the rebel group, and by counting system of physical apartheid of the radical and the base of the amino acid, the total number of atoms in the 64 coded is equal to:

1190 = 170 x 7

6. Arithmetical conclusions.

So, without the rebel group, the numbers of atoms, nucleons, protons and neutrons are all multiples of the prime number 7. This, with and without the counting system of physical apartheid. with the counting system of physical apartheid, the phenomena of multiples of 7 are very amplified.

Multiples of prime number 7 according to different entities:

counting configuration	entities	entities numbers
without the rebel group (base + radical which are united)	atoms	1078 =	22 x 7 x 7
	nucleons	7434 =	1062 x 7
	protons	4004 =	572 x 7
	neutrons	3430 =	10 x 7 x 7 x7

counting configuration	entities	entities numbers
without the rebel group and by counting system of physical apartheid	atoms	1190 =	170 x 7
	nucleons	7546 =	22 x 7 x 7 x7
	protons	4116 =	12 x 7 x 7 x7
	neutrons	3430 =	10 x 7 x 7 x7

The author suggests that these results are not due to chance and that the genetic code has not formed at random but responds to numerical constraints. Also, the proposed hypothesis on the atomic composition of the amino acid proline is a serious investigation to track in the study of the genetic code and in the field of physics.

Bibliographies :

[1] Shcherbak, V. I. Sixty-four triplets and 20 canonical amino acids of genetic code: the arithmetical regularities. Part II //J. theor. Biol., v. 166, p. 475-477, 1994)

[2] S.V.Petoukhov “Genetic Code and the Ancient Chinese “Book Of Changes””, “Symmetry: Culture and Science”, 1999, vol.10, № 3-4, p. 211

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To return to:

2. Shcherbak’s arithmetic and Boulay’s rebel group.

A

G

T

C

Rebel group only:

Symmetrical and identical configurations (without the rebel group)

Total nucleons numbers

Protons numbers only

Neutrons numbers only

Symmetrical and identical configurations (with the rebel group)

Total nucleons numbers

Protons numbers only

Neutrons numbers only