THE NUMERIC CONNECTIONS OF THE GENETIC CODE©

Jean-Yves BOULAY

 

 

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

63

24

39

Neutrons

52

17

35

Nucleons

115

41

74

Atoms

18

9

9

 

 

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

 

 

 

 

 

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 =

31 x 37

214 x 37

total number in the 64 coded without the rebel group

1078 =

7434 =

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

 

[3] The numeric connections of the genetic code - Jean-Yves Boulay 2001-2006©   (on the Web only)

 

[4] Connections between Sergei PETOUKHOV searches and Jean-Yves BOULAY searches 2005©   (on the Web only)

 

 

 

Shcherbak’s arithmetic and Boulay’s arithmetic: the proline hypothesis. Jean-Yves Boulay 2004-2010©

 

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