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MATHEMATIC LANGUAGE 

OF THE GENES

Today's science exercises a lot of effort to discover the essence of genetic processes. Realization of project "GENOME" is taking place at the very moment. That is one of the biggest scientific projects in history of humankind. However science hasn't been able to achieve noticeable results in that field of exploration yet. These results are not being achieved due to not using of regularities from God's formula for creation of the World. And these are, in the front of all: regularities of sequencing of molecules in shape of number 931.

P R O T E I N E

Experimental research of existence or non existence of amino acid code performs in science for a longer period, but that phenomenon is still not completely explained. Scientists, first able investigate possibility that genetic code has a stereo chemical origin (D. Grafstein, Anderson, Jukas, Yoshiyki Kuchino, Yamao, Cribbs, etc.) While that, they do not pay enough attention o. program cybernetic and information lawfulness in genetic processes. And, that it is necessary to explore that aspect of those problems points the discoveries, which we discovered in that researches of schedule of periodic in biochemical process. Detailed analysis of periodic schedule of genetic code tells us that periodicity is accomplished by sequencing of molecule and is based on a mathematical law.

Example:

Amino acids

 

Amino acid 1

     

Amino acid 2

 

å

 

ß

 

å

 

æ

HNH

 

COOH

 

HNH

 

COOH

ß

 

ß

 

ß

 

ß

1,7,1

 

6,8,8,1

 

1,7,1

 

6,8,8,1

Connection

 

Connection

 

Connection

 

Connection

ß

 

ß

 

ß

 

ß

171

 

6881

 

171

 

6881

æ

 

æ

 

å

 

å

     

14104

     
   

å

ß

æ

   

931+931+931

931

931+931+931

139| | 931

931+931+931

931

931+931+931

(171 + 6881 + 171 + 6881) = 14104;

14104 = [ (931+931+931+931+931+931+931)+ (139+931) +

+(931+931+931+931+931+931+931)] ;

.............................................................

Peptide the chain

 

Amino acid1

     

Amino acide2

 

å

 

æ

 

å

 

æ

HNH

 

CONH

 

COOH

 

HOH

ß

 

ß

 

ß

 

ß

1,7,1

 

6,8,7,1

 

6,8,8,1

 

1,8,1

Connection

 

Connection

 

Connection

 

Connection

ß

 

ß

 

ß

 

ß

171

 

6871

 

6881

 

181

æ

 

æ

 

å

 

å

     

14104

     
   

å

ß

æ

   

931+931+931

931

931+931+ 931

139| | 931

931+931+ 931

931

931+931+ 931

(171+6871+6881+181) = 14104;

14104 = (931+931+931+931+931+931+931+ (139+931) + +(931+931+931+931+931+931+931);

……………………………………………….

etc.

PERIODICITY AND COMPLEMENTARITIES

IN THE AMINO ACID MATRIX CODE

 

The functioning pf genetic code is not completely resolved. The confuss on exists in amino acids code which would be analogue to nucleotide and how to classify amino acids. Mathematical analysis of "Gray code" model which was completed not long ago discovers that in that model we can classify amino acids  into 16 complementary and corresponding groups. The criteria for this classification is the number of atoms in those amino acids. When we do this we will discover that mathematical base of periodical law really exists. We are going do discover that sequences of molecules in genetic process is possible, according to the program systems, cybernetic systems, information systems and according to the laws. These are concrete results:

There is no doubt and there should never be a doubt. The processes in genetics are not only the matter of physical-chemical issue of objective material relationship. First of all it is matter of mathematical , program, cybernetic and information system and lawfulness.

DECODING SCHEME

 

ATGC = ( C1, H11, O4, N15 )

(S1 + S11 + S4 + S15) = (1 + 66 + 10 + 120) = 197;

-----------------------------------------------

ATGC = 4 nucleotides; Analog code = 40;

A = 7 atoms; Analog code = 70;

T = 9 atoms; Analog code = 90;

G = 6 atoms; Analog code = 60;

C = 9 atoms; Analog code = 9o;

Amino acid Code Matrix = 20 amino acids;

= 382 atoms; Analog code = 283;

(4+40+7+70+9+90+6+60+9+90+20+382+283)= 1070 =(139 + 931)

----------------------------------------------------------------

ATGC = (A = 7 atoms; T = 9 atoms; G = 6 atoms; C = 9 atoms;)

 

(S7 + S9 + S6 + S9) = (28 + 45 + 21 + 45) = 139;

139 ½ ½ 931

…………………………………………………

In amino acid Matrix Code has 64 codons an 20 amino acids.

Connecting 64 and 20 = 6420;

 

6420 = (139 + 931 + 139 + 931 + 139 + 931 + 139 + 931 + 139 + 931 +139 + 931);

--------------------

Analog code in amino acid Code Matrix = (Number of atoms in codons +

+Number of atoms in amino acid)

Amino acid Code Matrix:

C=107; Analog code = 701:

H=197; Analog code = 791;

O=48; Analog code = 84;

N= 28; Analog code = 82;

S=2; Analog code = 20;

( 701 + 791 + 84 + 82 + 20 ) = 1678;

------------------------------

Number of atoms in codons = 1296;

Number of atoms in amino acids= 382;

(1296 + 382) = 1678;

--------------------

(701 + 791 + 84 +82 + 20) = (1296 + 382);

1678 = 1678;

---------------------------------------

 

(107+701+197+791+48+84+28+82+2+20)= 2060;

 

2060= (197 + 719) + ( 74 + 139 + 931);

-------------------

Atomic numbers of the chemical elements in amino acids:

107x6= 642; 197x1=197; 48x8=384; 28x7=196; 2x16=32;

(642+197+384+196+32)= 1451;

Analog code= (246+791+483+691+23)= 2234;

2234 = (139 + 139 + 1678 + 139 + 139);

139 ½ ½ 931

-------------------

(2234+1451) = 3685

3685 = [ (197 + 719) + (A1 + A2 + A3) + (719 + 197)] ;

A1 = Number of amino acids = 20;

A2 = Number of atoms in amino acids;

A3 = Number of protons (and electrons) in amino acid;

3685 = [ (197 + 719) + (20 + 382 + 1451) + (719 + 197)] ;

--------------------------------------------

These are only some of the fragments from matrix code in genetic processes. Those processes are sequenced with numbers: 19, 7 and 931. By using these regularities we can discover in a very short period the essence of these processes and find explenation for all the secrets from the field of genetics. It can be expected that great changes in that particular science are going to take place.

WHAT IS SO ESSENTIAL ABOUT THIS DISCOVERY:

This discovery, according to our opinion, will have great impact on the future development of biology, chemistry, physics, medicine, and especially genetic biochemistry. Now, it is going to be possible to use completely new strategy of research in all sciences, so we can expect rapid development of such fields especially genetics, medicine, and nuclear physics. This discovery will also have an impact on human nature because we will no longer be able to talk about some coincidental cases in the creation of our material world. With mathematical language, the nature is telling us that everything that exists - is pure physical-chemical determination.

 

 MATHEMATIC LANGUAGE OF THE NUCLEOTIDES

Introduction

The subject under this discussion is research of the cybernetic and information lawfulness in nucleotide code matrix. The scientific-research results that we found during our research of the phenomenons in genetics is conditioned and arranged not only with chemical and biochemical, but also with program-cybernetic and information lawfulness too.

The modern science is seeking for periodical law and periodical code. The question is does that code exists and how it looks like? During this scientific research of the phenomenons in genetics we find out some of those secrets. With this content  we wish to inform scientific public with program-cybernetics lawfulness in nucleotide matrix code .

Methods of research

In our scientific-research work, we use some new methods and techniques, which are not applied in contemporary science till now. It is a question of the following: for the sequences from the phenomenons, which we research, we fix a corresponding numerical value. In this manner, we  expressed this phenomenons  in numbers. After that, we research, if these numbers in this phenomenons are arranged according to corresponding lawfulness. In fact, we research program, cybernetic, information and systematic characteristic of this phenomenon. The main role in this new scientific method has lawfulness of groups of numbers

The pairs of nucleotides

Codes key of nucleotide Code Matrix are numbers: 7, 19, and 931. These numbers are the alphabet of genetic language. When these “letters” connect in words we get computer relations of a different kind, and fundamental one is a sequencing of these phenomenon's in the sign of number 77.

Pair AT

Adenine (A) = 37 electrons (and protons)

Timin (T) = 40 electrons (and protons)

A + T = 77 electrons and protons

--------------------------------------------------

Pair GC

Guanine (G) = 46 electrons (and protons)

Cytosine (C) = 31 electrons (and protons)

G + C = 77 electrons and protons

---------------------------------------------------

Well, Adenine (A) and Timin (T) represent a couple of nucleotides with 77 electrons, and the same number of protons. Guanine (G) and Cytosine (C) represent a couple of nucleotides with 77 electrons and protons too. In this example, the chemical balance in distribution of electrons and protons is achieved. This is the key to the matrix mechanism in biochemical information channels: DNA Þ Dna, DNA Þ RNA, and DNA Þ RNA Þ protein.

We can see that  from the next scheme:

Code ATGC

Nucleotides

Number of electrons, and protons

Total

T - A

40 – 37

77

A - T

37 – 40

77

Total

77

154

G - C

46 – 31

77

C - G

31 – 46

77

Total

77

154

etc.

Analog code

 

Every phenomenon in Nature has it's arithmetical expression, and analog arithmetical expression. This means that in matrix code of the Nature there is another analog code existing. Example: Analog code of code 197 is number 791. Analog code of code 931 is number 139, etc.

Analog code ATGC

 

Nucleotides

Code

Analog code

Total

T - A

40 – 37

04 – 73

77

A - T

37 – 40

73 – 04

77

Total

77

77

154

       

G - C

46 – 31

64 – 13

77

C - G

31 – 46

13 – 64

77

Total

77

77

154

etc.

As we can see these pairs of nucleotides are coded with analog codes.

Connecting electrons

TA Þ 40 and 37; Connection Þ 4037;

AT Þ 37 and 40; Connection Þ 3740;

(4037 + 3740) = 7777;

*************************

Analog code

TA Þ Code = 40 and 37; Analog code = 04 and 73;

Connection of analog code = 04 and 73 = 0473;

AT Þ Code = 37 and 40; Analog code = 73 and 04;

Connection of analog code = 73 and 04 = 7304;

(0473 + 7304 ) = 7777;

**********************************

GC Þ 46 and 31; Connection Þ 4631;

CG Þ 31 and 46; Connection Þ 3146;

(4631 + 3146) = 7777;

*************************

Analog code GCCG

GC Þ 46 and 31;Analog code = 64 and 13; Connection Þ 6413;

CG Þ 31 and 46; Analog code =13 and 64; Connection Þ 1364;

(6413 + 1364) = 7777;

**********************************

etc.

GENETIC MATRIX CODE

   

U

C

A

G

 

U

1

2

3

4

UUU

UUC

UUA

UUG

UCU

UCC

UCA

UCG

UAU

UAC

UAA

UAG

UGU

UGC

UGA

UGG

U

C

A

G

C

5

6

7

8

CUU

CUC

CUA

CUG

CCU

CCC

CCA

CCG

CAU

CAC

CAA

CAG

CGU

CGC

CGA

CGG

U

C

A

G

A

1

2

3

4

AUU

AUC

AUA

AUG

ACU

ACC

ACA

ACG

AAU

AAC

AAA

AAG

AGU

AGC

AGA

AGG

U

C

A

G

G

5

6

7

8

GUU

GUC

GUA

GUG

GCU

GCC

GCA

GCG

GAU

GAC

GAA

GAG

GGU

GGC

GGA

GGG

U

C

A

G

 

Number of atoms in Genetic Matrix Code

   

U

C

A

G

Total

 

U

1

2

3

4

UUU=15

UUC=16

UUA=17

UUG=19

UCU=16

UCC=17

UCA=18

UCG=20

UAU=17

UAC=18

UAA=19

UAG=21

UGU=19

UGC=20

UGA=21

UGG=23

67

71

75

83

U

C

A

G

 

Total

67

71

75

83

   

C

5

6

7

8

CUU=16

CUC=17

CUA=18

CUG=20

CCU=17

CCC=18

CCA=19

CCG=21

CAU=18

CAC=19

CAA=20

CAG=22

CGU=20

CGC=21

CGA=22

CGG=24

71

75

79

87

U

C

A

G

 

Total

71

75

79

87

   

A

1

2

3

4

AUU=17

AUC=18

AUA=19

AUG=21

ACU=18

ACC=19

ACA=20

ACG=22

AAU=19

AAC=20

AAA=21

AAG=23

AGU=21

AGC=22

AGA=23

AGG=25

75

79

83

91

U

C

A

G

 

Total

75

79

83

91

   

G

5

6

7

8

GUU=19

GUC=20

GUA=21

GUG=23

GCU=20

GCC=21

GCA=22

GCG=24

GAU=21

GAC=22

GAA=23

GAG=25

GGU=23

GGC=24

GGA=25

GGG=27

83

87

91

99

U

C

A

G

 

Total

83

87

91

99

   
 

Total

296

312

328

360

1296

 

In this example sequencing is conditioned with number of atoms in triplet of codons. In this table, mathematics legality in compression of amount of atoms is very obvious.

Correlation of triplet

Example 1

UGU, UAU, UCU, UUU = 19, 17, 16, 15 atoms,

UUU, UCU, UAU, UGU = 15, 16, 17, 19 atoms,

Connection:

(19,17,16,15) and (15,16,17,19) = (19171615 – 15161719) = 4009896;

********************

UGC, UAC, UCC, UUC = 20, 18, 17, 16 atoms,

UUC, UCC, UAC, UGC = 16, 17, 18, 20 atoms.

Connection:

(20,18,17,16) and (16,17,18,20) = (20181716 - 16171820) = 4009896;

********************

UGA, UAA, UCA, UUA = 21¸, 19, 18, 17 atoms,

UUA, UCA, UAA, UGA = 17, 18, 19, 21 atoms,

Connection:

(21,19,18,17) and (17,18,19,21) = (21191817 - 17181921) = 4009896;

********************

UGG, UAG, UCG, UUG = 23, 21, 20, 19 atoms,

UUG, UCG, UAG, UGG = 19, 20, 21, 23 atoms,

Connection:

(23,21,20,19) and (19,20,21,23) = (23212019 - 19202123) = 4009896;

********************

etc.

Example 2

UUU, UUC, UUA, UUG = (15, 16, 17, 19); Connection = 15161719;

UGU, UGC, UGA, UGG = (19, 20, 21, 23); Connection = 19202123;

Total  34363842

***********************

UCU, UCC, UCA, UCG = (16, 17, 18, 20); Connection = 16171819;

UAU, UAC, UAA, UAG = (17, 18, 19, 21); Connection= 17181921;

Total 33353741

*************************

( 34363842 – 33353741 ) = 1010101;

----------------------------------------------------------------------

CUU, CUC, CUA, CUG = (16, 17, 18, 20); Connection = 16171820;

CGU, CGC, CGA, CGG = (20, 21, 22, 24); Connection =20212224;

Total 36384044

**********************

CCU, CCC, CCA, CCG = (17, 18, 19, 21); Connection = 17181921;

CAU, CAC, CAA, CAG = (18, 19, 20, 22); Connection = 18192022;

Total 35373943

**********************

( 36384044 – 35373943 ) = 1010101;

----------------------------------------------------------------------

etc.

Example 3

UUG, UUA, UUC, UUU = (19, 17, 16, 15); Connection = 19171615;

UGG, UGA, UGC, UGU = (23, 21, 20, 19); Connection = 23212019;

Total 42383634

************************

UCG, UCA, UCC, UCU = (20, 18, 17, 16); Connection= 20181716;

UAG, UAA, UAC, UAU = (21, 19, 18, 17); Connection = 21191817;

Total 41373533

**********************

( 42383634 – 41373533 ) = 1010101;

---------------------------------------------------------------------

CUG, CUA, CUC, CUU = (20, 18, 17, 16); Connection = 20181716;

CGG, CGA, CGC, CGU = (24, 22, 21, 20); Connection = 24222120;

Total 44403836

************************

CCG, CCA, CCC, CCU = (21, 19, 18, 17); Connection = 21191817;

CAG, CAA, CAC, CAU = (22, 20, 19, 18); Connection = 22201918;

Total 43393735

************************

( 44403836 – 43393735 ) = 1010101;

---------------------------------------------------------------------

etc.

Example 4

UUU, UCU, UAU, UGU = (15, 16, 17, 19); Connection = 15161719;

GUG, GCG, GAG,GGG = (23, 24, 25, 27); Connection = 23242527;

Total 38404246

************************

UUG, UCC, UAC, UGC = (16, 17, 18, 20); Connection = 16171820;

GUA, GCA, GAA, GGA = (21, 22, 23, 25); Connection = 21222325;

Total 37394145

************************

( 38404246 – 37394145 ) = 1010101;

---------------------------------------------------------------------

UUA, UCA, UAA, UGA = (17, 18, 19, 21); Connection= 17181921;

GUC, GCC, GAC,GGC = (20, 21, 22, 24); Connection = 20212224;

Total  37394145

************************

UUG, UCG, UAG, UGG = (19, 20, 21, 23); Connection = 19202123;

GUU, GCU, GAU, GGU = (19, 20, 21, 23); Connection = 19202123;

Total 38404246

*************************

( 38404246 – 37394145 ) = 1010101;

---------------------------------------------------------------------

Example 5

Groups of atoms: 67, 71, 75, 83; Connection = 67717583;

Groups of atoms: 83, 75, 71, 67; Connection = 83757167;

(83757167 – 67717583) = 16039584;

************************

Groups of atoms:71,75, 79, 87; Connection = 71757987;

Groups of atoms: 87, 79, 75, 71; Connection = 87797571;

(87797571 – 71757987) = 16039584;

************************

Groups of atoms:75,79, 83, 91; Connection = 77798391;

Groups of atoms: 91, 83, 79, 75; Connection = 91837975;

(91837975 – 75798391) = 16039584;

************************

Groups of atoms: 83, 87, 91, 99; Connection = 83879199;

Groups of atoms: 99, 91, 87, 83; Connection = 99918783;

(99918783 – 83879199) = 16039584;

************************

etc.

In this examples, mathematics legality in comparation of amount of atoms is very obvious.

That mathematics legality can be seen from the following squares:

Binary code

This text is dealing with proofs of the binary arrangement rule for the characteristics of genetic code units.

Example 1:

Table 1 Binary code (Fragment 1777776)

(0)

000000

UUU

F

 

(0)

001000

UCU

S

(1)

000001

UUC

F

 

(1)

001001

UCC

S

(2)

000010

UUA

L

 

(2)

001010

UCA

S

(3)

000011

UUG

L

 

(3)

001011

UCG

S

(4)

000100

CUU

L

 

(4)

001100

CCU

P

(5)

000101

CUC

L

 

(5)

001101

CCC

P

(6)

000110

CUA

L

 

(6)

001110

CCA

P

(7)

000111

CUG

L

 

(7)

001111

CCG

P

Total

000444

 

 

 

Total

008444

 

 

(0)

010000

AUC

I

 

(0)

011000

ACU

T

(1)

010001

AUU

I

 

(1)

011001

ACC

T

(2)

010010

AUA

I

 

(2)

011010

ACA

T

(3)

010011

AUG

M

 

(3)

011011

ACG

T

(4)

010100

GUU

V

 

(4)

011100

GCU

A

(5)

010101

GUC

V

 

(5)

011101

GCC

A

(6)

010110

GUA

 

 

(6)

011110

GCA

A

(7)

010111

GUG

V

 

(7)

011111

GCG

A

Total

080444

 

 

 

Total

088444

 

 

(0)

101000

UGU

C

 

(0)

100000

UAU

Y

(1)

101001

UGC

C

 

(1)

100001

UAC

Y

(2)

101010

UGA

*

 

(2)

100010

UAA

¨

(3)

101011

UGG

W

 

(3)

100011

UAG

¨

(4)

101100

CGU

R

 

(4)

100100

CAU

H

(5)

101101

CGC

R

 

(5)

100101

CAC

H

(6)

101110

CGA

R

 

(6)

100110

CAA

Q

(7)

101111

CGG

R

 

(7)

100111

CAG

Q

Total

808444

 

 

 

Total

800444

 

 

(0)

111000

AGU

S

 

(0)

110000

AAU

N

(1)

111001

AGC

S

 

(1)

110001

AAC

N

(2)

111010

AGA

R

 

(2)

110010

AAA

K

(3)

111011

AGG

R

 

(3)

110011

AAG

K

(4)

111100

GGU

G

 

(4)

110100

GAU

D

(5)

111101

GGC

G

 

(5)

110101

GAC

D

(6)

111110

GGA

G

 

(6)

110110

GAA

E

(7)

111111

GGG

G

 

(7)

110111

GAG

E

Total

888444

 

 

 

Total

880444

 

 

Total

1777776

 

 

 

Total

1777776

 

 

 

In this table, mathematics legality in comparation of amount of binary units is very obvious.

Table 2 - Binary code (Fragment UCAG)

       

Atoms

Total

     

Atoms

Total

 

(0)

000000

F

UUU

5,5,5

15

001000

S

UCU

5,6,5

16

(0)

(1)

000001

F

UUC

5,5,6

16

001001

S

UCC

5,6,6

17

(1)

(2)

000010

L

UUA

5,5,7

17

001010

S

UCA

5,6,7

18

(2)

(3)

000011

L

UUG

5,5,9

19

001011

S

UCG

5,6,9

20

(3)

(4)

000100

L

CUU

6,5,5

16

001100

P

CCU

6,6,5

17

(4)

(5)

000101

L

CUC

6,5,6

17

001101

P

CCC

6,6,6

18

(5)

(6)

000110

L

CUA

6,5,7

18

001110

P

CCA

6,6,7

19

(6)

(7)

000111

L

CUG

6,5,9

20

001111

P

CCG

6,6,9

21

(7)

Total

000444

 

 

4854

138

008444

 

 

4934

146

 

(0)

011000

T

ACU

7,6,5

18

010000

I

AUC

7,5,6

18

(0)

(1)

011001

T

ACC

7,6,6

19

010001

I

AUU

7,5,5

17

(1)

(2)

011010

T

ACA

7,6,7

20

010010

I

AUA

7,5,7

19

(2)

(3)

011011

T

ACG

7,6,9

22

010011

M

AUG

7,5,9

21

(3)

(4)

011100

A

GCU

9,6,5

20

010100

V

GUU

9,5,5

19

(4)

(5)

011101

A

GCC

9,6,6

21

010101

V

GUC

9,5,6

20

(5)

(6)

011110

A

GCA

9,6,7

22

010110

V

GUA

9,5,7

21

(6)

(7)

011111

A

GCG

9,6,9

24

010111

V

GUG

9,5,9

23

(7)

Total

088444

 

 

6934

166

080444

 

 

6854

158

 

(0)

100000

Y

UAU

5,7,5

17

101000

C

UGU

5,9,5

19

(0)

(1)

100001

Y

UAC

5,7,6

18

101001

C

UGC

5,9,6

20

(1)

(2)

100010

¨

UAA

5,7,7

19

101010

¨

UGA

5,9,7

21

(2)

(3)

100011

¨

UAG

5,7,9

21

101011

W

UGG

5,9,9

23

(3)

(4)

100100

H

CAU

6,7,5

18

101100

R

CGU

6,9,5

20

(4)

(5)

100101

H

CAC

6,7,6

19

101101

R

CGC

6,9,6

21

(5)

(6)

100110

Q

CAA

6,7,7

20

101110

R

CGA

6,9,7

22

(6)

(7)

100111

Q

CAG

6,7,9

22

101111

R

CGG

6,9,9

24

(7)

Total

800444

 

 

5014

154

808444

 

 

5174

170

 

(0)

111000

S

AGU

7,9,5

21

110000

N

AAU

7,7,5

19

(0)

(1)

111001

S

AGC

7,9,6

22

110001

N

AAC

7,7,6

20

(1)

(2)

111010

R

AGA

7,9,7

23

110010

K

AAA

7,7,7

21

(2)

(3)

111011

R

AGG

7,9,9

25

110011

K

AAG

7,7,9

23

(3)

(4)

111100

G

GGU

9,9,5

23

110100

D

GAU

9,7,5

21

(4)

(5)

111101

G

GGC

9,9,6

24

110101

D

GAC

9,7,6

22

(5)

(6)

111110

G

GGA

9,9,7

25

110110

E

GAA

9,7,7

23

(6)

(7)

111111

G

GGG

9,9,9

27

110111

E

GAG

9,7,9

25

(7)

Total

888444

 

 

7174

190

880444

 

 

7014

174

 

Total

1777776

 

 

23976

648

1777776

 

 

23976

648

 

 In this example sequencing is conditioned with number of atoms in triplet of codons.

 Table 3

Binary code (Fragment CGTA)

 

 

 

Number of atoms

Total

 

Number of atoms

 

Total

 

(0)

000000

C,C,C

6,6,6

18

001000

C,G,C

6,9,6

21

(0)

(1)

000001

C,C,A

6,6,7

19

001001

C,G,A

6,9,7

22

(1)

(2)

000010

C,C,G

6,6,9

21

001010

C,G,G

6,9,9

24

(2)

(3)

000011

C,C,T

6,6,9

21

001011

C,G,T

6,9,9

24

(3)

(4)

000100

A,C,C

7,6,6

19

001100

A,G,C

7,9,6

22

(4)

(5)

000101

A,C,A

7,6,7

20

001101

A,G,A

7,9,7

23

(5)

(6)

000110

A,C,C

7,6,9

22

001110

A,G,G

7,9,9

25

(6)

(7)

000111

A,C,T

7,6,9

22

001111

A,G,T

7,9,9

25

(7)

Total

000444

 

5742

162

008444

 

5982

186

 

(0)

011000

C,T,C

6,9,6

21

010000

C,A,C

6,7,6

19

(0)

(1)

011001

C,T,A

6,9,7

22

010001

C,A,A

6,7,7

20

(1)

(2)

011010

C,T,G

6,9,9

24

010010

C,A,G

6,7,9

22

(2)

(3)

011011

C,T,T

6,9,9

24

010011

C,A,T

6,7,9

22

(3)

(4)

011100

A,T,C

7,9,6

22

010100

A,A,C

7,7,6

20

(4)

(5)

011101

A,T,A

7,9,7

23

010101

A,A,A

7,7,7

21

(5)

(6)

011110

A,T,G

7,9,9

25

010110

A,A,G

7,7,9

23

(6)

(7)

011111

A,T,T

7,9,9

25

010111

A,A,T

7,7,9

23

(7)

Total

088444

 

5982

186

080444

6854

5822

170

 

(0)

100000

T,A,C

9,7,6

22

101000

G,T,C

9,9,6

24

(0)

(1)

100001

T,A,A

9,7,7

23

101001

G,T,A

9,9,7

25

(1)

(2)

100010

T,A,G

9,7,9

25

101010

G,T,C

9,9,9

27

(2)

(3)

100011

T,A,T

9,7,9

25

101011

G,T,T

9,9,9

27

(3)

(4)

100100

G,A,C

9,7,6

22

101100

T,T,C

9,9,6

24

(4)

(5)

100101

G,A,A

9,7,7

23

101101

T,T,A

9,9,7

25

(5)

(6)

100110

G,A,G

9,7,9

25

101110

T,T,G

9,9,9

27

(6)

(7)

100111

G,A,T

9,7,9

25

101111

T,T,T

9,9,9

27

(7)

Total

800444

 

7822

190

808444

 

7982

206

 

(0)

111000

G,G,C

9,9,6

24

110000

T,C,C

9,6,6

21

(0)

(1)

111001

G,G,A

9,9,7

25

110001

T,C,A

9,6,7

22

(1)

(2)

111010

G,G,T

9,9,9

27

110010

T,C,G

9,6,9

24

(2)

(3)

111011

G,G,G

9,9,9

27

110011

T,C,T

9,6,9

24

(3)

(4)

111100

T,G,C

9,9,6

24

110100

G,C,C

9,6,6

21

(4)

(5)

111101

T,G,A

9,9,7

25

110101

G,C,A

9,6,7

22

(5)

(6)

111110

T,G,G

9,9,9

27

110110

G,C,G

9,6,9

24

(6)

(7)

111111

T,G,C

9,9,9

27

110111

G,C,T

9,6,9

24

(7)

Total

888444

 

7982

206

880444

7014

7742

182

 

Total

1777776

 

27528

744

1777776

 

27528

744

 

 

In this example sequencing is conditioned with number of atoms in triplet of nucleotides.

It is the fact the genetic nucleotide code can be reduced to a Gray code, using binary encoding scheme.

 The mathematically basis of the periodic law can be read directly out of table 1, 2 and 3.

AMINO ACID MATRIX CODE

Number of atoms

Group A

Group B

Group C

Group D

Cys (C)=14

Gly (G)=10

Ser (S)=14

 

Thr (T)=17

Ala (A)=13

Pro (P)=17

Asn (N)=17

Val (V)=19

Asp (D)=16

Glu (E)=19

 

His (H)=20

Lys (K)=24

Gln (Q)=20

Met (M)= 20

Jle (J)=22

Arg (R)=25

Leu (L)=22

 

Phe (F)=23

Trp (W)=27

Tyr (Y)=23

 

115

115

115

37

In this table, amino acids are divided into three corresponding groups with the same number of atoms.

 

Codes and analog codes in Amino acids Matrix Code

Group

“A”

Code

Analog code

Group “B”

Code

Analog

code

Group “C”

Code

Analog

code

Cys

14

41

Gly

10

01

Ser

14

41

Thr

17

71

Ala

13

31

Pro

17

71

Val

19

91

Asp

16

61

Glu

19

91

His

20

02

Lys

24

42

Gln

20

02

Jle

22

22

Arg

25

52

Leu

22

22

Phe

23

32

Trp

27

72

Tyr

23

32

Total

115

259

 

115

259

 

115

259

In this example we have mathematical unity in atom distribution of amino acids.

Atomic number

 

Group

“A”

Atomic number

Group “B”

Atomic number

Group “C”

Atomic number

Cys

64

Gly

40

Ser

56

Thr

64

Ala

48

Pro

62

Val

64

Asp

70

Glu

78

His

82

Lys

80

Gln

78

Jle

72

Arg

87

Leu

72

Phe

88

Trp

108

Tyr

88

Svega

434

 

433

 

434

In this table, amino acids are divided into two corresponding groups with same atomic numbers.

AMINO ACID MATRIX CODE

(Code 719)

 

Gly (G)=10

Ala (A)=13

Ser (S)=14

Cys (C)=14

Total

Asp (D)=16

Pro (P)=17

Thr (T)=17

Asn (N)=17

67

Val (V)=19

Glu (E)=19

Gln (Q)=20

Met (M)= 20

78

His (H)=20

Jle (J)=22

Leu (L)=22

Phe (F)=23

87

Tyr (Y)=23

Lys (K)=24

Arg (R)=25

Trp (W)=27

99

Total 88

95

98

101

382

Analog codes Þ 88

59

89

101

337

Total 176

154

187

202

719

In this table sequencing is conditioned with codes 7 and 19:

7 and 19 Þ connection = 719

Connection of amino acids

Number of atoms in amino acid code matrix =

10, 13, 14, 14, 16, 17, 17, 17, 19, 19, 20, 20, 20, 22, 22, 23, 23, 24, 25, 27;

 

Connection = 1013141416171717191920202022222323242527;

 

1013141416171717191920202022222323242527 ={ (197 + [ (139+931)x Y] } ;

In this example sequencing is conditioned with codes: 19, 7, 139 i 931.

Codon form Gxx

This codon could be decoded with only amino acids:

Val (V), Ala (A), Asp (D), Glu (E) i Gly (G).

First two are hydrophone and others are hydrofoil, while Gly (G) is neutral amino acid. Those codons and amino acids have responding number of atoms, so they depend on it, in the origin code of amino acid, dispersed into complementary and corresponding group. We can see that in the following examples:

Table 1

Fragment Gxx (1)

Codons

Number of atoms

 

Amino acids

Number of atoms

Codons

Number of atoms

 

Amino acids

Number of atoms

   

GROUP A

     

GROUP B

 

GUU

19

Val (V)

19

GUC

20

Val (V)

19

GCU

20

Ala (A)

13

GCC

21

Ala (A)

13

GAU

21

Asp (D)

16

GAC

22

Asp (D)

16

GGU

23

Gly (G)

10

GGC

24

Gly (G)

10

Total

83

 

58

 

87

 

58

 

In this table amino acids are divided into two corresponding groups with the same number of atoms. Also there is mathematical lawfulness in distribution of atoms in a triplet codons.

Table 2

Fragment Gxx(2)

Codons

Number of atoms

 

Amino acids

Number of atoms

Codons

Number of atoms

 

Amino acids

Number of atoms

   

GROUP C

     

GROUP D

 

GUA

21

Val (V)

19

GUG

23

Val (V)

19

GCA

22

Ala (A)

13

GCG

24

Ala (A)

13

GAA

23

Glu (E)

19

GAG

25

Glu (E)

19

GGA

25

Gly (G)

10

GGG

27

Gly (G)

10

Total

91

 

61

 

99

 

61

 

In this example we have mathematical unity in atom distribution of amino acids, as well as in triplets.

Codon form Cxx

This codon decodes the following amino acids:

Leu(L), Pro(P), His(H), Arg(R) i Gln(Q).

 

The codons and amino acids, also, in the table of genetic code are distributed into responding complementary and corresponding groups:

Table 3

Fragment Cxx(1)

Codons

Number of atoms

 

Amino acids

Number of atoms

Codons

Number of atoms

 

Amino acids

Number of atoms

   

GROUP E

     

GROUP F

 

CUU

16

Leu (L)

22

CUC

17

Leu (L)

22

CCU

17

Pro (P)

17

CCC

18

Pro (P)

17

CAU

18

His (H)

20

CAC

19

His (H)

20

CGU

20

Arg (R)

25

CGC

21

Arg (R)

25

Total

71

 

84

 

75

 

84

 

In this table, as well as in table 1. and 2., we have mathematical unity in atom distribution in amino acids and in triplets.

 

Fragment Cxx(2)

Table 4

Codons

Number of atoms

 

Amino acids

Number of atoms

Codons

Number of atoms

 

Amino acids

Number of atoms

   

GROUP G

     

GROUP H

 

CUA

18

Leu (L)

22

CUG

20

Leu (L)

22

CCA

19

Pro (P)

17

CCG

21

Pro (P)

17

CAA

20

Gln (Q)

20

CAG

22

Gln (Q)

20

CGA

22

Arg (R)

25

CGG

24

Arg (R)

25

Total

79

 

84

 

87

 

84

 

In this example corresponding groups of amino acids have the same number of atoms.

 

Codon form Axx

 

This codon decodes the following amino acids:

Ile(J), Thr(T), Asn(N), Ser(S), Lys(K), Arg(R) i Met(M).

Corresponding groups:

Fragment Axx(1)

Table 5

Codons

Number of atoms

Amino acide

Number of atoms

Codons

Number of atoms

Amino acide

Number of atoms

   

GROUP I

     

GROUP J

 

AUU

17

Ile (J)

22

AUC

18

Ile (J)

22

ACU

18

Thr ( T)

17

ACC

19

Thr (T)

17

AAU

19

Asn (N)

17

AAC

20

Asn (N)

17

AGU

21

Ser (S)

14

AGC

22

Ser (S)

14

Total

75

 

70

 

79

 

70

 

In this table amino acids are in sequences in two corresponding groups with the same number of atoms. Also, there is mathematical lawfulness in distribution of atoms in a triplet.

Codon form Uxx

This codon decodes the folloving amino acids:

 

Phe(F), Ser(S), Tyr(Y), Cys(C), Leu(L) i Trp (W)

 

These amino acids are distributed in appropriate corresponding groups:

Fragment Uxx(1)

Table 6

Codons

Total

Amino acids

Number of atoms

Codons

Total

Amino acids

Number of atoms

   

GROUP K

     

GROUP L

 

UUU

15

Phe (F)

23

UUC

16

Phe (F)

23

UCU

16

Ser (S)

14

UCC

17

Ser (S)

14

UAU

17

Tyr (Y)

23

UAC

18

Tyr (Y)

23

UGU

19

Cys (C)

14

UGC

20

Cys (C)

14

Total

67

 

74

 

71

 

74

 

From this table we can see that similarity cannot be the only criteria for classification of amino acids. For example: In amino acid code phenyl (F) and leucin (L) are shown as really similar. But, even though, that they are similar, first is aromatic, and the second is auphatic unit, so according to our opinion they should be separated. The previous table of mathematical lawfulness also represent verification for separation.

 

Table 7

BINARY ENCODING SCHEME

Codons

 

Atoms

 

Codons

 

Atoms

 

Codons

 

Atoms

 

Codons

 

Atoms

(0)

UUU

F

23

(1)

UUC

F

23

(2)

UUA

L

22

(3)

UUG

L

22

(0)

UCU

S

14

(1)

UCC

S

14

(2)

UCA

S

14

(3)

UCG

S

14

(0)

UAU

Y

23

(1)

UAC

Y

23

(2)

UAA

ˆ

 

(3)

UAG

Ž

 

(0)

UGU

C

14

(1)

UGC

C

14

(2)

UGA

O

 

(3)

UGG

W

27

Total

   

74

     

74

               

(4)

CUU

L

22

(5)

CUC

L

22

(6)

CUA

L

22

(7)

CUG

L

22

(4)

CCU

P

17

(5)

CCC

P

17

(6)

CCA

P

17

(7)

CCG

P

17

(4)

CAU

H

20

(5)

CAC

H

20

(6)

CAA

Q

29

(7)

CAG

Q

29

(4)

CGU

R

25

(5)

CGC

R

25

(6)

CGA

R

25

(7)

CGG

R

25

Total

   

84

     

84

     

84

     

84

(0)

AUU

J

22

(1)

AUC

J

22

(2)

AUA

J

22

(3)

AUG

M

20

(0)

ACU

T

17

(1)

ACC

T

17

(2)

ACA

T

17

(3)

ACG

T

17

(0)

AAU

N

17

(1)

AAC

N

17

(2)

AAA

K

24

(3)

AAG

K

24

(0)

AGU

S

14

(1)

AGC

S

14

(2)

AGA

R

25

(3)

AGG

R

25

Total

   

70

     

70

     

88

     

86

(4)

GUU

V

19

(5)

GUC

V

19

(6)

GUA

V

19

(7)

GUG

V

19

(4)

GCU

A

13

(5)

GCC

A

13

(6)

GCA

A

13

(7)

GCG

A

13

(4)

GAU

D

16

(5)

GAC

D

16

(6)

GAA

E

19

(7)

GAG

E

19

(4)

GGU

G

10

(5)

GGC

G

10

(6)

GGA

G

10

(7)

GGG

G

10

Total

   

58

     

58

     

61

     

61

 

These are only fragments of amino acids codes in GCAU(xx) codon form. From those examples we can see clearly that mathematical base of periodical law exists. The proof for that is the fact that amino acids in "Gray code" model are really grouped in corresponding groups with the same number of atoms, and also, there is mathematical lawfulness in distribution of atoms in triplets. We have a few mode things to explain such as mathematical lawfulness for grouping of some amino acids in codon forms Uxx and Axx but those secrets will be resolved according to our opinion, really soon.

MATHEMATICAL CONNECTION

OF TABLES OF GENETIC CODE AND PERIODIC SYSTEM

 

 

Genetic matrix code  (Fragment 70) Periodic System

Codons

Amino acides

Number of atoms

 

Chemical of elements

Atomic number

(0)

AUU

Ile (J)

22

(0)

Li

3

(0)

ACU

Thr (T)

17

(0)

Na

11

(0)

AAU

Asn (N)

17

(0)

K

19

(0)

AGU

Ser (S)

14

(0)

Rb

37

 

Total

 

70

   

70

 

Genetic matrix code  (Fragment 74) Periodic System

Codons

Amino acides

Number of atoms

 

Chemical of elements

Atomic number

(1)

UUC

Phe (F)

23

(1)

Be

4

(1)

UCC

Ser(S)

14

(1)

Mg

12

(1)

UAC

Tyr(Y)

23

(1)

Ca

20

(1)

UGC

Cys(C)

14

(1)

Sr

38

 

Total

 

74

   

74

etc.

 

There is no doubt and there should never be a doubt. The processes in genetics are not only the matter of physical-chemical issue of objective material relationship. First of all it is matter of mathematical , program, cybernetic and information system and lawfulness.

---------------------------------

These are only some of the fragments from matrix code in genetic processes. Those processes are sequenced with numbers: 19, 7 and 931. By using these regularities we can discover in a very short period the essence of these processes and find explanation for all the secrets from the field of genetics. It can be expected that great changes in that particular science are going to take place.

 

 

 

 

 

 

 

 

 

 

F,V,N,Q,H,L,C,G, S,H,L,V, E,A,L,Y,L,V,C,G,E, R,G,F,F,Y,T,P,K,A

 

23,19,17,20,20,22,14,10, 14, 20,22,19, 19,13,22,23,22,19,14,10,19,

25,10,23,23,23,17,17,24,13

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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