srijeda, 1. travnja 2015.

The Atomic Genetic Code

ABSTRACT

The modern science mainly treats the biochemical basis of sequencing in bio-macromolecules and processes in biochemistry. One can ask weather the language of biochemistry is the adequate scientific language to explain the phenomenon in that science. Is there maybe some other language, out of biochemistry, that determines how the biochemical processes will function and what the structure and organization of life systems will be? The research results provide some answers to these questions. They reveal to us that the process of sequencing in bio-macromolecules is conditioned and determined not only through biochemical, but also through cybernetic and information principles.

Keywords: Digital Genetics, Genetics Code, RNA Code, Amino acids Code, Evolution

METHODS

The genetic code tables used by the modern science are characterized and determined by principles of biochemistry. However, if in those tables, instead of the UCAG nucleotides we put the number of atoms of those nucleotides, we will get the new tables of the genetic code characterized and determined by programmatic and information principles. Therefore, biochemistry can be explained through a phenomenon out of biochemistry. Particularly interesting results we will get when determining numeric values for the information content of atoms and molecules. We will then find out that those values express physical and chemical characteristics of molecules. For example: in a DNA molecule, the polynucleotide chains are connected through an exact cyber-information connections. In those molecules there are also mathematical matrixes of DNA, represented by the number of atoms of four ATCG bases. These matrixes determine the positioning of nucleotides in that molecule. With this, the biological particularities of DNA are determined. Similar mathematical matrixes determine the positioning of nucleotides in the RNA molecule. In the amino acid proteins, they are interconnected into the respective mathematical chains. In those chains are also matrixes where particular mathematical principles apply, the principles that determine the positioning of each amino acid in the chain.



RESULTS

 The herewith discussed research results show that the process of sequencing in bio-macromolecules is conditioned and determined not only through biochemical, but also through cybernetic information principles.

We would particularly like to stress here that the genetic, as well as biochemical information in a broader sense of the word, is determined and characterized by very complex cybernetic and information principles. The constantans in those principles are: the number of atoms and molecules, atomic numbers, atomic weight, physical and chemical parameters, even and odd values, codes and analogue codes, standard deviations, frequencies, primary and secondary values, and many other things. How functioning of biochemistry is determined through cybernetic information principles, will be discussed further in this text. 

The Atomic Genetic Code (RNA)


A = 15 atoms; U = 12 atoms; C = 13 atoms; G = 16 atoms;

Number of atoms
UUU=36
 Phe=23

UUC=37
Phe=23

CUC=38
Leu=22

UUA=39
Leu=22

UUG=40
Leu=22

CUG=41
Leu=22

CGC=42
Arg=26

GAU=43
Asp=16

GAC=44
Asp=16

CGG=45
Arg=26

AGA=46
Arg=26

AGG=47
Arg=26

GGG=48
Gly=10

UCU=37
Ser=14

UCC=38
  Ser=14

AUU=39
Ile=22

AUC=40
Ile=22

UGC=41
Cys=14

AUA=42
    Ile=22

AUG=43
Met=20

UGG=44
  Trp=27

AAA=45
 Lys=24

AAG=46
 Lys=24

GGA=47
  Gly=10



CUU=37
 Leu=22

CCU=38
  Pro=17

CCC=39
  Pro=17

CUA=40
 Leu=22

CCA=41
  Pro=17

CCG=42
  Pro=17

AAC=43
 Asn=17

ACG=44
  Thr=17

GGC=45
  Gly=10

GAA=46
  Glu=19

GAG=47
  Glu=19





UAU=39
  Tyr=24

GUU=40
Val=19

GUC=41
  Val=19

GCC=42
  Ala=13

GUA=43
  Val=19

GUG=44
  Val=19

GCG=45
  Ala=13








UCA=40
Ser=14

UCG=41
  Ser=14

UAA=42

STOP
AGU=43
  Ser=14

AGC=44
  Ser=14









ACU=40
Thr=17

ACC=41
  Thr=17

AAU=42
 Asn=17

ACA=43
  Thr=17

GGU=44
  Gly=10









UAC=40
Tyr=24

GCU=41
  Ala=13


UAG=43

STOP
GCA=44
  Ala=13









CAU=40
His=20

CAC=41
  His=20


CAA=43
  Gln=20

CAG=44
  Gln=20









UGU=40
Cys=14

CGU=41
 Arg=26


UGA=43

STOP
CGA=44
 Arg=26











Number of atoms in triplets UCAG
UUU
36

UUC
37

CUC
38

UUA
39

UUG
40

CUG
41

CGC
42

GAU
43

GAC
44

CGG
45

AGA
46

AGG
47
GGG
48


UCU
37


UCC
38
 

AUU
39


AUC
40


UGC
41


AUA
42
   

AUG
43


UGG
44
 

AAA
45


AAG
46


GGA
47
 



CUU
37


CCU
38
 

CCC
39
 

CUA
40


CCA
41
 

CCG
42
 

AAC
43


ACG
44
 

GGC
45
 

GAA
46
 

GAG
47
 





UAU
39
 

GUU
40


GUC
41
 

GCC
42
 

GUA
43
 

GUG
44
 

GCG
45
 








UCA
40


UCG
41
 

UAA
42


AGU
43
 

AGC
44
 









ACU
40


ACC
41
 

AAU
42


ACA
43
 

GGU
44
 









UAC
40


GCU
41
 


UAG
43


GCA
44
 









CAU
40


CAC
41
 


CAA
43
 

CAG
44
 









UGU
40


CGU
41



UGA
43


CGA
44






.(36+48) = (37+47) = (38+46) = (39+45) = (40+44) = (41+43)
etc.

In fact, we discovered that the mathematical balance in the distribution of codons and amino acids in the genetic code is achieved.


Mathematical position of the nucleotides in codon

The development of prediction methods based on digital theory is focused on the exploration of new digital formulas and algorithms. The genetic code is stored in DNA molecules as sequences of bases: adenine (A) which pairs with thymine (T), and cytosine (C) which pairs with guanine (G), The analog of DNA in a digital genetic algorithm is a number of atoms, atomic numbers, analog codes, etc.

At mathematical evolution of genetic processes, nucleotides TCAG are being transformed to codons UCAG and later to amino acids and various organic composition.


Number of atoms
Second Position of Codon

T
C
A
G

13,13,15
41

Pro

13,13,13
39

Pro

13,13,15
41

Pro

13,13,16
42

Pro

   163  
15,16,15
46

Cys

15,16,13
44

Cys

15,16,15
46

Ter

15,16,16
47

Trp

    183
15,15,15
45

Tyr

15,15,13
43

Tyr

15,15,15
45

Ter

15,15,16
46

Ter

    179
16,15,15
46

Asp

16,15,13
44

Asp

16,15,15
46

Glu

16,15,16
47

Glu

   183
708
15,16,15
46

Ser

15,16,13
44

Ser

15,16,15
46

Arg

15,16,16
47

Arg

   183
15,15,15
45

Phe
15,15,13
43

Phe
15,15,15
45

Leu
15,15,16
46

Leu
    179
15,13,15
43

Ser

15,13,13
41

Ser

15,13,15
43

Ser

15,13,16
44

Ser

    171
13,16,15
44

Arg

13,16,13
42

Arg

13,16,15
44

Arg

13,16,16
45

Arg

  175



708



15,15,15
45

Ile

15,15,13
43

Ile

15,15,15
45

Ile

15,15,16
46

Met

  179
13,15,15
43

Leu
13,15,13
41

Leu
13,15,15
43

Leu
13,15,16
44

Leu
   171
16,16,15
47

Gly

16,16,13
45

Gly

16,16,15
47

Gly

16,16,16
48

Gly

   187 
13,15,15
43

His

13,15,13
41

His

13,15,15
43

Gln

13,15,16
44

Gln

  171
708

16,15,15
46

Val

16,15,13
44

Val

16,15,15
46

Val

16,15,16
47

Val

   183
1613,15
44

Ala

1613,13
42

Ala

16,13,15
44

Ala

16,13,16
45

Ala

   175
15,13,15
43

Thr

15,13,13
41

Thr

15,13,15
43

Thr

15,13,16
44

Thr

   171
15,15,15
45

Asn

15,15,13
43

Asn

15,15,15
45

Lys

15,15,16
46

Lys

  179
708

  708
  708
  708
 708

Diagonal D1 = 708Diagonal D2 = 708;

The digital genetic code describe a genotype, which is translated into an organism a phenotype by the processes of cell division.

Mathematical evolution of genetic processes is manifested in different ways. Evolution of groups of atoms is especially interesting.  Here are some examples




Digital codon square
A digital codon square of order n is an arrangement of n² numbers, usually distinct integers, in a square, such that the n numbers in all rows, all columns, and both diagonals sum to the same constant. A digital square contains the integers from 1 to n². The term "digital square" is also sometimes used to refer to any of various types of word square.
Number of atoms
163
183
179
183
708
183
179
171
175
708
179
171
187
171
708
183
175
171
179
708
708
708
708
708

D1 = (163+179+187+179) = 708;
D2 = (183+171+171+183) = 708;
The constant sum in every row, column and diagonal is called the magic analogue constant or magic sum, M.

163
183
179
183
183
179
171
175
179
171
187
171
183
175
171
179
(163+183+183+179) = 708;
(179+183+171+175) = 708;
(179+171+183+175) = 708;
187+171+171+179) =708;

163
183
179
183
183
179
171
175
179
171
187
171
183
175
171
179
ê
708

163
183
179
183
183
179
171
175
179
171
187
171
183
175
171
179
ê
708

etc.


Analogue Atomic Genetic Code

How could we adapt the program, ciberfnetic, and informational system to convey more information?  Here’s one way. This is an analogue code
“Theoretically the ancient book of DNA could have been analogue. But, for the same reason as for our analogue armada beacons, any ancient book copied and recopied in analogue language would degrade to meaninglessness in very few scribe generations. Fortunately, human writing is digital, at least in the sense we care about here. And the same is true of the DNA books of ancestral wisdom that we carry around inside us. Genes are digital, and in the full sense not shared by nerves”(20).
Correlation of the Code and Analogue Code
The atomic and analogue genetic code is the set of rules by which information encoded in genetic material (DNA or RNA sequences) is translated into proteins (amino acid sequences) by living cells. Specifically, those codes defines a mapping between tri-nucleotide sequences called codons and amino acids; every triplet of nucleotides in a nucleic acid sequence specifies a single amino acid. Because the vast majority of genes are encoded with exactly the same code.
Those codes are universal. The same codons are assigned to the same amino acids and to the same START and STOP signals in the vast majority of genes in animals, plants, and microorganisms.
Analogue Code||Code Code

Example:
Analogue Code of the number 12 is number 21:
21 ||12;
Analogue Code of the number 15 is number 51:
51 ||15;
etc.

At this stage of our research we replaced nucleotides from the Amino Acid Code Matrix with analogue numbers of the atoms in those nucleotides.
A = 15 atoms; T = 15 atoms; C = 13 atoms; G = 16 atoms                                                                                                                                                                                            A = 51; T = 51; C = 31; G = 61;



Analogue codon table

Mathematical position of the nucleotides in codon
Second Position of Codon

T
C
A
G

31,31,51
113

Pro

31,31,31
93

Pro

31,31,51
113

Pro

31,31,61
123

Pro

442
51,61,51
163

Cys

51,61,31
143

Cys

51,61,51
163

Ter

51,61,61
173

Trp

642
51,51,51
153

Tyr

51,51,31
133

Tyr

51,51,51
153

Ter

51,51,61
163

Ter

602
61,51,51
163

Asp

61,51,31
143

Asp

61,51,51
163

Glu

61,51,61
173

Glu

642
2328
51,61,51
163

Ser

51,61,31
143

Ser

51,61,51
163

Arg

15,16,16
173

Arg

642
51,51,51
153

Phe
51,51,31
133

Phe
51,51,51
153

Leu
51,51,61
163

Leu
602
51,31,51
133

Ser

51,31,31
113

Ser

51,31,51
133

Ser

51,31,61
143

Ser

522
31,61,51
143

Arg

31,61,31
123

Arg

31,61,51
143

Arg

31,61,61
153

Arg

562



2328



51,51,51
153

Ile

51,51,31
133

Ile

51,51,51
153

Ile

51,51,61
163

Met

602
31,51,51
133

Leu
31,51,31
113

Leu
31,51,51
133

Leu
31,51,61
143

Leu
522
61,61,51
173

Gly

61,61,31
153

Gly

61,61,51
173

Gly

61,61,61
183

Gly

682
31,51,51
133

His

31,51,31
113

His

31,51,51
133

Gln

31,51,61
143

Gln

522
2328

61,51,51
163

Val

61,51,31
143

Val

61,51,51
163

Val

61,51,61
173

Val

642
61,31,51
143

Ala

61,31,31
123

Ala

61,31,51
143

Ala

61,31,61
153

Ala

562
51,31,51
133

Thr

51,31,31
113

Thr

51,31,51
133

Thr

51,31,61
143

Thr

522
51,51,51
153

Asn

51,51,31
133

Asn

51,51,51
153

Lys

51,51,61
163

Lys

602
2328

2328
2328
2328
2328

Diagonal D1 = 2328;  Diagonal D2 = 2328;
Row 1 = Column 1;  Row 2 = Column 2;    Row 3 = Column 3;  Row 4 = Column 4;
Analogue codon square
A analogue codon square of order n is an arrangement of n² numbers, usually distinct integers, in a square, such that the n numbers in all rows, all columns, and both diagonals sum to the same constant
442
642
602
642
2328
642
602
522
562
2328
602
522
682
522
2328
642
562
522
602
2328
2328
2328
2328
2328

D1 = (442+602+682+602) = 2328;
D2 = (642+522+522+642) = 2328;

The constant sum in every row, column and diagonal is called the magic analogue constant or magic sum, M = 2328;

Correlation:
442
642
602
642
642
602
522
562
602
522
682
522
642
562
522
602
(442+642+642+602) = 2328;
(602+642+522+562) = 2328;
etc.

442
642
602
642
642
602
522
562
602
522
682
522
642
562
522
602
ê
2328

442
642
602
642
642
602
522
562
602
522
682
522
642
562
522
602
ê
2328

Determinsants in Digital analogue Genetic Code

DET (4 x 4)
442
642
602
642
642
602
522
562
602
522
682
522
642
562
522
602
ê
2681856000


 2681856000 = (2328 + 2328 + 2328…, + 2328);

There is a mathematical balance within all of the phenomena in the analogue genetic code matrix.                

Mathematical correlation of groups of nucleotides are a proof that genetic processes have evolved from one mathematical shape to another one. They are a proof that we can uncover some of hidden secrets in that science, with the help of mathematics.



Atomic numbers


U
C
A
G
F
i
r
s
t

P
o
s
i
t
i
o
n
U
58,58,58
174

Phe

58,58,58
174

Phe

58,58,70
186

Leu

58,58,78
194

Leu

   728  
70,78,58
206

Ser
70,78,58
206

Ser
70,78,70
218

Arg
70,78,78
226

Arg
856
58,70,58
186

Tyr

58,70,58
186

Tyr

58,70,70
198

Ter

58,70,78
206

Ter

    776
58,78,58
194

Cys


58,78,58
194

Cys


58,78,70
206

Ter

3168
58,78,78
214

Trp


             808
C
78,70,58
206

Asp

78,70,58
206

Asp

78,70,70
218

Glu

78,70,78
226

Glu

   856
58,58,58
174

Ser

58,58,58
174

Ser

58,58,70
186

Ser

58,58,78
194

Ser

    728
58,70,58
186

His

58,70,58
186

His

58,70,70
198

Gln

58,70,78
206

Gln

    776
58,78,58
194

Arg


58,78,58
194

Arg


58,78,70
206

Arg

3168
58,78,78
214

Arg


             808
A
70,58,58
186

Ile

70,58,58
186

Ile

70,58,70
198

Ile

70,58,78
206

Met

  776
70,58,58
186

Thr

70,58,58
186

Thr

70,58,70
198

Thr

70,58,78
206

Thr

   776
78,78,58
214

Gly
78,78,58
214

Gly
78,78,70
226

Gly
78,78,78
234

Gly
    888
58,58,58
174

Leu


58,58,58
174

Leu


58,58,70
186

Leu

3168
58,58,78
194

Leu


             728
G
78,58,58
194

Val

78,58,58
194

Val

78,58,70
206

Val

78,58,78
214

Val

   808
78,58,58
194

Ala

78,58,58
194

Ala

78,58,70
206

Ala

78,58,78
214

Ala

   808
58,58,58
174

Pro

58,58,58
174

Pro

58,58,70
186

Pro

58,58,78
194

Pro

   728
70,70,58
198

Asn


70,70,58
198

Asn


70,70,70
210

Lys

3168
70,70,78
218

Lys


             824 


3168
3168
3168
           3168
Diagonal D1 = 3168Diagonal D2 = 3168;

The atomic genetic code describe a genotype, which is translated into an organism a phenotype by the processes of cell division.

Mathematical evolution of genetic processes is manifested in different ways. Evolution of groups of atoms is especially interesting.  Here are some examples

Digital codon square
A atomic codon square of order n is an arrangement of n² numbers, usually distinct integers, in a square, such that the n numbers in all rows, all columns, and both diagonals sum to the same constant. A digital square contains the integers from 1 to n². The term "digital square" is also sometimes used to refer to any of various types of word square.
Number of atoms
728
856
776
808
3168
856
728
776
808
3168
776
776
888
728
3168
808
808
728
824
3168
3168
3168
3168
3168

D1 = (728+856+776+808) = 3168; D2 = (808+776+776+808) = 3168;

The constant sum in every row, column and diagonal is called the magic analogue constant or magic sum, M.

728
856
776
808
856
728
776
808
776
776
888
728
808
808
728
824
ê
3168

728
856
776
808
856
728
776
808
776
776
888
728
808
808
728
824
ê
3168

728
856
776
808
856
728
776
808
776
776
888
728
808
808
728
824
ê
3168

etc.

At this stage of our research we replaced nucleotides from the Amino Acid Code Matrix with analogue of the atomic numbers in those nucleotides.

A = 70; U = 58 atoms; G = 78 atoms; C = 58 atoms                                                                                                                                          A = 7; U = 85; G = 87; C = 85;

Analogue codon table


Atomic numbers


U
C
A
G
F
i
r
s
t

P
o
s
i
t
i
o
n
U
85,85,85
255

Phe

85,85,85
255

Phe

85,85,07
177

Leu

85,85,87
257

Leu

   944  
07,87,85
179

Ser
07,87,85
179

Ser
07,87,07
101

Arg
07,87,87
181

Arg
640
85,07,85
177

Tyr

85,07,85
177

Tyr

85,07,07
99

Ter

85,07,87
179

Ter

    632
85,87,85
257

Cys


85,87,85
257

Cys


85,87,07
179

Ter

3168
85,87,87
259

Trp


             952
C
87,07,85
179

Asp

87,07,85
179

Asp

87,07,07
101

Glu

87,07,87
181

Glu

   640
85,85,85
255

Ser

85,85,85
255

Ser

85,85,07
177

Ser

85,85,87
257

Ser

    944
85,07,85
177

His

85,07,85
177

His

85,07,07
99

Gln

85,07,87
179

Gln

    632
85,87,85
257

Arg


85,87,85
257

Arg


85,87,07
179

Arg

3168
85,87,87
259

Arg


             952
A
07,85,85
177

Ile

07,85,85
177

Ile

07,85,07
99

Ile

07,85,87
179

Met

  632
07,85,85
177

Thr

07,85,85
177

Thr

07,85,07
99

Thr

07,85,87
179

Thr

   632
87,87,85
259

Gly
87,87,85
259

Gly
87,87,07
181

Gly
87,87,87
261

Gly
    960
85,85,85
255

Leu


85,85,85
255

Leu


85,85,07
177

Leu

3168
85,85,87
257

Leu


             944
G
87,85,85
257

Val

87,85,85
257

Val

87,85,07
179

Val

87,85,87
259

Val

   952
87,85,85
257

Ala

87,85,85
257

Ala

87,85,07
179

Ala

87,85,87
259

Ala

   952
85,85,85
255

Pro

85,85,85
255

Pro

85,85,07
177

Pro

85,85,87
257

Pro

   944
07,07,85
99

Asn


07,07,85
99

Asn


07,07,07
21

Lys

3168
07,07,87
101

Lys


             320  


3168
3168
 3168
           3168

Diagonal D1 = 3168;  Diagonal D2 = 3168;
Row 1 = Column 1;  Row 2 = Column 2;    Row 3 = Column 3;  Row 4 = Column 4;

Analogue codon square
A analogue codon square of order n is an arrangement of n² numbers, usually distinct integers, in a square, such that the n numbers in all rows, all columns, and both diagonals sum to the same constant
944
640
632
952
3168
640
944
632
952
3168
632
632
960
944
3168
952
952
944
320
3168
3168
3168
3168
3168

D1 = (944+944+960+320) = 3168;
D2 = (952+632+632+952) = 3168;

The constant sum in every row, column and diagonal is called the magic analogue constant or magic sum, M = 3168;

Correlation:

944
640
632
952
640
944
632
952
632
632
960
944
952
952
944
320
ê
3168

944
640
632
952
640
944
632
952
632
632
960
944
952
952
944
320
ê
3168


944
640
632
952
640
944
632
952
632
632
960
944
952
952
944
320

ê
3168

Determinsants in Digital analogue Genetic Code

DET (4 x 4)
944
640
632
952
640
944
632
952
632
632
960
944
952
952
944
320
ê
197237145600

197237145600 = (3168+ 3168 + 3168…, + 3168);

There is a mathematical balance within all of the phenomena in the analogue genetic code matrix.                

Mathematical correlation of groups of nucleotides are a proof that genetic processes have evolved from one mathematical shape to another one. They are a proof that we can uncover some of hidden secrets in that science, with the help of mathematics.

Atomic weight

C
H
N
O
S

A
5
5
5
0
0
15
U
4
4
2
2
0
12
C
4
5
3
1
0
13
G
5
5
5
1
0
16

C = 12,0111;  H = 1,00797; N = 14,0067; O = 15,9994;  S = 32,064;

A = 135; U = 112; C = 111; G = 151;

The Digital Genetic Code

At the first stage of our research we replaced nucleotides from the Genetic Code with atomic weight of those nucleotides.
Mathematical position of the nucleotides in codon

The development of prediction methods based on digital theory is focused on the exploration of new digital formulas and algorithms. The genetic code is stored in DNA molecules as sequences of bases: adenine (A) which pairs with thymine (T), and cytosine (C) which pairs with guanine (G), The analog of DNA in a digital genetic algorithm is a number of atoms, atomic numbers, analog codes, etc.

At mathematical evolution of genetic processes, nucleotides TCAG are being transformed to codons UCAG and later to amino acids and various organic composition.



Second Position of Codon


U
C
A
G
F
i
r
s
t

P
o
s
i
t
i
o
n
U
112,111,112
335

Ser

112,111,111
334

Ser

112,111,135
358

Ser

112,111,151
374

Ser

       1401  
135,151,112
398

Ser

135,151,111
397

Ser

135,151,135
421

Arg

135,151,151
437

Arg

        1653
111,135,112
358

His

111,135,111
357

His

111,135,135
381

Gln

111,135,151
397

Gln

       1493
112,151,112
375

Cys

112,151,111
374

Cys

112,151,135
398

Ter
6108
112,151,151
414

Trp

  1561
C
151,135,112
398

Asp

151,135,111
397

Asp

151,135,135
421

Glu

151,135,151
437

Glu

       1653
111,112,112
335

Leu

111,112,111
334

Leu

111,112,135
358

Leu

111,112,151
374

Leu

        1401
135,111,112
359

Thr

135,111,111
358

Thr

135,111,135
382

Thr

135,111,151
398

Thr

       1493
151,112,112
375

Val

151,112,111
374

Val

151,112,135
398

Val
6108
151,112,151
414

Val

 1561
A
112,135,112
359

Tyr

112,135,111
358

Tyr

112,135,135
382

Ter

112,135,151
398

Ter

       1497
135,112,112
359

Ile

135,112,111
358

Ile

135,112,135
382

Ile

135,112,151
398

Met

        1497
151,151,112
414

Gly

151,151,111
413

Gly

151,151,135
437

Gly

151,151,151
453

Gly

       1717
111,111,112
334

Pro

111,111,111
333

Pro

111,111,135
357

Pro
6108
111,111,151
373

Pro

 1397
G
111,151,112
374

Arg

111,151,111
373

Arg

111,151,135
397

Arg

111,151,151
413

Arg

       1557
151,111,112
374

Ala

151,111,111
373

Ala

151,111,135
397

Ala

151,111,151
413

Ala

        1557
112,112,112
336

Phe

112,112,111
335

Phe

112,112,135
359

Leu

112,112,151
375

Leu

        1405
135,135,112
382

Asn

135,135,111
381

Asn

135,135,135
405

Lys
6108
135,135,151
421

Lys

 1589


       6108
          6108
         6108
                   6108

Diagonal D1 = 6108Diagonal D2 = 6108
The atomic genetic code describe a genotype, which is translated into an organism a phenotype by the processes of cell division.

Mathematical evolution of genetic processes is manifested in different ways. Evolution of groups of atoms is especially interesting.  Here are some examples


Atomic codon square
A atomic codon square of order n is an arrangement of n² numbers, usually distinct integers, in a square, such that the n numbers in all rows, all columns, and both diagonals sum to the same constant. A digital square contains the integers from 1 to n². The term "digital square" is also sometimes used to refer to any of various types of word square.
Number of atoms
1401
1653
1493
1561
6108
1653
1401
1493
1561
6108
1497
1497
1717
1397
6108
1557
1557
1405
1589
6108
6108
6108
6108
6108

D1 = (1401+1401+1717+1589) = 6108; D2 = (1561+1493+1497+1557) = 6108;

The constant sum in every row, column and diagonal is called the magic analogue constant or magic sum, M.

1401
1653
1493
1561
1653
1401
1493
1561
1497
1497
1717
1397
1557
1557
1405
1589
ê
6108

1401
1653
1493
1561
1653
1401
1493
1561
1497
1497
1717
1397
1557
1557
1405
1589
ê
6108

1401
1653
1493
1561
1653
1401
1493
1561
1497
1497
1717
1397
1557
1557
1405
1589
ê
6108
etc.

At this stage of our research we replaced nucleotides from the Amino Acid Code Matrix with analogue of the atomic weight in those nucleotides.

A = 135; U = 112; C = 111; G = 151;
A = 531; U = 211; C = 111; G = 151;
Analogue codon table


Second Position of Codon


U
C
A
G
F
i
r
s
t

P
o
s
i
t
i
o
n
U
211,111,211
533

Ser

211,111,111
433

Ser

211,111,531
853

Ser

211,111,151
473

Ser

        2292  
531,151,211
0893

Ser

531,151,111
0793

Ser

531,151,531
1213

Arg

531,151,151
0833

Arg

        3732
111,531,211
0853

His

111,531,111
0753

His

111,531,531
1173

Gln

111,531,151
0793

Gln

        3572
211,151,211
573

Cys

211,151,111
473

Cys

211,151,531
893

Ter
12048
211,151,151
513

Trp

                 2452
C
151,531,211
0893

Asp

151,531,111
0793

Asp

151,531,531
1213

Glu

151,531,151
0833

Glu

       3732
111,211,211
533

Leu

111,211,111
433

Leu

111,211,531
853

Leu

111,211,151
473

Leu

       2292
531,111,211
0853

Thr

531,111,111
0753

Thr

531,111,531
1173

Thr

531,111,151
0793

Thr

         3572
151,211,211
573

Val

151,211,111
473

Val

151,211,531
893

Val
12048
151,211,151
513

Val

                2452
A
211,531,211
0953

Tyr

211,531,111
0853

Tyr

211,531,531
1273

Ter

211,531,151
0893

Ter

       3972
531,211,211
0953

Ile

531,211,111
0853

Ile

531,211,531
1273

Ile

531,211,151
0893

Met

        3972
151,151,211
513

Gly

151,151,111
413

Gly

151,151,531
833

Gly

151,151,151
453

Gly

       2212
111,111,211
433

Pro

111,111,111
333

Pro

111,111,531
753

Pro
12048
111,111,151
373

Pro

                1892
G
111,151,211
473

Arg

111,151,111
373

Arg

111,151,531
793

Arg

111,151,151
413

Arg

      2052
151,111,211
473

Ala

151,111,111
373

Ala

151,111,531
793

Ala

151,111,151
413

Ala

       2052
211,211,211
633

Phe

211,211,111
533

Phe

211,211,531
953

Leu

211,211,151
573

Leu

      2692
531,531,211
1273

Asn

531,531,111
1173

Asn

531,531,531
1593

Lys
12048
531,531,151
1213

Lys

                 5252


     12048
       12048
      12048
                   12048

Diagonal D1 = 3168;  Diagonal D2 = 3168;


Analogue codon square
A analogue codon square of order n is an arrangement of n² numbers, usually distinct integers, in a square, such that the n numbers in all rows, all columns, and both diagonals sum to the same constant
2292
3732
3572
2452
12048
3732
2292
3572
2452
12048
3972
3972
2212
1892
12048
2052
2052
2692
5252
12048
 12048
 12048
 12048
 12048

D1 = 12048; D2 = 12048

The constant sum in every row, column and diagonal is called the magic analogue constant or magic sum, M = 12048;;

Correlation:

2292
3732
3572
2452
3732
2292
3572
2452
3972
3972
2212
1892
2052
2052
2692
5252
ê
12048

2292
3732
3572
2452
3732
2292
3572
2452
3972
3972
2212
1892
2052
2052
2692
5252
ê
12048

2292
3732
3572
2452
3732
2292
3572
2452
3972
3972
2212
1892
2052
2052
2692
5252
ê
12048

etc

Determinsants in Digital analogue Genetic Code

DET (4 x 4)
944
640
632
952
640
944
632
952
632
632
960
944
952
952
944
320

ê
74615095296000
ê
(12048+ 12048 + 12048…, + 12048);


There is a mathematical balance within all of the phenomena in the analogue genetic code matrix.                

Mathematical correlation of groups of nucleotides are a proof that genetic processes have evolved from one mathematical shape to another one. They are a proof that we can uncover some of hidden secrets in that science, with the help of mathematics.


It is obvious that digital matrix of amino acid code evolved from digital matrix of nucleotide code.

Mathematical correlation of groups of nucleotides are a proof that genetic processes have evolved from one mathematical shape to another one. They are a proof that we can uncover some of hidden secrets in that science, with the help of mathematics.

Perspectives


1. About importance of the proposal

Development of science in following period will be based on contemporary digital technology. To conquer new technology it would be far more efficient to use method of reverse engineering for comprehension of phenomen in genetics. We'll give a brief description of that method:
The genetic code tables used by the modern science are characterized and determined by principles of biochemistry. However, if in those tables, instead of the UCAG nucleotides we put the number of atoms of those nucleotides, we will get the new tables of the genetic code characterized and determined by programmatic and information principles. Therefore, biochemistry can be explained through a phenomenon out of biochemistry,
Particularly interesting results we will get when determining numeric values for the information content of atoms and molecules. We will then find out that those values express physical and chemical characteristics of molecules. For example: in a DNA molecule, the polynucleotide chains are connected through an exact cyber-information connections. In those molecules there are also mathematical matrixes of DNA, represented by the number of atoms of four ATCG bases. These matrixes determine the positioning of nucleotides in that molecule. With this, the biological particularities of DNA are determined. Similar mathematical matrixes determine the positioning of nucleotides in the RNA molecule. In the amino acid proteins, they are interconnected into the respective mathematical chains. In those chains are also matrixes where particular mathematical principles apply, the principles that determine the positioning of each amino acid in the chain. Therefore, the herewith discussed research results show that the process of sequencing in bio-macromolecules is conditioned and determined not only through biochemical, but also through cybernetic information principles. The hypothesis here is that the processes in an organism occur only when certain mathematical conditions are met, i.e. when there is a certain mathematical correlation between parameters in those processes. That correlation is expressed by the respective methodology. 
We would particularly like to stress here that the genetic, as well as biochemical information in a broader sense of the word, is determined and characterized by very complex cybernetic and information principles. The constantans in those principles are: the number of atoms and molecules, atomic numbers, atomic weight, physical and chemical parameters, even and odd values, codes and analogue codes, standard deviations, frequencies, primary and secondary values, and many other things

2. Where it might be useful

In view of this, our  findings might have a series of impacts to the aforementioned work. We are devoted to provide a digital code for each of 20 native amino acids. These digital codes should more complete and better reflect the essence of each of the 20 amino acids. Therefore, it might stimulate a series of future work by using the author’s digital codes to formulate the pseudo amino acid composition for predicting protein structure class, subcellular location, membrane protein type, enzyme family class, GPCR type, protease type, protein-protein interaction, metabolic pathways, protein quaternary structure, and other protein attributes.

We can expect that this discovery will significantly speed up the research of mutational genesis of humans, molecular etymology, in applied biology and genetic engineering, and also it will provide discoveries in new medicines and methods of medicinal treatments.

3. Future steps required

  1. Establish scientific-research project team for development of advanced   
      technologies in genetics, medicine and biochemistry.
  1. Project team should make concrete program of scientific-research work, where  
they should define goals of research, indispensable facilities for implementation of project, project duration, budget, and other conditions.
      3.  Define rights and duties of all participants in implementation of project.
      4.  To implement project defined by project documentation.

Research in the field of fundamental sciences

  1. Decode matrix of amino acid code and on the experimental way prove that the matrix really exists. And after that, use that matrix to conquer top technologies in the field of genetics.
  2. Decode matrix of nucleotide code and digital codes which connect that matrix with matrix of amino acid code. And use that matrix to conquer top technologies in the field of biochemistry.
  3. Decode matrix code in Tables of periodic system of chemical elements, and use that matrix to conquer top technologies in the field of chemistry.
  4. Decode matrix code in the nature, and use that matrix to conquer top technologies in the field of all natural sciences.
  5. Decode matrix code of chromosomes in human body.
  6. With the help of above mentioned matrixes, decode map of human DNA.
  7. Decode matrix code of processes in the field of nuclear physics.
  8. Decode insulin matrix code, as well as all other codes from the field of biochemistry.
  9. Other research (Matrix code in Pascal's triangle, Matrix code in astronomy, Matrix code in theoretical physics, determinism, etc.)


4.Paragraph of limitations


      1. Confirm that the manuscript has been submitted solely to this journal and is not 
           published, in press, or submitted elsewhere.
      2.  Confirm that all the research meets the ethical guidelines, including adherence to  
           the legal requirements of the study country.
3. Confirm that you have completed and sent a Copyright Transfer Agreement
    (CTA) to the Editorial Office.


5.The obtained results

The obtained results are valid. In this manuscript, we proposed the universal genetic code. Mathematics could confirm this fact with 100% scientific accuracy. For example, Table mathematical position of the nucleotides in codon, Digital codon square, Analogue atomic genetic code, Correlation of the code and analogue code Analogue codon table, Analogue codon square, Determinsants in Digital analogue Genetic Code, Determinsants in Digital analogue Genetic Code, Atomic weight Atomic codon square, etc.This mathematic system represents that very universal formula of the genetic code which 100% scientific accuracy. was looking for.
.
C O N C L U S I O N

It is a rewarding work to translate the biochemical language of amino acids into a digital language because it may be very useful for developing new methods for predicting protein sub cellular localization, membrane protein type, protein structure secondary prediction or any other protein attributes. 

This is because ever since the concept of Chou's pseudo amino acid composition was proposed many efforts have been made trying to use various digital numbers to represent the 20 native amino acids in order to better reflect the sequence-order effects through the vehicle of pseudo amino acid composition. Some investigators used complexity measure factor some used the values derived from the cellular automata, some used hydrophobic and/or hydrophilic values, some were through Fourier transform, and some used the physicochemical distance. 
 
Now, it is going to be possible to use the completely new strategy of research in genetics. However, observation of all these relations which are the outcome of the periodic law (actually, of the law of binary coding) is necessary, because it can be of great importance for decoding conformational forms and stereo-chemical and digital structure of proteins.