Algorithm and computational complexity of Insulin

ISSN:2229-6093 Lutvo Kurić, Int. J. Comp. Tech. Appl., Vol 2 (2), 216-241

Algorithm and computational complexity of Insulin Lutvo Kurić Bosnia and Herzegovina, Novi Travnik, Kalinska 7

Abstract:This paper discusses cyberinformation studies of the amino acid composition of insulin, in particular the identification of scientific terminology that could describe this phenomenon, ie, the study of genetic information, as well as the relationship between the genetic language of proteins and theoretical aspect of this system and cybernetics. The result of this research show that there is a matrix code for insulin. It also shows that the coding system within the amino acidic language gives detailed information, not only on the amino acid „record“, but also on its structure, configuration and its various shapes. The issue of the existence of an insulin code and coding of the individual structural elements of this protein are discussed. Answers to the following questions are sought. Does the matrix mechanism for biosynthesis of this protein function within the law of the general theory of information systems, and what is the significance of this for understanding the genetic language of insulin? What is the essence of existence and functioning of this language? Is the genetic information characterized only by biochemical, or also by cyberinformation principles? The potential effects of physical and chemical, as well as cybernetic and information ptinciples, on the biochemical basis of insulin are also investigated.This aper discusses new methods for developing genetic technologies, in particular more advanced digital technology based on programming, cybernetics, and informational laws and systems, and how this new technology could be useful in medicine, bioinformatics, genetics, biochemistry, and other natural sciences. Keywords biocoding, atomic progression, human insulin, insulin code, genetics code, amino acids

Introduction The biologic role of any given protein in essential life processes, eg, insulin, depends on the positioning of its component amino acids, and is understood by the „positioning of letters forming words“. Each of these words has its biochemical base. If this base is expressed by corresponding discrete numbers, it can be seen that any given base has its own program, along with its own unique cybernetics and information characteristics. Indeed, the sequencing of the molecule is determined not only by distin biochemical features, but also by cybernetic and information principles. For this reason, research in this field deals more with the quantitative rather than qualitative characteristcs of genetic information and its biochemical basis. For the purposes of this paper, specific physical and chemical factors have been selected in order to express the genetic information for insulin.Numerical values are them assigned to these factors, enabling them to be measured. In this way it is possible to determine oif a connection really exists between the quantitative ratios in the process of transfer of genetic information and the qualitative appearance of the insulin molecule. To select these factors, preference is given to classical physical and chemical parameters, including the number of atoms in the relevant amino acids, their analog values, the position in these amino acids in the peptide chain, and their frenquencies.There is a arge numbers of these parameters, and each of their gives important genetic information. Going through this process, it becomes clear that there is a mathematical relationship between quantitative ratios and the qualitative appearance of the biochemical „genetic processes“ and that there is a measurement method that can be used to describe the biochemistry of insulin.

216


Methods Insulin can be represented by two different forms, ie, a discrete form and a sequential form. In the discrete form, a molecule of insulin is represented by a set of discrete codes or a multiple dimension vector. In the sequential form, an insulin molecule is represent by a series of amino acids according to the order of their position in the chains 1AI0. Therefore, the sequential form can naturally reflect all the information about the sequence order and lenght of an insulin molecule. The key issue is whether we can develop a different discrete method of representing an insulin molecule that will allow accomodation of partial, if not all sequence order information? Because a protein sequence is usually represented by a series of amino acids should be assigned to these codes in order to optimally convert the sequence order information into a series of numbers for the discrete form representation?

Expression of Insulin Code Matrix- 1AI0 The matrix mechanism of Insulin, the evolution of biomacromolecules and, especially, the biochemical evolution of Insulin language, have been analyzed by the application of cybernetic methods, information theory and system theory, respectively. The primary structure of a molecule of Insulin is the exact specification of its atomic composition and the chemical bonds connecting those atoms.

Insulin Model The structure 1AI0 has in total 12 chains: A,B,C,D,E,F,G,H,I,J,K,L. 1AI0:A G

I

V

E

Q

C

C

T

S

I

C

S

L

Y

Q

L

E

N

Y

C

N

10

22

19

19

20

14

14

17

14

22

14

14

22

24

20

22

19

17

24

14

17

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

1AI0:B F

V

N

Q

H

I

C

G

S

H

L

V

E

A

L

23

19

17

20

20

22

14

10

14

20

22

19

19

13

22

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

Y

L

V

C

G

E

R

G

F

I

Y

T

P

K

T

24

22

19

14

10

19

26

10

23

22

24

17

17

24

17

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

etc. Figure 1. Group of chains A,B,C,D,E,F,G,H,I,J,K,L. Notes: Aforementioned aminoacids are positioned from number 1 to 306. Numbers 1, 2, 3, n... present the position of a certain aminoacid. This positioning is of the key importance for understanding of programmatic, cybernetic and information principles in this protein. The scientific key for interpretation of bio chemical processes is the same for insulin and as well as for the other proteins and other sequences in biochemistry.

217


The first aminoacid in this example has 10 atoms, the second one 22, the third one 19, etc. They have exactly these numbers of atoms because there are many codes in the insulin molecule, analog codes, and other voded features. In fact, there is a cybernetic algorithm which it is „recorded“ that the firs amino acid has to have 10 atoms, the second one 22, the third one 19, etc. The first amino acid has its own biochemistry, as does the second and the third, etc. The obvious conclusion is that there is a concrete relationship between quantitative ratios in the process of transfer of genetic information and qualitative appearance, ie, the characteristcs of the organism. ALGORITHM

We shall now give some mathematical evidences that will prove that in the biochemistry of hemoglob in there really is programmatic and cybernetic algorithm in which it is „recorded“, in the language of mathematics, how the molecule will be built and what will be the quantitative characteristics of the given genetic information. Atomic progression Step 1 (Amino acids from 1 to 306) AC1 = 10 atoms; AC2 = 22 atoms; AC3 = 19 atoms;... AC306 = 17 atoms; [AC1 + (AC1+ AC2) + (AC1+ AC2+ AC3)..., + (AC1+ AC2+ AC3..., + AC147)] = S1; AC1 = APa1 = 10; (AC1+ AC2) = (10+22) = APa2 = 32; (AC1+ AC2+ AC3) = (10+22+19) = APa3 = 51; (AC1+ AC2+ AC3..., + AC306) = APa306 = 5640 atoms; APa1,2,3,n = Atomic progression of amino acids 1,2,3,n [APa1+APa2+APa3)..., + APa306)] = (10+32+51…, + 5640) = S1; S1 = 863 208;

Example : Atomic progression 1 (APa) . . G I V E Q C P K T Sum . . 10 22 19 19 20 14 17 24 17 5640 . . 304 305 306 46971 1 2 3 4 5 6  . . Sum G I V E Q C P K T 5599 5623 5640 863 208 10 32 51 70 90 104 . . . . 1 2 3 4 5 6 304 305 306 46971 (0+10) = 10; (10+22)=32; (10+11+19) = 51; etc.

218


Figure 2. Atomic progression 1 (APa) of amino acids from 1 to 306. Notes: By using chemical-information procedures, we calculated the arithmetic progression for the information content of aforementioned aminoacids.

Step 2 (Amino acids from 306 to 1) AC306 = 17 atoms; AC305 = 24 atoms; AC304 = 17 atoms;... AC1 = 10 atoms; [AC306 + (AC306+ AC305) + (AC306+ AC305+ AC304)..., + (AC306+AC305+AC304..., +AC1)] = S2; AC306 = APb306 = 17; (AC306+ AC305) = (17+24) = APb306 = 41; (AC306+ AC305+ AC304) = (17+24+17) = APb304 = 58; (AC306+ AC305+ AC304..., + AC1) = APb1 = 5640 atoms; APb306,305,304, …,1 = Atomic progression of amino acids 306,305,304,…1; [APb306+APb305+APb1304)..., + APb1)] = (17+41+58…, + 5640) = 868 272; S2 = 868 272; Example: Atomic progression 2 (APb) G

I

V

.

.

I

Y

T

P

K

T

Sum

10

22

19

24

17

17

24

17

5640

2

3

. .

22

1

. .

302

303

304

305

306

46971

Sum 868 272 46971

301



G

I

V

.

.

I

Y

T

P

K

T

5640 1

5630 2

5608 3

. .

. .

121 301

99 302

75 303

58 304

41 305

17 306

(0+17) = 17; (17+24)=41; (17+24+17)=58; etc. Figure 3. Schematic representation of the atomic progression 2 from 306 to 1. Within the digital pictures in biochemistry, the physical and chemical parameters are in a strict compliance with programmatic, cybernetic and information principles. Each bar in the protein chain attracts only the corresponding aminoacid, and only the relevant aminoacid can be positioned at certain place in the chain. Each peptide chain can have the exact number of aminoacids necessary to meet the strictly determined mathematical conditioning. It can have as many atoms as necessary to meet the mathematical balance of the biochemical phenomenon at certain mathematical level, etc. The digital language of biochemistry has a countless number of codes and analogue codes, as well as other information content. These pictures enable us to realize the very essence of functioning of biochemical processes. There are some examples.

219


Table 1.

Bio intervals APa and APb (sequence from 1 to 306 AA)

Insulin Model The structure 1AI0 AA

S

N

C

L

E

G

T

S

N

C

L

E

G

T

Number of atoms

14

17

14

22

19

10

17

14

17

14

22

19

10

17

Rank

114

120

122

134

136

143

153

165

171

173

185

187

194

204





























2079

2203

2241

2459

2497

2621

2820

3019

3143

3181

3399

3437

3561

3760

APa





























-1681

-1358

-1196

-940

-684

-522

-199

+199

+522

+684

+940

+1196

+1358

+1681





























APb

3760

3561

3437

3399

3181

3143

3019

2820

2621

2497

2459

2241

2203

2079

AA

G

L

Y

N

V

A

E

G

L

Y

N

V

A

E

Number of atoms Rank

10

22

24

17

19

13

19

10

22

24

17

19

13

19

103

115

121

123

135

137

144

154

166

172

174

186

188

195

>

40420

>

40420

(2079-3760) = -1681; (2203-3561) = -1358; (2241-3437) ) =-1196; etc.

Table 1. Schematic representation of the bio intervals APa and APb (sequence from 1 to 306 AA). Notes: Namely, having mathematically analyzed the Bio intervals model of Insulin Model (Table 1) we have found out that the protein code is based on a periodic law. This being the only to „read“ the picture, the solution of the main problem (concering an arrangement where each amino acid takes only one, precisely determined position in the code), is quite manifest: Bio intervals model of insulin should, in fact, be „remodelled“ into a periodic system. Examples:

Insulin Model The structure 1AI0 Table 2 AA

S

N

C

L

E

G

T

S

N

C

L

E

G

T

Number of atoms

14

17

14

22

19

10

17

14

17

14

22

19

10

17

Rank

63

69

71

83

85

92

102

216

222

224

236

238

245

255





























1139

1263

1301

1519

1557

1681

1880

3959

4083

4121

4339

4377

4501

4700

APa





























-3561

-3238

-3076

-2820

-2564

-2402

-2079

2079

2402

2564

2820

3076

3238

3561





























>

220

40420


APb

4700

4501

4377

4339

4121

4083

3959

1880

1681

1557

1519

1301

1263

1139

AA

G

L

Y

N

V

A

E

G

L

Y

N

V

A

E

Number of atoms

10

22

24

17

19

13

19

10

22

24

17

19

13

19

52

64

70

72

84

86

93

205

217

223

225

237

239

246

Rank

>

40420

Table 2. Schematic representation of the bio intervals APa and APb (sequence from 52 to 255 AA).

Insulin Model The structure 1AI0 Table 3 AA

S

N

C

L

E

G

T

S

N

C

L

E

G

T

Number of atoms

14

17

14

22

19

10

17

14

17

14

22

19

10

17

Rank

12

18

20

32

34

41

51

267

273

275

287

289

296

306





























199

323

361

579

617

741

940

4899

5023

5061

5279

5317

5441

5640





























-5441

-5118

-4956

-4700

-4444

-4282

-3959

+3959

+4282

+4444

+4700

+4956

+5118

+5441





























APb

5640

5441

5317

5279

5061

5023

4899

940

741

617

579

361

323

199

AA

G

L

Y

N

V

A

E

G

L

Y

N

V

A

E

10

22

24

17

19

13

19

10

22

24

17

19

13

19

1

13

19

21

33

35

42

256

268

274

276

288

290

297

APa

Number of atoms Rank

Table 3. Schematic representation of the bio intervals APa and APb (sequence from 1 to 306 AA). The research we carried out have shown that atomic progression are one of quantitative characteristics in biochemistry. Atomic progression is, actually, a discrete code that protects and guards genetic information coded in bio-chemical processes. This a recently discovered code, and more detailed knowledge on it is yet to be discovered. In a similar way we shall calculate bio codes of other unions of amino acids. Once we do this, we will find out that all these unions of amino acids are connected by various bio codes, analogue codes as well as other quantitative features. Examples:

221

>

40420

>

40420


Insulin Model The structure 1AI0 Table 4. AA Number of atoms

S

N

C

L

E

G

T

14

17

14

22

19

10

17

Rank

12

18

20

32

34

41

51















199

323

361

579

617

741

940















-741

-418

-256

0

+256

+418

+741















APb

940

741

617

579

361

323

199

AA Number of atoms

G

L

Y

N

V

A

E

10

22

24

17

19

13

19

Rank

256

268

274

276

288

290

297

APa

>

3760

>

3760

Table 4. Schematic representation of the bio intervals APa and APb (sequence from 12 to 297. AA). (199-940) = -741; (323-741) = -418; (361-617) = -256;


S

N

C

L

E

G

T

14

17

14

22

19

10

17

Rank

63

69

71

83

85

92

102















1139

1263

1301

1519

1557

1681

1880















APa

-741 -418 -256 





0 

>

10340

+256 +418 +741 





222


APb

1880

1681

1557

1519

1301

1263

1139

AA Number of atoms

G

L

Y

N

V

A

E

10

22

24

17

19

13

19

Rank

205

217

223

225

237

239

246

>

10340

Table 5. Schematic representation of the bio intervals APa and APb (sequence from 63 to 246. AA).


S

N

C

L

E

G

T

14

17

14

22

19

10

17

Rank

114

120

122

134

136

143

153















APa

2079

2203

2241

2459

2497

2621

2820















-741 -418 -256

0

>

16920

>

16920

+256 +418 +741















APb

2820

2621

2497

2459

2241

2203

2079

AA Number of atoms

G

L

Y

N

V

A

E

10

22

24

17

19

13

19

Rank

154

166

172

174

186

188

195



S

N

C

L

E

G

T

14

17

14

22

19

10

17

Rank

165

171

173

185

187

194

204















APa

3019

3143

3181

3399

3437

3561

3760















>

23500

223


-741 -418 -256

0

256

418

741















APb

3760

3561

3437

3399

3181

3143

3019

AA Number of atoms

G

L

Y

N

V

A

E

10

22

24

17

19

13

19

Rank

103

115

121

123

135

137

144

>

23500



S

N

C

L

E

G

T

14

17

14

22

19

10

17

Rank

216

222

224

236

238

245

255















3959

4083

4121

4339

4377

4501

4700















0

256

418

741

APa

-741 -418 -256 













APb

4700

4501

4377

4339

4121

4083

3959

AA Number of atoms

G

L

Y

N

V

A

E

10

22

24

17

19

13

19

Rank

52

64

70

72

84

86

93

>

30080

>

30080



S

N

C

L

E

G

T

14

17

14

22

19

10

17

224


Rank

APa

267

273

275

287

289

296

306















4899

5023

5061

5279

5317

5441

5640















0

256

418

741

-741 -418 -256 













APb

5640

5441

5317

5279

5061

5023

4899

AA Number of atoms

G

L

Y

N

V

A

E

10

22

24

17

19

13

19

Rank

1

13

19

21

33

35

42

>

36660

>

36660

Table 9. Schematic representation of the bio intervals APa and APb (sequence from 1 to 306. AA). Those tables (4-9) contains an overview of all positive and negative values of bio codes. The values show some of the quantitative characteristics of the molecule of insulin. Actually, they show that there is an exact mathematical balance between positive and negative values. Therefore, there is a mathematical balance between the union of aminoacids with positive progression and those of negative progression. Aminoacids with a positive progression have a primary role in the mathematical picture of that protein, and the negative progression have a secondary role in it. We assume that aminoacids with a positive progression have a primary role in the biochemical picture of that protein, and the negative progression have a secondary role in it. If this really is the case and research on an experimental level proves it, a radically new way of learning about biochemical processes will be opened. The molecule of insulin we can understand as words built from letters, i.e. aminoacids. The meaning of words is determined by positioning of letters. Each of these words has its biochemical base. If this base is expressed by corresponding discrete numbers, we find out that the base has its own program, cybernetic and information characteristics. In fact, we will find out that the sequencing of the molecule is conditioned and determined not only by biochemical, but also by cybernetic and information principles. For this reason, in this research we will deal more with quantitative, and less with qualitative characteristics of the genetic information and its biochemical foundation. Here are some examples


G

G

G

G

G

G

10

10

10

10

10

10

Rank

256

205

154

103

52

1

225














940 1880 2820 3760 4700 5640

APb













741

741

741

741

741

741













199 1139 2079 3019 3959 4899

APa













AA Number of atoms

S

S

S

S

S

S

14

14

14

14

14

14

Rank

12

63

114

165

216

267

Table 10. Schematic representation of the bio intervals APa and APb (G and S. AA). (940-199)=741; (1880-1139) = 741: (2820-2079) = 741; etc.


L

L

L

L

L

L

22

22

22

22

22

22

Rank

13

64

115

166

217

268













5441

4501

3561

2621

1681

741













418

418

418

418

418

418













5023

4083

3143

2203

1263

323













APa

APb

AA Number of atoms

N

N

N

N

N

N

17

17

17

17

17

17

Rank

273

222

171

120

69

18

Table 11. Schematic representation of the bio intervals APa and APb (L and N. AA). .

226



L

L

L

L

L

L

22

22

22

22

22

22

Rank

32

83

134

185

236

287













579

1519

2459

3399

4339

5279













0

0

0

0

0

0













1519

2459

3399

4339

5279













APa

APb

579

AA Number of atoms

N

N

N

N

N

N

17

17

17

17

17

17

Rank

276

225

174

123

72

21

Table 12. Schematic representation of the bio intervals APa and APb (L and N. AA).


G

G

G

G

G

G

10

10

10

10

10

10

Rank

41

92

143

194

245

296













741

1681

2621

3561

4501

5441













5764

5764

5764

5764

5764

5764













5023

4083

3143

2203

1263













A

A

A

A

A

A

APa

APb

AA

323

227


Number of atoms

13

13

13

13

13

13

Rank

35

86

137

188

239

290

Table 13. Schematic representation of the bio intervals APa and APb (G and A. AA). (741+5023) = 5764; (1681+4083) = 5764; (2621+3143) = 5764; etc.


C

C

C

C

C

C

14

14

14

14

14

14

Rank

20

71

122

173

224

275













361

1301

2241

3181

4121

5061













APa

5678 5678 5678 5678 5678 5678 APb













5317

4377

3437

2497

1557

617













AA Number of atoms

Y

Y

Y

Y

Y

Y

24

24

24

24

24

24

Rank

19

70

121

172

223

274

Table 14. Schematic representation of the bio intervals APa and APb (C and Y. AA). (361+5317) = 5678; (1301+4377) = 5678; (2241+3437) = 5678; etc.


E

E

E

E

E

E

19

19

19

19

19

19

228


Rank

APa

34

85

136

187

238

289













617

1557

2497

3437

4377

5317













5678 5678 5678 5678 5678 5678 APb













5061

4121

3181

2241

1301













361

AA Number of atoms

V

V

V

V

V

V

19

19

19

19

19

19

Rank

33

84

135

186

237

288

Table 15. Schematic representation of the bio intervals APa and APb (E and V. AA). (617+5061) = 5678; (1557+4121) = 5678; (2497+3181) = 5678; ets.


T

T

T

T

T

T

17

17

17

17

17

17

Rank

51

102

153

204

255

306













940

1880

2820

3760

4700

5640













APa

5839 5839 5839 5839 5839 5839 APb













4899

3959

3019

2079

1139













199

AA Number of atoms

E

E

E

E

E

E

19

19

19

19

19

19

Rank

42

93

144

195

246

297

Table 16. Schematic representation of the bio intervals APa and APb (T and E. AA). (940+4899) = 5839; (1880+3959) = 5839; (3760+2079) = 5839; ets.

229



E

E

E

E

E

E

19

19

19

19

19

19

Rank

34

85

136

187

238

289













617

1557

2497

3437

4377

5317













0

0

0

0

0

0













617

1557

2497

3437

4377

5317













APa

APb

AA Number of atoms

Y

Y

Y

Y

Y

Y

24

24

24

24

24

24

Rank

274

223

172

121

70

19

Table 17. Schematic representation of the bio intervals APa and APb (E and Y. AA).


C

C

C

C

C

C

14

14

14

14

14

14

Rank

20

71

122

173

224

275













361

1301

2241

3181

4121

5061













0

0

0

0

0

0













1301

2241

3181

4121

5061













V

V

V

V

V

V

APa

APb

AA

361

230


Number of atoms

19

19

19

19

19

19

Rank

288

237

186

135

84

33

Table 18. Schematic representation of the bio intervals APa and APb (C and V. AA).


T

T

T

T

T

T

17

17

17

17

17

17

Rank

51

102

153

204

255

306













940

1880

2820

3760

4700

5640













741

741

741

741

741

741













199

1139

2079

3019

3959

4899













APa

APb

AA Number of atoms

E

E

E

E

E

E

19

19

19

19

19

19

Rank

297

246

195

144

93

42

(940-199) = 741; (1880-1139) = 741; (940-2079) = 741; etc. Table 19. Schematic representation of the bio intervals APa and APb (T and E. AA). Atomic progression presented in Tables 1-19 are calculated using the relationship between corresponding groups of amino acids. These are groups with different numbers of amino acids. There are different ways and methods of selecting these groups of amino acids, which method is most efficient some We hope that science will determine which method is most efficient for this selection. Biological particularity of proteins depends on the order of amino acids in their molecules. Change of that order will lead to the change of their biological particularity. The base parameters that determine the change of status of biosynthesis matrix of macromolecules are the system entropy, volume of information transferred and the level of probability that the genetic information will be transferred as a whole.

231


System is any group of objects (elements), their relations (number of atoms, atomic number, atomic weight, co-valent radius, molar rotation, electrical negativity, etc...), as well as relations among its attributes. Such is the example of insulin, but also all other proteins. An identical scenario we have in the example of all natural sequences. Therefore, if G (10 atoms) is replaced by an amino acid with the same polarity of characteristics, but different number of atoms, the biological particularity of insulin will change, reflected in genetic changes and mutagenesis.

Insulin Model The structure 1AI0 Table 20. G AA Number of atoms

Rank

G

G

G

G

G

10

10

10

10

10

10













256

205

154

103

52

1













268 268 268 268 268 268 Rank

AA Number of atoms













12

63

114

165

216

267













S

S

S

S

S

S

14

14

14

14

14

14

(256+12) = 268; (205+63) = 268; (154+114) = 268; etc. Table 20. Schematic representation of the ranks APa and APb (G and S. AA).


Rank

L

L

L

L

L

L

22

22

22

22

22

22













13

64

115

166

217

268













286 286 286 286 286 286

232


Rank

AA Number of atoms













273

222

171

120

69

18













N

N

N

N

N

N

17

17

17

17

17

17

(273+13) = 286; (222+64) = 286; (171+115) = 286; etc. Table 21. Schematic representation of the ranks APa and APb (L and N. AA).

Insulin Model The structure 1AI0 Table 22. L AA Number of atoms

Rank

L

L

L

L

L

22

22

22

22

22

22













32

83

134

185

236

287













308 308 308 308 308 308 Rank

AA Number of atoms













276

225

174

123

72

21













N

N

N

N

N

N

17

17

17

17

17

17

(32+276) = 308; (83+225) = 308; (134+174) = 308; etc. Table 22. Schematic representation of the ranks APa and APb (L and N. AA).


Rank

G

G

G

G

G

G

10

10

10

10

10

10













296

245

194

143

92

41

233














331 331 331 331 331 331 Rank

AA Number of atoms













35

86

137

188

239

290













A

A

A

A

A

A

13

13

13

13

13

13

(296+35) = 331; (245+86) = 331; (194+137) = 331; etc. Table 23. Schematic representation of the ranks APa and APb (G and A. AA).

Insulin Model The structure 1AI0

Table 24. AA Number of atoms

Rank

C

C

C

C

C

C

14

14

14

14

14

14













20

71

122

173

224

275













294 294 294 294 294 294 Rank

AA Number of atoms













274

223

172

121

70

19













Y

Y

Y

Y

Y

Y

24 24 24 24 24 24 (20+274) = 294; (71+223) = 294; (122+172) = 294; etc. Table 24. Schematic representation of the ranks APa and APb (G and A. AA).

Insulin Model The structure 1AI0 Table 25. AA

E

E

E

E

E

E

234


Number of atoms

Rank

19

19

19

19

19

19













34

85

136

187

238

289













322 322 322 322 322 322 Rank

AA Number of atoms













288

237

186

135

84

33













V

V

V

V

V

V

19

19

19

19

19

19

(34+288) = 322; (85+237) = 322; (136+186) = 322; etc. Table 25. Schematic representation of the ranks APa and APb (E and V. AA).

Insulin Model The structure 1AI0

Table 26. AA Number of atoms

Rank

T

T

T

T

T

T

17

17

17

17

17

17













51

102

153

204

255

306













348 348 348 348 348 348 Rank

AA Number of atoms













297

246

195

144

93

42













E

E

E

E

E

E

19

19

19

19

19

19

(51+297) = 348; (102+246) = 348; (153+195) = 348; etc. Table 26. Schematic representation of the ranks APa and APb (T and E. AA). As it cam be observed, quantitative characteristics of the biochemistry of insulin apply to the position number. It can be concluded that there is a connection between quantitative

235


characteristics in the process of transfer of genetic information and the qualitative appearance of given genetic processes. 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. There are some examples.

Amino acids with atomic progression

Insulin Model The structure 1AI0, chains: A,B,C,D,E,F,G,H,I,J,K,L.

Table 27. G I V E Q C C T S I C S L Y Q L E N Y C N F V N Q H I C G S H L V E A L Y L V C G E R G F I Y T P K T G I V E Q C C T S I C S L Y Q L E N Y C N F V N Q H I C G S H L V E A L Y L V C G E R G F I Y T P K T G I V E Q C C T S I C S L Y Q L E N Y C N F V N Q H I C G S H L V E A L Y L V C G E R G F I Y T P K T G I V E Q C C T S I C S L Y Q L E N Y C N F V N Q H I C G S H L V E A L Y L V C G E R G F I Y T P K T G I V E Q C C T S I C S L Y Q L E N Y C N F V N Q H I C G S H L V E A L Y L V C G E R G F I Y T P K T G I V E Q C C T S I C S L Y Q L E N Y C N F V N Q H I C G S H L V E A L Y L V C G E R G F I Y T P K T Table 27. Schematic representation of the amino acids with atomic progression .

236


Amino acids without atomic progression Table 28. G I V E Q C C

T

S

I

C S

L

Y Q L

E

N Y C N F V N Q H I C G S H L V E A L Y L V C G E R G F I Y T P K T G I V E Q C C T S I C S L Y Q L E N Y C N F V N Q H I C G S H L V E A L Y L V C G E R G F I Y T P K T G I V E Q C C T S I C S L Y Q L E N Y C N F V N Q H I C G S H L V E A L Y L V C G E R G F I Y T P K T G I V E Q C C T S I C S L Y Q L E N Y C N F V N Q H I C G S H L V E A L Y L V C G E R G F I Y T P K T G I V E Q C C T S I C S L Y Q L E N Y C N F V N Q H I C G S H L V E A L Y L V C G E R G F I Y T P K T G I V E Q C C T S I C S L Y Q L E N Y C N F V N Q H I C G S H L V E A L Y L V C G E R G F I Y T P K T Table 28. Schematic representation of the amino acids without atomic progression

The structure 1AI0, chains: A,B,C,D,E,F,G,H,I,J,K,L. Prima sequences Table 29. 10

22

19

19

20 14 14 17 14 22 14 14 22 24 20 22 19

17 24 14 17 23 19 17 20 20 22 14 10 14 20 22 19 19 13

22

24

22

19 14 10 19 26 10 23 22

24

17

17

24

17

10

22

19

19

20 14 14 17 14 22 14 14 22 24 20 22 19

17 24 14 17 23 19 17 20 20 22 14 10 14 20 22 19 19 13

22

24

22

19 14 10 19 26 10 23 22

24

17

17

24

17

20 14 14 17 14 22 14 14 22 24 20 22 19 17 24 14 17 23 19 17 20 20 22 14 10 14 20 22 19 19 10

22

19

19

13

22

24

22

10

22

19

19

19 14 10 19 26 10 23 22

20 17 24 14 17 23 13 22 24 22 19 10 22 19 19 20

14 19 14 14

14 17 10 14

17 20 19 17

14 20 26 14

22 22 10 22

14 14 23 14

24

17

17

24

17

14 22 24 20 22 19 10 14 20 22 19 19 22 24 17 17 24 17 14 22 24 20 22 19

237


17 24 14 17 23 19 17 20 20 22 14 10 14 20 22 19 19 13 10

22 22

24 19

22 19

19 14 10 19 26 10 23 22 24 17 17 24 17 20 14 14 17 14 22 14 14 22 24 20 22 19

17 24 14 17 23 19 17 20 20 22 14 10 14 20 22 19 19 13

22

24

22

19 14 10 19 26 10 23 22

24

17

17

24

17

Table 29. Schematic representation of the amino acids - prima sequences Prima numbers 19, 19, 17,…, 17 = Prima sequences V,E,T,…T In the previous examples we translated the physical and chemical parameters from the language of biochemistry into the digital language of programmatic, cybernetic and information principles. This we did by using the adequate mathematical algorithms. By using chemical-information procedures, we calculated the numerical value for the information content of molecules. What we got this way is the digital picture of the phenomenon of biochemistry. These digital pictures reveal to us a whole new dimension of this science. They reveal to us that the biochemical process is strictly conditioned and determined by programmatic, cybernetic and information principles. From the previous examples we can see that this protein really has its quantitative characteristics. It can be concluded that there is a connection between quantitative characteristics in the process of transfer of genetic information and the qualitative appearance of given genetic processes.

DISCUSSION The results of our research show that the processes of sequencing the molecules are conditioned and arranged not only with chemical and biochemical lawfulness, but also with program, cybernetic and informational lawfulness too. At the first stage of our research we replaced nucleotides from the Amino Acid Code Matrix with numbers of the atoms and atomic numbers in those nucleotides. Translation of the biochemical language of these amino acids into a digital language may be very useful for developing new methods of predicting protein sub-cellular localization, membrane protein type, protein structure secondary prediction or any other protein attributes. Since the concept of Chou's pseudo amino acid composition was proposed [1-2], there have been many efforts to try 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 [3], some used the values derived from the cellular automata [4-7], some used hydrophobic and/or hydrophilic values [8-16], some were through Fourier transform [17-18], and some used the physicochemical distance [19]. The author [34-44] is 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 [20-22], subcellular location [23,24], membrane protein type [9,25], enzyme family class [26,27], GPCR type [28, 29], protease type [30], protein-protein interaction [31], metabolic pathways [32], protein quaternary structure [33], and other protein attributes. It is going to be possible to use a completely new strategy of research in genetics in the future. However, close observation of

238


all these relationships, which are the outcomes of periodic laws (more specifically the law of binary coding), stereo-chemical and digital structure of proteins.

Conclusions The process of sequencing in bio-macromolecules is conditioned and determined not only through biochemical, but also through cybernetic and information principles. The digital pictures of biochemistry provide us with cybernetic and information interpretation of the scientific facts. Now we have the exact scientific proofs that there is a genetic language that can be described by the theory of systems and cybernetics, and which functions in accordance with certain principles.

DISCLOSURE The author reports no conflict of interest in this research.

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