The Digital Genetic Codes

The Digital Genetic Codes

Lutvo Kurić

Independent Researcher

Bosnia and Herzegovina

72290 Novi Travnik

Kalinska 7

Tel. 061 763 917

lutvokuric@yahoo.com

*abstract

Motivation: Many important problems in cell biology require the dense nonlinear interactions between functional modules to be considered. The importance of computer simulation in understanding cellular processes is now widely accepted, and a variety of simulations algorithms useful for studying certain subsystems have been designed. Genetic algorithms try to model digital evolution by genetic processes. The digital 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 numbers of atoms, atomic numbers, analog code, etc.

1.introduction

At mathematical evolution of genetic processes, nucleotides at are being transformed to codons UCAG and later to amino acids and various organic composition. That transformacion has it's mathematical language which contains mathematical description of all genetic processes. This is how the way of transformation of nucleotides ATCG to codons UCAG is writen in that mathematical language.In this text we will give experimental proof that the mathematical evolution of sequence in genetics does exist. We will prove that the process of sequencing of molecules in genetics is conditioned and determined not only by biochemical, but by programme, cybernetic, and informational laws.

2.metods

Digital image of the ATCG

First we made a digital image of the ATCG nucleotide and discovered that there are 59 atoms:

A = 15 atoms; T = 15 atoms; C = 13 atoms; G = 16 atoms;

ATCG = (15 + 15 + 13 + 16) = 59;

Digital image of the AUCG

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

UCAG = (15 + 15 + 13 + 16) = 56;

The Standard Code (transl_table=1)

By default all transl_table in GenBank flatfiles are equal to id 1, and this is not shown. When transl_table is not equal to id 1, it is shown as a qualifier on the CDS feature.

    AAs  = FFLLSSSSYY**CC*WLLLLPPPPHHQQRRRRIIIMTTTTNNKKSSRRVVVVAAAADDEEGGGG

  Starts = ---M---------------M---------------M----------------------------

  Base1  = TTTTTTTTTTTTTTTTCCCCCCCCCCCCCCCCAAAAAAAAAAAAAAAAGGGGGGGGGGGGGGGG

  Base2  = TTTTCCCCAAAAGGGGTTTTCCCCAAAAGGGGTTTTCCCCAAAAGGGGTTTTCCCCAAAAGGGG

  Base3  = TCAGTCAGTCAGTCAGTCAGTCAGTCAGTCAGTCAGTCAGTCAGTCAGTCAGTCAGTCAGTCAG

The Digital Standard Code (transl_table=1)

By default all transl_table in GenBank flatfiles are equal to id 1, and this is not shown. When transl_table is not equal to id 1, it is shown as a qualifier on the CDS feature.

    AAs  = FFLLSSSSYY**CC*WLLLLPPPPHHQQRRRRIIIMTTTTNNKKSSRRVVVVAAAADDEEGGGG

ê

23,23,22,22,14,14,14,14,24,24,××14,14,×27,22,22,22,22,17,17,17,1720,20,20,20,26,26,26,26,22,22,22,20,22,17,17,17,17,17,24,24,14,14,26,26,19,1919,19,13,13,13,13,16,16,19,19,10,10,10,10 = 1148 atoms;

AmAt = 1148;

Nucleotides UCAG

Base 1 =

UUUUUUUUUUUUUUUUCCCCCCCCCCCCCCCCAAAAAAAAAAAAAAAAGGGGGGGGGGGGGGGG

ê

12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,13,13,13,13,13,1313,13,13,13,13,13,13,13,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,1516,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16 = 896 atoms;

AT1 =896;

Base 2

UUUUCCCCAAAAGGGGUUUUCCCCAAAAGGGGUUUUCCCCAAAAGGGGUUUUCCCCAAAAGGGG

ê

12,12,12,12,13,13,13,13,15,15,15,15,15,16,16,16,16,12,12,12,12,13,13,13   13,15,15,15,15,16,16,16,16,12,12,12,12,13,13,13,13,15,15,15,15,16,16,1616,12,12,12,12,13,13,13,13,15,15,15,15,16,16,16,16 = 896 atoms;

AT2 =896;

Base 3

UCAGUCAGUCAGUCAGUCAGUCAGUCAGUCAGUCAGUCAGUCAGUCAGUCAGUCAGUCAGUCAG

  ê

12,13,15,16,12,13,15,16,12,13,15,16,12,13,15,16,12,13,15,16,12,13,15,16,12,13,15,16,12,13,15,16,12,13,15,16,12,13,15,16,12,13,15,16,12,13,15,16,12,13,15,16,12,13,15,16,12,13,15,16,12,13,15,16 = 896 atoms;

AT3 =896;

First we made a digital image of the ATCG nucleotide and discovered that there are 59 atoms:

A = 15 atoms; T = 15 atoms; C = 13 atoms; G = 16 atoms;

(15+15+13+16) = 59;

3.results

Nucleotides UCAG

Base 1	Base 2	Base 3
ê	ê	ê
896 atoms	896 atoms	896 atoms
î	ê	í
	2688 atoms

AT = (896+896+896) = 2 688;

AT = The number of atoms in digital image AUCG.

Nucleotides ATCG

Base1  = TTTTTTTTTTTTTTTTCCCCCCCCCCCCCCCCAAAAAAAAAAAAAAAAGGGGGGGGGGGGGGGG

ê

15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,13,13,13,13,13,13,13,1313,13,13,13,13,13,13,13,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,1516,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16, = 944 atoms;

At1 =944;

Base2  = TTTTCCCCAAAAGGGGTTTTCCCCAAAAGGGGTTTTCCCCAAAAGGGGTTTTCCCCAAAAGGGG

ê

15,15,15,15,13,13,13,13,15,15,15,15,16,16,16,16,15,15,15,15,13,13,13,1315,15,15,15,16,16,16,16,15,15,15,15,13,13,13,13,15,15,15,15,16,16,16,1615,15,15,15,13,13,13,13,15,15,15,15,16,16,16,16 = 944 atoms;

At2 =944;

Base3  = TCAGTCAGTCAGTCAGTCAGTCAGTCAGTCAGTCAGTCAGTCAGTCAGTCAGTCAGTCAGTCAG

ê

15,13,15,16,15,13,15,16,15,13,15,16,15,13,15,16,15,13,15,16,15,13,15,16,15,13,15,16,1513,15,16,15,13,15,16,15,13,15,16,15,13,15,16,15,13,15,16,15,13,15,16,15,13,15,16,15,1315,16,15,13,15,16 = 944 atoms;

At3 =944;

Base 1	Base 2	Base 3
ê	ê	ê
944 atoms	944 atoms	944 atoms
î	ê	í
	2832 atoms

At = (944+944+944) = 2832;

At = The number of atoms in digital image ATCG.

We have discovered the mathematical balance in distribution of atoms in Digital Format for Aligned nucleotides is achieved.

3.1.Data Structure This is Heading 2 style

Groups of nucleotides ATCG and UCAG have evolved to amino acids on following way:

(At1,2,3,n : ATCG) = (AT1,2,3,n : UCAG)

(AT1,2,3,n x UCAG) = (ATCG x AT1,2,3,n)

Example 1

At1 = 944; UCAG = 56; ATCG = 59; AT1 = 896;

At1 : ATCG = AT1 : UCAG

(At1 x UCAG) = (ATCG x AT1)

(944 x 56) = (59 x 896);

52864 = 52864;

Example 2

Base 1 - ATCG (5-53)

TTTTTTTTTTTTCCCCCCCCCCCCCCCCAAAAAAAAAAAAAAAAGGGGG

ê

15,15,15,15,15,15,15,15,15,15,15,15,13,13,13,13,13,13,13,13,13,13,13,1313,13,13,13,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,16,16,16, 16,16 = 708 atoms;

Atn =708;

Base 1 – UCAG (5-53)

UUUUUUUUUUUUCCCCCCCCCCCCCCCCAAAAAAAAAAAAAAAAGGGGG

ê

12,12,12,12,12,12,12,12,12,12,12,12,13,13,13,13,13,13,13,13,13,13,13,1313,13,13,13,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,16,16,16,1616= 672 atoms;

ATn = 672;

Atn = 708; UCAG = 56; ATCG = 59; ATn = 896;

Atn : ATCG = ATn : UCAG

(Atn x UCAG) = (ATCG x AT1)

(708 x 56) = (59 x 672);

39 648 = 39 648;

Example 3

Base 2 (1-16)

T	T	T	T	C	C	C	C	A	A	A	A	G	G	G	G
15	15	15	15	13	13	13	13	15	15	15	15	16	16	16	16
U	U	U	U	C	C	C	C	A	A	A	A	G	G	G	G
12	12	12	12	13	13	13	13	15	15	15	15	16	16	16	16

Atn = 236; ATn = 224; UCAG = 56; ATCG = 59;

(Atn x UCAG) = (ATCG x ATn)

(236x56) = (59x224);

Example 4

Base 2 (1-32)

T	T	T	T	C	C	C	C	A	A	A	A	G	G	G	G
15	15	15	15	13	13	13	13	15	15	15	15	16	16	16	16
U	U	U	U	C	C	C	C	A	A	A	A	G	G	G	G
12	12	12	12	13	13	13	13	15	15	15	15	16	16	16	16

T	T	T	T	C	C	C	C	A	A	A	A	G	G	G	G
15	15	15	15	13	13	13	13	15	15	15	15	16	16	16	16
U	U	U	U	C	C	C	C	A	A	A	A	G	G	G	G
12	12	12	12	13	13	13	13	15	15	15	15	16	16	16	16

Atn = 472; ATn = 448; UCAG = 56; ATCG = 59;

(Atn x UCAG) = (ATCG x ATn)

(472x56) = (59x448);

Example 5

Base 2 (1-48)

T	T	T	T	C	C	C	C	A	A	A	A	G	G	G	G
15	15	15	15	13	13	13	13	15	15	15	15	16	16	16	16
U	U	U	U	C	C	C	C	A	A	A	A	G	G	G	G
12	12	12	12	13	13	13	13	15	15	15	15	16	16	16	16

T	T	T	T	C	C	C	C	A	A	A	A	G	G	G	G
15	15	15	15	13	13	13	13	15	15	15	15	16	16	16	16
U	U	U	U	C	C	C	C	A	A	A	A	G	G	G	G
12	12	12	12	13	13	13	13	15	15	15	15	16	16	16	16

T	T	T	T	C	C	C	C	A	A	A	A	G	G	G	G
15	15	15	15	13	13	13	13	15	15	15	15	16	16	16	16
U	U	U	U	C	C	C	C	A	A	A	A	G	G	G	G
12	12	12	12	13	13	13	13	15	15	15	15	16	16	16	16

Atn = 708; ATn = 672; UCAG = 56; ATCG = 59;

(Atn x UCAG) = (ATCG x ATn)

(708x56) = (59x672);

Example 6

Base 2 (3-18)

T	T	C	C	C	C	A	A	A	A	G	G	G	G	T	T
15	15	13	13	13	13	15	15	15	15	16	16	16	16	15	15
U	U	C	C	C	C	A	A	A	A	G	G	G	G	U	U
12	12	13	13	13	13	15	15	15	15	16	16	16	16	12	12

Atn = 236; ATn = 224; UCAG = 56; ATCG = 59;

(Atn x UCAG) = (ATCG x ATn)

(236 x 56) = (59 x 224);

39 648 = 39 648;

Example 7

Base 3 (1-4)

T	C	A	G
15	13	15	16
U	C	A	G
12	13	15	16

Atn = 59; ATn = 56; UCAG = 56; ATCG = 59;

(Atn x UCAG) = (ATCG x ATn)

(59x56) = (59x56);

Example 8

Base 3 (1-8)

T	C	A	G	T	C	A	G
15	13	15	16	15	13	15	16
U	C	A	G	U	C	A	G
12	13	15	16	12	13	15	16

Atn = 118; ATn = 112; UCAG = 56; ATCG = 59;

(Atn x UCAG) = (ATCG x ATn)

(118x56) = (59x112);

Example 9

Base 3 (1-12)

T	T	T	T	T	T	T	T	T	T	T	T
15	13	15	16	15	13	15	16	15	13	15	16
U	C	A	G	U	C	A	G	U	C	A	G
12	13	15	16	12	13	15	16	12	13	15	16

Atn = 177; ATn = 168; UCAG = 56; ATCG = 59;

(Atn x UCAG) = (ATCG x ATn)

(177x56) = (59x168);

etc.

In these formulas are determined macro proportions of mathematical evolution of nucleotides in genetic processes.

acknowledgements

Results of our research show that the processes of sequencing in genetic conditioned and arranged not only with chemical and biochemical, but also with program, cybernetic and informational lawfulness too. This discovery, according to our opinion, will have great impact on the future development of genetics, medicine, biology and biochemistry. Now, it is going to be possible to use completely new strategy of research in these sciences. However, observation of all these relation 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.

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*To whom correspondence should be addressed.