Lutvo Kuriæ

Independent Researcher, Bosnia and Herzegovina, 72290 Novi Travnik, Kalinska 7

Citation: Lutvo Kuriæ (2009) The Atomic Genetic Code. J Comput Sci Syst Biol 2: 101-116.

Copyright:© 2009 Lutvo Kuriæ. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

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

Number of atoms in triplets UCAG

.(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.

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

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
2328
442 642 602 642 642 602 522 562 602 522 682 522 642 562 522 602
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
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.

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
3168
728 856 776 808 856 728 776 808 776 776 888 728 808 808 728 824
3168
728 856 776 808 856 728 776 808 776 776 888 728 808 808 728 824
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.

Analogue Codon Table

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
3168
944 640 632 952 640 944 632 952 632 632 960 944 952 952 944 320
3168
944 640 632 952 640 944 632 952 632 632 960 944 952 952 944 320
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
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 Codon3
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.

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

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
12048
2292 3732 3572 2452 3732 2292 3572 2452 3972 3972 2212 1892 2052 2052 2692 5252
12048
2292 3732 3572 2452 3732 2292 3572 2452 3972 3972 2212 1892 2052 2052 2692 5252
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
74615095296000
(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

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.

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.

Future Steps Required

1. Establish scientific-research project team for development of advanced technologies in genetics, medicine and biochemistry.
2. 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. 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.).
   

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.

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.

Conclusion
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.

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