It is generally accepted that DNA contains the information or codes that are necessary to build life. But why are there mathematical patterns in DNA and why is DNA fine-tuned by the Golden Ratio – is this necessary for the creation of life?

**Jean-Claude Perez**

Frequencies of the 64 codons in the whole human genome scale are a self-similar fractal expansion of the universal genetic code. The original genetic code kernel governs not only the micro scale but the macro scale as well. Particularly, the 6 folding steps of codon populations modeled by the binary divisions of the “Dragon fractal paper folding curve” show evidence of 2 attractors. The numerical relationship between the attractors is derived from the Golden Ratio.

**Vladimir F. Shcherbak**

http://www.freewebs.com/genetics37/shcherbakPages.htm

Shcherbak’s patterns are based on the number of nucleons in each amino acid. The number of nucleons = number of protons + number of neutrons. Each amino acid consists of a radical and a base. The base is the same in all amino acids, and consists of 74 nucleons, whilst the number of nucleons in the radical varies.The table shows the number of nucleons in the radical as R =.. and the number of nucleons in the base as B = ..

Shcherbak noted that in 8 of the 16 cells shown above, all four codons code for only one amino acid. These cells are shown in yellow above. Taking a single molecule of each of the amino acids found in these cells, Shcherbak counted the number of nucleons in the amino acids and found the following

Arithmetic inside the universal genetic code

The first information system emerged on the earth as primordial version of the genetic code and genetic texts. The natural appearance of arithmetic power in such a linguistic milieu is theoretically possible and practicalto producing information systems of extremely high efficiency. In this case, the arithmetic symbols should be incorporated into an alphabet, i.e. the genetic code. A number is the fundamental arithmetic symbol produced by the system of numeration. If the system of numeration were detected inside the genetic code, it would be natural to expect that its purpose is arithmetic calculation e.g., for the sake of control, safety, and precise alteration of the genetic texts.

**Miloje M. Rakočević**

Genetic code as a harmonic system

In a certain way, this paper presents the continuation of the previous one which discussed the harmonic structure of the genetic code (Rakočević, 2004). Several new harmonic structures presented in this paper, through specific unity and coherence, together with the previously presented(Rakočević, 2004), show that it makes sense to understand genetic code as a set of several different harmonic structures.

**Tidjani Négadi**

In this short paper, which follows a recent one [1], we propose a numerical connection between the beautiful arithmetical approach to the genetic code by Shcherbak, [2], based on the use of the nucleon numbers-as-digital-signs, and involving a distinguished (prime) number, Shcherbak’s

Prime Quantum 37, which appears to occupy a central role in his work, and the recent theory by Yang, [3], a topological approach, to classify the amino acids and based on a particular polyhedron, the quasi-28-gon or ikosicaioctagon.

In the case of the genetic code 64 codons system, we re–derive the chain of groups and show that the last member of the chain, C2, leaves 16 codons of type GNN invariant and this invariance is maintained across all species with respect to their “non–standard” use of the genetic code, including nuclear genomes as well as mitochondrial genomes. Moreover, we show that this symmetry is suited, in fact it fits, the “bisections” of the set of 64 codons, used by Shcherbak to derive many striking arithmetical regularities and balances, involving the nucleon numbers in the amino acids.

**Chi Ming Yang**

The naturally designed spherical symmetry in the genetic code

**Victor A. Gusev**

**Zvonimir M. Damjanović and Miloje M. Rakočević**

GENETIC CODE: A NEW UNDERSTANDING OF CODON

**Sergei V. Petoukhov **