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 practical for 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. The nucleons of amino acids and the bases of nucleic acids seem most suitable for embodiments of digits. These assumptions were used for the analyzing the genetic code. The compressed, life-size, and split representation of the Escherichia coli and Euplotes octocarinatus code versions were considered simultaneously. An exact equilibration of the nucleon sums of the amino acid standard blocks and/or side chains was found repeatedly within specified sets of the genetic code. Moreover, the digital notations of the balanced sums acquired, in decimal representation, the unique form 111, 222...., 999. This form is a consequence of the criterion of divisibility by 037. The criterion could simplify some computing mechanism of a cell if any and facilitate its computational procedure. The cooperative symmetry of the genetic code demonstrates that possibly a zero was invented and used by this mechanism. Such organization of the genetic code could be explained by activities of some hypothetical molecular organelles working as natural biocomputers of digital genetic texts. It is well known that if mutation replaces an amino acid, the change of hydrophobicity is generally weak, while that of size is strong. The antisymmetrical correlation between the amino acid size and the degeneracy number is known as well. It is shown that these and some other familiar properties may be a physicochemical effect of arithmetic inside the genetic code. The "frozen accident" model, giving unlimited freedom to the mapping function, could optimally support the appearance of both arithmetic symbols and physicochemical protection inside the genetic code.