Arithmetic inside the universal genetic code

**Vladimir I. shCherbak**

Department of Applied Mathematics, al-Faraby Kazakh National University, 71 al-Faraby Avenue, Almaty 480078, Kazakhstan, CIS

Received 28 October 2001;  revised 23 April 2002;  accepted 10 December 2002.  Available online 28 June 2003

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 𠇏rozen 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.

**Author Keywords: **Genetic code; Genetic
language; Arithmetic power; Natural biocomputer; Mathematical
model

Biosystems:
Volume 70, Issue 3, August 2003, Pages 187-209 |