Universal dynamical function behind all genetic codes: P-adic attractor dynamical model

Abstract

The genetic code is a map which gives the correspondence between codons in DNA and amino acids. In the attractor dynamical model (ADM), genetic codes can be described as the sets of the cyclic attractors of discrete dynamical systems - the iterations of functions acting in the ring of 2-adic integers $Z_2.$ This ring arises from representation of nucleotides by binary vectors and hence codons by triples of binary vectors. We construct a Universal Function $B$ such that the dynamical functions for all known genetic codes can be obtained from $B$ by simple transformations on the set of codon cycles - the “Addition” and “Division” operations. ADM can be employed for study of phylogenetic dynamics of genetic codes. One can speculate that the “common ancestor genetic code” was caused by $B.$ We remark that this function has 24 cyclic attractors which distribution coincides with the distribution for the hypothetical pre-LUCA code. This coupling of the Universal Function with the pre-LUCA code assigns the genetic codes evolution perspective to ADM. All genetic codes are generated from $B$ through the special chains of the “Addition” and “Division” operations. The challenging problem is to assign the biological meaning to these mathematical operations.