Noise immunity of the genetic code

Summary

A model is suggested explaining uneven frequencies distribution of code series and the strong correlation between the degree of degeneracy of codon series and usage frequencies of codons of these series in the primary structure of cistrons (genetic text).

The replication of a cistron sequence with its subsequent transcription and translation in offspring is considered as a process of information transmission through a noisy communicating channel. If P _i is series frequency in the genetic text, N is the number of codons in the text, and is the conditional probability that a codon of an i series mutates without lethal effect (if it does mutate at all), then is the probability that the transmission of a text of length N is not accompanied by a lethal mutation.

The average quantity of information received by offsprings of a population of haploid organisms ( ȳ ) is a function of the N . Frequencies P _i , which provide maximum ȳ at a given length of the text. are correlated with the degree of codon series degeneracy. If mutation constant is μ ≃ 10 ^–8 per position per genome per generation, minimum deviations of these frequencies from the actual frequencies is attained at N ≃ 10 ⁷ codons.

The results obtained may be interpreted as follows. If genomes are short ( N ≪ 10 ⁷ codons), mutation losses are negligibly small ( G > 0,9) and have slight evolutionary consequences. If genomes are sufficiently large ( N ≃ 10 ⁷ ), mutation losses become appreciable ( G ≃ 0,5), and the redistribution of the occurrence frequencies of codon series considerably increases noise immunity of the text. When N ≫ 10 ⁷ , no redistribution will protect haploid organisms from large mutation losses ( G < 0.1).

Thus, a natural limit of genome size N ≃ 10 ⁷ – 10 ⁸ nucleotide pairs, which is determined by mutation losses, has been set for haploid organisms.