A general rule for ranged series of codon frequencies in different genomes

Information science widely uses descriptions of the distribution of information units (words) according to the frequency of occurrence with the help of a corresponding ranged series, i.e., the sequence of occurrence frequencies p1, p2, ..., pr as taken in decreasing order. A model called the Zipf rule or Zipflaw is the most commonly used. In this model pr is inversly proportional to a certain degree of range r: pr = C/r2 (C, z greater than 0). Upon analysis, the correspondence of codon distribution and the Zipf model is found unsatisfactory. The distribution of letters (in English and some other languages) by the occurrence frequency does not obey the Zipf rule either. A new model is proposed for a similar distribution in which pr = C.(ln(n + 1)-ln r), where n is the quantity of various symbols (codons). This dependence is approximated by a straight line not in the co-ordinate system (ln r, ln p), like the Zipf model, but in the (ln r, p) system of co-ordinates. It is shown on the basis of statistical criteria that this model is in good agreement with the ranged series of codon frequencies for the best-studied genoms to date. This result may be regarded as an additional reason in favor of the codon-letter analogy (not the codon-word analogy) in genetic texts.