DNA and its Mosaic Structure

We consider that the DNA is an information processing system, receiving, registering and transferring information. In DNA we encounter four different nucleotides, which may be considered as the “letters” of an alphabet. Each distinct DNA base may be represented equally well by a specific number and a DNA strand by a unique Gödel number G, where G is a product of prime numbers raised to appropriate powers. We studied the statistical distribution of g, the logarithm of G, in the case of equal probability for the four DNA bases. In the present work we extend our analysis in two different directions We consider unequal probabilities for the DNA bases We raise the issue of scaling. For relatively small DNA strands we use the prime number theorem and we obtain a Poisson distribution for the average g. The Poisson distribution depends upon a parameter λ, which connects together the DNA pattern and the prime number density. Different values for λ lead to a mosaic structure of DNA. Our work indicates a strong link between DNA structure, its representation by Gödel’s numbers and the distribution of the prime numbers.