Ising model description of long range correlations in DNA sequences

Abstract

We model long range correlations of nucleotides in the human DNA sequence using the long range one dimensional Ising model. We show that for distances between $10^3$ and $10^6$ bp the correlations show an universal behaviour and may be described by the non-mean field limit of the long range 1d Ising model. This allows us to make some testable hypothesis on the nature of the interaction between distant portions of the DNA chain which led to the DNA structure that we observe today in higher eukaryotes.