Ising model description of long range correlations in DNA sequences

TL;DR

This paper models long-range correlations in human DNA sequences using the one-dimensional Ising model, revealing universal behavior at large distances and suggesting hypotheses about DNA structural interactions.

Contribution

It introduces an Ising model framework to describe DNA correlations, providing new insights into the interactions shaping DNA structure in higher eukaryotes.

Findings

Correlations follow a universal pattern between 10^3 and 10^6 base pairs.

The non-mean field limit of the Ising model describes DNA correlations.

Hypotheses on the interaction mechanisms in DNA structure are proposed.

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.