# Allosteric interactions in a birod model of DNA

## TL;DR

This paper develops a birod model of DNA to quantitatively analyze allosteric interactions, showing that the interaction energy decays exponentially with distance and oscillates with the DNA's helical periodicity, aligning with experimental observations.

## Contribution

The study introduces a birod elasticity model to explain allosteric interactions in DNA, linking mechanical properties to interaction decay length and sequence composition.

## Key findings

- Interaction energy decays exponentially with distance
- Energy oscillates with DNA's helical periodicity
- Decay length depends on DNA's mechanical properties

## Abstract

Allosteric interactions between molecules bound to DNA at distant locations have been known for a long time. The phenomenon has been studied via experiments and numerical simulations, but a comprehensive understanding grounded in a theory of DNA elasticity remains a challenge. Here we quantify allosteric interactions between two entities bound to DNA by using the theory of birods. We recognize that molecules bound to DNA cause local deformations that can be captured in a birod model which consists of two elastic strands interacting via an elastic web representing the base-pairs. We show that the displacement field caused by bound entities decays exponentially with distance from the binding site. We compute the interaction energy between two proteins on DNA as a function of distance between them and find that it decays exponentially while oscillating with the periodicity of the double-helix, in excellent agreement with experiments. The decay length of the interaction energy can be determined in terms of the mechanical properties of the strands and the webbing in our birod model, and it varies with the GC content of the DNA. Our model provides a framework for viewing allosteric interactions in DNA within the ambit of configurational forces of continuum elasticity.