A length-dynamic Tonks gas theory of histone isotherms

TL;DR

This paper develops an exact 1D particle theory modeling DNA wrapping around histones, revealing complex adsorption behaviors, density fluctuations, and correlation functions relevant to chromatin structure.

Contribution

It introduces a length-dynamic Tonks gas model for histone-DNA interactions, providing exact solutions and insights into adsorption and correlation phenomena.

Findings

Histone density shows a two-stage adsorption process.

Mean histone coverage peaks at certain chemical potentials.

Coverage fluctuations are maximized at specific conditions.

Abstract

We find exact solutions to a new one-dimensional (1D) interacting particle theory and apply the results to the adsorption and wrapping of polymers (such as DNA) around protein particles (such as histones). Each adsorbed protein is represented by a Tonks gas particle. The length of each particle is a degree of freedom that represents the degree of DNA wrapping around each histone. Thermodynamic quantities are computed as functions of wrapping energy, adsorbed histone density, and bulk histone concentration (or chemical potential); their experimental signatures are also discussed. Histone density is found to undergo a two-stage adsorption process as a function of chemical potential, while the mean coverage by high affinity proteins exhibits a maximum as a function of the chemical potential. However, {\it fluctuations} in the coverage are concurrently maximal. Histone-histone correlation functions are also computed and exhibit rich two length scale behavior.