An exact theory of histone-DNA adsorption and wrapping

We find exact solutions to a 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, fluctuations in the coverage are concurrently maximal. Histone-histone correlation functions are also computed and exhibit rich two - length- scale behavior.