Potential function describing the folding of the 30 nm fiber

Most of the DNA in a eucaryotic cell nucleus is accurately described as an extremely long thin fiber which is smoothly folded by histones into a thicker fiber called the 30 nm fiber. For the DNA to remain biologically functional, the 30 nm fiber must be only marginally stable. Therefore, we assume that the 30 nm fiber has fluidlike properties under physiologic conditions. It does not possess a single well-defined structure, but rather at any given instant it will possess a structure that lies within specified limits in an energy landscape. We predict an energy landscape for the 30 nm fiber by modeling the fiber as an elastic rod (DNA) subjected to an external potential (histones). For this purpose, closed-form helix-on-a-linear-helix solutions for the equilibrium configuration of an elastic rod are parametrized to fit the dimensions of the so-called solenoid model of the 30 nm fiber. We introduce a method of including a Lennard-Jones type potential function into the elastic rod model that represents histone-DNA interactions, and we parametrize the potential according to known thermodynamic data. The resulting energy landscape for the 30 nm fiber allows for structural irregularities under physiologic conditions and for unfolding of the fiber when the DNA is sufficiently over- or underwound. Our model predicts that forcing a change in the amount of twist in DNA of -6.5% or +4.5% from an intrinsic twist of 10.5 base pairs per turn is sufficient to unfold the 30 nm fiber. These results describe a self-activating mechanism which enables RNA polymerase to unfold chromatin during transcription. According to our model, formation of the open complex itself is sufficient to unfold over 200 base pairs of DNA.