An elastic model for conformational transitions of spacer DNA in chromatin; first results

We study the elastic stability of the trajectory of DNA in the solenoid model for the 30 nm chromatin fiber, as extended by McGhee et al. [J.D. McGhee, J.M. Nickol, G. Felsenfeld and D.C. Rau, Cell 33, 831-841 (1983)] to visualize both internucleosomal (spacer) DNA and DNA bound to the core histones. Actually, we idealize this trajectory by neglecting the shallow pitch of the solenoid. The DNA trajectory is then transversely wound on a torus, like a helix on a cylinder. We then neglect the shallow pitch of the transverse winding. We find that there is a threshold length for the elastic stability of a DNA segment in the resulting trajectory, even if the DNA is not allowed to straighten away from the torus surface. For most organisms the length of spacer DNA exceeds the threshold. This result does not imply that anything is wrong with the solenoid model, wherein two nucleosomal turns of DNA are stabilized by interaction with core and linker histones. The result does suggest, however, that if internucleosomal DNA follows a path similar to nucleosomal DNA, then this path would also have to be stabilized, possibly by interaction with linker histone. A second result of the analysis is that the extent of instability depends significantly on the location of the starting point of the DNA. If the DNA starts on the outside of the torus, it is less unstable than if it starts on the inside. In the extended solenoid model, some turns of internucleosomal DNA are on the outside of the solenoid, some on the inside. This result thus suggests the possibility that localized structural disruptions are more likely for some nucleosome neighboring pairs than others. Of intrinsic theoretical interest is the reduction of the problem through a series of approximations to the solution of Mathieu's equation.