Statistical mechanics of the extensible and shearable elastic rod and of DNA

Abstract

We have developed a new statistical mechanical theory for wormlike chains and elastic rods which will account for deformations of bending, twisting, shear, and axial extension/stretching. We have derived a Fokker–Planck equation for Green’s function. We have also obtained an exact expression for the mean square end-to-end distance. Our new theoretical model is the most general statistical mechanical model for wormlike chain polymers available to date. The Kratky–Porod wormlike chain and the Yamakawa–Fujii helical wormlike chain models are found to be special cases of this new model. This new theory may provide deeper understanding of recent experimental data regarding overstretching single DNA molecules.