Folding of polymer chains with short-range binormal interactions

We study the structure of chains which have anisotropic short-range contact interactions that depend on the alignment of the binormal vectors of chain segments. This represents a crude model of hydrogen bonding or 'stacking' interactions out of the plane of curvature. The polymers are treated as ribbon-like semi-flexible chains, where the plane of the ribbon is determined by the local binormal. We show that with dipole-dipole interactions between the binormals of contacting chain segments, mean-field theory predicts a first-order transition to a binormally aligned state. We describe the onset of this transition as a function of the temperature-dependent parameters that govern the chain stiffness and the strength of the binormal interaction, as well as the binormal alignment's coupling to chain collapse. We also examine a metastable state governing the folding kinetics. Finally, we discuss the possible mesoscopic structure of the aligned phase, and application of our model to secondary structure motifs like beta-sheets and alpha-helices, as well as composite structures like beta-(amyloid) fibrils.