Density of states for a short overlapping-bead polymer: Clues to a mechanism for helix formation?

The densities of states are evaluated for very short chain molecules made up of overlapping monomers, using a model which has previously been shown to produce helical structure. The results of numerical calculations are presented for tetramers and pentamers. We show that these models demonstrate behaviors relevant to the behaviors seen in longer, helix-forming chains, particularly "magic numbers" of the overlap parameter, where the derivatives of the densities of states change discontinuously, and a region of bimodal energy probability distributions, reminiscent of a first-order phase transition in a bulk system.