Origins of helicity in a simple polymer model
Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, Genova, Italy, (9-13 July 2007)Abstract
Recently, several authors have shown that simple, isotropic and achiral polymer models can adopt thermodynamically stable helical configurations. Since Pauling's classic work on the $\alpha$-helix in polypeptides, descriptions of how helices form in nature have focused on strongly directional interactions and innate chirality. These recent models indicate that helix formation is more fundamental than such descriptions allow.
We have previously presented a model of overlapping spherical monomers which can form two separate helical phases in Monte Carlo simulations (Phys. Rev. Lett. 96, 207802 (2006)). In this work, we use analytic and numerical methods to evaluate the partition functions for such 4- and 5-monomer length model polymers. By considering the coupling between the torsional angles $\phi$ around bonds, and using physical insight from the calculation of the partition functions, we seek an explanation for how this model can show helical structure at all, the shape of the observed phase diagram, and whether the observed behaviours can be considered to be general, or artefacts of the particular model.