Monte Carlo calculations on polypeptide chains. IX. A study of the effect of long-range interactions on the helix-coil transition.

A Monte Carlo statistical mechanical study of the helix-coil transition for a hard-sphere model of poly(L-alanine) has been conducted base on the theory of Lifson and Roig but including the effects of long-range interactions. A stochastic model of the kinetics of the helix-coil transition is presented, and a Monte Carlo stimulation of the kinetics based on this model was used to generate equilibrium chain samples, each chain of which consisted of Lifson-Roig weighted sequences of helix and coil residues. Each of the chains in this sample was then used many times by assigning at random specific sterically allowed coil states from a hard-sphere Ramachandran dipeptide map. Unperturbed properties were then calculated using this sample and perturbed properties by using only the non-self-conflicting subset. The properties calculated were the average degree of hydrogen bonding, the average length of a helical sequence, the mean-square end-to-end distance, the mean-square radius of gyration, and the distribution functions for the end-to-end distance and radius of gyration. This study was conducted at chain lengths 10, 34, and 85 residues. Helix-coil transition theory was fit to the perturbed transition curves in an attempt to ascertain if theory could then predict the perturbed values of the dimensions. For the hard-sphere model used in these calculations, it was found that current helix-coil transition theory does not predict the correct perturbed dimensions.