Helix-Coil, Liquid Crystal, and Spin Glass Transitions of a Collapsed Heteropolymer

Abstract

Using simple statistical mechanical models, we investigate secondary structure formation in the molten globule state of a helix-forming heteropolymer. The theory based on the helix-coil model of Bragg and Zimm correctly treats the one-dimensional aspect of the helix-coil transition but has been modified to include the randomness effects of the tertiary interactions in a heteropolymer. Rough approximations to the effects of confinement, excluded volume, and packing order of the helices are used to give the resulting generalization of the random energy model. In this model the packing effects give rise to a liquid crystalline order in the molten globule state. For reasonable values of parameters at the spin glass transition, we estimate that the heteropolymer is about 80% helical with helix lengths of order 20. Analysis of this simple model allows an estimate of the effective Levinthal entropy and determines that about 10^(11) configurations would have to be searched at the glass transition for a 100-mer.