HELIX-COIL, LIQUID-CRYSTAL, AND SPIN-GLASS TRANSITIONS OF A COLLAPSEDHETEROPOLYMER

Using simple statistical mechanical models, we investigate secondary s tructure formation in the molten globule state of a helix-forming hete ropolymer. The theory based on the helix-coil model of Bragg and Zimm correctly treats the one-dimensional aspect of the helix-coil transiti on but has been modified to include the randomness effects of the tert iary interactions in a heteropolymer. Rough approximations to the effe cts of confinement, excluded volume, and packing order of the helices are used to give the resulting generalization of the random energy mod el. In this model the packing effects give rise to a liquid crystallin e order in the molten globule state. For reasonable values of paramete rs at the spin glass transition, we estimate that the heteropolymer is about 80% helical with helix lengths of order 20. Analysis of this si mple model allows an estimate of the effective Levinthal entropy and d etermines that about 10(11) configurations would have to be searched a t the glass transition for a 100-mer.