  The thermodynamic properties for three different types of off-lattice
four-strand beta-sheet protein models interacting via a hybrid Go-type
potential have been investigated. Discontinuous molecular dynamic simulations
have been performed for different sizes of the bias gap g, an artificial
measure of a model protein's preference for its native state. The thermodynamic
transition temperatures are obtained by calculating the squared radius of
gyration, the root-mean-squared pair separation fluctuation, the specific heat,
the internal energy of the system, and the Lindemann disorder parameter. In
spite of the simplicity, the protein-like heteropolymers have shown a complex
set of protein transitions as observed in experimental studies. Starting from
high temperature, these transitions include a collapse transition, a
disordered-to-ordered globule transition, a folding transition, and a
liquid-to-solid transition. These transitions strongly depend on the
native-state geometry of the model proteins and the size of the bias gap. A
strong transition from the disordered globule state to the ordered globule
state with large energy change and a weak transition from the ordered globule
state to the native state with small energy change were observed for the large
gap models. For the small gap models no native structures were observed at any
temperature, all three beta-sheet proteins fold into a partially-ordered
globule state which is geometrically different from the native state. For small
bias gaps at even lower temperatures, all protein motions are frozen indicating
an inactive solid-like phase.
