DYNAMIC MONTE-CARLO SIMULATIONS OF GLOBULAR PROTEIN FOLDING UNFOLDING PATHWAYS .1. 6-MEMBER, GREEK KEY BETA-BARREL PROTEINS

In the context of a simplified diamond lattice model of a six-member, Greek key β-barrel protein that is closely related in topology to plastocyanin, the nature of the folding and unfolding pathways have been investigated using dynamic Monte Carlo techniques. The mechanism of Greek key assembly is best described as punctuated "on site construction". Folding typically starts at or near a β-turn, and then the β-strands sequentially form by using existing folded structure as a scaffold onto which subsequent tertiary structure assembles. On average, β-strands tend to zip up from one tight bend to the next. After the four-member, β-barrel assembles, there is a long pause as the random coil portion of the chain containing the long loop thrashes about trying to find the native state. Thus, there is an entropic barrier that must be surmounted. However, while a given piece of the protein may be folding, another section may be unfolding. A competition therefore exists to assemble a fairly stable intermediate before it dissolves. Folding may initiate at any of the tight turns, but the turn closer to the N terminus seems to be preferred due to well-known excluded volume effects. When the protein first starts to fold, there are a multiplicity of folding pathways, but the number of options is reduced as the system gets closer to the native state. In the early stages, the excluded volume effect exerted by the already assembled protein helps subsequent assembly. Then, near the native conformation, the folded parts reduce the accessible conformational space available to the remaining unfolded sections. Unfolding essentially occurs in reverse. Employing a simple statistical mechanical theory, the configurational free energy along the reaction co-ordinate for this model has been constructed. The free energy surface, in agreement with the simulations, provides the following predictions. The transition state is quite near the native state, and consists of five of the six β-strands being fully assembled, with the remaining long loop plus sixth β-strand in place, but only partially assembled. It is separated from the β-barrel intermediate by a free energy barrier of mainly entropic origin and from the native state by a barrier that is primarily energetic in origin. The latter feature is in agreement with the "Cardboard Box" model described by Goldenberg and Creighton but, unlike their model, the transition state is not a high-energy distorted form of the native state. The theory predicts that the rate of folding is less sensitive to changes in folding conditions than is the rate of unfolding, in agreement with experiment. Finally, the simple theory provides a means of assessing the effects of amino acid substitutions that favor native-like turn formation. By stabilizing the intermediate, they enhance the rate of folding to the intermediate from the denatured state and the rate of unfolding out of the native state, and they act to slow down the rate of folding from the intermediate to the native state. But even when every turn residue is modified, the effect is relatively small. © 1990.