Abstract
The cluster model of protein folding [Kanehisa, M. I. & Tsong, T. Y. (1978) J. Mol. Biol. 124, 177โ194] is further investigated for the thermodynamic and kinetic properties of protein foldingโunfolding transitions. A cluster is a locally formed ordered region in the polypeptide chain due to cooperative interactions among residues. In the cluster model a cooperative term is assigned as proportional to the surface area of a globular cluster. This assignment is compared with that for the helixโcoil transition of homopolypeptides, where the cooperative term is proportional to the two ends of a linear helical sequence. The dynamics of the cluster model exhibit a slow phase, which is wellโseparated from other faster phases, because of the cooperative interaction of the macrosystem. This slow phase not only appears within the transition region, but can also persist well below the transition region if the cooperativity depends on the external condition. The amplitudes of certain kinetic phases can vary depending on the choice of physical parameters monitoring the reaction. Thus the same reaction may display different time courses. The qualitative aspects of the folding dynamics are as follows. In one case the rateโlimiting formation of a criticalโsize cluster is followed by its rapid growth, while in the other the rateโlimiting step appears in a later stage, where preformed smaller clusters merge into larger ones. The former case is similar to the dynamics of the helixโcoil transition, and the latter represents a stepwise mechanism of protein structure formation.