  A kinetic model for the nucleation mechanism of protein folding is proposed.
A protein is modeled as a heteropolymer consisting of hydrophobic and
hydrophilic beads with equal constant bond lengths and bond angles. The total
energy of the heteropolymer is determined by the repulsive/attractive
interactions of non-linked beads and the contribution from the dihedral angles
involved. Their parameters can be rigorously defined, unlike the ill defined
surface tension of a cluster of protein residues which is the basis of the
previous model. As a crucial idea of the model, the dihedral potential in which
a selected bead is involved is averaged over all possible configurations of
neighboring beads along the protein chain. The resulting average dihedral
potential of the residue is constant far enough from the cluster, but increases
monotonically with decreasing distance below a threshold value. An overall
potential around the cluster wherein a residue performs a chaotic motion is a
combination of the average dihedral and pairwise potentials. As a function of
distance from the cluster it has a double well shape. Residues in the inner
well are considered as belonging to the cluster (folded part of the protein)
while those in the outer well are treated as belonging to the unfolded
(although compact) part of the protein. A double well shape of the potential
around the cluster allows one to determine its emission and absorption rates by
using a first passage time analysis and develop a self-consistent kinetic
theory for the nucleation mechanism of protein folding. Numerical calculations
for a protein of 2500 residues with the diffusion coefficient of residues in
the native state ranging from 10^{-6} cm^2/s to 10^{-8} cm^2/s predict folding
times in the range from several seconds to several hundreds of seconds.
