Role of the dihedral angle potential in the nucleation pathway of   protein folding
  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. 
Yuri S. Djikaev