Effect of ionized protein residues on the nucleation pathway of protein folding

Using a ternary nucleation formalism, we have recently [Y. S. Djikaev and E. Ruckenstein, J. Chem. Phys. 126, 175103 (2007)] proposed a kinetic model for the nucleation mechanism of protein folding. A protein was considered as a heteropolymer consisting of hydrophobic, hydrophilic, and neutral beads with all the bonds having the same constant length and all the bond angles equal and fixed. In this paper, we further develop that model by taking into account of the ionizability of some of the protein residues. As previously, an overall potential around the cluster wherein a protein residue performs a chaotic motion is considered to be a combination of the average dihedral and average pairwise potentials (the latter now including an electrostatic contribution for ionized residues) assigned to the residue and the confining potential due to the polymer connectivity constraint. The overall potential as a function of the distance from the cluster has a double well shape (even for ionized beads) which allows one to determine the rates of emission and absorption of residues by the cluster by using a first passage time analysis. Assuming the equality of the ratios of the numbers of negatively and positively ionized residues in the cluster and in the entire protein, one can keep the modified model within the framework of the ternary nucleation formalism and evaluate the size and composition of the nucleus and the protein folding time as in the previous model. As an illustration, the model is again applied to the folding of bovine pancreatic ribonuclease consisting of 124 amino acids, whereof 40 are hydrophobic, 81 hydrophilic (of which 10 are negatively and 18 positively ionizable), and 3 neutral. Numerical calculations at pH=6.3, pH=7.3, and pH=8.3 show that for this protein the time of folding via nucleation is significantly affected by electrostatic interactions only for the unusually low pH of 6.3 and that among all pH's considered pH=7.3 provides the lowest folding time.