Algorithmic approach to quantifying the hydrophobic force contribution in protein folding.

Though the electrostatic, ionic, van der Waals, Lennard-Jones, hydrogen bonding, and other forces play an important role in the energy function minimized at a protein's native state, it is widely believed that the hydrophobic force is the dominant term in protein folding. Here we attempt to quantify the extent to which the hydrophobic force determines the positions of the backbone alpha-carbon atoms in PDB data, by applying Monte-Carlo and genetic algorithms to determine the predicted conformation with minimum energy, where only the hydrophobic force is considered (i.e. Dill's HP-model, and refinements using Woese's polar requirement). This is done by computing the root mean square deviation between the normalized distance matrix D = (di,j) (di,j is normalized Euclidean distance between residues ri and rj) for PDB data with that obtained from the output of our algorithms. Our program was run on the database of ancient conserved regions drawn from GenBank 101 generously supplied by W. Gilbert's lab, as well as medium-sized proteins (E. Coli RecA, 2reb, Erythrocruorin, 1eca, and Actinidin 2act). The root mean square deviation (RMSD) between distance matrices derived from the PDB data and from our program output is quite small, and by comparison with RMSD between PDB data and random coils, allows a quantification of the hydrophobic force contribution. A preliminary version of this paper appeared at GCB'99 (http:¿bibiserv.techfak.uni-bielefeld.de/gcb9 9/).