Comparative Study of Hydrophobic-Polar and Miyazawa-Jernigan Energy Functions in Protein Folding on a Cubic Lattice Using Pruned-Enriched Rosenbluth Monte Carlo Algorithm

In this analysis of the contact energies guiding the protein folding, the performance of the PERM algorithm on a simple, cubic lattice is examined when Miyazawa-Jernigan (MJ) and Hydrophobic-Polar (HP) energy matrices are applied. Geometric similarity of minimum energy conformations of twenty proteins, generated when HP and MJ are used, is determined by the Root Mean Square Difference (RMSD) and the fraction of Common Contacts (CC). RMSD is a measure of global similarity, while CC indicates local similarity. On average, RMSD is one lattice edge, which is the resolution of the model. More contacts are formed when the MJ energies are used, as opposed to HP energies. This difference is attributed to the greater likelihood of contact formation between two polar residues in the MJ model. The local and global differences in conformations predicted by HP and MJ, increase with protein length, and decrease with hydrophobic fraction. A novel parameter, protein ”foldability”, is introduced. It is a measure of the simplicity of folding a protein. RMSD has a negative correlation with foldability. Conversely, CC demonstrates a positive, linear correlation with foldability. For highly foldable proteins, HP and MJ energy functions predict both globally and locally similar structures, while the opposite is true of low foldability proteins. Moreover, the search for conformation with optimal energy is more efficient for foldable proteins. For proteins with low foldability, the use of known secondary structure facilitates the search for lowest energy structure. For all twenty proteins, our method identified conformations with lower energy states than those previously reported.