Simulation of protein folding by reaction path annealing

We present a systematic application of reaction path sampling to computer simulations of the folding of peptides and small proteins at atomic resolution in the presence of solvent. We use a simulated annealing protocol to generate an ensemble of room temperature folding trajectories of fixed length, which connect predetermined initial and final states. The trajectories are distributed according to a discretized version of the Onsager–Machlup action functional. We show that, despite the enormous practical restrictions placed on the number of time slices which can be explored, some of the basic kinetic features found experimentally for the folding of peptides and small proteins are exhibited in the nature of the reaction paths sampled. We test the method on three systems: A 12 residue α-helical peptide, a 16 residue β-hairpin peptide, and the 36 residue avian Pancreatic Polypeptide (aPP). All systems are represented at atomic resolution, and include explicit water molecules. For the 12 residue α-helix, we find that $\text{(i,i+3)}$ hydrogen bonds can play a significant role in the folding pathway, with specific $\text{(i,i+3)}$ bonds appearing, then transforming to the corresponding $\text{(i,i+4)}$ hydrogen bond for some, but not all of the native hydrogen bonds. For the β-hairpin and aPP, hydrophobic interactions play a dominant role, with nonbonded interactions consistently appearing before hydrogen bonds. This is true both at the level of tertiary structure, and at the level of individual hydrogen bonds which tend to form only after stabilizing nonbonded interactions have already formed between the residues involved.