Generating Pathways for Free Energy Calculations in Proteins Using Constraint-Based Conformational Sampling

Abstract

Constraint-based sampling [1] is a computational method for quickly exploring the allowed motions of a protein. Sampling of protein conformations is guided by a set of geometric constraints instead of a molecular mechanics force field. The geometric constraints preserve covalent bonding geometry, maintain favorable non-bonded contacts, and prevent steric overlap. We have tuned the constraints so that sampled conformations are low in energy according to a molecular mechanics force field (Amber). In this work, we apply the constraint-based sampling method in a targeted fashion to generate a pathway between two conformational end states in the protein dihydrofolate reductase (DHFR). The pathway we generate bridges the so-called “closed” and “occluded” states of DHFR, a transition that involves loop rearrangement near the binding site and relative rotations of subdomains. We then use this pathway as a starting point for free energy calculations. By performing molecular dynamics umbrella sampling [2] along the pathway, we obtain the free energy difference between the end states. Although the generated pathway is not necessarily the actual transition pathway, accurate calculation of the free energy difference between end states only requires that the pathway be low in free energy in the umbrella sampling method.[1] Wells S, Menor S, Hespenheide B M, and Thorpe M F. Constrained geometric simulation of the diffusive motions in proteins. Phys Bio 2 S127-S136 (2005).[2] Mamonova T and Kurnikova M. Structure and energetics of channel-forming protein-polysaccharide complexes inferred via computational statistical thermodynamics. J Phys Chem 110(49) 25091-25100 (2006).