Atomic Simulations of Trp-Cage Folding by Umbrella Sampling using Q Function as Reaction Coordinate

Abstract

Spontaneous transitions between different protein conformations, especially the transition between native and non-native states, typically occur rarely in an unbiased molecular dynamics simulation. Recently, it was shown that the thermodynamics of protein folding can be described by a Q function, which is the collective fraction of the native contacts of protein atoms. In this study, we implement Umbrella Sampling with Hamiltonian replica exchange, using Q as the reaction coordinate, to model the folding of Trp-Cage protein. The CHARMM force field and the NAMD2 program were used in the molecular dynamics simulations. The simulations show a satisfactory convergence along Q. Besides the native structure, multiple folded states can be observed in the reconstructed equilibrium ensemble. Even without native contacts, some protein structures are stabilized by hydrogen bonds not present in the native state. Overall, our result showed that although Q is a reasonably reliable parameter to analyze the simulations, it is not necessarily the best reaction coordinate for enhanced sampling. In particular, the folding of the α-helix is a slow degree of freedom for Trp-Cage, and the reaction coordinate may probably be improved by incorporating parameters that describe the α-helix conformation as well.