Peptide backbone sampling convergence with the adaptive biasing force algorithm

Complete Boltzmann sampling of reaction coordinates in biomolecular systems continues to be a challenge for unbiased molecular dynamics simulations. A growing number of methods have been developed for applying biases to biomolecular systems to enhance sampling while enabling recovery of the unbiased (Boltzmann) distribution of states. The adaptive biasing force (ABF) algorithm is one such method and works by canceling out the average force along the desired reaction coordinate(s) using an estimate of this force progressively accumulated during the simulation. Upon completion of the simulation, the potential of mean force, and therefore Boltzmann distribution of states, is obtained by integrating this average force. In an effort to characterize the expected performance in applications such as protein loop sampling, ABF was applied to the full ranges of the Ramachandran φ/ψ backbone dihedral reaction coordinates for dipeptides of the 20 amino acids using all-atom explicit-water molecular dynamics simulations. Approximately half of the dipeptides exhibited robust and rapid convergence of the potential of mean force as a function of φ/ψ in triplicate 50 ns simulations, while the remainder exhibited varying degrees of less complete convergence. The greatest difficulties in achieving converged ABF sampling were seen in the branched-side chain amino acids threonine and valine, as well as the special case of proline. Proline dipeptide sampling was further complicated by trans-to-cis peptide bond isomerization not observed in unbiased control molecular dynamics simulations. Overall, the ABF method was found to be a robust means of sampling the entire φ/ψ reaction coordinate for the 20 amino acids, including high free-energy regions typically inaccessible in standard molecular dynamics simulations.