Efficient and accurate calculation of proline cis/trans isomerization free energies from Hamiltonian replica exchange molecular dynamics simulations

Proline cis/trans isomerization plays an important role in many biological processes but occurs on time scales not accessible to brute-force molecular dynamics (MD) simulations. We have designed a new Hamil-tonian replica exchange scheme, &-bias potential replica exchange molecular dynamics (&BP-REMD), to efficiently and accurately calculate proline cis/trans isomerization free energies. &BP-REMD is applied to various proline-containing tripeptides and a biologically important proline residue in the N2-domain of the gene-3-protein of phage fd in the wildtype and mutant variants of the protein. Excellent cis/trans transition rates are obtained. Reweighting of the sampled probability distribution along the peptide bond dihedral angle allows construction of the corresponding free-energy profile and calculation of the cis/trans isomerization free energy with high statistical precision. Very good agreement with experimental data is obtained. &BP-REMD outperforms standard umbrella sampling in terms of convergence and agreement with experiment and strongly reduces perturbation of the local structure near the proline residue.