Hamiltonian replica exchange approach and its application to the study of side-chain type and neighbor effects on peptide backbone conformations

We presented a Hamiltonian replica exchange approach and applied it to investigate the effects of various factors on the conformational equilibrium of peptide backbone. In different replicas, biasing potentials of varying strengths are applied to all backbone (phi,psi) torsional angle pairs to overcome sampling barriers. A general form of constructing biasing potentials based on a reference free energy surface is employed to minimize sampling in physically irrelevant parts of the conformational space. An extension of the weighted histogram analysis formulation allows for conformational free energy surfaces to be computed using all replicas, including those with biased Hamiltonians. This approach can significantly reduce the statistical uncertainties in computed free energies. For the peptide systems considered, it allows for effects of the order of 0.5-1 kJ/mol to be quantified using explicit solvent simulations. We applied this approach to capped peptides of 2-5 peptide units containing Ala, Phe, or Val in explicit water solvent and focused on how the conformational equilibrium of a single pair of backbone angles are influenced by changing the residue types of the same and neighboring residues as well as conformations of neighboring residues. For the effects of changing side-chain types of the same residue, our results consistently showed increased preference of beta for Phe and Val relative to Ala. As for neighbor effects, our results not only indicated that they can be as large as the effects of changing the side-chain type of the same residue but also led to several new insights. We found that for the N-terminal neighbors, their conformations seem to have large effects. Relative to the beta conformer of an N-terminal neighbor, its a conformer stabilizes the beta conformer of its next Ala disregarding the residue type of the neighbor. For C-terminal neighbors, their chemical identities seem to play more important roles. Val as the C-terminal neighbor significantly increases the PII propensity of its previous Ala disregarding its own conformational state. These results are in good accordance with reported statistics of protein coil structure libraries, proving the persistent presence of such effects in short peptides as well as in proteins. We also observed other side-chain identity and neighbor effects which have been consistently reproduced in our simulations of different small peptide systems but not displayed by coil library statistics.