Connecting the mechanistic steps of cyclic dipeptide formation by a proton-transfer network: pH, temperature, pressure, and nuclear quantum effects.

We expanded our previous mapping of the peptide condensation reaction mechanism from the linear dipeptide formation to the cyclization reaction that results in diketopiperazines. The overarching theme of our computational investigations is a reaction network that connects all intermediates proton-transfer pathways. We conducted the simulations designed to be predictive in a range of environments, such as the gas phase, hydrothermal aqueous conditions, deliquescent salts, and bulk water. While the free-energy profiles are similar to the linear peptide, the presence of the amide bond leading to a pre-arranged vicinity of the two reacting groups and the role of explicit solvent molecules revealed new mechanistic insights that differentiate the linear cyclic peptide formation/hydrolysis reactions. The rate-determining step corresponds to the final water-elimination reaction using the most realistic computational models with both implicit and explicit water solvation models at neutral pH. At high pH, the highest barrier corresponds to the C-N bond formation at a significantly lower free energy, while at low pH, the water elimination step's barrier increases by close to 30%; thus, effectively shutting down the reaction in agreement with experiments. Due to the central role of proton transfer, we studied the impact of nuclear wave functions on all active H-centers. By utilizing two quantum protons, we document up to 0.1 Å impact on H positions, 20 kJ mol tunneling effects, and a significant change in the shape of the potential energy surface in comparison with the classical DFT calculations. The calculated reaction rates well reproduce the experimentally determined values under hydrothermal conditions.