Extracting Realistic Kinetics of Rare Activated Processes from Accelerated Molecular Dynamics Using Kramers' Theory

The cis-trans isomerization of peptide bonds is very slow, occurring in hundreds of seconds. Kinetic studies of such processes using straightforward molecular dynamics are currently not possible. Here, we use Kramers' rate theory in the high friction regime in combination with accelerated molecular dynamics in explicit solvent to successfully retrieve the normal rate of cis to trans switching in the glycyl prolyl dipeptide. Our approach bypasses the time-reweighting problem of the hyperdynamics scheme, wherein the addition of the bias potential alters the transition state regions and avoids an accurate estimation of kinetics. By performing accelerated molecular dynamics at a few different levels of acceleration, the rate of isomerization is enhanced as much as 10(10) to 10(11) times. Remarkably, the normal rates obtained by simply extrapolating to zero bias are within an order of experimental estimates. This provides validation from a kinetic standpoint of the omega torsional parameters of the AMBER force field that were recently revised by matching to experimentally measured equilibrium properties. We also provide a comparative analysis of the performance of the widely used water models, i.e., TIP3P and SPC/E, in estimating the kinetics of cis-trans isomerization. Furthermore, we show that the dynamic properties of bulk water can be corrected by adjusting the collision frequency in a Langevin thermostat, which then allows for better reproduction of cis-trans isomerization kinetics and a closer agreement of rates between experiments and simulations.