Free Energy Barrier Estimation with Milestoning for Alanine Dipeptide Dynamics
iv, 53 p.
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Although the molecular dynamics (MD) is highly useful tool for complement experiments and to look motions of microstates, MD have some restriction. The time scale is one major problem that can disturb the analysis of MD for biological supramolecular systems. Many algorithms and methods have been developed to try to overcome this problem, such as milestoning. The fundamental idea of milestoning is that it is possible to divide the reaction paths represented on the hyperspace into several short reaction trajectories and to recover the original by joining the divided reaction paths back together. The milestone is a hyperspace that is orthogonal to the reaction path, and it divides long time reaction path into several short reaction trajectories. A milestoning simulation is consisted of orthogonal equilibrium (OEQ) mode and first passage (FP) mode. A normal Verlet algorithm with seven constraints runs structures on the milestone until the trajectories reach neighbor milestones in OEQ mode. These trajectories are sampled using a canonical ensemble for describing the local kinetics. In FP mode, the results of OEQ mode are joined together to recover the global kinetics of the original reaction path. To test accuracy of milestoning, the ψ dihedral rotation of alanine dipeptide is simulated on the MOIL program and normal Langevin dynamics is run for reference long trajectory MD on the Groningen Machine for Chemical Simulations (GROMACS). The free energy profile of milestoning simulation result matches well to the reference, if milestoning approximations are not broken. Milestoning has three benefits when comparing long trajectory MD simulation methds: parallelization, diffusive enhancement and exponential bootstrapping. Parallelization improves the efficiency of the simulation by running independent short reaction trajectories simultaneously. Diffusive enhancement reduces simulation time, because the total simulation time is proportional to length of the distance between the reactant and product, short paths provide a short simulation time than typical MD. Exponential bootstrapping means that probability of following accurate reaction trajectory is greater than for general long trajectory MD. To improve, milestoning needs to overcome two weak points: Milestone determination and the preparation of the initial temporary reaction path. However, preparing the initial temporary reaction trajectory determines the value of simulation and making a long time path is extremely difficult. As such, milestoning uses similar approaches for making long time reaction paths or improved milestoning equations. Determining milestones is more important for simulation, if the distance between milestones is shorter than the correlation time at zero, milestoning approximations will be broken, and results lose their reliability.