Rare Events and Enhanced Sampling

  • Molecular dynamics algorithms have time reversibility and ergodic hypotheses. We assume that all states of a molecule have a probability to be explored (or traversed/sampled) after a sufficiently long simulation. These states include ground states, meta-stable states, and some high-energy states (unstable states). When the simulation reaches equilibrium, the distribution of molecular conformations in the system satisfies the Boltzmann distribution under its ensemble.

  • Different states have different probabilities to be sampled. In most cases, the molecules are stuck in a local minimum on the energy surface, and it is difficult to jump over the energy barriers. Therefore, under finite-time simulations, the probability of sampling some high-energy state or another meta-state separated by an energy barrier is very low. These are rare events.

    • Here, it can be compared with Monte Carlo (MC) simulations of a high-dimensional function, starting from a random value of the high-dimensional function to explore the global minima of the function. This can take a lot of time and computational resources.

  • To increase the probability of rare events occurring in MD simulations, the simulation process can be interfered with using various methods:

    • Enhanced sampling based on temperature:

      • Raise the temperature, lower the energy barriers, and increase the probability of rare events.

      • Replica-Exchange Molecular Dynamics (REMD)[5], selective integrated tempering sampling (SITS)[6], etc.

    • Enhanced sampling based on bias potential:

      • Collective variables (CV), are functions of system coordinates. The free energy are defined on collective variables. (Please refer to the difference between free energy and potential energy)

      • Add bias potential to the given CVs during the simulations, which can push the trajectory out of the local minima on the energy surface to explore other states.

      • Metadynamics[7], VES[8], RiD[9], etc.

      • Traditional boosted sampling methods based on bias potential suffer from the curse of dimensionality.