Replica-exchange molecular dynamics

Replica-exchange MD simulations execute multiple versions of the same molecule in parallel, at different conditions (typically different temperatures). This is motivated by using a “ladder” of simulations to connect a target low-temperature distribution with a high-temperature, easier-to-sample distribution, accelerating sampling of the former (1).

Details

For a set of $M+1$ replicas ranging from $p_0(\text{x})=p(\text{x})$ to $p_M(\text{x})=q(\text{x})$, each replica $i$ has $u_i(\text{x})=(k_B{T}_i{)}^{-1}U(\text{x})$ where $U(\text{x})$ is the potential energy and $T_i$ interpolates between $T_0$ and $T_M$. Total replicas $M$ scales as $M\propto \sqrt{N}$ with system degrees of freedom.

Configurations ${\text{x}}_i$ and ${\text{x}}_j$ are exchanged with probability:

$${\alpha }_{REX}=\min \left\{1,\exp \left(\Delta u_{ij}({\text{x}}_i)-\Delta u_{ij}({\text{x}}_j)\right)\right\}$$ $$\Delta u_{ij}(\text{x})=u_i(\text{x})-u_j(\text{x})$$

1.

Invernizzi M, Krämer A, Clementi C, Noé F. Skipping the Replica Exchange Ladder with Normalizing Flows. The Journal of Physical Chemistry Letters. 2022;13(50):11643–9. Available from: https://doi.org/10.1021/acs.jpclett.2c03327