  Generalized ensemble methods such as Hamiltonian replica exchange (HREX) and
expanded ensemble (EE) have been shown effective in free energy calculations
for various contexts, given their ability to circumvent free energy barriers
via nonphysical pathways defined by states with different modified
Hamiltonians. However, both HREX and EE methods come with drawbacks, such as
limited flexibility in parameter specification, or the lack of
parallelizability for more complicated applications. To address this challenge,
we present the method of replica exchange of expanded ensembles (REXEE), which
integrates the principles of HREX and EE methods by periodically exchanging
coordinates of EE replicas sampling different yet overlapping sets of
alchemical states. With the solvation free energy calculation of anthracene and
binding free energy calculation of the CB7-10 binding complex, we show that the
REXEE method achieves the same level of accuracy in free energy calculations as
the HREX and EE methods, while offering enhanced flexibility and
parallelizability. Additionally, we examined REXEE simulations with various
setups to understand how different exchange frequencies and replica
configurations influence the sampling efficiency in the fixed-weight phase and
the weight convergence in the weight-updating phase. The REXEE approach can be
further extended to support asynchronous parallelization schemes, allowing
looser communications between larger numbers of loosely coupled processors such
as cloud computing and therefore promising much more scalable and adaptive
executions of alchemical free energy calculations. All algorithms for the REXEE
method are available in the Python package ensemble_md, which offers an
interface for REXEE simulation management without modifying the source code in
GROMACS.
