Ensemble of expanded ensembles: A generalized ensemble approach with enhanced flexibility and parallelizability

Abstract

Over the past decade, alchemical free energy methods like Hamiltonian replica exchange (HREX) and expanded ensemble (EXE) have gained popularity for the computation of solvation free energies and binding free energies. These methods connect the end states of interest via nonphysical pathways defined by states with different modified Hamiltonians. However, there exist systems where traversing all alchemical intermediate states is challenging, even if alchemical biases (e.g., in EXE) or coordinate exchanges (e.g., in HREX) are applied. This issue is exacerbated when the state space is multidimensional, which can require extensive communications between hundreds of cores that current parallelization schemes do not fully support. To address this challenge, we present the method of ensemble of expanded ensembles (EEXE), which integrates the principles of EXE and HREX. Specifically, the EEXE method periodically exchanges coordinates of EXE replicas sampling different ranges of states and allows combining weights across replicas. With the solvation free energy calculation of anthracene, we show that the EEXE method achieves accuracy akin to the EXE and HREX methods in free energy calculations, while offering higher flexibility in parameter specification. Additionally, its parallelizability opens the door to wider applications, such as estimating free energy profiles of serial mutations. Importantly, extensions to the EEXE approach can be done asynchronously, allowing looser communications between larger numbers of loosely coupled processors, such as when using cloud computing, than methods such as replica exchange. They also allow adaptive changes to the parameters of ensembles in response to data collected. All algorithms for the EEXE method are available in the Python package ensemble_md, which offers an interface for EEXE simulation management without modifying the source code in GROMACS