Search

Relative free energy calculations are now widely used in academia and industry, but the accuracy is often limited by poor sampling of the complexes conformational ensemble. To address this, we have developed a novel method termed Multi-Topology Replica Exchange of Expanded Ensembles (MT-REXEE). This method enables parallel expanded ensemble calculations, facilitating iterative relative free energy computations while allowing conformational exchange between parallel transformations. These iterative transformations are adaptable to any set of systems with a common backbone or central substructure. We demonstrate that the MT-REXEE method maintains thermodynamic cycle closure to the same extent as standard expanded ensemble for both solvation free energy and relative binding free energy. The transformations tested involve simple systems that incorporate diverse heavy atoms and multi-site perturbations of a small molecule core resembling multi-site $\lambda$ dynamics, without necessitating modifications to the MD code, which in our initial implementation is GROMACS. We outline a systematic approach for topology set-up and provide instructions on how to perform inter-replicate coordinate modifications. This work shows that MT-REEXE can be used to perform accurate and reproducible free energy estimates and prompts expansion to more complex test systems and other molecular dynamics simulation infrastructures.

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.

Performing alchemical transformations, in which one molecular system is nonphysically changed to another system, is a popular approach adopted in performing free energy calculations associated with various biophysical processes, such as protein-ligand binding or the transfer of a molecule between environments. While the sampling of alchemical intermediate states in either parallel (e.g. Hamiltonian replica exchange) or serial manner (e.g. expanded ensemble) can bridge the high-probability regions in the configurational space between two end states of interest, alchemical methods can fail in scenarios where the most important slow degrees of freedom in the configurational space are in large part orthogonal to the alchemical variable, or if the system gets trapped in a deep basin extending in both the configurational and alchemical space. To alleviate these issues, we propose to use alchemical variables as an additional dimension in metadynamics, augmenting the ability both to sample collective variables and to enhance sampling in free energy calculations. In this study, we validate our implementation of alchemical metadynamics in PLUMED with test systems and alchemical processes with varying complexities and dimensions of collective variable space, including the interconversion between the torsional metastable states of a toy system and the methylation of a nucleoside both in the isolated form and in a duplex. We show that multi-dimensional alchemical metadynamics can address the challenges mentioned above and further accelerate sampling by introducing configurational collective variables. The method can trivially be combined with other metadynamics-based algorithms implemented in PLUMED. The necessary PLUMED code changes have already been released for general use in PLUMED 2.8.