Free Energy Methods

Replica-Exchange Enveloping Distribution Sampling (RE-EDS)

In molecular dynamics (MD) simulations, free-energy differences are often calculated using free energy perturbation (FEP) or thermodynamic integration (TI) methods. However, both techniques are only suited to calculate free-energy differences between two end states. Enveloping distribution sampling (EDS) presents an attractive alternative that allows the calculation of multiple free-energy differences in a single simulation. In EDS, a reference state is simulated which “envelopes” the end states. The challenge of this methodology is the determination of optimal reference-state parameters to ensure equal sampling of all end states. Currently, the automatic determination of the reference-state parameters for multiple end states is an unsolved issue that limits the application of the methodology. To overcome this challenge, we have generalised the replica-exchange EDS (RE-EDS) approach introduced by Lee et al. for constant-pH MD simulations [J. Chem. Theory Comput., 10, 2738 (2014)] to arbitrary systems [1]. By exchanging configurations between replicas with different reference-state parameters, the complexity of the parameter-choice problem can be substantially reduced. In a next step, we have developed an efficient algorithm to optimize distribution of the replicas [2]. With this, we could obtain all 36 free-energy differences between nine ligands of a protein from a single simulation.

[1] Sidler et al., J. Chem. Phys. (2016), 145, 154114.
[2] Sidler et al., J. Chem. Theory Comput. (2017), 13, 3020.

To illustrate the performance of the methodology on a more challenging system, the relative binding free energies were calculated for a series of checkpoint kinase 1 (CHK1) inhibitors, which contain difficult transformations such as ring size, ring opening/closing, and ring extension, which reflect changes observed in scaffold hopping [3]. The accuracy of RE-EDS was found to be comparable while being computationally more efficient than state-of-the-art methods. Importantly, Ref. [3] provides an automated pipeline for RE-EDS simulations, and our RestraintMaker algorithm [4] makes it straightforward to use a "dual topology" approach for free-energy calculations.

[3] external pageRies et al., J. Comput.-Aided Mol. Des. (2022), 36, 117.
[4] external pageRies et al., J. Comput.-Aided Mol. Des. (2022), 36, 175.

To enable the use of force fields such as GAFF (and OpenFF) with RE-EDS, we developed the amber2gromos program for topology conversion [5]. When applied to compute relative hydration free energies of up to 28 benzene derivatives, the same accuracy was achieved with RE-EDS as with state-of-the-art methods, although at a fraction of the computational costs (about five times less) [5]. An implementation of RE-EDS in OpenMM is also available [6].

[5] external pageRieder et al., J. Chem. Inf. Model. (2022), 62, 3043.
[6] external pageRieder et al., J. Chem. Phys. (2022), 157, 104117.

RE-EDS for Water Energetics in Binding Pockets

Water molecules are ubiquitous in biology and chemistry, but their unique properties make their exploitation for tuning of biological processes extremely challenging, with often unexpected outcomes. In drug design, for example, the thermodynamic contribution of water molecules can have a pronounced role in ligand binding, and thus a range of computational methods have been developed for the characterization of hydration sites in protein binding pockets. However, due to methodological limitations, calculations are typically restricted to an apo pocket in a static protein structure, neglecting the cooperativity and solvation effects that can be expected in water networks formed in such enclosed environments. A major advantage of RE-EDS over other free-energy methods is that multiple end states can be considered simultaneously in a single simulation. RE-EDS is therefore perfectly suited to investigate the effects that perturbations to water networks in protein binding sites have on their thermodynamics. The multistate property of the method allows for the consideration of the conjoint effects of replacing combinations of water molecules in the pocket in a single set of simulations, and thus to probe solvation correlation effects explicitly and efficiently. Through studies on five protein systems, we demonstrated how these perturbations of the water networks and associated changes to the pocket environment can have a significant effect on the stability of the remaining water molecules, and be exploited for the design of selective inhibitors [7].

[7] external pageBarros et al., J. Chem. Inf. Model. (2023), 63, 1794.

λ-EDS

EDS can be combined with a coupling parameter λ to obtain better intermediate states for alchemical free-energy calculations [8, 9]. Alchemical free-energy calculations typically rely on intermediate states to bridge between the relevant phase spaces of the two end states. These intermediate states are usually created by mixing the energies or parameters of the end states according to a coupling parameter λ. The choice of the procedure has a strong impact on the efficiency of the calculation, as it affects both the encountered energy barriers and the phase space overlap between the states. A particularly attractive feature of λ-EDS is its ability to emulate the use of soft-core potential while avoiding the associated computational overhead when applying efficient free energy estimators such as (M)BAR. The performance of λ-EDS was compared to conventional intermediate states using standard free-energy estimators for different simplified test systems [8]. By using simple free energy estimates such as linear interaction energy as energy offsets, λ-EDS has also been applied to calculation hydration free energies of organic molecules [9].

[8] external pageKönig et al., J. Chem. Inf. Model. (2020), 60, 5407.
[9] external pageKönig et al., J. Chem. Theory Comput. (2021), 17, 5805.