A Benchmark of Electrostatic Methods Performance in Relative Binding Free Energy Calculations

Accurate in silico predictions of how strongly small molecules bind to proteins, such as those afforded by relative binding free energy (RBFE) calculations, can greatly increase the efficiency of the hit-to-lead and lead optimization stages of the drug discovery process. The success of such calculations, however, relies heavily on their precision. Here, we show that a recently developed alchemical enhanced sampling (ACES) approach can consistently improve the precision of RBFE calculations on a large and diverse set of proteins and small molecule ligands. The addition of ACES to conventional RBFE calculations lowered the average hysteresis by over 35% (0.3-0.4 kcal/mol) and the average replicate spread by over 25% (0.2-0.3 kcal/mol) across a set of 10 protein targets and 213 small molecules while maintaining similar or improved accuracy. We show in atomic detail how ACES improved convergence of several representative RBFE calculations through enhancing the sampling of important slowly transitioning ligand degrees of freedom.

We present an extension of the alchemical transfer method (ATM) for the estimation of relative binding free energies of molecular complexes applicable to conventional, as well as scaffold-hopping, alchemical transformations. Named ATM-RBFE, the method is implemented in the free and open-source OpenMM molecular simulation package and aims to provide a simpler and more generally applicable route to the calculation of relative binding free energies than what is currently available. ATM-RBFE is based on sound statistical mechanics theory and a novel coordinate perturbation scheme designed to swap the positions of a pair of ligands such that one is transferred from the bulk solvent to the receptor binding site while the other moves simultaneously in the opposite direction. The calculation is conducted directly in a single solvent box with a system prepared with conventional setup tools, without splitting of electrostatic and nonelectrostatic transformations, and without pairwise soft-core potentials. ATM-RBFE is validated here against the absolute binding free energies of the SAMPL8 GDCC host-guest benchmark set and against protein-ligand benchmark sets that include complexes of the estrogen receptor ERα and those of the methyltransferase EZH2. In each case the method yields self-consistent and converged relative binding free energy estimates in agreement with absolute binding free energies and reference literature values, as well as experimental measurements.

Our interest is relative binding free energy (RBFE) calculations based on molecular simulations. These are promising tools for lead optimization in drug discovery, computing changes in binding free energy due to modifications of a lead compound. However, in the "alchemical" framework for RBFE calculations, some types of mutations have the potential to introduce error into the computed binding free energies. Here we explore the magnitude of this error in several different model binding calculations. We find that some of the calculations involving ring breaking have significant errors, and these errors are especially large in bridged ring systems. Since the error is a function of ligand strain, which is unpredictable in advance, we believe that ring breaking should be avoided when possible.

Multisite λ‐dynamics (MSλD) is a novel method for the calculation of relative free energies of binding for ligands to their targeted receptors. It can be readily used to examine a large number of molecules with multiple functional groups at multiple sites around a common core. This makes MSλD a powerful tool in structure‐based drug design. In the present study, MSλD is applied to calculate the relative binding free energies of 1296 inhibitors to the testis specific serine kinase 1B (TSSK1B), a validated target for male contraception. For this system, MSλD requires significantly fewer computational resources compared to traditional free energy methods like free energy perturbation or thermodynamic integration. From MSλD simulations, we examined whether modifications of a ligand at two different sites are coupled or not. Based on our calculations, we established a quantitative structure–activity relationship (QSAR) for this set of molecules and identified a site in the ligand where further modification, such as adding more polar groups, may lead to increased binding affinity.

The combination of quantum mechanics (QM) with molecular mechanics (MM) offers a route to improved accuracy in the study of biological systems, and there is now significant research effort being spent to develop QM/MM methods that can be applied to the calculation of relative free energies. Currently, the computational expense of the QM part of the calculation means that there is no single method that achieves both efficiency and rigor; either the QM/MM free energy method is rigorous and computationally expensive, or the method introduces efficiency-led assumptions that can lead to errors in the result, or a lack of generality of application. In this paper we demonstrate a combined approach to form a single, efficient, and, in principle, exact QM/MM free energy method. We demonstrate the application of this method by using it to explore the difference in hydration of water and methane. We demonstrate that it is possible to calculate highly converged QM/MM relative free energies at the MP2/aug-cc-pVDZ/OPLS level within just two days of computation, using commodity processors, and show how the method allows consistent, high-quality sampling of complex solvent configurational change, both when perturbing hydrophilic water into hydrophobic methane, and also when moving from a MM Hamiltonian to a QM/MM Hamiltonian. The results demonstrate the validity and power of this methodology, and raise important questions regarding the compatibility of MM and QM/MM forcefields, and offer a potential route to improved compatibility.

Relative binding free energy calculations in drug design are becoming a useful tool in facilitating lead binding affinity optimization in a cost- and time-efficient manner. However, they have been limited by technical challenges such as the manual creation of large numbers of input files to set up, run, and analyze free energy simulations. In this Application Note, we describe FEPrepare, a novel web-based tool, which automates the setup procedure for relative binding FEP calculations for the dual-topology scheme of NAMD, one of the major MD engines, using OPLS-AA force field topology and parameter files. FEPrepare provides the user with all necessary files needed to run a FEP/MD simulation with NAMD. FEPrepare can be accessed and used at https://feprepare.vi-seem.eu/.

Discovery of highly potent phosphodiesterase-1 inhibitors by a combined-structure free energy perturbation approach

While relative binding free energy (RBFE) calculations using alchemical methods are routinely carried out for many pharmaceutically relevant protein targets, challenges remain. For example, open-source tools do not support the easy setup and simulation of metalloproteins, particularly when ligands directly coordinate to the metal site. Here, we evaluate the performance of RBFE methods for KPC-2, a serine-β-lactamase (SBL), and two nonbonded metal parameter setups for VIM-2, a metallo-β-lactamase (MBL) with two active site zinc ions. We tested two different ways of modeling the ligand-zinc interactions. First, a restraint-based approach, in which FF14SB zinc parameters are combined with harmonic restraints between the zincs and their coordinating residues. The second approach uses an upgraded Amber force field (UAFF) for zinc-metalloproteins with adjusted partial charges and nonbonded terms of zinc-coordinating residues. Molecular mechanics (MM) and quantum mechanics/molecular mechanics (QM/MM) simulations show that the crystallographically observed zinc coordination is not retained in MM simulations with either zinc parameter set for a series of known phosphonic acid-based inhibitors bound to VIM-2. These phosphonic acid-based inhibitors exhibit known cross-class affinity for SBLs and MBLs and serve as a benchmark for RBFE calculations for VIM-2, after validation with KPC-2. The KPC-2 free energy of binding estimates are within expected literature accuracies for the ligand series with a mean absolute error of kcal/mol and a Pearson's correlation coefficient of . For VIM-2, the UAFF approach has improved correlation from to , compared to the restraint approach. The presented strategies for handling ligands coordinating to metal sites highlight that simple metal parameter models can provide some predictive free energy estimates for metalloprotein-ligand systems, but leave room for improvement in their ease of use, modeling of coordination sites and as a result, their accuracy.

Reaction Control in Fungal Fatty Acid Synthase

We present calculations of the absolute and relative binding free energies of complexation of streptavidin with biotin and its analogs by means of a thermodynamic free energy perturbation method implemented with molecular dynamics. Using the recently solved crystal structure of the streptavidin-biotin complex, biotin was mutated into a dummy molecule as well as thiobiotin and iminobiotin both in the protein and in solution. The calculated absolute binding free energy was dependent on the simulation model used. Encouragingly, the "best models" provided a reasonable semiquantitative reproduction (-20 to -22 kcal/mol) of the experimental free energy (-18.3 kcal/mol). Furthermore, the calculated results give clear insights into the binding nature of the protein-ligand complex, showing that the van der Waals energy dominates the electrostatic and hydrogen bonding energies in the binding of biotin by streptavidin. Specifically, the mutation of biotin into a dummy molecule in solution has a delta G (van der Waals) approximately -4 kcal/mol, due to the cancellation of dispersion and repulsion "cavity" effects. On the other hand, in the protein, a very small free energy price must be paid to create a cavity since one already exists and the mutation of biotin into a dummy molecule has a delta G (van der Waals) approximately 15 kcal/mol. These results are also consistent with the interpretation that the entropy increase to be expected from hydrophobic interactions from desolvation of biotin is counterbalanced by a decrease in entropy accompanying the formation of buried hydrogen bonds, which have been derived from the apparently conflicting experimental data. They provide an alternative interpretation of the reason for the extremely high affinity of the biotin-streptavidin interaction than that recently proposed by Weber et al. (J. Am. Chem. Soc. 114:3197, 1992). In the case of the relative binding free energies, the calculated values of 3.8 +/- 0.6 and 7.2 +/- 0.6 kcal/mol compare well with the experimental values of 3.6 and 6.2 kcal/mol for the perturbation of biotin to thiobiotin and iminobiotin, respectively in the related protein avidin. The calculations indicate that desolvation of the ligand is important in understanding the relative affinity of the ligands with the protein. The above successful simulations suggest that the molecular dynamics/free energy perturbation method is useful for understanding the energetic features affecting the binding between proteins and ligands, since it is generally difficult to determine these factors unambiguously by experiment.(ABSTRACT TRUNCATED AT 400 WORDS)

The solid-fluid coexistence properties of the n - 6 Lennard-Jones system, n from 7 to 12, are reported. The procedure relies on determining Helmholtz free energy curves as a function of volume for each phase independently, from several NVT simulations, and then connecting it to points of known absolute free energy. For n = 12 this requires connecting the simulated points to states of very low densities on the liquid phase, and to a harmonic crystal for the solid phase, which involves many extra simulations for each temperature. For the reference points of the remaining systems, however, the free energy at a given density and temperature can be calculated relative to the n = 12 system. The method presented here involves a generalization of the multiple histogram method to combine simulations performed with different potentials, provided they visit overlapping regions of the phase space, and allows for a precise calculation of relative free energies. The densities, free energies, average potential energies, pressure, and chemical potential at coexistence are presented for up to T∗ = 5.0 and new estimations of the triple points are given for the n - 6 Lennard-Jones system.

Relative binding free energy (RBFE) prediction methods such as free energy perturbation (FEP) are important today for estimating protein-ligand binding affinities. Significant hardware and algorithmic improvements now allow for simulating congeneric series within days. Therefore, RBFE calculations have an enormous potential for structure-based drug discovery. As typically only a few representative crystal structures for a series are available, other ligands and design proposals must be reliably superimposed for meaningful results. An observed significant effect of the alignment on FEP led us to develop an alignment approach combining docking with maximum common substructure (MCS) derived core constraints from the most similar reference pose, named MCS-docking workflow. We then studied the effect of binding pose generation on the accuracy of RBFE predictions using six ligand series from five pharmaceutically relevant protein targets. Overall, the MCS-docking workflow generated consistent poses for most of the ligands in the investigated series. While multiple alignment methods often resulted in comparable FEP predictions, for most of the cases herein, the MCS-docking workflow produced the best accuracy in predictions. Furthermore, the FEP analysis data strongly support the hypothesis that the accuracy of RBFE predictions depends on input poses to construct the perturbation map. Therefore, an automated workflow without manual intervention minimizes potential errors and obtains the most useful predictions with significant impact for structure-based design.

We have extended and applied a multicoordinate free energy method, chemical Monte Carlo/Molecular Dynamics (CMC/MD), to calculate the relative free energies of different amino acid side-chains. CMC/MD allows the calculation of the relative free energies for many chemical species from a single free energy calculation. We have previously shown its utility in host:guest chemistry (Pitera and Kollman, J Am Chem Soc 1998;120:7557-7567)1 and ligand design (Eriksson et al., J Med Chem 1999;42:868-881)2, and here demonstrate its utility in calculations of amino acid properties and protein stability. We first study the relative solvation free energies of N-methylated and acetylated alanine, valine, and serine amino acids. With careful inclusion of rotameric states, internal energies, and both the solution and vacuum states of the calculation, we calculate relative solvation free energies in good agreement with thermodynamic integration (TI) calculations. Interestingly, we find that a significant amount of the unfavorable solvation of valine seen in prior work (Sun et al., J Am Chem Soc 1992;114:6798-6801)3 is caused by restraining the backbone in an extended conformation. In contrast, the solvation free energy of serine is calculated to be less favorable than expected from experiment, due to the formation of a favorable intramolecular hydrogen bond in the vacuum state. These monomer calculations emphasize the need to accurately consider all significant conformations of flexible molecules in free energy calculations. This development of the CMC/MD method paves the way for computations of protein stability analogous to the biochemical technique of "exhaustive mutagenesis." We have carried out just such a calculation at position 133 of T4 lysozyme, where we use CMC/MD to calculate the relative stability of eight different side-chain mutants in a single free energy calculation. Our T4 calculations show good agreement with the prior free energy calculations of Veenstra et al. (Prot Eng 1997;10:789-807)4 and excellent agreement with the experiments of Mendel et al. (Science 1992;256:1798-1802).

Decision letter for "Data-driven generation of perturbation networks for relative binding free energy calculations"

Molecular mechanics (MM) potentials have long been a workhorse of computational chemistry. Leveraging accuracy and speed, these functional forms find use in a wide variety of applications in biomolecular modeling and drug discovery, from rapid virtual screening to detailed free energy calculations. Traditionally, MM potentials have relied on human-curated, inflexible, and poorly extensible discrete chemical perception rules (atom types) for applying parameters to small molecules or biopolymers, making it difficult to optimize both types and parameters to fit quantum chemical or physical property data. Here, we propose an alternative approach that uses graph neural networks to perceive chemical environments, producing continuous atom embeddings from which valence and nonbonded parameters can be predicted using invariance-preserving layers. Since all stages are built from smooth neural functions, the entire process-spanning chemical perception to parameter assignment-is modular and end-to-end differentiable with respect to model parameters, allowing new force fields to be easily constructed, extended, and applied to arbitrary molecules. We show that this approach is not only sufficiently expressive to reproduce legacy atom types, but that it can learn to accurately reproduce and extend existing molecular mechanics force fields. Trained with arbitrary loss functions, it can construct entirely new force fields self-consistently applicable to both biopolymers and small molecules directly from quantum chemical calculations, with superior fidelity than traditional atom or parameter typing schemes. When adapted to simultaneously fit partial charge models, espaloma delivers high-quality partial atomic charges orders of magnitude faster than current best-practices with low inaccuracy. When trained on the same quantum chemical small molecule dataset used to parameterize the Open Force Field ("Parsley") openff-1.2.0 small molecule force field augmented with a peptide dataset, the resulting espaloma model shows superior accuracy vis-á-vis experiments in computing relative alchemical free energy calculations for a popular benchmark. This approach is implemented in the free and open source package espaloma, available at https://github.com/choderalab/espaloma.