Alchemical Free Energy Calculations Research Articles

Prediction of octanol-water partition coefficients for the SAMPL6-$$\log P$$ molecules using molecular dynamics simulations with OPLS-AA, AMBER and CHARMM force fields

All-atom molecular dynamics simulations with stratified alchemical free energy calculations were used to predict the octanol-water partition coefficient [Formula: see text] of eleven small molecules as part of the SAMPL6-[Formula: see text] blind prediction challenge using four different force field parametrizations: standard OPLS-AA with transferable charges, OPLS-AA with non-transferable CM1A charges, AMBER/GAFF, and CHARMM/CGenFF. Octanol parameters for OPLS-AA, GAFF and CHARMM were validated by comparing the density as a function of temperature, the chemical potential, and the hydration free energy to experimental values. The partition coefficients were calculated from the solvation free energy for the compounds in water and pure ("dry") octanol or "wet" octanol with 27 mol% water dissolved. Absolute solvation free energies were computed by thermodynamic integration (TI) and the multistate Bennett acceptance ratio with uncorrelated samples from data generated by an established protocol using 5-ns windowed alchemical free energy perturbation (FEP) calculations with the Gromacs molecular dynamics package. Equilibration of sets of FEP simulations was quantified by a new measure of convergence based on the analysis of forward and time-reversed trajectories. The accuracy of the [Formula: see text] predictions was assessed by descriptive statistical measures such as the root mean square error (RMSE) of the data set compared to the experimental values. Discarding the first 1 ns of each 5-ns window as an equilibration phase had a large effect on the GAFF data, where it improved the RMSE by up to 0.8 log units, while the effect for other data sets was smaller or marginally worsened the agreement. Overall, CGenFF gave the best prediction with RMSE 1.2 log units, although for only eight molecules because the current CGenFF workflow for Gromacs does not generate files for certain halogen-containing compounds. Over all eleven compounds, GAFF gave an RMSE of 1.5. The effect of using a mixed water/octanol solvent slightly decreased the accuracy for CGenFF and GAFF and slightly increased it for OPLS-AA. The GAFF and OPLS-AA results displayed a systematic error where molecules were too hydrophobic whereas CGenFF appeared to be more balanced, at least on this small data set.

Alchemical Hydration Free-Energy Calculations Using Molecular Dynamics with Explicit Polarization and Induced Polarity Decoupling: An On-the-Fly Polarization Approach.

We present a methodology using fixed charge force fields for alchemical solvation free energy calculations which accounts for the change in polarity that the solute experiences as it transfers from the gas-phase to the condensed phase. We update partial charges using QM/MM snapshots, decoupling the electric field appropriately when updating the partial charges. We also show how to account for the cost of self-polarization. We test our methodology on 30 molecules ranging from small polar to large druglike molecules. We use Minimum Basis Iterative Stockholder (MBIS), Restrained Electrostatic Potential (RESP), and AM1-BCC partial charge methodologies. Using our method with MP2/cc-pVTZ and MBIS partial charges yields an average absolute deviation (AAD) of 6.3 kJ·mol-1 in comparison with the AM1-BCC result of 8.6 kJ·mol-1. AM1-BCC is within experimental uncertainty on 10% of the data compared to 30% with our method. We conjecture that results can be further improved by using Lennard-Jones and torsional parameters refitted to MBIS and RESP partial charge methods that use high levels of theory.

Best Practices for Alchemical Free Energy Calculations [Article v1.0

Alchemical free energy calculations are a useful tool for predicting free energy differences associated with the transfer of molecules from one environment to another. The hallmark of these methods is the use of "bridging" potential energy functions representing alchemical intermediate states that cannot exist as real chemical species. The data collected from these bridging alchemical thermodynamic states allows the efficient computation of transfer free energies (or differences in transfer free energies) with orders of magnitude less simulation time than simulating the transfer process directly. While these methods are highly flexible, care must be taken in avoiding common pitfalls to ensure that computed free energy differences can be robust and reproducible for the chosen force field, and that appropriate corrections are included to permit direct comparison with experimental data. In this paper, we review current best practices for several popular application domains of alchemical free energy calculations performed with equilibrium simulations, in particular relative and absolute small molecule binding free energy calculations to biomolecular targets.

Large scale relative protein ligand binding affinities using non-equilibrium alchemy.

Ligand binding affinity calculations based on molecular dynamics (MD) simulations and non-physical (alchemical) thermodynamic cycles have shown great promise for structure-based drug design. However, their broad uptake and impact is held back by the notoriously complex setup of the calculations. Only a few tools other than the free energy perturbation approach by Schrödinger Inc. (referred to as FEP+) currently enable end-to-end application. Here, we present for the first time an approach based on the open-source software pmx that allows to easily set up and run alchemical calculations for diverse sets of small molecules using the GROMACS MD engine. The method relies on theoretically rigorous non-equilibrium thermodynamic integration (TI) foundations, and its flexibility allows calculations with multiple force fields. In this study, results from the Amber and Charmm force fields were combined to yield a consensus outcome performing on par with the commercial FEP+ approach. A large dataset of 482 perturbations from 13 different protein–ligand datasets led to an average unsigned error (AUE) of 3.64 ± 0.14 kJ mol−1, equivalent to Schrödinger's FEP+ AUE of 3.66 ± 0.14 kJ mol−1. For the first time, a setup is presented for overall high precision and high accuracy relative protein–ligand alchemical free energy calculations based on open-source software.

Effects of Mutating Trp42 Residue on γD-Crystallin Stability

Oligomerization and aggregation of γD-crystallins (HγDC) in the eye lens is one of the main causes of cataract development. To date, several congenital mutations related to this protein are known to promote the formation of aggregates. Previous studies have demonstrated that mutations in W42 residue of HγDC lead to the generation of partially unfolded intermediates that are more prone to aggregate. To understand the role of W42 in the stability of HγDC, we performed alchemical free-energy calculations and all-atom molecular dynamics simulations of different W42 mutant models. Our results suggest that substitution of W42 by small size and/or polar residues promotes HγDC denaturation due to the entry of water molecules into the hydrophobic core of the N-terminal domain. Similar behavior was observed in the C-terminal domain of HγDC when mutating the W130 residue located in a homologous position. Moreover, the exposure of the hydrophobic core residues could lead to the formation of aggregation-prone partially unfolded species. Overall, this study takes a step toward understanding the role of HγDC in cataract development.

Dissecting the Energetics of Intrinsically Disordered Proteins via a Hybrid Experimental and Computational Approach.

Intrinsically disordered proteins (IDPs) play important roles in biology, but little is known about the energetics of their inter-residue interactions. Methods that have been successfully applied to analyze the energetics of globular proteins are not applicable to the fluctuating partially ordered ensembles populated by IDPs. A combined computational experimental strategy is introduced for analyzing the energetic role of individual residues in the free state of IDPs. The approach combines experimental measurements of the binding of wild-type and mutant IDPs to their partners with alchemical free energy calculations of the structured complexes. These data allow quantitative information to be deduced about the free state via a thermodynamic cycle. The approach is validated by the analysis of the effects of mutations upon the binding free energy of the ovomucoid inhibitor third binding domain to its partners and is applied to the C-terminal domain of the measles virus nucleoprotein, a 125-residue IDP involved in the RNA transcription and replication of measles virus. The analysis reveals significant inter-residue interactions in the unbound IDP and suggests a biological role for them. The work demonstrates that advances in force fields and computational hardware have now led to the point where it is possible to develop methods, which integrate experimental and computational techniques to reveal insights that cannot be studied using either technique alone.

Absolute Protein Binding Free Energy Simulations for Ligands with Multiple Poses, a Thermodynamic Path That Avoids Exhaustive Enumeration of the Poses.

We propose a free energy calculation method for receptor-ligand binding, which have multiple binding poses that avoids exhaustive enumeration of the poses. For systems with multiple binding poses, the standard procedure is to enumerate orientations of the binding poses, restrain the ligand to each orientation, and then, calculate the binding free energies for each binding pose. In this study, we modify a part of the thermodynamic cycle in order to sample a broader conformational space of the ligand in the binding site. This modification leads to more accurate free energy calculation without performing separate free energy simulations for each binding pose. We applied our modification to simple model host-guest systems as a test, which have only two binding poses, by using a single decoupling method (SDM) in implicit solvent. The results showed that the binding free energies obtained from our method without knowing the two binding poses were in good agreement with the benchmark results obtained by explicit enumeration of the binding poses. Our method is applicable to other alchemical binding free energy calculation methods such as the double decoupling method (DDM) in explicit solvent. We performed a calculation for a protein-ligand system with explicit solvent using our modified thermodynamic path. The results of the free energy simulation along our modified path were in good agreement with the results of conventional DDM, which requires a separate binding free energy calculation for each of the binding poses of the example of phenol binding to T4 lysozyme in explicit solvent. © 2019 Wiley Periodicals, Inc.

Perturbation potentials to overcome order/disorder transitions in alchemical binding free energy calculations.

We investigate the role of order/disorder transitions in alchemical simulations of protein-ligand absolute binding free energies. We show, in the context of a potential of mean force description, that for a benchmarking system (the complex of the L99A mutant of T4 lysozyme with 3-iodotoluene) and for a more challenging system relevant for medicinal applications (the complex of the farnesoid X receptor with inhibitor 26 from a recent D3R challenge) that order/disorder transitions can significantly hamper Hamiltonian replica exchange sampling efficiency and slow down the rate of equilibration of binding free energy estimates. We further show that our analytical model of alchemical binding combined with the formalism developed by Straub et al. for the treatment of order/disorder transitions of molecular systems can be successfully employed to analyze the transitions and help design alchemical schedules and soft-core functions that avoid or reduce the adverse effects of rare binding/unbinding transitions. The results of this work pave the way for the application of these techniques to the alchemical estimation with explicit solvation of hydration free energies and absolute binding free energies of systems undergoing order/disorder transitions.

Blinded prediction of protein-ligand binding affinity using Amber thermodynamic integration for the 2018 D3R grand challenge 4.

In the framework of the 2018 Drug Design Data Resource grand challenge 4, blinded predictions on relative binding free energy were performed for a set of 39 ligands of the Cathepsin S protein. We leveraged the GPU-accelerated thermodynamic integration of Amber 18 to advance our computational prediction. When our entry was compared to experimental results, a good correlation was observed (Kendall's τ: 0.62, Spearman's ρ: 0.80 and Pearson's R: 0.82). We designed a parallelized transformation map that placed ligands into several groups based on common alchemical substructures; TI transformations were carried out for each ligand to the relevant substructure, and between substructures. Our calculations were all conducted using the linear potential scaling scheme in Amber TI because we believe the softcore potential/dual-topology approach as implemented in current Amber TI is highly fault-prone for some transformations. The issue is illustrated by using two examples in which typical preparation for the dual-topology approach of Amber TI fails. Overall, the high accuracy of our prediction is a result of recent advances in force fields (ff14SB and GAFF), as well as rapid calculation of ensemble averages enabled by the GPU implementation of Amber. The success shown here in a blinded prediction strongly suggests that alchemical free energy calculation in Amber is a promising tool for future commercial drug design.

Compressing physics with an autoencoder: Creating an atomic species representation to improve machine learning models in the chemical sciences

We define a vector quantity which corresponds to atomic species identity by compressing a set of physical properties with an autoencoder. This vector, referred to here as the elemental modes, provides many advantages in downstream machine learning tasks. Using the elemental modes directly as the feature vector, we trained a neural network to predict formation energies of elpasolites with improved accuracy over previous works on the same task. Combining the elemental modes with geometric features used in high-dimensional neural network potentials (HD-NNPs) solves many problems of scaling and efficiency in the development of such neural network potentials. Whereas similar models in the past have been limited to typically four atomic species (H, C, N, and O), our implementation does not scale in cost by adding more atomic species and allows us to train an HD-NNP model which treats molecules containing H, C, N, O, F, P, S, Cl, Se, Br, and I. Finally, we establish that our implementation allows us to define feature vectors for alchemical intermediate states in the HD-NNP model, which opens up new possibilities for performing alchemical free energy calculations on systems where bond breaking/forming is important.

Overcoming Challenging Substituent Perturbations with Multisite λ-Dynamics: A Case Study Targeting β-Secretase 1.

Alchemical free energy calculations have made a dramatic impact upon the field of structure-based drug design by allowing functional group modifications to be explored computationally prior to experimental synthesis and assay evaluation, thereby informing and directing synthetic strategies. In furthering the advancement of this area, a series of 21 β-secretase 1 (BACE1) inhibitors developed by Janssen Pharmaceuticals were examined to evaluate the ability to explore large substituent perturbations, some of which contain scaffold modifications, with multisite λ-dynamics (MSλD), an innovative alchemical free energy framework. Our findings indicate that MSλD is able to efficiently explore all structurally diverse ligand end-states simultaneously within a single MD simulation with a high degree of precision and with reduced computational costs compared to the widely used approach TI/MBAR. Furthermore, computational predictions were shown to be accurate to within 0.5-0.8 kcal/mol when CM1A partial atomic charges were combined with CHARMM or OPLS-AA-based force fields, demonstrating that MSλD is force field independent and a viable alternative to FEP or TI approaches for drug design.

Thermodynamic Stability of Human γD-Crystallin Mutants Using Alchemical Free-Energy Calculations.

γD-Crystallin (HγDC) is a key structural protein in the human lens, whose aggregation has been associated with the development of cataracts. Single-point mutations and post-translational modifications destabilize HγDC interactions, forming partially folded intermediates, where hydrophobic residues are exposed and thus triggering its aggregation. In this work, we used alchemical free-energy calculations to predict changes in thermodynamic stability (ΔΔG) of 10 alanine-scanning variants and 12 HγDC mutations associated with the development of congenital cataract. Our results show that W42R is the most destabilizing mutation in HγDC. This has been corroborated through experimental determination of ΔΔG employing differential scanning calorimetry. Calculations of hydration free energies from the HγDC WT and the W42R mutant suggested that the mutant has a higher aggregation propensity. Our combined theoretical and experimental results contribute to understand HγDC destabilization and aggregation mechanisms in age-onset cataracts.

A double exponential potential for van der Waals interaction.

Van der Waals (vdw) interaction is an important force between atoms and molecules. Many potential functions have been proposed to model vdw interaction such as the Lennard-Jones (L-J) potential. To overcome certain drawbacks of existing function forms, this work proposes a double exponential (DE) potential that contains a repulsive exponential term and an attractive exponential term. This potential decays faster than the L-J potential and has a soft core. The DE potential is very flexible and its two exponential parameters can be adjusted continuously to mimic many potential functions. Combined with the isotropic periodic sum (IPS) method, the DE potential can efficiently and accurately describe non-bonded interactions and is convenient for alchemical free energy calculation.

Computational Fluorine Scanning Using Free-Energy Perturbation.

We present perturbative fluorine scanning, a computational fluorine scanning approach using free-energy perturbation. This method can be applied to molecular dynamics simulations of a single compound and make predictions for the best binders out of numerous fluorinated analogues. We tested the method on nine test systems: renin, DPP4, menin, P38, factor Xa, CDK2, AKT, JAK2, and androgen receptor. The predictions were in excellent agreement with more rigorous alchemical free-energy calculations and in good agreement with experimental data for most of the test systems. However, the agreement with experiment was very poor in some of the test systems, and this highlights the need for improved force fields in addition to accurate treatment of tautomeric and protonation states. The method is of particular interest due to the wide use of fluorine in medicinal chemistry to improve binding affinity and ADME properties. The promising results on this test case suggest that perturbative fluorine scanning will be a useful addition to the available arsenal of free-energy methods.

Effect of set up protocols on the accuracy of alchemical free energy calculation over a set of ACK1 inhibitors.

Hit-to-lead virtual screening frequently relies on a cascade of computational methods that starts with rapid calculations applied to a large number of compounds and ends with more expensive computations restricted to a subset of compounds that passed initial filters. This work focuses on set up protocols for alchemical free energy (AFE) scoring in the context of a Docking–MM/PBSA–AFE cascade. A dataset of 15 congeneric inhibitors of the ACK1 protein was used to evaluate the performance of AFE set up protocols that varied in the steps taken to prepare input files (using previously docked and best scored poses, manual selection of poses, manual placement of binding site water molecules). The main finding is that use of knowledge derived from X-ray structures to model binding modes, together with the manual placement of a bridging water molecule, improves the R2 from 0.45 ± 0.06 to 0.76 ± 0.02 and decreases the mean unsigned error from 2.11 ± 0.08 to 1.24 ± 0.04 kcal mol-1. By contrast a brute force automated protocol that increased the sampling time ten-fold lead to little improvements in accuracy. Besides, it is shown that for the present dataset hysteresis can be used to flag poses that need further attention even without prior knowledge of experimental binding affinities.

Alchemical Free-Energy Calculations by Multiple-Replica λ-Dynamics: The Conveyor Belt Thermodynamic Integration Scheme.

A new method is proposed to calculate alchemical free-energy differences based on molecular dynamics (MD) simulations, called the conveyor belt thermodynamic integration (CBTI) scheme. As in thermodynamic integration (TI), K replicas of the system are simulated at different values of the alchemical coupling parameter λ. The number K is taken to be even, and the replicas are equally spaced on a forward-turn-backward-turn path, akin to a conveyor belt (CB) between the two physical end-states; and as in λ-dynamics (λD), the λ-values associated with the individual systems evolve in time along the simulation. However, they do so in a concerted fashion, determined by the evolution of a single dynamical variable Λ of period 2π controlling the advance of the entire CB. Thus, a change of Λ is always associated with K/2 equispaced replicas moving forward and K/2 equispaced replicas moving backward along λ. As a result, the effective free-energy profile of the replica system along Λ is periodic of period 2 πK-1, and the magnitude of its variations decreases rapidly upon increasing K, at least as K-1 in the limit of large K. When a sufficient number of replicas is used, these variations become small, which enables a complete and quasi-homogeneous coverage of the λ-range by the replica system, without application of any biasing potential. If desired, a memory-based biasing potential can still be added to further homogenize the sampling, the preoptimization of which is computationally inexpensive. The final free-energy profile along λ is calculated similarly to TI, by binning of the Hamiltonian λ-derivative as a function of λ considering all replicas simultaneously, followed by quadrature integration. The associated quadrature error can be kept very low owing to the continuous and quasi-homogeneous λ-sampling. The CBTI scheme can be viewed as a continuous/deterministic/dynamical analog of the Hamiltonian replica-exchange/permutation (HRE/HRP) schemes or as a correlated multiple-replica analog of the λD or λ-local elevation umbrella sampling (λ-LEUS) schemes. Compared to TI, it shares the advantage of the latter schemes in terms of enhanced orthogonal sampling, i.e. the availability of variable-λ paths to circumvent conformational barriers present at specific λ-values. Compared to HRE/HRP, it permits a deterministic and continuous sampling of the λ-range, is expected to be less sensitive to possible artifacts of the thermo- and barostating schemes, and bypasses the need to carefully preselect a λ-ladder and a swapping-attempt frequency. Compared to λ-LEUS, it eliminates (or drastically reduces) the dead time associated with the preoptimization of a biasing potential. The goal of this article is to provide the mathematical/physical formulation of the proposed CBTI scheme, along with an initial application of the method to the calculation of the hydration free energy of methanol.

Computational Insights on Small Molecule Binding to the Hv1 Proton Channel

Hv1 is a voltage-gated proton channel whose main function is to extrude excess protons from the cell. It appears to be involved in a variety of maladies (e.g., breast cancer metastasis, brain damage in ischemic stroke). Despite extensive recent research, details of the gating mechanism, proton permeation pathway, and exquisite selectivity of Hv1 remain elusive. We have previously developed an atomistic model of human Hv1 in its open state using molecular dynamics (MD) simulations on the microsecond timescale. This model has been validated by comparison with electrophysiology data. Further investigation of the model with respect to small molecule inhibitor binding may further support the structure and lead to the design and development of effective channel blockers. The objective of this work is to understand and improve the binding of small molecules that have been experimentally shown to block Hv1. Our approach utilizes the docking of these inhibitors to our open state model, atomistic molecular dynamics simulations, and alchemical free energy calculations. Here, we present results on the relative binding free energies of one prototypical Hv1 inhibitor with comparison to experimental mutagenesis and electrophysiology data.

Best Practices for Alchemical Free Energy Calculations [Article v1.0

Best Practices for Alchemical Free Energy Calculations [Article v1.0

Analytical Model of the Free Energy of Alchemical Molecular Binding.

We present a parametrized analytic statistical model of the thermodynamics of alchemical molecular binding within the solvent potential of mean force formalism. The model describes the free energy profiles of linear single-decoupling alchemical binding free energy calculations accurately. The parameters of the model, which are physically motivated, are derived by maximum likelihood inference from data obtained from alchemical molecular simulations. The validity of the model has been assessed on a set of host-guest complexes. The model faithfully reproduces both the binding free energy profiles and the probability densities of the perturbation energy as a function of the alchemical progress parameter. The model offers a rationalization for the characteristic shape of binding free energy profiles. The parameters obtained from the model are potentially useful descriptors of the association equilibrium of molecular complexes. Potential applications of the model for the classification of molecular complexes and the design of alchemical molecular simulations are envisioned.

Approaching protein design with multisite λ dynamics: Accurate and scalable mutational folding free energies in T4 lysozyme.

The estimation of changes in free energy upon mutation is central to the problem of protein design. Modern protein design methods have had remarkable success over a wide range of design targets, but are reaching their limits in ligand binding and enzyme design due to insufficient accuracy in mutational free energies. Alchemical free energy calculations have the potential to supplement modern design methods through more accurate molecular dynamics based prediction of free energy changes, but suffer from high computational cost. Multisite λ dynamics (MSλD) is a particularly efficient and scalable free energy method with potential to explore combinatorially large sequence spaces inaccessible with other free energy methods. This work aims to quantify the accuracy of MSλD and demonstrate its scalability. We apply MSλD to the classic problem of calculating folding free energies in T4 lysozyme, a system with a wealth of experimental measurements. Single site mutants considering 32 mutations show remarkable agreement with experiment with a Pearson correlation of 0.914 and mean unsigned error of 1.19 kcal/mol. Multisite mutants in systems with up to five concurrent mutations spanning 240 different sequences show comparable agreement with experiment. These results demonstrate the promise of MSλD in exploring large sequence spaces for protein design.