Alchemical Free Energy Calculations Research Articles

Alchemical Design of Pharmacological Chaperones with Higher Affinity for Phenylalanine Hydroxylase.

Phenylketonuria (PKU) is a rare metabolic disease caused by variations in a human gene, PAH, encoding phenylalanine hydroxylase (PAH), and the enzyme converting the essential amino acid phenylalanine into tyrosine. Many PKU-causing variations compromise the conformational stability of the encoded enzyme, decreasing or abolishing its catalytic activity, and leading to an elevated concentration of phenylalanine in the blood, which is neurotoxic. Several therapeutic approaches have been developed to treat the more severe manifestations of the disorder, but they are either not entirely effective or difficult to adhere to throughout life. In a search for novel pharmacological chaperones to treat PKU, a lead compound was discovered (compound IV) that exhibited promising in vitro and in vivo chaperoning activity on PAH. The structure of the PAH-IV complex has been reported. Here, using alchemical free energy calculations (AFEC) on the structure of the PAH-IV complex, we design a new generation of compound IV-analogues with a higher affinity for the enzyme. Seventeen novel analogues were synthesized, and thermal shift and isothermal titration calorimetry (ITC) assays were performed to experimentally evaluate their stabilizing effect and their affinity for the enzyme. Most of the new derivatives bind to PAH tighter than lead compound IV and induce a greater thermostabilization of the enzyme upon binding. Importantly, the correspondence between the calculated alchemical binding free energies and the experimentally determined ΔΔGb values is excellent, which supports the use of AFEC to design pharmacological chaperones to treat PKU using the X-ray structure of their complexes with the target PAH enzyme.

GROMACS in the Cloud: A Global Supercomputer to Speed Up Alchemical Drug Design.

We assess costs and efficiency of state-of-the-art high-performance cloud computing and compare the results to traditional on-premises compute clusters. Our use case is atomistic simulations carried out with the GROMACS molecular dynamics (MD) toolkit with a particular focus on alchemical protein–ligand binding free energy calculations. We set up a compute cluster in the Amazon Web Services (AWS) cloud that incorporates various different instances with Intel, AMD, and ARM CPUs, some with GPU acceleration. Using representative biomolecular simulation systems, we benchmark how GROMACS performs on individual instances and across multiple instances. Thereby we assess which instances deliver the highest performance and which are the most cost-efficient ones for our use case. We find that, in terms of total costs, including hardware, personnel, room, energy, and cooling, producing MD trajectories in the cloud can be about as cost-efficient as an on-premises cluster given that optimal cloud instances are chosen. Further, we find that high-throughput ligand-screening can be accelerated dramatically by using global cloud resources. For a ligand screening study consisting of 19 872 independent simulations or ∼200 μs of combined simulation trajectory, we made use of diverse hardware available in the cloud at the time of the study. The computations scaled-up to reach peak performance using more than 4 000 instances, 140 000 cores, and 3 000 GPUs simultaneously. Our simulation ensemble finished in about 2 days in the cloud, while weeks would be required to complete the task on a typical on-premises cluster consisting of several hundred nodes.

Exploring the Effect of Enhanced Sampling on Protein Stability Prediction.

Changes in protein stability due to side-chain mutations are evaluated by alchemical free-energy calculations based on classical molecular dynamics (MD) simulations in explicit solvent using the GROMOS force field. Three proteins of different complexity with a total number of 93 single-point mutations are analyzed, and the relative free-energy differences are discussed with respect to configurational sampling and (dis)agreement with experimental data. For the smallest protein studied, a 34-residue WW domain, the starting structure dependence of the alchemical free-energy changes, is discussed in detail. Deviations from previous simulations for the two other proteins are shown to result from insufficient sampling in the earlier studies. Hamiltonian replica exchange in combination with multiple starting structures and sufficient sampling time of more than 100 ns per intermediate alchemical state is required in some cases to reach convergence.

Molecular dynamics study of fission gas behaviour and solubility in molten FLiNaK salt

The solubility of fission products in molten salts is an important factor in predicting their rate of release, and their buildup can affect the salts’ performance. In this work, a molecular dynamics study of dissolved Ar, Xe, Cs+ and I− in molten FLiNaK is undertaken. The work includes a method for the determination of the interatomic potential parameters based on DFT calculations and tuned such that experimentally determined densities are achieved. Simulations were used to estimate diffusion coefficients for each solute. Additionally, the effects of dissolved CsI on the thermophysical properties, such as heat capacity, viscosity and thermal conductivity of the salt, are also predicted. Alchemical free energy calculations are used to determine the solutes’ solvation free energies, and trends due to changes in concentration and temperature are examined and compared favourably to experimental results found in the literature. Thus, it was found that molecular dynamics simulations can be used to predict the behaviour of solutes in molten salts, and the effects of their presence on the properties of the salt.

Alchemical binding free energy calculations guided design of novel human topoisomerase II inhibitors

Human topoisomerase II (topoII) enzymes are critical in DNA topology modulation within the cell. Importantly, topoII are validated anticancer drug targets due to their association with cancer cell proliferation. The clinically available topoII targeted anticancer drugs such as etoposide, often show harmful side effects and drug resistance. Therefore, new studies revolving around the design of topoII inhibitors are crucial for the discovery of novel, potent and safer anti-cancer therapeutics. We present an ongoing drug design campaign to optimize compounds centered on a recently patented chemical class of topoIIα inhibitors.

Data-driven discovery of cardiolipin-selective small molecules by computational active learning.

Subtle variations in the lipid composition of mitochondrial membranes can have a profound impact on mitochondrial function. The inner mitochondrial membrane contains the phospholipid cardiolipin, which has been demonstrated to act as a biomarker for a number of diverse pathologies. Small molecule dyes capable of selectively partitioning into cardiolipin membranes enable visualization and quantification of the cardiolipin content. Here we present a data-driven approach that combines a deep learning-enabled active learning workflow with coarse-grained molecular dynamics simulations and alchemical free energy calculations to discover small organic compounds able to selectively permeate cardiolipin-containing membranes. By employing transferable coarse-grained models we efficiently navigate the all-atom design space corresponding to small organic molecules with molecular weight less than ≈500 Da. After direct simulation of only 0.42% of our coarse-grained search space we identify molecules with considerably increased levels of cardiolipin selectivity compared to a widely used cardiolipin probe 10-N-nonyl acridine orange. Our accumulated simulation data enables us to derive interpretable design rules linking coarse-grained structure to cardiolipin selectivity. The findings are corroborated by fluorescence anisotropy measurements of two compounds conforming to our defined design rules. Our findings highlight the potential of coarse-grained representations and multiscale modelling for materials discovery and design.

End-to-end differentiable construction of molecular mechanics force fields.

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.

Precise Binding Free Energy Calculations for Multiple Molecules Using an Optimal Measurement Network of Pairwise Differences

Alchemical binding free energy (BFE) calculations offer an efficient and thermodynamically rigorous approach to in silico binding affinity predictions. As a result of decades of methodological improvements and recent advances in computer technology, alchemical BFE calculations are now widely used in drug discovery research. They help guide the prioritization of candidate drug molecules by predicting their binding affinities for a biomolecular target of interest (and potentially selectivity against undesirable antitargets). Statistical variance associated with such calculations, however, may undermine the reliability of their predictions, introducing uncertainty both in ranking candidate molecules and in benchmarking their predictive accuracy. Here, we present a computational method that substantially improves the statistical precision in BFE calculations for a set of ligands binding to a common receptor by dynamically allocating computational resources to different BFE calculations according to an optimality objective established in a previous work from our group and extended in this work. Our method, termed Network Binding Free Energy (NetBFE), performs adaptive BFE calculations in iterations, re-optimizing the allocations in each iteration based on the statistical variances estimated from previous iterations. Using examples of NetBFE calculations for protein binding of congeneric ligand series, we demonstrate that NetBFE approaches the optimal allocation in a small number (≤5) of iterations and that NetBFE reduces the statistical variance in the BFE estimates by approximately a factor of 2 when compared to a previously published and widely used allocation method at the same total computational cost.

Inhibition Mechanism of SARS-CoV-2 Main Protease with Ketone-Based Inhibitors Unveiled by Multiscale Simulations: Insights for Improved Designs*.

We present the results of classical and QM/MM simulations for the inhibition of SARS‐CoV‐2 3CL protease by a hydroxymethylketone inhibitor, PF‐00835231. In the noncovalent complex the carbonyl oxygen atom of the warhead is placed in the oxyanion hole formed by residues 143 to 145, while P1–P3 groups are accommodated in the active site with interactions similar to those observed for the peptide substrate. According to alchemical free energy calculations, the P1′ hydroxymethyl group also contributes to the binding free energy. Covalent inhibition of the enzyme is triggered by the proton transfer from Cys145 to His41. This step is followed by the nucleophilic attack of the Sγ atom on the carbonyl carbon atom of the inhibitor and a proton transfer from His41 to the carbonyl oxygen atom mediated by the P1′ hydroxyl group. Computational simulations show that the addition of a chloromethyl substituent to the P1′ group may lower the activation free energy for covalent inhibition

Inhibition Mechanism of SARS‐CoV‐2 Main Protease with Ketone‐Based Inhibitors Unveiled by Multiscale Simulations: Insights for Improved Designs**

AbstractWe present the results of classical and QM/MM simulations for the inhibition of SARS‐CoV‐2 3CL protease by a hydroxymethylketone inhibitor, PF‐00835231. In the noncovalent complex the carbonyl oxygen atom of the warhead is placed in the oxyanion hole formed by residues 143 to 145, while P1–P3 groups are accommodated in the active site with interactions similar to those observed for the peptide substrate. According to alchemical free energy calculations, the P1′ hydroxymethyl group also contributes to the binding free energy. Covalent inhibition of the enzyme is triggered by the proton transfer from Cys145 to His41. This step is followed by the nucleophilic attack of the Sγ atom on the carbonyl carbon atom of the inhibitor and a proton transfer from His41 to the carbonyl oxygen atom mediated by the P1′ hydroxyl group. Computational simulations show that the addition of a chloromethyl substituent to the P1′ group may lower the activation free energy for covalent inhibition

Expanded Ensemble Methods Can be Used to Accurately Predict Protein-Ligand Relative Binding Free Energies.

Alchemical free energy methods have become indispensable in computational drug discovery for their ability to calculate highly accurate estimates of protein-ligand affinities. Expanded ensemble (EE) methods, which involve single simulations visiting all of the alchemical intermediates, have some key advantages for alchemical free energy calculation. However, there have been relatively few examples published in the literature of using expanded ensemble simulations for free energies of protein-ligand binding. In this paper, as a test of expanded ensemble methods, we compute relative binding free energies using the Open Force Field Initiative force field (codename "Parsley") for 24 pairs of Tyk2 inhibitors derived from a congeneric series of 16 compounds. The EE predictions agree well with the experimental values (root-mean-square error (RMSE) of 0.94 ± 0.13 kcal mol-1 and mean unsigned error (MUE) of 0.75 ± 0.12 kcal mol-1). We find that while increasing the number of alchemical intermediates can improve the phase space overlap, faster convergence can be obtained with fewer intermediates, as long as acceptance rates are sufficient. We also find that convergence can be improved using more aggressive updating of biases, and that estimates can be improved by performing multiple independent EE calculations. This work demonstrates that EE is a viable option for alchemical free energy calculation. We discuss the implications of these findings for rational drug design, as well as future directions for improvement.

Efficient Alchemical Intermediate States in Free Energy Calculations Using λ-Enveloping Distribution Sampling.

Alchemical free energy calculations generally require intermediate states along a coupling parameter λ to establish sufficient phase space overlap for obtaining converged results. Such intermediate states can also be engineered to lower the energy barriers and, consequently, reduce the required sampling time. The recently introduced λ-enveloping distribution sampling (λ-EDS) scheme combines the properties of the minimum variance pathway and the EDS methods to improve sampling and allow for larger steps along the alchemical pathway compared to conventional approaches. This scheme also eliminates the need for soft-core potentials and retains the behavior of conventional λ-intermediate states as a limiting case. In this study, an automated procedure is developed to select the parameters of λ-EDS for optimal performance. The underlying theory is illustrated based on simulations of simple test systems (bond length changes in harmonic oscillators, mutations of dihedral angles, and charge creation in water), as well as on the calculation of the absolute hydration free energies of 12 small organic molecules.

Molecular Environment-Specific Atomic Charges Improve Binding Affinity Predictions of SAMPL5 Host-Guest Systems.

Host-guest systems are widely used in benchmarks as model systems to improve computational methods for absolute binding free energy predictions. Recent advances in sampling algorithms for alchemical free energy calculations and the increase in computational power have made their binding affinity prediction primarily dependent on the quality of the force field. Here, we propose a new methodology to derive the atomic charges of host-guest systems based on quantum mechanics/molecular mechanics calculations and minimal basis iterative stockholder (MBIS) partitioning of the polarized electron density. A newly developed interface between the OpenMM and ORCA software packages provides D-MBIS charges that represent the guest's average electrostatic interactions in the hosts or the solvent. The simulation workflow also calculates the average energy required to polarize the guest in the bound and unbound state. Alchemical free energy calculations using the general Amber force field parameters with D-MBIS charges improve the binding affinity prediction of six guests bound to two octa acid hosts compared to the AM1-BCC charge set after correction with the average energetic polarization cost. This correction originates from the difference in potential energy that is required to polarize the guest in the bound and unbound state and contributes significantly to the binding affinity of anionic guests.

Dummy Atoms in Alchemical Free Energy Calculations.

In calculations of relative free energy differences, the number of atoms of the initial and final states is rarely the same. This necessitates the introduction of dummy atoms. These placeholders interact with the physical system only by bonded energy terms. We investigate the conditions necessary so that the presence of dummy atoms does not influence the result of a relative free energy calculation. On the one hand, one has to ensure that dummy atoms only give a multiplicative contribution to the partition function so that their contribution cancels from double-free energy differences. On the other hand, the bonded terms used to attach a dummy atom (or group of dummy atoms) to the physical system have to maintain it in a well-defined position and orientation relative to the physical system. A detailed theoretical analysis of both aspects is provided, illustrated by 24 calculations of relative solvation free energy differences, for which all four legs of the underlying thermodynamic cycle were computed. Cycle closure (or lack thereof) was used as a sensitive indicator to probing the effects of dummy atom treatment on the resulting free energy differences. We find that a naive (but often practiced) treatment of dummy atoms results in errors of up to kBT when calculating the relative solvation free energy difference between two small solutes, such as methane and ammonia. While our analysis focuses on the so-called single topology approach to set up alchemical transformations, similar considerations apply to dual topology, at least many widely used variants thereof.

The accelerated weight histogram method for alchemical free energy calculations.

The accelerated weight histogram method is an enhanced sampling technique used to explore free energy landscapes by applying an adaptive bias. The method is general and easy to extend. Herein, we show how it can be used to efficiently sample alchemical transformations, commonly used for, e.g., solvation and binding free energy calculations. We present calculations and convergence of the hydration free energy of testosterone, representing drug-like molecules. We also include methane and ethanol to validate the results. The protocol is easy to use, does not require a careful choice of parameters, and scales well to accessible resources, and the results converge at least as quickly as when using conventional methods. One benefit of the method is that it can easily be combined with other reaction coordinates, such as intermolecular distances.

Challenges Encountered Applying Equilibrium and Nonequilibrium Binding Free Energy Calculations.

Binding free energy calculations have become increasingly valuable to drive decision making in drug discovery projects. However, among other issues, inadequate sampling can reduce accuracy, limiting the value of the technique. In this paper, we apply absolute binding free energy calculations to ligands binding to T4 lysozyme L99A and HSP90 using equilibrium and nonequilibrium approaches. We highlight sampling problems encountered in these systems, such as slow side chain rearrangements and slow changes of water placement upon ligand binding. These same types of challenges are also likely to show up in other protein-ligand systems, and we propose some strategies to diagnose and test for such problems in alchemical free energy calculations. We also explore similarities and differences in how the equilibrium and the nonequilibrium approaches handle these problems. Our results show the large amount of work still to be done to make free energy calculations robust and reliable and provide insight for future research in this area.

Implementation of the QUBE Force Field in SOMD for High-Throughput Alchemical Free-Energy Calculations.

The quantum mechanical bespoke (QUBE) force-field approach has been developed to facilitate the automated derivation of potential energy function parameters for modeling protein-ligand binding. To date, the approach has been validated in the context of Monte Carlo simulations of protein-ligand complexes. We describe here the implementation of the QUBE force field in the alchemical free-energy calculation molecular dynamics simulation package SOMD. The implementation is validated by demonstrating the reproducibility of absolute hydration free energies computed with the QUBE force field across the SOMD and GROMACS software packages. We further demonstrate, by way of a case study involving two series of non-nucleoside inhibitors of HIV-1 reverse transcriptase, that the availability of QUBE in a modern simulation package that makes efficient use of graphics processing unit acceleration will facilitate high-throughput alchemical free-energy calculations.

A strategy for proline and glycine mutations to proteins with alchemical free energy calculations.

Computation of the thermodynamic consequences of protein mutations holds great promise in protein biophysics and design. Alchemical free energy methods can give improved estimates of mutational free energies, and are already widely used in calculations of relative and absolute binding free energies in small molecule design problems. In principle, alchemical methods can address any amino acid mutation with an appropriate alchemical pathway, but identifying a strategy that produces such a path for proline and glycine mutations is an ongoing challenge. Most current strategies perturb only side chain atoms, while proline and glycine mutations also alter the backbone parameters and backbone ring topology. Some strategies also perturb backbone parameters and enable glycine mutations. This work presents a strategy that enables both proline and glycine mutations and comprises two key elements: a dual backbone with restraints and scaling of bonded terms, facilitating backbone parameter changes, and a soft bond in the proline ring, enabling ring topology changes in proline mutations. These elements also have utility for core hopping and macrocycle studies in computer-aided drug design. This new strategy shows slight improvements over an alternative side chain perturbation strategy for a set T4 lysozyme mutations lacking proline and glycine, and yields good agreement with experiment for a set of T4 lysozyme proline and glycine mutations not previously studied. To our knowledge this is the first report comparing alchemical predictions of proline mutations with experiment. With this strategy in hand, alchemical methods now have access to the full palette of amino acid mutations.

Binding thermodynamics and interaction patterns of human purine nucleoside phosphorylase-inhibitor complexes from extensive free energy calculations.

Human purine nucleoside phosphorylase (hPNP) plays a significant role in the catabolism of deoxyguanosine. The trimeric protein is an important target in the treatment of T-cell cancers and autoimmune disorders. Experimental studies on the inhibition of the hPNP observe that the first ligand bound to one of three subunits effectively inhibits the protein, while the binding of more ligands to the subsequent sites shows negative cooperativities. In this work, we performed extensive end-point and alchemical free energy calculations to determine the binding thermodynamics of the trimeric protein-ligand system. 13 Immucillin inhibitors with experimental results are under calculation. Two widely accepted charge schemes for small molecules including AM1-BCC and RESP are adopted for ligands. The results of RESP are in better agreement with the experimental reference. Further investigations of the interaction networks in the protein-ligand complexes reveal that several residues play significant roles in stabilizing the complex structure. The most commonly observed ones include PHE200, GLU201, MET219, and ASN243. The conformations of the protein in different protein-ligand complexes are observed to be similar. We expect these insights to aid the development of potent drugs targeting hPNP.

Sensitivity of Binding Free Energy Calculations to Initial Protein Crystal Structure.

Binding free energy calculations using alchemical free energy (AFE) methods are widely considered to be the most rigorous tool in the computational drug discovery arsenal. Despite this, the calculations suffer from accuracy, precision, and reproducibility issues. In this publication, we perform a high-throughput study of more than a thousand AFE calculations, utilizing over 220 μs of total sampling time, on three different protein systems to investigate the impact of the initial crystal structure on the resulting binding free energy values. We also consider the influence of equilibration time and discover that the initial crystal structure can have a significant effect on free energy values obtained at short timescales that can manifest itself as a free energy difference of more than 1 kcal/mol. At longer timescales, these differences are largely overtaken by important rare events, such as torsional ligand motions, typically resulting in a much higher uncertainty in the obtained values. This work emphasizes the importance of rare event sampling and long-timescale dynamics in free energy calculations even for routinely performed alchemical perturbations. We conclude that an optimal protocol should not only concentrate computational resources on achieving convergence in the alchemical coupling parameter (λ) space but also on longer simulations and multiple repeats.