An introduction to best practices in free energy calculations

Insights and Challenges in Correcting Force Field Based Solvation Free Energies Using a Neural Network Potential

We present a comprehensive study investigating the potential gain in accuracy for calculating absolute solvation free energies (ASFE) using a neural network potential to describe the intramolecular energy of the solute. We calculated the ASFE for most compounds from the FreeSolv database using the Open Force Field (OpenFF) and compared them to earlier results obtained with the CHARMM General Force Field (CGenFF). By applying a nonequilibrium (NEQ) switching approach between the molecular mechanics (MM) description (either OpenFF or CGenFF) and the neural net potential (NNP)/MM level of theory (using ANI-2x as the NNP potential), we attempted to improve the accuracy of the calculated ASFEs. The predictive performance of the results did not change when this approach was applied to all 589 small molecules in the FreeSolv database that ANI-2x can describe. When selecting a subset of 156 molecules, focusing on compounds where the force fields performed poorly, we saw a slight improvement in the root-mean-square error (RMSE) and mean absolute error (MAE). The majority of our calculations utilized unidirectional NEQ protocols based on Jarzynski's equation. Additionally, we conducted bidirectional NEQ switching for a subset of 156 solutes. Notably, only a small fraction (10 out of 156) exhibited statistically significant discrepancies between unidirectional and bidirectional NEQ switching free energy estimates.

Mechanism of Ligand Discrimination by the NMT1 Riboswitch

Riboswitches are conserved functional domains in mRNA that almost exclusively exist in bacteria. They regulate the biosynthesis and transport of amino acids and essential metabolites such as coenzymes, nucleobases, and their derivatives by specifically binding small molecules. Due to their ability to precisely discriminate between different cognate molecules as well as their common existence in bacteria, riboswitches have become potential antibacterial drug targets that could deliver urgently needed antibiotics with novel mechanisms of action. In this work, we report the recognition mechanisms of four oxidization products (XAN, AZA, UAC, and HPA) generated during purine degradation by an RNA motif termed the NMT1 riboswitch. Specifically, we investigated the physical interactions between the riboswitch and the oxidized metabolites by computing the changes in the free energy on mutating key nucleobases in the ligand binding pocket of the riboswitch. We discovered that the electrostatic interactions are central to ligand discrimination by this riboswitch. The relative binding free energies of the mutations further indicated that some of the mutations can also strengthen the binding affinities of the ligands (AZA, UAC, and HPA). These mechanistic details are also potentially relevant in the design of novel compounds targeting riboswitches.

Active Learning Guided Drug Design Lead Optimization Based on Relative Binding Free Energy Modeling

In silico identification of potent protein inhibitors commonly requires prediction of a ligand binding free energy (BFE). Thermodynamics integration (TI) based on molecular dynamics (MD) simulations is a BFE calculation method capable of acquiring accurate BFE, but it is computationally expensive and time-consuming. In this work, we have developed an efficient automated workflow for identifying compounds with the lowest BFE among thousands of congeneric ligands, which requires only hundreds of TI calculations. Automated machine learning (AutoML) orchestrated by active learning (AL) in an AL-AutoML workflow allows unbiased and efficient search for a small set of best-performing molecules. We have applied this workflow to select inhibitors of the SARS-CoV-2 papain-like protease and were able to find 133 compounds with improved binding affinity, including 16 compounds with better than 100-fold binding affinity improvement. We obtained a hit rate that outperforms that expected of traditional expert medicinal chemist-guided campaigns. Thus, we demonstrate that the combination of AL and AutoML with free energy simulations provides at least 20× speedup relative to the naïve brute force approaches.

Martini 3 Coarse-Grained Force Field for Carbohydrates

The Martini 3 force field is a full reparametrization of the Martini coarse-grained model for biomolecular simulations. Due to the improved interaction balance, it allows for a more accurate description of condensed phase systems. In the present work, we develop a consistent strategy to parametrize carbohydrate molecules accurately within the framework of Martini 3. In particular, we develop a canonical mapping scheme which decomposes arbitrarily large carbohydrates into a limited number of fragments. Bead types for these fragments have been assigned by matching physicochemical properties of mono- and disaccharides. In addition, guidelines for assigning bonds, angles, and dihedrals were developed. These guidelines enable a more accurate description of carbohydrate conformations than in the Martini 2 force field. We show that models obtained with this approach are able to accurately reproduce osmotic pressures of carbohydrate water solutions. Furthermore, we provide evidence that the model differentiates correctly the solubility of the polyglucoses dextran (water-soluble) and cellulose (water insoluble but soluble in ionic liquids). Finally, we demonstrate that the new building blocks can be applied to glycolipids. We show they are able to reproduce membrane properties and induce binding of peripheral membrane proteins. These test cases demonstrate the validity and transferability of our approach.

Absolute binding free energies of mucroporin and its analog mucroporin-M1 with the heptad repeat 1 domain and RNA-dependent RNA polymerase of SARS-CoV-2

The peptide Mucroporin and its analog Mucroporin-M1 were studied using the molecular docking and molecular dynamics simulation of their complexation with two protein targets, the Heptad Repeat 1 (HR1) domain and RNA-dependent RNA polymerase (RdRp) of SARS-CoV-2. The molecular docking of the peptide-protein complexes was performed using the glowworm swarm optimization algorithm. The lowest energy poses were submitted to molecular dynamics simulation. Then, the binding free energies of Mucroporin and its analog Mucroporin-M1 with these two protein targets were calculated using the Multistate Bennett Acceptance Ratio (MBAR) method. It was verified that the peptides/HR1 domain complex showed stability in the interaction site determined by molecular docking. It was also found that Mucroporin-M1 has a much higher affinity than Mucroporin to the HR1 protein target. The peptides showed similar stability and affinity at the NTP binding site in the RdRp protein. Additional experimental studies are needed to confirm the antiviral activity of Mucroporin-M1 and a possible mechanism of action against SARS-CoV-2. However, here we indicate that Mucroporin-M1 may have potential antiviral activity against the HR1 domain with the possibility for further peptide optimization.Communicated by Ramaswamy H. Sarma.

Relative Binding Free Energy between Chemically Distant Compounds Using a Bidirectional Nonequilibrium Approach

In the context of advanced hit-to-lead drug design based on atomistic molecular dynamics simulations, we propose a dual topology alchemical approach for calculating the relative binding free energy (RBFE) between two chemically distant compounds. The method (termed NE-RBFE) relies on the enhanced sampling of the end-states in bulk and in the bound state via Hamiltonian Replica Exchange, alchemically connected by a series of independent and fast nonequilibrium (NE) simulations. The technique has been implemented in a bidirectional fashion, applying the Crooks theorem to the NE work distributions for RBFE predictions. The dissipation of the NE process, negatively affecting accuracy, has been minimized by introducing a smooth regularization based on shifted electrostatic and Lennard-Jones non bonded potentials. As a challenging testbed, we have applied our method to the calculation of the RBFEs in the recent host–guest SAMPL international contest, featuring a macrocyclic host with guests varying in the net charge, volume, and chemical fingerprints. Closure validation has been successfully verified in cycles involving compounds with disparate Tanimoto coefficients, volume, and net charge. NE-RBFE is specifically tailored for massively parallel facilities and can be used with little or no code modification on most of the popular software packages supporting nonequilibrium alchemical simulations, such as Gromacs, Amber, NAMD, or OpenMM. The proposed methodology bypasses most of the entanglements and limitations of the standard single topology RBFE approach for strictly congeneric series based on free-energy perturbation, such as slowly relaxing cavity water, sampling issues along the alchemical stratification, and the need for highly overlapping molecular fingerprints.

Coarse-Grained Model of Thiol-Epoxy-Based Alternating Copolymers in Explicit Solvents

The cosolvent method has been widely used in the self-assembly of amphiphilic alternating copolymers (ACPs), but the role of good and selective solvents is rarely investigated. Here, we have developed a coarse-grained (CG) model for the widely studied thiol-epoxy-based amphiphilic ACPs and a three-bead CG model for tetrahydrofuran (THF) as the good solvent, which is compatible with the MARTINI water model. The accuracy of both the CG polymer and THF models was validated by reproducing the structural and thermodynamic properties obtained from experiments or atomistic simulation results. Density in bulk, the radius of gyration, and solvation free energy in water or THF showed a good agreement between CG and atomistic models. The CG models were further employed to explore the self-assembly of ACPs in THF/water mixtures with different compositions. Chain folding and liquid-liquid phase separation behaviors were found with increasing water fractions, which were the key steps of the self-assembly process. This work will provide a basic platform to explore the self-assembly of amphiphilic ACPs in solvent mixtures and to reveal the real role of different solvents in self-assembly.

Multiscale Modeling of Bio-Nano Interactions of Zero-Valent Silver Nanoparticles

Understanding the specifics of interaction between the protein and nanomaterial is crucial for designing efficient, safe, and selective nanoplatforms, such as biosensor or nanocarrier systems. Routing experimental screening for the most suitable complementary pair of biomolecule and nanomaterial used in such nanoplatforms might be a resource-intensive task. While a range of computational tools are available for prescreening libraries of proteins for their interactions with small molecular ligands, choices for high-throughput screening of protein libraries for binding affinities to new and existing nanomaterials are very limited. In the current work, we present the results of the systematic computational study of interaction of various biomolecules with pristine zero-valent noble metal nanoparticles, namely, AgNPs, by using the UnitedAtom multiscale approach. A set of blood plasma and dietary proteins for which the interaction with AgNPs was described experimentally were examined computationally to evaluate the performance of the UnitedAtom method. A set of interfacial descriptors (log P^NM, adsorption affinities, and adsorption affinity ranking), which can characterize the relative hydrophobicity/hydrophilicity/lipophilicity of the nanosized silver and its ability to form bio(eco)corona, was evaluated for future use in nano-QSAR/QSPR studies.

Mechanism of the enhancing effect of glycyrrhizin on nifedipine penetration through a lipid membrane

The saponin glycyrrhizin from liquorice root shows the ability to enhance the therapeutic activity of other drugs when used as a drug delivery system. Due to its amphiphilic properties, glycyrrhizin can form self-associates (dimers, micelles) and supramolecular complexes with a wide range of hydrophobic drugs, which leads to an increase in their solubility, stability and bioavailability. That is why the mechanism of the biological activity of glycyrrhizin is of considerable interest and has been the subject of intensive physical and chemical research in the last decade. Two mechanisms have been proposed to explain the effect of glycyrrhizin on drug bioavailability, namely, the increase in drug solubility in water and enhancement of the membrane permeability. Interest in the membrane-modifying ability of glycyrrhizic acid (GA) is also growing at present due to its recently discovered antiviral activity against SARS-CoV-2 Bailly and Vergoten (2020) [1]. In the present study, the passive permeability of the DOPC lipid membrane for the calcium channel blocker nifedipine was elucidated by parallel artificial membrane permeability assay (PAMPA) and full atomistic molecular dynamics (MD) simulation with free energy calculations. PAMPA experiments show a remarkable increase in the amount of nifedipine (NF) permeated with glycyrrhizin compared to free NF. In previous studies, we have shown using MD techniques that glycyrrhizin molecules can integrate into the lipid bilayer. In this study, MD simulation demonstrates a significant decrease in the energy barrier of NF penetration through the lipid bilayer in the presence of glycyrrhizin both in the pure DOPC membrane and in the membrane with cholesterol. This effect can be explained by the formation of hydrogen bonds between NF and GA in the middle of the bilayer.

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.

Deciphering nucleotide modification-induced structure and stability changes

Nucleotide modification in RNA controls a bevy of biological processes, including RNA degradation, gene expression, and gene editing. In turn, misregulation of modified nucleotides is associated with a host of chronic diseases and disorders. However, the molecular mechanisms driving these processes remain poorly understood. To partially address this knowledge gap, we used alchemical and temperature replica exchange molecular dynamics (TREMD) simulations on an RNA duplex and an analogous hairpin to probe the structural effects of modified and/or mutant nucleotides. The simulations successfully predict the modification/mutation-induced relative free energy change for complementary duplex formation, and structural analyses highlight mechanisms driving stability changes. Furthermore, TREMD simulations for a hairpin-forming RNA with and without modification provide reliable estimations of the energy landscape. Illuminating the impact of methylated and/or mutated nucleotides on the structure-function relationship and the folding energy landscape, the simulations provide insights into modification-induced alterations to the folding mechanics of the hairpin. The results here may be biologically significant as hairpins are widespread structure motifs that play critical roles in gene expression and regulation. Specifically, the tetraloop of the probed hairpin is phylogenetically abundant, and the stem mirrors a miRNA seed region whose modification has been implicated in epilepsy pathogenesis.

Alchemical Binding Free Energy Calculations in AMBER20: Advances and Best Practices for Drug Discovery

Predicting protein-ligand binding affinities and the associated thermodynamics of biomolecular recognition is a primary objective of structure-based drug design. Alchemical free energy simulations offer a highly accurate and computationally efficient route to achieving this goal. While the AMBER molecular dynamics package has successfully been used for alchemical free energy simulations in academic research groups for decades, widespread impact in industrial drug discovery settings has been minimal because of the previous limitations within the AMBER alchemical code, coupled with challenges in system setup and postprocessing workflows. Through a close academia-industry collaboration we have addressed many of the previous limitations with an aim to improve accuracy, efficiency, and robustness of alchemical binding free energy simulations in industrial drug discovery applications. Here, we highlight some of the recent advances in AMBER20 with a focus on alchemical binding free energy (BFE) calculations, which are less computationally intensive than alternative binding free energy methods where full binding/unbinding paths are explored. In addition to scientific and technical advances in AMBER20, we also describe the essential practical aspects associated with running relative alchemical BFE calculations, along with recommendations for best practices, highlighting the importance not only of the alchemical simulation code but also the auxiliary functionalities and expertise required to obtain accurate and reliable results. This work is intended to provide a contemporary overview of the scientific, technical, and practical issues associated with running relative BFE simulations in AMBER20, with a focus on real-world drug discovery applications.

Titratable Martini model for constant pH simulations

In this work, we deliver a proof of concept for a fast method that introduces pH effects into classical coarse-grained (CG) molecular dynamics simulations. Our approach is based upon the latest version of the popular Martini CG model to which explicit proton mimicking particles are added. We verify our approach against experimental data involving several different molecules and different environmental conditions. In particular, we compute titration curves, pH dependent free energies of transfer, and lipid bilayer membrane affinities as a function of pH. Using oleic acid as an example compound, we further illustrate that our method can be used to study passive translocation in lipid bilayers via protonation. Finally, our model reproduces qualitatively the expansion of the macromolecule dendrimer poly(propylene imine) as well as the associated pKa shift of its different generations. This example demonstrates that our model is able to pick up collective interactions between titratable sites in large molecules comprising many titratable functional groups.

Alchemical free energy calculations via metadynamics: Application to the theophylline-RNA aptamer complex

We propose a computational workflow for robust and accurate prediction of both binding poses and their affinities at early stage in designing drug candidates. Small, rigid ligands with few intramolecular degrees of freedom, for example, fragment-like molecules, have multiple binding poses, even at a single binding site, and their affinities are often close to each other. We explore various structures of ligand binding to a target through metadynamics using a small number of collective variables, followed by reweighting to obtain the atomic coordinates. After identifying each binding pose by cluster analysis, we perform alchemical free energy calculations on each structure to obtain the overall value. We applied this protocol in computing free energy of binding for the theophylline-RNA aptamer complex. Of the six (meta)stable structures found, the most favorable binding structure is consistent with the structure obtained by NMR. The overall free energy of binding reproduces the experimental values very well.

Identification of potential binders of the main protease 3CLpro of the COVID-19 via structure-based ligand design and molecular modeling

We have applied a computational strategy, using a combination of virtual screening, docking and molecular dynamics techniques, aimed at identifying possible lead compounds for the non-covalent inhibition of the main protease 3CL^pro of the SARS-CoV2 Coronavirus. Based on the X-ray structure (PDB code: 6LU7), ligands were generated using a multimodal structure-based design and then docked to the monomer in the active state. Docking calculations show that ligand-binding is strikingly similar in SARS-CoV and SARS-CoV2 main proteases. The most potent docked ligands are found to share a common binding pattern with aromatic moieties connected by rotatable bonds in a pseudo-linear arrangement.

Confining Liquids inside Carbon Nanotubes: Accelerated Molecular Dynamics with Spliced, Soft-Core Potentials and Simulated Annealing

Understanding emergent phenomena of fluids under physical confinement requires the development of advanced tools for rapid and accurate simulation of their physiochemical properties. Simulating liquid molecules commensurate in size with the nanoscale enclosures that confine them is a key challenge. We demonstrate an accelerated molecular dynamics simulation technique that combines soft-core potentials (SCP) and simulated annealing (SA) to analyze confined liquids. This integrated SCP/SA method relies on a new spliced soft-core potential (SSCP), which enables tunable accuracy with respect to the target hard-core potential (HCP). SCP/SA enables the packing of enclosures with bulk material in a controlled, thermodynamically consistent manner. The enhanced SSCP accuracy is a critical feature of SCP/SA, enabling a smooth transition between the SCP and the HCP at a desired SCP hardness. We applied SCP/SA to the problem of filling a carbon nanotube (CNT) in periodic boundary conditions with a popular ionic liquid (IL), 1-butyl-3-methylimidazolium hexafluorophosphate [BMIM⁺][PF₆^-]. We performed a series of triplicate simulations on systems with varying CNT diameter and charge to demonstrate SCP/SA's versatility. Beyond this IL/CNT system, the SCP/SA simulation framework has a broad range of potential applications, not limited to nanoscale enclosures and interfaces, including both solid-state and biological systems.

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.

SAMPL6 blind predictions of water-octanol partition coefficients using nonequilibrium alchemical approaches

In this paper, we compute, by means of a non equilibrium alchemical technique, the water-octanol partition coefficients (LogP) for a series of drug-like compounds in the context of the SAMPL6 challenge initiative. Our blind predictions are based on three of the most popular non-polarizable force fields, CGenFF, GAFF2, and OPLS-AA and are critically compared to other MD-based predictions produced using free energy perturbation or thermodynamic integration approaches with stratification. The proposed non-equilibrium method emerges has a reliable tool for LogP prediction, systematically being among the top performing submissions in all force field classes for at least two among the various indicators such as the Pearson or the Kendall correlation coefficients or the mean unsigned error. Contrarily to the widespread equilibrium approaches, that yielded apparently very disparate results in the SAMPL6 challenge, all our independent prediction sets, irrespective of the adopted force field and of the adopted estimate (unidirectional or bidirectional) are, mutually, from moderately to strongly correlated.

Quantum Mechanical and Molecular Mechanics Modeling of Membrane-Embedded Rhodopsins

Computational chemistry provides versatile methods for studying the properties and functioning of biological systems at different levels of precision and at different time scales. The aim of this article is to review the computational methodologies that are applicable to rhodopsins as archetypes for photoactive membrane proteins that are of great importance both in nature and in modern technologies. For each class of computational techniques, from methods that use quantum mechanics for simulating rhodopsin photophysics to less-accurate coarse-grained methodologies used for long-scale protein dynamics, we consider possible applications and the main directions for improvement.

Application of the Movable Type Free Energy Method to the Caspase-Inhibitor BindingAffinity Study

Many studies have provided evidence suggesting that caspases not only contribute to the neurodegeneration associated with Alzheimer’s disease (AD) but also play essential roles in promoting the underlying pathology of this disease. Studies regarding the caspase inhibition draw researchers’ attention through time due to its therapeutic value in the treatment of AD. In this work, we apply the “Movable Type” (MT) free energy method, a Monte Carlo sampling method extrapolating the binding free energy by simulating the partition functions for both free-state and bound-state protein and ligand configurations, to the caspase-inhibitor binding affinity study. Two test benchmarks are introduced to examine the robustness and sensitivity of the MT method concerning the caspase inhibition complexing. The first benchmark employs a large-scale test set including more than a hundred active inhibitors binding to caspase-3. The second benchmark includes several smaller test sets studying the relative binding free energy differences for minor structural changes at the caspase-inhibitor interaction interfaces. Calculation results show that the RMS errors for all test sets are below 1.5 kcal/mol compared to the experimental binding affinity values, demonstrating good performance in simulating the caspase-inhibitor complexing. For better understanding the protein-ligand interaction mechanism, we then take a closer look at the global minimum binding modes and free-state ligand conformations to study two pairs of caspase-inhibitor complexes with (1) different caspase targets binding to the same inhibitor, and (2) different polypeptide inhibitors targeting the same caspase target. By comparing the contact maps at the binding site of different complexes, we revealed how small structural changes affect the caspase-inhibitor interaction energies. Overall, this work provides a new free energy approach for studying the caspase inhibition, with structural insight revealed for both free-state and bound-state molecular configurations.

Insights into Membrane Protein-Lipid Interactions from Free Energy Calculations

Integral membrane proteins are regulated by specific interactions with lipids from the surrounding bilayer. The structures of protein–lipid complexes can be determined through a combination of experimental and computational approaches, but the energetic basis of these interactions is difficult to resolve. Molecular dynamics simulations provide the primary computational technique to estimate the free energies of these interactions. We demonstrate that the energetics of protein–lipid interactions may be reliably and reproducibly calculated using three simulation-based approaches: potential of mean force calculations, alchemical free energy perturbation, and well-tempered metadynamics. We employ these techniques within the framework of a coarse-grained force field and apply them to both bacterial and mammalian membrane protein–lipid systems. We demonstrate good agreement between the different techniques, providing a robust framework for their automated implementation within a pipeline for annotation of newly determined membrane protein structures.

Computing Relative Binding Affinity of Ligands to Receptor: An Effective Hybrid Single-Dual-Topology Free-Energy Perturbation Approach in NAMD

An effective hybrid single-dual-topology protocol is designed for the calculation of relative binding affinities of small ligands to a receptor. The protocol was developed as an extension of the NAMD molecular dynamics program, which exclusively supports a dual-topology framework for relative alchemical free-energy perturbation (FEP) calculations. In this protocol, the alchemical end states are represented as two separate molecules sharing a common substructure identified through maximum structural mapping. Within the substructure, an atom-to-atom correspondence is established, and each pair of corresponding atoms is holonomically constrained to share identical coordinates at all time throughout the simulation. The forces are projected and combined at each step for propagation. Following this formulation, a set of illustrative calculations of reliable experiment/simulation data, including relative solvation free energies of small molecules and relative binding affinities of drug compounds to proteins, are presented. To enhance sampling of the dual-topology region, the FEP calculations were carried out within a replica-exchange MD scheme supported by the multiple-copy algorithm module of NAMD, with periodically attempted swapping of the thermodynamic coupling parameter λ between neighboring states. The results are consistent with experiments and benchmarks reported in the literature, lending support to the validity of the current protocol. In summary, this hybrid single-dual-topology approach combines the conceptual simplicity of the dual-topology paradigm with the advantageous sampling efficiency of the single-topology approach, making it an ideal strategy for high-throughput in silico drug design.

Solvation free energies via alchemical simulations: let's get honest about sampling, once more

Free energy perturbation (FEP) approaches with stratification have seen widespread and increasing use in computational studies of biologically relevant molecules. However, when the molecular systems are characterized by a complex conformational free energy landscape, the assessment of convergence remains a concern for many practitioners. The sampling problem in FEP has been authoritatively addressed in a recent perspective paper [D. Mobley, J. Comput.-Aided Mol. Des., 2012, 26, 93], incisively entitled "Let's get honest about sampling". Here, I return to the issue of sampling in the determination of the octanol-water partition coefficient for a synthetic precursor of kinase inhibitors that has been included in the recent extension of the SAMPL6 blind challenge of log P coefficients. I will show that even for this simple compound, whose conformational space is essentially dictated by two sp₃ rotable bonds connecting rigid planar units, canonical sampling using standard techniques can be surprisingly hard to achieve. I will also show how the conformational sampling problem can be effectively bypassed using unidirectional and bidirectional nonequilibrium work methods, reliably recovering the solvation energy with minimal methodological uncertainty.

Glycyrrhizin-Assisted Transport of Praziquantel Anthelmintic Drug through the Lipid Membrane: An Experiment and MD Simulation

Praziquantel (PZQ) is one of the most widespread anthelmintic drugs. However, the frequent insufficient application of PZQ after oral administration is associated with its low solubility, penetration rate, and bioavailability. In the present study, the permeation of PZQ through a 1,2-dioleoyl- sn-glycero-3-phosphocholine (DOPC) membrane was investigated to probe glycyrrhizin-assisted transport. Glycyrrhizin (or glycyrrhizic acid, GA), a natural saponin, shows the ability to enhance the therapeutic activity of various drugs when it is used as a drug delivery system. However, the molecular mechanism of this effect is still under debate. In the present study, the transport rate was measured experimentally by a parallel artificial membrane permeation assay (PAMPA) and molecular dynamics (MD) simulation with DOPC lipid bilayers. The formation of the noncovalent supramolecular complex of PZQ with disodium salt of GA (Na2GA) in an aqueous solution was proved by the NMR relaxation technique. PAMPA experiments show a strong increase in the amount of the penetrating praziquantel molecules in comparison with a saturated aqueous solution of pure drug used as a control. MD simulation of PZQ penetration through the bilayer demonstrates an increase in permeability into the membrane in the presence of a glycyrrhizin molecule. A decrease in the free energy barrier in the middle of the lipid bilayer was obtained, associated with the hydrogen bond between PZQ and GA. Also, GA reduces the local bilayer surface resistance to penetration of PZQ by rearranging the surface lipid headgroups. This study clarifies the mechanism of increasing the drug's bioavailability in the presence of glycyrrhizin.

The Good, the Bad, and the Ugly: "HiPen", a New Dataset for Validating (S)QM/MM Free Energy Simulations

Indirect (S)QM/MM free energy simulations (FES) are vital to efficiently incorporating sufficient sampling and accurate (QM) energetic evaluations when estimating free energies of practical/experimental interest. Connecting between levels of theory, i.e., calculating Δ A l o w → h i g h , remains to be the most challenging step within an indirect FES protocol. To improve calculations of Δ A l o w → h i g h , we must: (1) compare the performance of all FES methods currently available; and (2) compile and maintain datasets of Δ A l o w → h i g h calculated for a wide-variety of molecules so that future practitioners may replicate or improve upon the current state-of-the-art. Towards these two aims, we introduce a new dataset, "HiPen", which tabulates Δ A g a s M M → 3 o b (the free energy associated with switching from an M M to an S C C - D F T B molecular description using the 3ob parameter set in gas phase), calculated for 22 drug-like small molecules. We compare the calculation of this value using free energy perturbation, Bennett's acceptance ratio, Jarzynski's equation, and Crooks' equation. We also predict the reliability of each calculated Δ A g a s M M → 3 o b by evaluating several convergence criteria including sample size hysteresis, overlap statistics, and bias metric ( Π ). Within the total dataset, three distinct categories of molecules emerge: the "good" molecules, for which we can obtain converged Δ A g a s M M → 3 o b using Jarzynski's equation; "bad" molecules which require Crooks' equation to obtain a converged Δ A g a s M M → 3 o b ; and "ugly" molecules for which we cannot obtain reliably converged Δ A g a s M M → 3 o b with either Jarzynski's or Crooks' equations. We discuss, in depth, results from several example molecules in each of these categories and describe how dihedral discrepancies between levels of theory cause convergence failures even for these gas phase free energy simulations.

Predicting the Effect of Mutations on Protein Folding and Protein-Protein Interactions

The function of a protein is largely determined by its three-dimensional structure and its interactions with other proteins. Changes to a protein's amino acid sequence can alter its function by perturbing the energy landscapes of protein folding and binding. Many tools have been developed to predict the energetic effect of amino acid changes, utilizing features describing the sequence of a protein, the structure of a protein, or both. Those tools can have many applications, such as distinguishing between deleterious and benign mutations and designing proteins and peptides with attractive properties. In this chapter, we describe how to use one of such tools, ELASPIC, to predict the effect of mutations on the stability of proteins and the affinity between proteins, in the context of a human protein-protein interaction network. ELASPIC uses a wide range of sequential and structural features to predict the change in the Gibbs free energy for protein folding and protein-protein interactions. It can be used both through a web server and as a stand-alone application. Since ELASPIC was trained using homology models and not crystal structures, it can be applied to a much broader range of proteins than traditional methods. It can leverage precalculated sequence alignments, homology models, and other features, in order to drastically lower the amount of time required to evaluate individual mutations and make tractable the analysis of millions of mutations affecting the majority of proteins in a genome.

Accelerating QM/MM Free Energy Computations via Intramolecular Force Matching

The calculation of free energy differences between levels of theory has numerous potential pitfalls. Chief among them is the lack of overlap, i.e., ensembles generated at one level of theory (e.g., "low") not being good approximations of ensembles at the other (e.g., "high"). Numerous strategies have been devised to mitigate this issue. However, the most straightforward approach is to ensure that the "low" level ensemble more closely resembles that of the "high". Ideally, this is done without increasing computational cost. Herein, we demonstrate that by reparametrizing classical intramolecular potentials to reproduce high level forces (i.e., force matching) configurational overlap between a "low" (i.e., classical) and "high" (i.e., quantum) level can be significantly improved. This procedure is validated on two test cases and results in vastly improved convergence of free energy simulations.

Reproducibility of Free Energy Calculations across Different Molecular Simulation Software Packages

Alchemical free energy calculations are an increasingly important modern simulation technique to calculate free energy changes on binding or solvation. Contemporary molecular simulation software such as AMBER, CHARMM, GROMACS, and SOMD include support for the method. Implementation details vary among those codes, but users expect reliability and reproducibility, i.e., for a given molecular model and set of force field parameters, comparable free energy differences should be obtained within statistical bounds regardless of the code used. Relative alchemical free energy (RAFE) simulation is increasingly used to support molecule discovery projects, yet the reproducibility of the methodology has been less well tested than its absolute counterpart. Here we present RAFE calculations of hydration free energies for a set of small organic molecules and demonstrate that free energies can be reproduced to within about 0.2 kcal/mol with the aforementioned codes. Absolute alchemical free energy simulations have been carried out as a reference. Achieving this level of reproducibility requires considerable attention to detail and package-specific simulation protocols, and no universally applicable protocol emerges. The benchmarks and protocols reported here should be useful for the community to validate new and future versions of software for free energy calculations.

Transferable MARTINI Model of Poly(ethylene Oxide)

Motivated by the deficiencies of the previous MARTINI models of poly(ethylene oxide) (PEO), we present a new model featuring a high degree of transferability. The model is parametrized on (a) a set of 8 free energies of transfer of dimethoxyethane (PEO dimer) from water to solvents of varying polarity; (b) the radius of gyration in water at high dilution; and (c) matching angle and dihedral distributions from atomistic simulations. We demonstrate that our model behaves well in five different areas of application: (1) it produces accurate densities and phase behavior or small PEO oligomers and water mixtures; (2) it yields chain dimensions in good agreement with the experiment in three different solvents (water, diglyme, and benzene) over a broad range of molecular weights (∼1.2 kg/mol to 21 kg/mol); (3) it reproduces qualitatively the structural features of lipid bilayers containing PEGylated lipids in the brush and mushroom regime; (4) it is able to reproduce the phase behavior of several PEO-based nonionic surfactants in water; and (5) it can be combined with the existing MARTINI PS to model PS-PEO block copolymers. Overall, the new PEO model outperforms previous models and features a high degree of transferability.

The Role of the Active Site Flap in Streptavidin/Biotin Complex Formation

Obtaining a detailed description of how active site flap motion affects substrate or ligand binding will advance structure-based drug design (SBDD) efforts on systems including the kinases, HSP90, HIV protease, ureases, etc. Through this understanding, we will be able to design better inhibitors and better proteins that have desired functions. Herein we address this issue by generating the relevant configurational states of a protein flap on the molecular energy landscape using an approach we call MT_Flex-b and then following this with a procedure to estimate the free energy associated with the motion of the flap region. To illustrate our overall workflow, we explored the free energy changes in the streptavidin/biotin system upon introducing conformational flexibility in loop_3-4 in the biotin unbound ( apo) and bound ( holo) state. The free energy surfaces were created using the Movable Type free energy method, and for further validation, we compared them to potential of mean force (PMF) generated free energy surfaces using MD simulations employing the FF99SBILDN and FF14SB force fields. We also estimated the free energy thermodynamic cycle using an ensemble of closed-like and open-like end states for the ligand unbound and bound states and estimated the binding free energy to be approximately -16.2 kcal/mol (experimental -18.3 kcal/mol). The good agreement between MT_Flex-b in combination with the MT method with experiment and MD simulations supports the effectiveness of our strategy in obtaining unique insights into the motions in proteins that can then be used in a range of biological and biomedical applications.

Assessment of a Single Decoupling Alchemical Approach for the Calculation of the Absolute Binding Free Energies of Protein-Peptide Complexes

The computational modeling of peptide inhibitors to target protein-protein binding interfaces is growing in interest as these are often too large, too shallow, and too feature-less for conventional small molecule compounds. Here, we present a rare successful application of an alchemical binding free energy method for the calculation of converged absolute binding free energies of a series of protein-peptide complexes. Specifically, we report the binding free energies of a series of cyclic peptides derived from the LEDGF/p75 protein to the integrase receptor of the HIV1 virus. The simulations recapitulate the effect of mutations relative to the wild-type binding motif of LEDGF/p75, providing structural, energetic and dynamical interpretations of the observed trends. The equilibration and convergence of the calculations are carefully analyzed. Convergence is aided by the adoption of a single-decoupling alchemical approach with implicit solvation, which circumvents the convergence difficulties of conventional double-decoupling protocols. We hereby present the single-decoupling methodology and critically evaluate its advantages and limitations. We also discuss some of the challenges and potential pitfalls of binding free energy calculations for complex molecular systems which have generally limited their applicability to the quantitative study of protein-peptide binding equilibria.

Fast Calculation of Protein-Protein Binding Free Energies Using Umbrella Sampling with a Coarse-Grained Model

Determination of protein–protein binding affinity values is key to understanding various underlying biological phenomena, such as how missense variations change protein–protein binding. Most existing non-rigorous (fast) and rigorous (slow) methods that rely on all-atom representation of the proteins force the user to choose between speed and accuracy. In an attempt to achieve balance between speed and accuracy, we have combined rigorous umbrella sampling molecular dynamics simulation with a coarse-grained protein model. We predicted the effect of missense variations on binding affinity by selecting three protein–protein systems and comparing results to empirical relative binding affinity values and to non-rigorous modeling approaches. We obtained significant improvement both in our ability to discern stabilizing from destabilizing missense variations and in the correlation between predicted and experimental values compared to non-rigorous approaches. Overall our results suggest that using a rigorous affinity calculation method with coarse-grained protein models could offer fast and reliable predictions of protein–protein binding free energies.

Absolute Alchemical Free Energy Calculations for Ligand Binding: A Beginner's Guide

Many thermodynamic quantities can be extracted from computer simulations that generate an ensemble of microstates according to the principles of statistical mechanics. Among these quantities is the free energy of binding of a small molecule to a macromolecule, such as a protein. Here, we present an introductory overview of a protocol that allows for the estimation of ligand binding free energies via molecular dynamics simulations. While we focus on the binding of organic molecules to proteins, the approach is in principle transferable to any pair of molecules.

Computation of Hemagglutinin Free Energy Difference by the Confinement Method

Hemagglutinin (HA) mediates membrane fusion, a crucial step during influenza virus cell entry. How many HAs are needed for this process is still subject to debate. To aid in this discussion, the confinement free energy method was used to calculate the conformational free energy difference between the extended intermediate and postfusion state of HA. Special care was taken to comply with the general guidelines for free energy calculations, thereby obtaining convergence and demonstrating reliability of the results. The energy that one HA trimer contributes to fusion was found to be 34.2 ± 3.4kBT, similar to the known contributions from other fusion proteins. Although computationally expensive, the technique used is a promising tool for the further energetic characterization of fusion protein mechanisms. Knowledge of the energetic contributions per protein, and of conserved residues that are crucial for fusion, aids in the development of fusion inhibitors for antiviral drugs.

Predicting Binding Free Energies: Frontiers and Benchmarks

Binding free energy calculations based on molecular simulations provide predicted affinities for biomolecular complexes. These calculations begin with a detailed description of a system, including its chemical composition and the interactions among its components. Simulations of the system are then used to compute thermodynamic information, such as binding affinities. Because of their promise for guiding molecular design, these calculations have recently begun to see widespread applications in early-stage drug discovery. However, many hurdles remain in making them a robust and reliable tool. In this review, we highlight key challenges of these calculations, discuss some examples of these challenges, and call for the designation of standard community benchmark test systems that will help the research community generate and evaluate progress. In our view, progress will require careful assessment and evaluation of new methods, force fields, and modeling innovations on well-characterized benchmark systems, and we lay out our vision for how this can be achieved.

Computing converged free energy differences between levels of theory via nonequilibrium work methods: Challenges and opportunities

We demonstrate that Jarzynski's equation can be used to reliably compute free energy differences between low and high level representations of systems. The need for such a calculation arises when employing the so-called "indirect" approach to free energy simulations with mixed quantum mechanical/molecular mechanical (QM/MM) Hamiltonians; a popular technique for circumventing extensive simulations involving quantum chemical computations. We have applied this methodology to several small and medium sized organic molecules, both in the gas phase and explicit solvent. Test cases include several systems for which the standard approach; that is, free energy perturbation between low and high level description, fails to converge. Finally, we identify three major areas in which the difference between low and high level representations make the calculation of ΔAlow→high difficult: bond stretching and angle bending, different preferred conformations, and the response of the MM region to the charge distribution of the QM region. © 2016 Wiley Periodicals, Inc.

Relative Binding Free Energy Calculations Applied to Protein Homology Models

A significant challenge and potential high-value application of computer-aided drug design is the accurate prediction of protein-ligand binding affinities. Free energy perturbation (FEP) using molecular dynamics (MD) sampling is among the most suitable approaches to achieve accurate binding free energy predictions, due to the rigorous statistical framework of the methodology, correct representation of the energetics, and thorough treatment of the important degrees of freedom in the system (including explicit waters). Recent advances in sampling methods and force fields coupled with vast increases in computational resources have made FEP a viable technology to drive hit-to-lead and lead optimization, allowing for more efficient cycles of medicinal chemistry and the possibility to explore much larger chemical spaces. However, previous FEP applications have focused on systems with high-resolution crystal structures of the target as starting points-something that is not always available in drug discovery projects. As such, the ability to apply FEP on homology models would greatly expand the domain of applicability of FEP in drug discovery. In this work we apply a particular implementation of FEP, called FEP+, on congeneric ligand series binding to four diverse targets: a kinase (Tyk2), an epigenetic bromodomain (BRD4), a transmembrane GPCR (A2A), and a protein-protein interaction interface (BCL-2 family protein MCL-1). We apply FEP+ using both crystal structures and homology models as starting points and find that the performance using homology models is generally on a par with the results when using crystal structures. The robustness of the calculations to structural variations in the input models can likely be attributed to the conformational sampling in the molecular dynamics simulations, which allows the modeled receptor to adapt to the "real" conformation for each ligand in the series. This work exemplifies the advantages of using all-atom simulation methods with full system flexibility and offers promise for the general application of FEP to homology models, although additional validation studies should be performed to further understand the limitations of the method and the scenarios where FEP will work best.

Understanding the large solubility of lidocaine in 1-n-butyl-3-methylimidazolium based ionic liquids using molecular simulation

Room temperature ionic liquids have been proposed as replacement solvents in a wide range of industrial separation processes. Here, we focus on the use of ionic liquids as solvents for the pharmaceutical compound lidocaine. We show that the solubility of lidocaine in seven common 1-n-butyl-3-methylimidazolium based ionic liquids is greatly enhanced relative to water. The predicted solubility is greatest in [BMIM](+)[CH3CO2](-), which we find results from favorable hydrogen bonding between the lidocaine amine hydrogen and the [CH3CO2](-) oxygen, favorable electrostatic interactions between the lidocaine amide oxygen with the [BMIM](+) aromatic ring hydrogens, while lidocaine does not interfere with the association of [BMIM](+) with [CH3CO2](-). Additionally, by removing functional groups from the lidocaine scaffold while maintaining the important amide group, we found that as the van der Waals volume increases, solubility in [BMIM](+)[CH3CO2](-) relative to water increases.