Free Energy Perturbation Hamiltonian Replica-Exchange Molecular Dynamics (FEP/H-REMD) for Absolute Ligand Binding Free Energy Calculations

Free Energy Perturbation with Replica Exchange Molecular Dynamics (FEP/REMD) offers a powerful strategy to improve the convergence of free energy computations. In particular, it has been shown previously that a FEP/REMD scheme allowing random moves within an extended replica ensemble of thermodynamic coupling parameters "lambda" can improve the statistical convergence in calculations of absolute binding free energy of ligands to proteins [J. Chem. Theory Comput. 2009, 5, 2583]. In the present study, FEP/REMD is extended and combined with an accelerated MD simulations method based on Hamiltonian replica-exchange MD (H-REMD) to overcome the additional problems arising from the existence of kinetically trapped conformations within the protein receptor. In the combined strategy, each system with a given thermodynamic coupling factor lambda in the extended ensemble is further coupled with a set of replicas evolving on a biased energy surface with boosting potentials used to accelerate the inter-conversion among different rotameric states of the side chains in the neighborhood of the binding site. Exchanges are allowed to occur alternatively along the axes corresponding to the thermodynamic coupling parameter lambda and the boosting potential, in an extended dual array of coupled lambda- and H-REMD simulations. The method is implemented on the basis of new extensions to the REPDSTR module of the biomolecular simulation program CHARMM. As an illustrative example, the absolute binding free energy of p-xylene to the nonpolar cavity of the L99A mutant of T4 lysozyme was calculated. The tests demonstrate that the dual lambda-REMD and H-REMD simulation scheme greatly accelerates the configurational sampling of the rotameric states of the side chains around the binding pocket, thereby improving the convergence of the FEP computations.     

Effects of Water Placement on Predictions of Binding Affinities for p38α MAP Kinase Inhibitors

Monte Carlo free energy perturbation (MC/FEP) calculations have been applied to compute the relative binding affinities of 17 congeneric pyridazo-pyrimidinone inhibitors of the protein p38α MAP kinase. Overall correlation with experiment was found to be modest when the complexes were hydrated using a traditional procedure with a stored solvent box. Significant improvements in accuracy were obtained when the MC/FEP calculations were repeated using initial solvent distributions optimized by the water placement algorithm JAWS. The results underscore the importance of accurate placement of water molecules in a ligand binding site for the reliable prediction of relative free energies of binding.     

Alternative approaches to potential of mean force calculations: Free energy perturbation versus thermodynamic integration. Case study of some representative nonpolar interactions

We investigated the convergence behavior of potential of mean force (PMF) calculations using free energy perturbation (FEP), thermodynamic integration (TI), and “slow growth” (SG) techniques. The critical comparison of these alternative approaches is illustrated by the study of three different systems: two tagged argon atoms in a periodic box of argon, two methane molecules, and two benzene molecules maintained in a “T-shaped” conformation, both dimers embedded in a periodic box of water. The complete PMF simulations were carried out considering several protocols, in which the number of intermediate “λ” states, together with the amount of sampling per individual state, were varied. In most cases, as much as 1 ns of molecular dynamics (MD) sampling was used to derive each free energy profile. For the different systems examined, we find that FEP and TI unquestionably constitute robust computational methods leading to results of comparable accuracy. We also show that proper convergence of the free energy calculations, and further quantitative interpretation of the PMFs, requires total simulation times much higher than has been hitherto estimated. In some circumstances, the free energy profiles derived from FEP calculations tend to be slightly poorer than those obtained with TI, as a probable consequence of the greater sensitivity of FEP to the window spacing δλ. In the context of TI, and to a lesser extent FEP, simulations, it appears preferable to employ a limited number of “λ” points of the integrand involving extensive sampling, rather than numerous points with fewer samplings. Finally, we note that, at least in the case of nonpolar interactions, PMFs of reasonable quality can be generated using SG, and at a substantially lower cost than with either FEP or TI. © 1996 by John Wiley & Sons, Inc.     

X‐Ray Crystallography and Free Energy Calculations Reveal the Binding Mechanism of A2A Adenosine Receptor Antagonists

We present a robust protocol based on iterations of free energy perturbation (FEP) calculations, chemical synthesis, biophysical mapping and X‐ray crystallography to reveal the binding mode of an antagonist series to the A_2A adenosine receptor (AR). Eight A_2AAR binding site mutations from biophysical mapping experiments were initially analyzed with sidechain FEP simulations, performed on alternate binding modes. The results distinctively supported one binding mode, which was subsequently used to design new chromone derivatives. Their affinities for the A_2AAR were experimentally determined and investigated through a cycle of ligand‐FEP calculations, validating the binding orientation of the different chemical substituents proposed. Subsequent X‐ray crystallography of the A_2AAR with a low and a high affinity chromone derivative confirmed the predicted binding orientation. The new molecules and structures here reported were driven by free energy calculations, and provide new insights on antagonist binding to the A_2AAR, an emerging target in immuno‐oncology.     

A displaced-solvent functional analysis of model hydrophobic enclosures

Calculation of protein-ligand binding affinities continues to be a hotbed of research. Although many techniques for computing protein-ligand binding affinities have been introduced--ranging from computationally very expensive approaches, such as free energy perturbation (FEP) theory; to more approximate techniques, such as empirically derived scoring functions, which, although computationally efficient, lack a clear theoretical basis--there remains pressing need for more robust approaches. A recently introduced technique, the displaced-solvent functional (DSF) method, was developed to bridge the gap between the high accuracy of FEP and the computational efficiency of empirically derived scoring functions. In order to develop a set of reference data to test the DSF theory for calculating absolute protein-ligand binding affinities, we have pursued FEP theory calculations of the binding free energies of a methane ligand with 13 different model hydrophobic enclosures of varying hydrophobicity. The binding free energies of the methane ligand with the various hydrophobic enclosures were then recomputed by DSF theory and compared with the FEP reference data. We find that the DSF theory, which relies on no empirically tuned parameters, shows excellent quantitative agreement with the FEP. We also explored the ability of buried solvent accessible surface area and buried molecular surface area models to describe the relevant physics, and find the buried molecular surface area model to offer superior performance over this dataset.     

Calculation of relative binding free energy differences for fructose 1,6-bisphosphatase inhibitors using the thermodynamic cycle perturbation approach.

An iterative, computer-assisted, drug design strategy that combines molecular design, molecular mechanics, molecular dynamics (MD), and free energy perturbation (FEP) calculations with compound synthesis, biochemical testing of inhibitors, and crystallographic structure determination of protein-inhibitor complexes was successfully used to predict the rank order of a series of nucleoside monophosphate analogues as fructose 1,6-bisphosphatase (FBPase) inhibitors. The X-ray structure of FBPase complexed with 5-aminoimidazole-4-carboxamide-1-beta-D-ribofuranosyl 5'-monophosphate (ZMP) provided structural information used for subsequent analogue design and free energy calculations. The FEP protocol was validated by calculating the free energy differences for the mutation of ZMP (1) to AMP (2). The calculated results showed a net gain of 1.7 kcal/mol, which agreed with the experimental result of 1.3 kcal/mol. FEP calculations were performed for 18 other AMP analogues. Inhibition constants were determined for over half of these analogues, usually after completion of the calculation, and were consistent with the predictions. Solvation free energy differences between AMP and various AMP analogues proved to be an important factor in binding free energies, suggesting that increased desolvation costs associated with the addition of polar groups to an inhibitor must be overcome by stronger ligand-protein interactions if the structural modification is to enhance inhibitor potency. The results indicate that FEP calculations predict relative binding affinities with high accuracy and provide valuable insight into the factors that influence inhibitor binding and therefore should greatly aid efforts to optimize initial lead compounds and reduce the time required for the discovery of new drug candidates.     

A water-swap reaction coordinate for the calculation of absolute protein-ligand binding free energies

The accurate prediction of absolute protein-ligand binding free energies is one of the grand challenge problems of computational science. Binding free energy measures the strength of binding between a ligand and a protein, and an algorithm that would allow its accurate prediction would be a powerful tool for rational drug design. Here we present the development of a new method that allows for the absolute binding free energy of a protein-ligand complex to be calculated from first principles, using a single simulation. Our method involves the use of a novel reaction coordinate that swaps a ligand bound to a protein with an equivalent volume of bulk water. This water-swap reaction coordinate is built using an identity constraint, which identifies a cluster of water molecules from bulk water that occupies the same volume as the ligand in the protein active site. A dual topology algorithm is then used to swap the ligand from the active site with the identified water cluster from bulk water. The free energy is then calculated using replica exchange thermodynamic integration. This returns the free energy change of simultaneously transferring the ligand to bulk water, as an equivalent volume of bulk water is transferred back to the protein active site. This, directly, is the absolute binding free energy. It should be noted that while this reaction coordinate models the binding process directly, an accurate force field and sufficient sampling are still required to allow for the binding free energy to be predicted correctly. In this paper we present the details and development of this method, and demonstrate how the potential of mean force along the water-swap coordinate can be improved by calibrating the soft-core Coulomb and Lennard-Jones parameters used for the dual topology calculation. The optimal parameters were applied to calculations of protein-ligand binding free energies of a neuraminidase inhibitor (oseltamivir), with these results compared to experiment. These results demonstrate that the water-swap coordinate provides a viable and potentially powerful new route for the prediction of protein-ligand binding free energies.     

X-Ray Crystallography and Free Energy Calculations Reveal the Binding Mechanism of A2A Adenosine Receptor Antagonists

We present a robust protocol based on iterations of free energy perturbation (FEP) calculations, chemical synthesis, biophysical mapping and X-ray crystallography to reveal the binding mode of an antagonist series to the A_2A adenosine receptor (AR). Eight A_2AAR binding site mutations from biophysical mapping experiments were initially analyzed with sidechain FEP simulations, performed on alternate binding modes. The results distinctively supported one binding mode, which was subsequently used to design new chromone derivatives. Their affinities for the A_2AAR were experimentally determined and investigated through a cycle of ligand-FEP calculations, validating the binding orientation of the different chemical substituents proposed. Subsequent X-ray crystallography of the A_2AAR with a low and a high affinity chromone derivative confirmed the predicted binding orientation. The new molecules and structures here reported were driven by free energy calculations, and provide new insights on antagonist binding to the A_2AAR, an emerging target in immuno-oncology.     

Improved precision and efficiency of free energy calculations for small systems using lambda-scaled atomic masses and separating conformational and transformational sampling

We present results showing the importance of appropriate treatment of atomic masses in molecular dynamics (MD)-based single topology free-energy perturbations (FEPs) on small molecule systems. The reversibility of gas phase simulations is significantly improved by scaling the atomic mass of mutated atoms with the lambda variable normally used for the scaling of energy terms. Because this effect is less pronounced for solvated systems, it will not cancel in estimates of the relative hydration free energy difference. The advantage of mass scaling is demonstrated by a null mutation of ethane to ethane and the calculation of the relative hydration free energy difference between ethane and n-propane. Furthermore, it is found that the simulation time necessary for converged MD/FEPs is prohibitively large for relative hydration free energy calculations on cyclic alkanes. Therefore, we explore an alternative free energy pathway including strongly constrained conformations to improve convergence in FEP simulations of flexible molecules.     

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.

Relative 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.     

Computing Alchemical Free Energy Differences with Hamiltonian Replica Exchange Molecular Dynamics (H-REMD) Simulations

Alchemical free energy calculations play a very important role in the field of molecular modeling. Efforts have been made to improve the accuracy and precision of those calculations. One of the efforts is to employ a Hamiltonian replica exchange molecular dynamics (H-REMD) method to enhance conformational sampling. In this paper, we demonstrated that HREMD method not only improves convergence in alchemical free energy calculations but also can be used to compute free energy differences directly via the Free Energy Perturbation (FEP)algorithm. We show a direct mapping between the H-REMD and the usual FEP equations, which are then used directly to compute free energies. The H-REMD alchemical free energy calculation (Replica exchange Free Energy Perturbation, REFEP) was tested on predicting the pK(a) value of the buried Asp26 in thioredoxin. We compare the results of REFEP with TI and regular FEP simulations. REFEP calculations converged faster than those from TI and regular FEP simulations. The final predicted pK(a) value from the H-REMD simulation was also very accurate, only 0.4 pK(a) unit above the experimental value. Utilizing the REFEP algorithm significantly improves conformational sampling, and this in turn improves the convergence of alchemical free energy simulations.     

Large scale free energy calculations for blind predictions of protein–ligand binding: the D3R Grand Challenge 2015

We describe binding free energy calculations in the D3R Grand Challenge 2015 for blind prediction of the binding affinities of 180 ligands to Hsp90. The present D3R challenge was built around experimental datasets involving Heat shock protein (Hsp) 90, an ATP-dependent molecular chaperone which is an important anticancer drug target. The Hsp90 ATP binding site is known to be a challenging target for accurate calculations of ligand binding affinities because of the ligand-dependent conformational changes in the binding site, the presence of ordered waters and the broad chemical diversity of ligands that can bind at this site. Our primary focus here is to distinguish binders from nonbinders. Large scale absolute binding free energy calculations that cover over 3000 protein–ligand complexes were performed using the BEDAM method starting from docked structures generated by Glide docking. Although the ligand dataset in this study resembles an intermediate to late stage lead optimization project while the BEDAM method is mainly developed for early stage virtual screening of hit molecules, the BEDAM binding free energy scoring has resulted in a moderate enrichment of ligand screening against this challenging drug target. Results show that, using a statistical mechanics based free energy method like BEDAM starting from docked poses offers better enrichment than classical docking scoring functions and rescoring methods like Prime MM-GBSA for the Hsp90 data set in this blind challenge. Importantly, among the three methods tested here, only the mean value of the BEDAM binding free energy scores is able to separate the large group of binders from the small group of nonbinders with a gap of 2.4 kcal/mol. None of the three methods that we have tested provided accurate ranking of the affinities of the 147 active compounds. We discuss the possible sources of errors in the binding free energy calculations. The study suggests that BEDAM can be used strategically to discriminate binders from nonbinders in virtual screening and to more accurately predict the ligand binding modes prior to the more computationally expensive FEP calculations of binding affinity.     

Interaction between water molecules and zinc sulfide nanoparticles studied by temperature-programmed desorption and molecular dynamics simulations

We have investigated the bonding of water molecules to the surfaces of ZnS nanoparticles (approximately 2-3 nm sphalerite) using temperature-programmed desorption (TPD). The activation energy for water desorption was derived as a function of the surface coverage through kinetic modeling of the experimental TPD curves. The binding energy of water equals the activation energy of desorption if it is assumed that the activation energy for adsorption is nearly zero. Molecular dynamics (MD) simulations of water adsorption on 3 and 5 nm sphalerite nanoparticles provided insights into the adsorption process and water binding at the atomic level. Water binds with the ZnS nanoparticle surface mainly via formation of Zn-O bonds. As compared with bulk ZnS crystals, ZnS nanoparticles can adsorb more water molecules per unit surface area due to the greatly increased curvature, which increases the distance between adjacent adsorbed molecules. Results from both TPD and MD show that the water binding energy increases with decreasing the water surface coverage. We attribute the increase in binding energy with decreasing surface water coverage to the increasing degree of surface under-coordination as removal of water molecules proceeds. MD also suggests that the water binding energy increases with decreasing particle size due to the further distance and hence lower interaction between adsorbed water molecules on highly curved smaller particle surfaces. Results also show that the binding energy, and thus the strength of interaction of water, is highest in isolated nanoparticles, lower in nanoparticle aggregates, and lowest in bulk crystals. Given that water binding is driven by surface energy reduction, we attribute the decreased binding energy for aggregated as compared to isolated particles to the decrease in surface energy that occurs as the result of inter-particle interactions.     

Grand canonical Monte Carlo simulations of water in protein environments

The grand canonical simulation algorithm is considered as a general methodology to sample the configuration of water molecules confined within protein environments. First, the probability distribution of the number of water molecules and their configuration in a region of interest for biochemical simulations, such as the active site of a protein, is derived by considering a finite subvolume in open equilibrium with a large system serving as a bulk reservoir. It is shown that the influence of the bulk reservoir can be represented as a many-body potential of mean force acting on the atoms located inside the subvolume. The grand canonical Monte Carlo (GCMC) algorithm, augmented by a number of technical advances to increase the acceptance of insertion attempts, is implemented, and tested for simple systems. In particular, the method is illustrated in the case of a pure water box with periodic boundary conditions. In addition, finite spherical systems of pure water and containing a dialanine peptide, are simulated with GCMC while the influence of the surrounding infinite bulk is incorporated using the generalized solvent boundary potential [W. Im, S. Berneche, and B. Roux, J. Chem. Phys. 114, 2924 (2001)]. As a last illustration of water confined in the interior of a protein, the hydration of the central cavity of the KcsA potassium channel is simulated.     

Free Energy Peturbation and Molecular Dynamics Simulation Studies on the Enantiomeric Discrimination of Amines by Dimethyldiketopyridino-18-Crown-6

Abstract

Discrimination of chiral amines by dimethyldiketopyridino-18-crown-6 (1) is studied by free energy peturbation (FEP) and molecular dynamics (MD) methods. 1 has two (S)-chiral centers and discriminates chiral amines through host-guest interactions. The optically active amines in this study are α-(1-naphthyl)ethylamine, methylbenzylamine, cyclohexylethylamine, and sec-butylamine. The trends in binding free energy differences obtained from FEP calculations were in excellent agreement with experimental results obtained in the gas phase. In order to explain the enantioselectivity of the host in terms of the host-guest interactions at the molecular level, we analyzed the structures generated by 10-ns MD simulations of host-guest complexes. The suggested chiral discrimination mechanism, the π-π interaction and the steric repulsion between the guest and the host, was verified by our MD simulation analysis.     

Free enthalpies of replacing water molecules in protein binding pockets

Water molecules in the binding pocket of a protein and their role in ligand binding have increasingly raised interest in recent years. Displacement of such water molecules by ligand atoms can be either favourable or unfavourable for ligand binding depending on the change in free enthalpy. In this study, we investigate the displacement of water molecules by an apolar probe in the binding pocket of two proteins, cyclin-dependent kinase 2 and tRNA-guanine transglycosylase, using the method of enveloping distribution sampling (EDS) to obtain free enthalpy differences. In both cases, a ligand core is placed inside the respective pocket and the remaining water molecules are converted to apolar probes, both individually and in pairs. The free enthalpy difference between a water molecule and a CH₃ group at the same location in the pocket in comparison to their presence in bulk solution calculated from EDS molecular dynamics simulations corresponds to the binding free enthalpy of CH₃ at this location. From the free enthalpy difference and the enthalpy difference, the entropic contribution of the displacement can be obtained too. The overlay of the resulting occupancy volumes of the water molecules with crystal structures of analogous ligands shows qualitative correlation between experimentally measured inhibition constants and the calculated free enthalpy differences. Thus, such an EDS analysis of the water molecules in the binding pocket may give valuable insight for potency optimization in drug design.     

Using physics-based pose predictions and free energy perturbation calculations to predict binding poses and relative binding affinities for FXR ligands in the D3R Grand Challenge 2

Computer-aided drug design has become an integral part of drug discovery and development in the pharmaceutical and biotechnology industry, and is nowadays extensively used in the lead identification and lead optimization phases. The drug design data resource (D3R) organizes challenges against blinded experimental data to prospectively test computational methodologies as an opportunity for improved methods and algorithms to emerge. We participated in Grand Challenge 2 to predict the crystallographic poses of 36 Farnesoid X Receptor (FXR)-bound ligands and the relative binding affinities for two designated subsets of 18 and 15 FXR-bound ligands. Here, we present our methodology for pose and affinity predictions and its evaluation after the release of the experimental data. For predicting the crystallographic poses, we used docking and physics-based pose prediction methods guided by the binding poses of native ligands. For FXR ligands with known chemotypes in the PDB, we accurately predicted their binding modes, while for those with unknown chemotypes the predictions were more challenging. Our group ranked #1st (based on the median RMSD) out of 46 groups, which submitted complete entries for the binding pose prediction challenge. For the relative binding affinity prediction challenge, we performed free energy perturbation (FEP) calculations coupled with molecular dynamics (MD) simulations. FEP/MD calculations displayed a high success rate in identifying compounds with better or worse binding affinity than the reference (parent) compound. Our studies suggest that when ligands with chemical precedent are available in the literature, binding pose predictions using docking and physics-based methods are reliable; however, predictions are challenging for ligands with completely unknown chemotypes. We also show that FEP/MD calculations hold predictive value and can nowadays be used in a high throughput mode in a lead optimization project provided that crystal structures of sufficiently high quality are available.     

Overcoming dissipation in the calculation of standard binding free energies by ligand extraction

This article addresses calculations of the standard free energy of binding from molecular simulations in which a bound ligand is extracted from its binding site by steered molecular dynamics (MD) simulations or equilibrium umbrella sampling (US). Host–guest systems are used as test beds to examine the requirements for obtaining the reversible work of ligand extraction. We find that, for both steered MD and US, marked irreversibilities can occur when the guest molecule crosses an energy barrier and suddenly jumps to a new position, causing dissipation of energy stored in the stretched molecule(s). For flexible molecules, this occurs even when a stiff pulling spring is used, and it is difficult to suppress in calculations where the spring is attached to the molecules by single, fixed attachment points. We, therefore, introduce and test a method, fluctuation‐guided pulling, which adaptively adjusts the spring's attachment points based on the guest's atomic fluctuations relative to the host. This adaptive approach is found to substantially improve the reversibility of both steered MD and US calculations for the present systems. The results are then used to estimate standard binding free energies within a comprehensive framework, termed attach‐pull‐release, which recognizes that the standard free energy of binding must include not only the pulling work itself, but also the work of attaching and then releasing the spring, where the release work includes an accounting of the standard concentration to which the ligand is discharged. © 2013 Wiley Periodicals, Inc.     

Involvement of water in carbohydrate-protein binding.

The interactions of trimannosides 1 and 2 with Con A were studied to reveal the effects of displacement of well-ordered water molecules on the thermodynamic parameters of protein-ligand complexation. Trisaccharide 2 is a derivative of 1, in which the hydroxyl at C-2 of the central mannose unit is replaced by a hydroxyethyl moiety. Upon binding, this moiety displaces a conserved water molecule present in the Con A binding site. Structural studies by NMR spectroscopy and MD simulations showed that the two compounds have very similar solution conformational properties. MD simulations of the complexes of Con A with 1 and 2 demonstrated that the hydroxyethyl side chain of 2 can establish the same hydrogen bonds in a low energy conformation with the protein binding site as those mediated by the water molecule in the complex of 1 with Con A. Isothermal titration microcalorimetry (ITC) measurements showed that 2 has a more favorable entropy of binding compared to 1. This term, which was expected, arises from the return of the highly ordered water molecule to bulk solution. The favorable entropy term was, however, offset by a relatively large unfavorable enthalpy term. This observation was rationalized by comparing the extent of hydrogen bond and solvation changes during binding. It is proposed that an indirect interaction through a water molecule will provide a larger number of hydrogen bonds in the complex that have higher occupancies than in bulk solution, thereby stabilizing the complex.