Alchemical Free Energy Methods Research Articles

Uncertainty Quantification in Alchemical Free Energy Methods.

Alchemical free energy methods have gained much importance recently from several reports of improved ligand–protein binding affinity predictions based on their implementation using molecular dynamics simulations. A large number of variants of such methods implementing different accelerated sampling techniques and free energy estimators are available, each claimed to be better than the others in its own way. However, the key features of reproducibility and quantification of associated uncertainties in such methods have barely been discussed. Here, we apply a systematic protocol for uncertainty quantification to a number of popular alchemical free energy methods, covering both absolute and relative free energy predictions. We show that a reliable measure of error estimation is provided by ensemble simulation—an ensemble of independent MD simulations—which applies irrespective of the free energy method. The need to use ensemble methods is fundamental and holds regardless of the duration of time of the molecular dynamics simulations performed.

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.

Robust Prediction of Resistance to Trimethoprim in Staphylococcus aureus

The rise of antibiotic resistance threatens modern medicine; to combat it new diagnostic methods are required. Sequencing the whole genome of a pathogen offers the potential to accurately determine which antibiotics will be effective to treat a patient. A key limitation of this approach is that it cannot classify rare or previously unseen mutations. Here we demonstrate that alchemical free energy methods, a well-established class of methods from computational chemistry, can successfully predict whether mutations in Staphylococcus aureus dihydrofolate reductase confer resistance to trimethoprim. We also show that the method is quantitatively accurate by calculating how much the most common resistance-conferring mutation, F99Y, reduces the binding free energy of trimethoprim and comparing predicted and experimentally measured minimum inhibitory concentrations for seven different mutations. Finally, by considering up to 32 free energy calculations for each mutation, we estimate its specificity and sensitivity.

D3R Grand Challenge 2: blind prediction of protein-ligand poses, affinity rankings, and relative binding free energies.

The Drug Design Data Resource (D3R) ran Grand Challenge 2 (GC2) from September 2016 through February 2017. This challenge was based on a dataset of structures and affinities for the nuclear receptor farnesoid X receptor (FXR), contributed by F. Hoffmann-La Roche. The dataset contained 102 IC50 values, spanning six orders of magnitude, and 36 high-resolution co-crystal structures with representatives of four major ligand classes. Strong global participation was evident, with 49 participants submitting 262 prediction submission packages in total. Procedurally, GC2 mimicked Grand Challenge 2015 (GC2015), with a Stage 1 subchallenge testing ligand pose prediction methods and ranking and scoring methods, and a Stage 2 subchallenge testing only ligand ranking and scoring methods after the release of all blinded co-crystal structures. Two smaller curated sets of 18 and 15 ligands were developed to test alchemical free energy methods. This overview summarizes all aspects of GC2, including the dataset details, challenge procedures, and participant results. We also consider implications for progress in the field, while highlighting methodological areas that merit continued development. Similar to GC2015, the outcome of GC2 underscores the pressing need for methods development in pose prediction, particularly for ligand scaffolds not currently represented in the Protein Data Bank ( http://www.pdb.org ), and in affinity ranking and scoring of bound ligands.

Free Energy Methods in Drug Design: Prospects of "Alchemical Perturbation" in Medicinal Chemistry.

Underpinning all drug discovery projects is the interaction between a drug and its target, usually a protein. Thus, improved methods for predicting the magnitude of protein-ligand interactions have the potential to improve the efficiency of drug development. In this review, we describe the principles of free energy methods used for the calculation of protein-ligand binding free energies, the challenges associated with these methods, and recent advances developed to address these difficulties. We then present case studies from 2005 to 2017, each demonstrating that alchemical free energy methods can assist rational drug design projects. We conclude that alchemical methods are becoming a feasible reality in medicinal chemistry research due to improved computational resources and algorithms and that alchemical free energy predictions methods are close to becoming a mainstream tool for medicinal chemists.

Computational methodology for solubility prediction: Application to the sparingly soluble solutes.

The solubility of a crystalline substance in the solution can be estimated from its absolute solid free energy and excess solvation free energy. Here, we present a numerical method, which enables convenient solubility estimation of general molecular crystals at arbitrary thermodynamic conditions where solid and solution can coexist. The methodology is based on standard alchemical free energy methods, such as thermodynamic integration and free energy perturbation, and consists of two parts: (1) systematic extension of the Einstein crystal method to calculate the absolute solid free energies of molecular crystals at arbitrary temperatures and pressures and (2) a flexible cavity method that can yield accurate estimates of the excess solvation free energies. As an illustration, via classical Molecular Dynamic simulations, we show that our approach can predict the solubility of OPLS-AA-based (Optimized Potentials for Liquid Simulations All Atomic) naphthalene in SPC (Simple Point Charge) water in good agreement with experimental data at various temperatures and pressures. Because the procedure is simple and general and only makes use of readily available open-source software, the methodology should provide a powerful tool for universal solubility prediction.

Gibbs Sampler-Based λ-Dynamics and Rao–Blackwell Estimator for Alchemical Free Energy Calculation

λ-dynamics is a generalized ensemble method for alchemical free energy calculations. In traditional λ-dynamics, the alchemical switch variable λ is treated as a continuous variable ranging from 0 to 1 and an empirical estimator is utilized to approximate the free energy. In the present article, we describe an alternative formulation of λ-dynamics that utilizes the Gibbs sampler framework, which we call Gibbs sampler-based λ-dynamics (GSLD). GSLD, like traditional λ-dynamics, can be readily extended to calculate free energy differences between multiple ligands in one simulation. We also introduce a new free energy estimator, the Rao-Blackwell estimator (RBE), for use in conjunction with GSLD. Compared with the current empirical estimator, the advantage of RBE is that RBE is an unbiased estimator and its variance is usually smaller than the current empirical estimator. We also show that the multistate Bennett acceptance ratio equation or the unbinned weighted histogram analysis method equation can be derived using the RBE. We illustrate the use and performance of this new free energy computational framework by application to a simple harmonic system as well as relevant calculations of small molecule relative free energies of solvation and binding to a protein receptor. Our findings demonstrate consistent and improved performance compared with conventional alchemical free energy methods.

Multiple binding modes of ibuprofen in human serum albumin identified by absolute binding free energy calculations.

Human serum albumin possesses multiple binding sites and transports a wide range of ligands that include the anti-inflammatory drug ibuprofen. A complete map of the binding sites of ibuprofen in albumin is difficult to obtain in traditional experiments, because of the structural adaptability of this protein in accommodating small ligands. In this work, we provide a set of predictions covering the geometry, affinity of binding and protonation state for the pharmaceutically most active form (S-isomer) of ibuprofen to albumin, by using absolute binding free energy calculations in combination with classical molecular dynamics (MD) simulations and molecular docking. The most favorable binding modes correctly reproduce several experimentally identified binding locations, which include the two Sudlow's drug sites (DS2 and DS1) and the fatty acid binding sites 6 and 2 (FA6 and FA2). Previously unknown details of the binding conformations were revealed for some of them, and formerly undetected binding modes were found in other protein sites. The calculated binding affinities exhibit trends which seem to agree with the available experimental data, and drastically degrade when the ligand is modeled in a protonated (neutral) state, indicating that ibuprofen associates with albumin preferentially in its charged form. These findings provide a detailed description of the binding of ibuprofen, help to explain a wide range of results reported in the literature in the last decades, and demonstrate the possibility of using simulation methods to predict ligand binding to albumin.

Ribose 2'-Hydroxyl Groups Stabilize RNA Hairpin Structures Containing GCUAA Pentaloop.

The chemical structure of RNA and DNA is very similar; however, the three-dimensional conformation of these two nucleic acids is very different. Whereas the DNA adopts a repetitive structure of a double-stranded helix, RNA is primarily single stranded with a complex three-dimensional structure in which the hairpin is the most common secondary structure. Apart from the difference between uracil and thymine, the difference in the chemical structure between RNA and DNA is the presence of a hydroxyl group at position 2' of the sugar (ribose) instead of a hydrogen (deoxyribose). In this paper, we present molecular dynamics simulations addressing the contribution of 2'-hydroxyls to the stability of a GCUAA pentaloop motif. The results indicate that the 2'-hydroxyls stabilize the hairpin conformation of the GCUAA pentaloop relative to an analogous oligonucleotide in which the ribose sugars in the loop region were substituted with deoxyriboses. The magnitude of the stabilization was found to be 23.8 ± 4.1 kJ/mol using an alchemical mutations free energy method and 4.2 ± 6.5 kJ/mol using potential of mean force calculations. The latter indicates that in addition to its larger thermodynamic stability the RNA hairpin is also kinetically more stable. We find that the excess stability is a result of intrahairpin hydrogen bonds in the loop region between the 2'-hydroxyls and sugars, bases, and phosphates. The hydrogen bonds with the sugars and phosphates involve predominantly interactions with adjacent nucleotides. However, the hydrogen bonds with the bases involve also interactions between groups on opposite sides of the loop or with the middle base of the loop and are therefore likely to contribute significantly to the stability of the loop. Of these hydrogen bonds, the most frequent is observed between the 2'-hydroxyl at the first position of the pentaloop with N6/N7 of adenine at the forth position, as well as between the 2'-hydroxyl at position -1 with N6 of adenine at the fifth position. Our results contribute to the notion that one of the important roles of the ribose sugars in RNA is to facilitate hairpin formation.

Thermodynamic integration to predict host-guest binding affinities

An alchemical free energy method with explicit solvent molecular dynamics simulations was applied as part of the blind prediction contest SAMPL3 to calculate binding free energies for seven guests to an acyclic cucurbit-[n]uril host. The predictions included determination of protonation states for both host and guests, docking pose generation, and binding free energy calculations using thermodynamic integration. We found a root mean square error (RMSE) of 3.6 kcal mol(-1) from the reference experimental results, with an R(2) correlation of 0.51. The agreement with experiment for the largest contributor to this error, guest 6, is improved by 1.7 kcal mol(-1) when a periodicity-induced free energy correction is applied. The corrections for the other ligands were significantly smaller, and altogether the RMSE was reduced by 0.4 kcal mol(-1). We link properties of the host-guest systems during simulation to errors in the computed free energies. Overall, we show that charged host-guest systems studied here, initialized in unconfirmed docking poses, present a challenge to accurate alchemical simulation methods.

Predicting Ligand Binding Affinity with Alchemical Free Energy Methods in a Polar Model Binding Site

We present a combined experimental and modeling study of organic ligand molecules binding to a slightly polar engineered cavity site in T4 lysozyme (L99A/M102Q). For modeling, we computed alchemical absolute binding free energies. These were blind tests performed prospectively on 13 diverse, previously untested candidate ligand molecules. We predicted that eight compounds would bind to the cavity and five would not; 11 of 13 predictions were correct at this level. The RMS error to the measurable absolute binding energies was 1.8 kcal/mol. In addition, we computed “relative” binding free energies for six phenol derivatives starting from two known ligands: phenol and catechol. The average RMS error in the relative free energy prediction was 2.5 kcal/mol (phenol) and 1.1 kcal/mol (catechol). To understand these results at atomic resolution, we obtained x-ray co-complex structures for nine of the diverse ligands and for all six phenol analogs. The average RMSD of the predicted pose to the experiment was 2.0 Å (diverse set), 1.8 Å (phenol-derived predictions), and 1.2 Å (catechol-derived predictions). We found that predicting accurate affinities and rank-orderings required near-native starting orientations of the ligand in the binding site. Unanticipated binding modes, multiple ligand binding, and protein conformational change all proved challenging for the free energy methods. We believe that these results can help guide future improvements in physics-based absolute binding free energy methods.

Application of Computer Simulation Free-Energy Methods to Compute the Free Energy of Micellization as a Function of Micelle Composition. 2. Implementation

In this paper, the implementation of the CS-FE/MT model introduced in article 1 is discussed, and computer simulations are performed to evaluate the feasibility of the new theoretical approach. As discussed in article 1, making predictions of surfactant/solubilizate aqueous solution behavior using the CS-FE/MT model requires evaluation of DeltaDeltaG for multiple surfactant-to-solubilizate or surfactant-to-cosurfactant transformations. The central goal of this article is to evaluate the quantitative accuracy of the alchemical computer simulation method used in the CS-FE/MT modeling approach to predict DeltaDeltaG for a single surfactant-to-solubilizate or for a single surfactant-to-cosurfactant transformation. A hybrid single/dual topology approach was used to morph the ionic surfactant sodium dodecyl sulfate (SDS) into the ionic solubilizate ibuprofen (IBU), and a dual topology approach was used to morph the nonionic surfactant octyl glucoside (OG) into the nonionic solubilizate p-aminobenzoate (PAB). In addition, a single topology approach was used to morph the nonionic surfactant n-decyl dimethylphosphine oxide (C10PO) into the nonionic cosurfactant n-decyl methyl sulfoxide (C10SO), the nonionic surfactant octylsulfinyl ethanol (C8SE) into the nonionic cosurfactant decylsulfinyl ethanol (C10SE), and the nonionic surfactant n-decyl methyl sulfoxide (C10SO) into the nonionic cosurfactant n-octyl methyl sulfoxide (C8SO). Each DeltaDeltaG value was computed by using thermodynamic integration to determine the difference in free energy associated with (i) transforming a surfactant molecule of type A into a cosurfactant/solubilizate molecule of type B in a micellar environment (referred to as DeltaG2) and (ii) transforming a surfactant molecule of type A into a cosurfactant/solubilizate molecule of type B in aqueous solution (referred to as DeltaG1). CS-FE/MT model predictions of DeltaDeltaG for each alchemical transformation were made at a number of simulation conditions, including (i) different equilibration times at each value of the coupling parameter lambda, (ii) different data-gathering times at each lambda value, and (iii) simulation at a different number of lambda values. For the three surfactant-to-cosurfactant transformations considered here, the DeltaDeltaG values predicted by the CS-FE/MT model were compared with DeltaDeltaG values predicted by an accurate molecular thermodynamic (MT) model developed by fitting to experimental CMC data. Even after performing lengthy equilibration and data gathering at each lambda value, physically unrealistic values of DeltaDeltaG were predicted by the CS-FE/MT model for the transformations of SDS into IBU and of OG into PAB. However, more physically realistic DeltaDeltaG values were predicted for the transformation of C10PO into C10SO, and reasonable free-energy predictions were obtained for the transformations of C8SE into C10SE and C10SO into C8SO. Each of the surfactant-to-cosurfactant transformations considered here involved less extensive structural changes than the surfactant-to-solubilizate transformations. As computer power increases and as improvements are made to alchemical free-energy methods, it may become possible to apply the CS-FE/MT model to make accurate predictions of the free-energy changes associated with forming multicomponent surfactant and solubilizate micelles in aqueous solution where the chemical structures of the surfactants, cosurfactants, and solubilizates differ significantly.

Treating entropy and conformational changes in implicit solvent simulations of small molecules.

Implicit solvent models are increasingly popular for estimating aqueous solvation (hydration) free energies in molecular simulations and other applications. In many cases, parameters for these models are derived to reproduce experimental values for small molecule hydration free energies. Often, these hydration free energies are computed for a single solute conformation, neglecting solute conformational changes upon solvation. Here, we incorporate these effects using alchemical free energy methods. We find significant errors when hydration free energies are estimated using only a single solute conformation, even for relatively small, simple, rigid solutes. For example, we find conformational entropy (TDeltaS) changes of up to 2.3 kcal/mol upon hydration. Interestingly, these changes in conformational entropy correlate poorly (R2 = 0.03) with the number of rotatable bonds. The present study illustrates that implicit solvent modeling can be improved by eliminating the approximation that solutes are rigid.