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Ensemble Simulations and Experimental Free Energy Distributions: Evaluation and Characterization of Isoxazole Amides as SMYD3 Inhibitors
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Computational Biochemistry

Ensemble Simulations and Experimental Free Energy Distributions: Evaluation and Characterization of Isoxazole Amides as SMYD3 Inhibitors
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  • Shunzhou Wan
    Shunzhou Wan
    Centre for Computational Science, Department of Chemistry, University College London, London WC1H 0AJ, U.K.
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    Orcidhttps://orcid.org/0000-0001-7192-1999
  • Agastya P. Bhati
    Agastya P. Bhati
    Centre for Computational Science, Department of Chemistry, University College London, London WC1H 0AJ, U.K.
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  • David W. Wright
    David W. Wright
    Centre for Computational Science, Department of Chemistry, University College London, London WC1H 0AJ, U.K.
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    Orcidhttps://orcid.org/0000-0002-5124-8044
  • Ian D. Wall
    Ian D. Wall
    GlaxoSmithKline, Gunnels Wood Road, Stevenage, Hertfordshire SG1 2NY, U.K.
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  • Alan P. Graves
    Alan P. Graves
    GlaxoSmithKline, 1250 South Collegeville Road, Collegeville, Pennsylvania 19426, United States
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  • Darren Green
    Darren Green
    GlaxoSmithKline, Gunnels Wood Road, Stevenage, Hertfordshire SG1 2NY, U.K.
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  • Peter V. Coveney*
    Peter V. Coveney
    Centre for Computational Science, Department of Chemistry, University College London, London WC1H 0AJ, U.K.
    Advanced Research Computing Centre, University College London, London WC1H 0AJ U.K.
    Institute for Informatics, Faculty of Science, University of Amsterdam, 1098XH Amsterdam, The Netherlands
    *Email: [email protected]
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    Orcidhttps://orcid.org/0000-0002-8787-7256
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Cite this: J. Chem. Inf. Model. 2022, 62, 10, 2561–2570
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https://doi.org/10.1021/acs.jcim.2c00255
Published May 4, 2022

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Abstract

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Optimization of binding affinities for ligands to their target protein is a primary objective in rational drug discovery. Herein, we report on a collaborative study that evaluates various compounds designed to bind to the SET and MYND domain-containing protein 3 (SMYD3). SMYD3 is a histone methyltransferase and plays an important role in transcriptional regulation in cell proliferation, cell cycle, and human carcinogenesis. Experimental measurements using the scintillation proximity assay show that the distributions of binding free energies from a large number of independent measurements exhibit non-normal properties. We use ESMACS (enhanced sampling of molecular dynamics with approximation of continuum solvent) and TIES (thermodynamic integration with enhanced sampling) protocols to predict the binding free energies and to provide a detailed chemical insight into the nature of ligand–protein binding. Our results show that the 1-trajectory ESMACS protocol works well for the set of ligands studied here. Although one unexplained outlier exists, we obtain excellent statistical ranking across the set of compounds from the ESMACS protocol and good agreement between calculations and experiments for the relative binding free energies from the TIES protocol. ESMACS and TIES are again found to be powerful protocols for the accurate comparison of the binding free energies.

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1. Introduction

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SMYD3 has been characterized as a versatile lysine methyltransferase and is associated with multiple types of cancer, including colorectal, liver, and breast cancer. A range of histone and non-histone protein substrates are lysine N-methylated by methyl transfer from the SAM (S-adenosyl-l-methionine) cofactor of SMYD3. Notably, loss of SMYD3 catalytic activity inhibited tumorigenesis in the presence of oncogenic Ras, (1) suggesting that inhibition of SMYD3 in cancers with elevated RAS pathway signaling may be a useful therapeutic strategy. However, few SMYD3 inhibitors have been described. (2) GSK has previously reported a crystal structure of the ternary complex of SMYD3, SAH [S-adenosylhomocysteine, a reaction product of the methyl group donor SAM] and MEKK2 [MAPK/ERK (mitogen-activated protein kinase/extracellular signal-regulated kinase) kinase 2] and a second crystal structure showing GSK2807 binding in the SAM pocket. (3) More recently, the identification and optimization of a series of isoxazole amides as SMYD3 inhibitors was reported. (4) The ability of computational binding free energy calculations to predict the affinity of that series of ligands is presented here.
The last 10 years have seen substantial progress in the use of computational chemistry methods within both academia and the pharmaceutical industry for quantitative structure-based drug discovery, thanks to burgeoning computational power, the increasing number of crystal structures, the accuracy of force fields, the improvement of the sampling methods and control of errors, alongside the automation and general usability of the approaches. Many pharmaceutical companies have adopted free energy predictions as a routine tool to support their drug discovery efforts. (5,6) This progress has been prompted by Schrödinger’s drug discovery platform, especially the FEP+ implementation. (7) There are other packages and workflows used in academia and/or industry, which integrate and automate the process of free energy calculation, including the steps of planning, set up, simulation, and analyses. (8,9)
In the last few years, our team at UCL has developed two ensemble-based protocols for free energy calculations, termed “enhanced sampling of molecular dynamics with approximation of continuum solvent” (ESMACS) (8,10) and “thermodynamic integration with enhanced sampling” (TIES). (8,11) ESMACS is based on the molecular mechanics Poisson–Boltzmann surface area (MMPBSA) method, (12) while TIES centers on thermodynamic integration (TI). Although the protocols are built around the standard MMPBSA and TI methodologies, the names and abbreviations of these protocols are used to emphasize the central importance of the ensemble-based nature of the protocols employed. (8,10,13−16) The term “ensemble” here refers to a set of individual (often called “replica”) simulations conducted for the same physical system, starting from different initial conformations (13) (and possibly also with varying model parameters (14)). Advances in high-end computing capabilities offer the opportunity to run all of the replicas concurrently, ensuring that the results can be delivered rapidly, exactly as has been done in climate and weather forecasting for the past 20 years. Ensemble approaches lead to increased reliability and reproducibility, with tighter control of standard uncertainty for nonlinear systems which are chaotic in nature. (8,17,18) Ensemble approaches provide probabilistic statements about quantities of interest and the likelihood of various outcomes. Only by large scale ensemble sampling can the nature of statistical distributions of free energies be assessed; we have previously shown that they exhibit non-normal behavior. (8,16,18,19) Binding free energies obtained from independent replica simulations of the same molecular system can vary by a wide range, while their distributions deviates from the Gaussian behavior usually assumed as we have reported. (16) Such properties are important for the proper use of many statistical methods (discussed further in Section 3.5). ESMACS and TIES are performed using a binding affinity calculator (BAC), (20) which is a computational pipeline to automate the processes of building, running, and marshaling the molecular dynamics simulations, as well as collecting and analyzing data. It is notable that until now virtually no other groups have been using or reporting results based on ensemble calculations which hitherto remain anything but routine methods within the entire field of classical molecular dynamics. (8,16,18)
Depending on the usability, reliability, rapidity, and throughput, these automated packages could find application at various stages of the drug discovery process across the wider pharmaceutical industry. In practice, however, the application of computational approaches is still dependent on the experience and knowledge of the practitioner. It remains a challenge for non-expert users to apply these existing tools to make robust predictions on a timescale that can substantially impact drug discovery programs. For a given approach, the success of predictions also varies significantly across different protein targets with different sets of compounds. Studies have shown that the initial crystal structures and the existence of multiple conformations can have a significant effect on the quality of free energy predictions. (21,22) Based on the experience, knowledge, and intuition we have accumulated, we propose the following criteria to predict the quality of the calculations: (1) how well the binding site is defined and structured; (2) how well a compound fits into the binding pocket; and (3) how many rotamers and/or binding poses a compound may manifest.
The purpose of the present study is to evaluate the ability of ESMACS and TIES to estimate binding affinities of a set of 22 ligands (Table 1) to the protein target. For the SMYD3 systems studied here, the binding site of the protein is well structured (Figure 1), and the binding mode for the scaffold of the congeneric compounds (Table 1) is well-defined in the crystal structure. It is thus likely, based on our foregoing criteria, that a reasonable prediction can be achieved, although the relatively large size of the binding site, the presence of multiple components in the structure including several crystallographic water molecules involved in binding, and the rotatable bonds at the R2 site of the compounds (Table 1) still pose a challenge for the conformational sampling and hence the accuracy and precision of the predictions.

Figure 1

Figure 1. Structure of SMYD3, complexed with one of the compounds in this study. The N-terminal SET domain, the MYND domain, the post-SET domain, and the C-terminal region are colored in orange, yellow, pink, and white, respectively. The cofactor SAH is shown with a bond representation and the ligand (S01) in a ball-and-stick model. The Zn2+ ions are shown with sphere models and colored green.

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Table 1. Compounds Investigated in This Study
a

The binding free energy is estimated by ΔGexp = RT × ln (IC50) = – RT × ln (10) × pIC50, where R is the gas constant and T is temperature, which is set to 300 K in this study.

b

There was no activity at the highest concentration (250 μM) tested.

2. Material and Methods

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The X-ray structure of SMYD3 consists of a co-factor SAH and three zinc ions which are important for the folding of the protein (Figure 1).

2.1. Experiments

A series of isoxazole amides was chosen to cover a range of binding affinity and chemical structure. These include a diversity of lipophilicity, aromaticity, and formal charge; the variation of formal charge has historically been challenging for free energy predictions. The IC50s acquired for the compounds were measured using the scintillation proximity assay using MEKK2-based peptide as a substrate previously reported. (4)

2.2. Computational Approach

2.2.1. Compounds

A set of compounds named SXX were provided by GSK, where XX was a two-digit number where integers lower than 10 were preceded by a 0 (Table 1), with mean values of pIC50 from experimental assay. Two of the compounds, S21 and S22, were reported as C01 and C28 in a previous publication. (4) All compounds shared the same scaffold (Table 1). The compounds were docked into the binding pocket of SMYD3 using Glide. (23) Modeling was carried out on a GSK internal structural precursor to 6P7Z. The rmsd between the structure used and 6P7Z is approximately 0.3 Å. The compounds were docked into the structure with a substructural constraint on the isoxazole-amide-piperidine-sulfone substructure (as shown in Table 1) using Glide XP in Maestro 2015-2.

2.2.2. Model Preparation

The preparation and setup of the simulations were implemented using BAC, (20) including parameterization of the compounds, solvation of the complexes, addition of counterions to electrostatically neutralize the systems, and generation of configurations files for the simulations. The Amber package (24) was used for the parameterization of the compounds, the setup of the systems, and the analyses of the results. The Amber ff14SB force field was used for the protein and TIP3P for water molecules. The protonation states were assigned using the “reduce” module of AmberTools. Parameters of the ligands were produced using the general Amber force field 2 (GAFF2) with Gaussian 16 to optimize compound geometries and to determine electrostatic potentials at the Hartree–Fock level with 6-31G** basis functions. The restrained electrostatic potential module in the AmberTools was used to calculate the partial atomic charges for the compounds. All systems were solvated in orthorhombic water boxes with a minimum extension from the protein of 14 Å.

2.2.3. ESMACS

We used the ESMACS (10) protocol for the simulations and analyses. The protocol uses replica simulations to obtain reproducible binding affinity predictions with robust uncertainty estimates. It is based on the molecular mechanics Poisson–Boltzmann surface area (MMPBSA), which is an approximate method for calculating absolute binding affinities from molecular dynamics trajectories. It is an endpoint free energy calculation, in which the difference in binding free energy, ΔG, is calculated using
(1)
where Gi is the free energy of component i which corresponds to either complex (com), protein (pro), or ligand (lig), and is calculated from a set of structures from MD simulations. The free energies can be broken down into a number of components, including the molecular mechanics energy in the gas phase and the solvation free energy. While the former is derived from the molecular modeling force field used, the latter is estimated as the sum of the electrostatic solvation free energy calculated using the Poisson–Boltzmann equation and the nonpolar solvation free energy calculated from the solvent accessible surface area. The binding free energy is calculated from the difference between calculations performed for the complex, ligand, and receptor conformations obtained from simulation. The 1-trajectory approach was used here, in which conformations of the protein and the ligands were extracted from the ligand–protein complex simulations. The ESMACS protocol has options to include configurational entropy within the free energy calculations, obtained from normal model analyses or other approximations. In most situations, however, the inclusion of entropic contributions fails to improve the rankings of predicted binding affinities. (25−28) In the current ESMACS study, the entropic term is neglected because of its minor contribution to the predicted rankings.

2.2.4. Thermodynamic Integration with Enhanced Sampling

We used TIES (11) to calculate the relative binding free energies for pairs of compounds. In TIES, an alchemical transformation for the mutated entity is used in both aqueous solution and within the ligand–protein complex. The free energy changes of the alchemical mutation processes, ΔGaqalch and ΔGcomplexalch, are calculated by
(2)
where λ (0 ≤ λ ≤ 1) is an alchemical coupling parameter such that λ = 0 and λ = 1 correspond to the initial and final thermodynamic states, and ∂V(λ)/∂λ is the partial derivative of the hybrid potential energy V(λ) at an intermediate state λ. ⟨···⟩λ denotes an ensemble average over configurations representative of the state λ. For each transformation, 13 λ windows are used with fixed values 0.0, 0.05, 0.1, 0.2, ..., 0.9, 0.95, 1.0.
The binding free energy difference is then calculated from
(3)

2.2.5. Simulations

The BAC, (20) an automated workflow tool for free energy calculations, was used to prepare and execute ESMACS and TIES simulations. The standard protocol (10,11,29) was used, in which NAMD (30) simulations with 25 and 5 replicas were performed for ESMACS and TIES, respectively. Each replica in the ensemble started with identical atomic coordinates, with different initial velocities generated independently from a Maxwell–Boltzmann distribution.
To avoid the well-known “end-point catastrophe,” (31) a soft-core potential was used for van der Waals (vdW) interactions involving the perturbed atoms. The electrostatic interactions were linearly scaled but at a faster rate than the vdW interactions, so that the partial charges were removed for the disappearing atoms before they were fully annihilated and were introduced on the appearing atoms after they already partially appeared.
The MD package NAMD2.12 (30) was used throughout the equilibration and production runs of all simulations. For each replica in an ensemble, energy minimizations were first performed with heavy protein atoms restrained at their initial positions. The initial velocities were then generated independently from a Maxwell–Boltzmann distribution at 50 K, and the systems were heated up to and kept at 300 K within 60 ps. A series of equilibration runs, totaling 2 ns, were conducted, while the restraints on heavy atoms were gradually reduced. Finally, 4 ns production simulations were run for each replica for all ESMACS and TIES simulations.
The ESMACS simulations for the compounds S01–S20 were initially conducted using 10-replica ensembles on the DNAnexus platform (https://www.dnanexus.com/) which provides strong cybersecurity. Previous studies (10,19,29,32,33) have established a standard ESMACS protocol with 25 replicas and have shown that the combination of the simulation length and the size of the ensemble provides a trade-off between computational cost and precision. The choice of a smaller number here was designed to reduce computational cost on the cloud environment. The study was later extended to include two more compounds, C01 and C28 from Su et al., (4) renamed as S21 and S22, to extend ESMACS to 25 replicas and, more importantly, to perform TIES studies on the selected compound pairs. The Blue Waters supercomputer at the National Center for Supercomputing Applications (NCSA) in the US was used for the extended ESMACS simulations. The SuperMUC supercomputer at Leibniz Supercomputing Centre in Germany was used for the TIES simulations. For 1 ns simulation, it took ∼5.4 h on a single GRID K520 card using DNAnexus, ∼2.1 h on 128 CPUs on Blue Waters, and ∼0.9 h on 220 CPUs on SuperMUC. It should be noted that Nvidia GRID K520 GPUs are now discontinued and that both the supercomputers referenced here are now retired. As a result, any state-of-the-art supercomputers and cloud services are much faster than the ones used for this study.

3. Results

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To assess the accuracy and precision of the method, we evaluated the binding affinities of the ligands (Table 1) to SMYD3 and compared the computed results with experimental data. ESMACS was used for the full set of the ligands, while TIES was applied to some selected pairs of the ligands with the same net charge. When making a direct comparison of specific correlation coefficients, we also quote the 95% confidence intervals (CI).

3.1. Reproducibility of the ESMACS Simulations

It is well known that the differences of the initial conditions among individual simulations lead to rapid divergence of trajectories. (13) Many complex systems hence exhibit sensitive dependence on initial conditions. The calculated thermodynamic properties from individual simulations will therefore inevitably differ. Two sets of ESMACS simulations were performed for the complexes SXX (Table 1) independently on Blue Waters and DNAnexus (see the Material and Methods section above). Figure 2 shows the variances and correlation of the calculated binding free energies from the two sets of simulations. Excellent agreement was observed between calculations using two different computational platforms: the HPC machine Blue Waters and the cloud environment DNAnexus, with a highly significant Spearman correlation of 0.98 [CI: 0.94–0.99]. No statistical differences were seen between the two sets of calculated binding free energies: 16 out of 20 compounds having identical results, within error bars, and the remaining 4 within two error bars (Figure 2). The two simulations produce consistent results, with a mean signed difference of 0.13 kcal/mol and a mean unsigned difference of 0.63 kcal/mol. Both of the calculations have good correlations with the experimental measurement, with correlation coefficients of 0.80 [CI: 0.56–0.92] and 0.78 [CI: 0.52–0.91] for the simulations on Blue Waters and DNAnexus, respectively. Because of the smaller number of replicas used in the DNAnexus simulations, the error bars in these simulations are ∼1.5 times larger than those from Blue Waters simulations. As the two simulations produce similar accuracies, only the results from Blue Waters are reported in the following analyses.

Figure 2

Figure 2. Comparison of calculated binding free energies from two independent studies of the ligand-SMYD3 models performed on Blue Waters (bw, horizontal axis) and DNAnexus (DNA, vertical axis). The dashed line shows an ideal y = x regression. The standard errors are calculated using a bootstrapping method.

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3.2. Correlations between ESMACS Calculations and Experimental Measurements

The predicted binding free energies from the 1-trajectory approach exhibit a high correlation with the experimental data (Figure 3), with a Pearson correlation coefficient of 0.84 [CI: 0.65–0.93]. In a pharmaceutical drug development project, compounds are designed or selected for the same protein target. The ranking of the binding affinities is not affected by the energy of the protein Gpro (eq 1) when the conformational space is sufficiently sampled. Free energies of a protein differ in its bound and unbound states. The difference, called the adaptation free energy, (10) provides an indication of the conformational changes of the protein and the energetic costs upon binding. Inclusion of adaptation free energies improves the correlations between simulations and experimental measurements in some cases (10,34,35) and does not have obvious effects in other cases. (26) For the current data set of compounds, the binding site is relatively large. No significant strain is induced within protein upon compound binding. The inclusion of adaptation free energies of the protein degrades the correlations, with a correlation coefficient of 0.70 [CI: 0.40–0.87].

Figure 3

Figure 3. Comparison of calculated binding free energies and experimental binding affinity data from 1-traj ESMACS approach. The dotted line shows a linear regression. A correlation coefficient of 0.84 [CI: 0.65–0.93] is obtained for the entire set of compounds. The +1e charged compounds are shown in blue and electrostatically neutral ones in black.

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The calculations correctly distinguish the charged compounds from the neutral ones (Figure 3). The R2 group (Table 1) locates in a hydrophilic pocket in which negatively charged residues GLU192, ASP241, and GLU294 form favorable electrostatic interactions with the positively charged R2 group (Figure 4). This makes the binding of charged compounds more favorable in general than the electrostatically neutral ones. The two variants at R1 studied here may not affect the binding affinities significantly because the ethyl group and the cyclopropyl ring are similar in their hydrophobic properties and their sizes. The two compounds, S01 and S21, differing only at the R1 group, have similar binding affinities from both experimental measurements and the ESMACS calculations (Figure 3). It should be noted that no activity was detected for S08 at the highest concentration (250 μM) in the experiments (Table 1), indicating that its binding affinity is likely to be less negative than that presented in Figure 3. This makes the point deviate even farther from the regression line. Our TIES calculations also show that S08 is an outlier (see details below).

Figure 4

Figure 4. Electrostatic interactions between the R2 group and the protein. The negatively charged residues GLU192, ASP241, and GLU294, and positively charged R2 group, along with positively charged LYS 329, form favorable electrostatic interactions.

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3.3. TIES Results

Relative binding free energies (ΔΔG) are calculated using TIES for selected pairs of compounds. Each compound is paired at least once with other compounds. No compounds are paired if they have different net charges, as alchemical methods encounter specific difficulties when changes in the net charge arise and charge corrections are required. The results of these relative binding free energy calculations are compared with the data derived from experimental measurements (Figure 5).

Figure 5

Figure 5. Comparison between TIES-predicted relative binding affinities and experimental data for a total of 19 compound pairs. The long dashed line represents y = x, whereas dashed and dotted lines represent 1 kcal/mol and 2 kcal/mol ranges, respectively. The pairs involving S08 are highlighted in blue.

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As the compound S08 may be denoted as an outlier (see details below), the analyses are performed separately for the data set with and without the compound. The overall mean unsigned error is 1.21 kcal/mol for the entire data set and 0.68 kcal/mol when pairs involving S08 are excluded. The mean signed errors are 0.62 kcal/mol and –0.06 kcal/mol for the data set with and without S08, respectively. Except the pairs with S08, only one compound pair, S22–S20, has a predicted ΔΔG value which differs from the experimental data by >2 kcal/mol. The main difference between the two compounds are the three rotatable bonds at R2 (Table 1). The rotation of these rotatable bonds leads to large conformational flexibilities in S22, which may need longer simulation time to get reliable prediction.

3.4. S08 Remains an Outlier

Our initial TIES calculations only contained one compound pair involving S08, of which the deviation between the calculation and the experimental data is large. As the ESMACS simulation also shows that it is an outlier, we have paired S08 with three other compounds for TIES simulations. The results only confirm that there is a systematic deviation in the binding free energy for S08 between calculations and experimental measurements. Based on the four TIES calculations for S08, the average difference between calculations and experimental data is 3.21 kcal/mol. In other words, the compound S08 needs to have a binding affinity 3.21 kcal/mol more negative in the experiments or 3.21 kcal/mol less negative in the calculations to make them agree with each other. This value is also in a good agreement with the ESMACS calculation, with which the data point for S08 can be shifted much closer to the regression line (Figure 3).
The compound S08 consists of a nitrile group of which the nitrogen is highly electronegative. Although the negatively charged residues at the R2 pocket are unfavorable for the presentence of the nitrile group, the positively charged residue LYS329 and the relatively spacious pocket appear to be able to tolerate the group. The detailed analyses of the simulation trajectories do not provide more insights. Further searching in the experimental data set identified another compound, which is very similar to S08 and shares the same nitrile group at the R2. The compound also does not show any activity at the highest concentration tested in the assay (data not shown). Although it could be an experimental issue, it is more likely to be a force field or possibly a sampling issue. As there are no satisfactory explanations for the disagreement between the experiments and the calculations, S08 remains as an unexplained outlier. Such unexplained outliers are not unusual in drug discovery and development projects. Machine learning approaches have been proposed to identify the differences between the calculations and the experimental data and to provide empirical correction terms to the predictions from the alchemical approaches, but these too depend on assumptions which are rarely articulated concerning the way in which the data are distributed. (36)

3.5. Non-normal Distributions of Free Energy Calculations and Measurement

Normal distributions have been typically assumed in experimental measurements and calculations of binding free energies. The assumptions are commonly made for the true ΔGbinding for a large number of compounds, for the experimentally determined and computationally predicted ΔGbinding for a given compound, as well as for the relative binding free energies ΔΔGbinding. The normal distributions are characterized by an average μ and a standard deviation σ. Although the presence of uncertainties is known to the scientific community broadly, they are still “known unknowns”: in many cases, we do not know the order of magnitude of the various uncertainties, the sources and the consequences of them, not to mention how to reduce them. It is important to describe the free energy distribution carefully as many statistical analyses are based on it. The most important assumption in regression dilution, (37) for example, is that all the variables under consideration are normally distributed. If this is not the case, regression dilution may not be applied.
The assertion that the calculated binding free energies ΔGcal or binding free energy differences ΔΔGcal follow a normal distribution conflicts with our observation that such data are not in general normally distributed. (8,16,18,19) Newtonian molecular dynamics is inherently nonlinear, and this is the underlying reason why the dynamics is chaotic in the technical sense. Not only are individual trajectories extremely sensitive to initial conditions, they become increasingly inaccurate as the duration of such a simulation unfolds. They manifest long range correlations which are not present in Gaussian statistics.
In experimental measurement of binding free energies, uncertainties on the order of 0.3–0.5 kcal/mol for ΔGexp and 0.4–0.7 kcal/mol for ΔΔGexp have been claimed from high-quality experimental measurements. (7) It is, however, very often the case that experimental data are reported as single numbers, without quantification of the uncertainties. We have no knowledge about the statistics of ΔGexp or ΔΔGexp reported, let alone the distribution of these quantities. This means that the unknown and unstated error bars may be varying in all manner of ways, so claiming that they are normally distributed is not credible.
There are four compounds in the current project, which have been tested >100 times for their activities to SMYD3. One of them is S21 (Figure 6a), which has been computationally investigated here. The other three are for more potent compounds that are from a related but slightly different series. The relatively large number of tests makes it possible to verify the distributions of the experimental data. It should be noted that while compounds a and b do not show any drift in the assay over time, compounds c and d (Table 2 and Figure 6) show a small amount of time dependency.

Figure 6

Figure 6. Distributions of experimental pIC50 values shown as histogram and kernel density curve. Four compounds from the current project (a–d) are used, which have been tested more than 100 times. A bin size of 0.05 is used. The dashed lines indicate the means of the experimental measurements.

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Table 2. Statistics of the Experimental Measurements pIC50 for the Compounds with >100 Tests
compoundno. of testaverageSDskewnesskurtosis
a2645.290.100.881.47
b1147.310.12–0.350.23
c1247.470.192.047.56
d1167.090.212.115.30
All of the four distributions are skewed from a normal distribution, with skewness deviating from 0. Three of them are highly skewed with positive skewness (Table 2), indicating that the distributions have longer tails on the right side than those on the left (Figure 6). The other one is moderately skewed with a negative skewness and a longer tail on the left. The excess kurtoses are all positive, meaning that compared to a normal distribution, the tails are longer and heavier. It should be noted that the experimental data shown in Figure 6 are representative of the behavior of such ligand–protein binding affinities more widely and that other data remain confidential to GSK. Overall, these results imply the presence of non-normal distributions in the experimental measurements.
The fat-tailed distribution of binding affinities indicates that the expectation value of this quantity lies far from the most probable value of the distribution (Figure 6). The probability of observing a high value of the binding affinity is far higher than for a normal distribution (Table 3). The skewness (Table 2) characterizes the deviation of the distribution from symmetry, evidenced by the unequal distributions in the corresponding bins centered at their means and by the presence of longer tails on one side than the other (Table 3). The lack of symmetry is highlighted in Figure 6 for compounds c and d, which exhibit large skewness (Table 2). The high values of kurtosis indicate the existence of outliers in the distribution. The measured binding free energies for compound d, for example, have a probability of 5.2% to be found more than two standard deviations from the mean on the left side, compared with a probability of 2.3% were the distribution normal. Asymmetric distributions with a long tail on one side have been commonly observed in climate studies. (38) One such study, (39) which highlights the impact of fat-tailed distributions, found that, because of the probability distribution being fat-tailed at higher temperatures, there was a predicted 3% chance of an increase in global surface temperature by 8 °C or more following a doubling of carbon dioxide concentrations, whereas if the distribution were normal, this probability would be only 0.3%.
Table 3. Percentages of Samples in Different Binsa
compound(−∞, −2σ)[−2σ, −σ)[−σ, 0)[0, σ)[σ, 2σ)[2σ, ∞)
a4.99.829.543.911.00.8
b1.815.832.536.89.63.5
c3.27.328.254.86.50
d5.24.328.455.26.90
normal2.313.634.134.113.62.3
a

The experimental binding affinities pIC50 have been converted into binding free energies using ΔG = RT ln (IC50). σ values are the standard deviations of the normal distributions which best fit the binding free energies for each of the compounds. The percentages from a normal distribution are listed for reference.

4. Conclusions

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Using the TIES and ESMACS protocols, we have computed the binding free energies of a series of ligands to zinc finger protein SMYD3. Although an unexplained outlier exists, we obtain excellent statistical rankings across the set of compounds from the two protocols. ESMACS and TIES are again found to be powerful protocols for the accurate comparison of the binding free energies.
We have previously reported the non-normal properties of calculated binding free energies. In the current study, we investigate the distributions of experimentally measured free energies and find that the distributions are highly skewed. The practical implications of this discovery are important to apprehend. Non-normal distributions imply the occurrence of more “outliers”, making it essential to perform multiple measurements to pin down average behavior. It is also a call to exercise caution in the use of statistical methods for the comparison of experimental data and computational predictions, as the assumption of normal distributions is not generally valid.

Author Information

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  • Corresponding Author
    • Peter V. Coveney - Centre for Computational Science, Department of Chemistry, University College London, London WC1H 0AJ, U.K.;  Advanced Research Computing Centre, University College London, London WC1H 0AJ U.K.;  Institute for Informatics, Faculty of Science, University of Amsterdam, 1098XH Amsterdam, The Netherlands;  Orcidhttps://orcid.org/0000-0002-8787-7256;  Email: [email protected]
  • Authors
    • Shunzhou Wan - Centre for Computational Science, Department of Chemistry, University College London, London WC1H 0AJ, U.K.;  Orcidhttps://orcid.org/0000-0001-7192-1999
    • Agastya P. Bhati - Centre for Computational Science, Department of Chemistry, University College London, London WC1H 0AJ, U.K.
    • David W. Wright - Centre for Computational Science, Department of Chemistry, University College London, London WC1H 0AJ, U.K.;  Orcidhttps://orcid.org/0000-0002-5124-8044
    • Ian D. Wall - GlaxoSmithKline, Gunnels Wood Road, Stevenage, Hertfordshire SG1 2NY, U.K.
    • Alan P. Graves - GlaxoSmithKline, 1250 South Collegeville Road, Collegeville, Pennsylvania 19426, United States
    • Darren Green - GlaxoSmithKline, Gunnels Wood Road, Stevenage, Hertfordshire SG1 2NY, U.K.
  • Notes
    The authors declare no competing financial interest.

    The structures for the SMYD3 protein and the compounds are freely available at https://doi.org/10.23728/b2share.8e650caf35cb437dbf9007afc84c5257.

Acknowledgments

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We are grateful for funding for the UK MRC Medical Bioinformatics project (grant no. MR/L016311/1), the EPSRC funded UK Consortium on Mesoscale Engineering Sciences (UKCOMES grant no. EP/L00030X/1), the European Commission for EU H2020 CompBioMed2 Centre of Excellence (grant no. 823712) and for EU H2020 EXDCI-2 project (grant no. 800957), and NSF award (https://www.nsf.gov/pubs/2017/nsf17542/nsf17542.htm, Award No. NSF 1713749). We made use of the Blue Waters supercomputer at the National Center for Supercomputing Applications of the University of Illinois at Urbana-Champaign, access to which was made available through the aforementioned NSF award. Additional calculations were conducted using an award of computer time on the Theta machine at Argonne Leadership Computing Facility provided by the US Department of Energy’s Innovative and Novel Computational Impact on Theory and Experiment (INCITE) program (through the INSPIRE project and a 2021 award “COMPBIO”). We are grateful to DNAnexus for both computational resources and technical support from Fiona Ford, Brett Hannigan and Chai Fungtammasan. We acknowledge the Leibniz Supercomputing Centre for providing access to SuperMUC (https://www.lrz.de/services/compute/) and the very able assistance of its scientific support staff.

References

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This article references 39 other publications.

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    On the calculation of equilibrium thermodynamic properties from molecular dynamics
    Coveney, Peter V.; Wan, Shunzhou
    Physical Chemistry Chemical Physics (2016), 18 (44), 30236-30240CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
    The purpose of statistical mechanics is to provide a route to the calcn. of macroscopic properties of matter from their constituent microscopic components. It is well known that the macrostates emerge as ensemble avs. of microstates. However, this is more often stated than implemented in computer simulation studies. Here we consider foundational aspects of statistical mechanics which are overlooked in most textbooks and research articles that purport to compute macroscopic behavior from microscopic descriptions based on classical mechanics and show how due attention to these issues leads in directions which have not been widely appreciated in the field of mol. dynamics simulation.
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  14. 14
    Vassaux, M.; Wan, S.; Edeling, W.; Coveney, P. V. Ensembles Are Required to Handle Aleatoric and Parametric Uncertainty in Molecular Dynamics Simulation. J. Chem. Theory Comput. 2021, 17, 5187– 5197,  DOI: 10.1021/acs.jctc.1c00526
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    14
    Aleatoric and parametric uncertainty in molecular dynamics simulation
    Vassaux, Maxime; Wan, Shunzhou; Edeling, Wouter; Coveney, Peter V.
    Journal of Chemical Theory and Computation (2021), 17 (8), 5187-5197CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
    Classical mol. dynamics is a computer simulation technique that is in widespread use across many areas of science, from physics and chem. to materials, biol. and medicine. The method continues to attract criticism due its oft-reported lack of reproducibility which is in part due to a failure to submit it to reliable uncertainty quantification (UQ). Here we show that the uncertainty arises from a combination of (i) the input parameters and (ii) the intrinsic stochasticity of the method controlled by the random seeds. To illustrate the situation, we make a systematic UQ anal. of a widely used mol. dynamics code (NAMD), applied to est. binding free energy of a ligand-bound to a protein. In particular, we replace the usually fixed input parameters with random variables, systematically distributed about their mean values, and study the resulting distribution of the simulation output. We also perform a sensitivity anal., which reveals that, out of a total of 175 parameters, just six dominate the variance in the code output. Furthermore, we show that binding energy calcn. damps the input uncertainty, in the sense that the variation around the mean output free energy is less than the variation around the mean of the assumed input distributions, if the output is ensemble-averaged over the random seeds. Without such ensemble averaging, the predicted free energy is five times more uncertain. The distribution of the predicted properties is thus strongly dependent upon the random seed. Owing to this substantial uncertainty, robust statistical measures of uncertainty in mol. dynamics simulation require the use of ensembles in all contexts.
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  15. 15
    Wade, A.; Bhati, A. P.; Wan, S.; Coveney, P. V. Alchemical Free Energy Estimators and Molecular Dynamics Engines: Accuracy Precision and Reproducibility. ChemRxiv 2021,  DOI: 10.26434/chemrxiv-2021-nqp8r .
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  16. 16
    Bhati, A. P.; Coveney, P. V. Large Scale Study of Ligand-Protein Relative Binding Free Energy Calculations: Actionable Predictions from Statistically Robust Protocols. J. Chem. Theory Comput. 2022, 18, 2687– 2702,  DOI: 10.1021/acs.jctc.1c01288
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    16
    Large Scale Study of Ligand-Protein Relative Binding Free Energy Calculations: Actionable Predictions from Statistically Robust Protocols
    Bhati, Agastya P.; Coveney, Peter V.
    Journal of Chemical Theory and Computation (2022), 18 (4), 2687-2702CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
    The accurate and reliable prediction of protein-ligand binding affinities can play a central role in the drug discovery process as well as in personalized medicine. Of considerable importance during lead optimization are the alchem. free energy methods that furnish an estn. of relative binding free energies (RBFE) of similar mols. Recent advances in these methods have increased their speed, accuracy, and precision. This is evident from the increasing no. of retrospective as well as prospective studies employing them. However, such methods still have limited applicability in real-world scenarios due to a no. of important yet unresolved issues. Here, we report the findings from a large data set comprising over 500 ligand transformations spanning over 300 ligands binding to a diverse set of 14 different protein targets which furnish statistically robust results on the accuracy, precision, and reproducibility of RBFE calcns. We use ensemble-based methods which are the only way to provide reliable uncertainty quantification given that the underlying mol. dynamics is chaotic. These are implemented using TIES (Thermodn. Integration with Enhanced Sampling). Results achieve chem. accuracy in all cases. Ensemble simulations also furnish information on the statistical distributions of the free energy calcns. which exhibit non-normal behavior. We find that the "enhanced sampling" method known as replica exchange with solute tempering degrades RBFE predictions. We also report definitively on numerous assocd. alchem. factors including the choice of ligand charge method, flexibility in ligand structure, and the size of the alchem. region including the no. of atoms involved in transforming one ligand into another. Our findings provide a key set of recommendations that should be adopted for the reliable application of RBFE methods.
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  17. 17
    Knapp, B.; Ospina, L.; Deane, C. M. Avoiding False Positive Conclusions in Molecular Simulation: The Importance of Replicas. J. Chem. Theory Comput. 2018, 14, 6127– 6138,  DOI: 10.1021/acs.jctc.8b00391
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    17
    Avoiding False Positive Conclusions in Molecular Simulation: The Importance of Replicas
    Knapp, Bernhard; Ospina, Luis; Deane, Charlotte M.
    Journal of Chemical Theory and Computation (2018), 14 (12), 6127-6138CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
    Mol. simulations are a computational technique used to investigate the dynamics of proteins and other mols. The free energy landscape of these simulations is often rugged, and minor differences in the initial velocities, floating-point precision, or underlying hardware can cause identical simulations (replicas) to take different paths in the landscape. In this study the authors investigated the magnitude of these effects based on 310 000 ns of simulation time. The authors performed 100 identically parametrized replicas of 3000 ns each for a small 10 amino acid system as well as 100 identically parametrized replicas of 100 ns each for an 827 residue T-cell receptor/MHC system. Comparing randomly chosen subgroups within these replica sets, the authors estd. the reproducibility and reliability that can be achieved by a given no. of replicas at a given simulation time. These results demonstrate that conclusions drawn from single simulations are often not reproducible and that conclusions drawn from multiple shorter replicas are more reliable than those from a single longer simulation. The actual no. of replicas needed will always depend on the question asked and the level of reliability sought. On the basis of the data, it appears that a good rule of thumb is to perform a min. of five to 10 replicas.
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  18. 18
    Wan, S.; Sinclair, R. C.; Coveney, P. V. Uncertainty Quantification in Classical Molecular Dynamics. Philos. Trans. R. Soc., A 2021, 379, 20200082  DOI: 10.1098/rsta.2020.0082
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    18
    Uncertainty quantification in classical molecular dynamics
    Wan, Shunzhou; Sinclair, Robert C.; Coveney, Peter V.
    Philosophical Transactions of the Royal Society, A: Mathematical, Physical & Engineering Sciences (2021), 379 (2197), 20200082CODEN: PTRMAD; ISSN:1364-503X. (Royal Society)
    Mol. dynamics simulation is now a widespread approach for understanding complex systems on the atomistic scale. It finds applications from physics and chem. to engineering, life and medical science. In the last decade, the approach has begun to advance from being a computer-based means of rationalizing exptl. observations to producing apparently credible predictions for a no. of real-world applications within industrial sectors such as advanced materials and drug discovery. However, key aspects concerning the reproducibility of the method have not kept pace with the speed of its uptake in the scientific community. Here, we present a discussion of uncertainty quantification for mol. dynamics simulation designed to endow the method with better error ests. that will enable it to be used to report actionable results. The approach adopted is a std. one in the field of uncertainty quantification, namely using ensemble methods, in which a sufficiently large no. of replicas are run concurrently, from which reliable statistics can be extd. Indeed, because mol. dynamics is intrinsically chaotic, the need to use ensemble methods is fundamental and holds regardless of the duration of the simulations performed. We discuss the approach and illustrate it in a range of applications from materials science to ligand-protein binding free energy estn.
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  19. 19
    Bieniek, M. K.; Bhati, A. P.; Wan, S.; Coveney, P. V. TIES 20: Relative Binding Free Energy with a Flexible Superimposition Algorithm and Partial Ring Morphing. J. Chem. Theory Comput. 2021, 17, 1250– 1265,  DOI: 10.1021/acs.jctc.0c01179
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    19
    TIES 20: Relative Binding Free Energy with a Flexible Superimposition Algorithm and Partial Ring Morphing
    Bieniek, Matuesz K.; Bhati, Agastya P.; Wan, Shunzhou; Coveney, Peter V.
    Journal of Chemical Theory and Computation (2021), 17 (2), 1250-1265CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
    The TIES (Thermodn. Integration with Enhanced Sampling) protocol is a formally exact alchem. approach in computational chem. to the calcn. of relative binding free energies. The validity of TIES relies on the correctness of matching atoms across compared pairs of ligands, laying the foundation for the transformation along an alchem. pathway. We implement a flexible topol. superimposition algorithm which uses an exhaustive joint-traversal for computing the largest common component(s). The algorithm is employed to enable matching and morphing of partial rings in the TIES protocol along with a validation study using 55 transformations and five different proteins from our previous work. We find that TIES 20 with the RESP charge system, using the new superimposition algorithm, reproduces the previous results with mean unsigned error of 0.75 kcal/mol with respect to the exptl. data. Enabling the morphing of partial rings decreases the size of the alchem. region in the dual-topol. transformations resulting in a significant improvement in the prediction precision. We find that increasing the ensemble size from 5 to 20 replicas per λ window only has a minimal impact on the accuracy. However, the non-normal nature of the relative free energy distributions underscores the importance of ensemble simulation. We further compare the results with the AM1-BCC charge system and show that it improves agreement with the exptl. data by slightly over 10%. This improvement is partly due to AM1-BCC affecting only the charges of the atoms local to the mutation, which translates to even fewer morphed atoms, consequently reducing issues with sampling and therefore ensemble averaging. TIES 20, in conjunction with the enablement of ring morphing, reduces the size of the alchem. region and significantly improves the precision of the predicted free energies.
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  20. 20
    Sadiq, S. K.; Wright, D.; Watson, S. J.; Zasada, S. J.; Stoica, I.; Coveney, P. V. Automated Molecular Simulation Based Binding Affinity Calculator for Ligand-Bound HIV-1 Proteases. J. Chem. Inf. Model. 2008, 48, 1909– 1919,  DOI: 10.1021/ci8000937
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    20
    Automated Molecular Simulation Based Binding Affinity Calculator for Ligand-Bound HIV-1 Proteases
    Sadiq, S. Kashif; Wright, David; Watson, Simon J.; Zasada, Stefan J.; Stoica, Ileana; Coveney, Peter V.
    Journal of Chemical Information and Modeling (2008), 48 (9), 1909-1919CODEN: JCISD8; ISSN:1549-9596. (American Chemical Society)
    The successful application of high throughput mol. simulations to det. biochem. properties would be of great importance to the biomedical community if such simulations could be turned around in a clin. relevant timescale. An important example is the detn. of antiretroviral inhibitor efficacy against varying strains of HIV through calcn. of drug-protein binding affinities. We describe the Binding Affinity Calculator (BAC), a tool for the automated calcn. of HIV-1 protease-ligand binding affinities. The tool employs fully atomistic mol. simulations alongside the well established mol. mechanics Poisson-Boltzmann solvent accessible surface area (MMPBSA) free energy methodol. to enable the calcn. of the binding free energy of several ligand-protease complexes, including all nine FDA approved inhibitors of HIV-1 protease and seven of the natural substrates cleaved by the protease. This enables the efficacy of these inhibitors to be ranked across several mutant strains of the protease relative to the wildtype. BAC is a tool that utilizes the power provided by a computational grid to automate all of the stages required to compute free energies of binding: model prepn., equilibration, simulation, postprocessing, and data-marshaling around the generally widely distributed compute resources utilized. Such automation enables the mol. dynamics methodol. to be used in a high throughput manner not achievable by manual methods. This paper describes the architecture and workflow management of BAC and the function of each of its components. Given adequate compute resources, BAC can yield quant. information regarding drug resistance at the mol. level within 96 h. Such a timescale is of direct clin. relevance and can assist in decision support for the assessment of patient-specific optimal drug treatment and the subsequent response to therapy for any given genotype.
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  21. 21
    Suruzhon, M.; Bodnarchuk, M. S.; Ciancetta, A.; Viner, R.; Wall, I. D.; Essex, J. W. Sensitivity of Binding Free Energy Calculations to Initial Protein Crystal Structure. J. Chem. Theory Comput. 2021, 17, 1806– 1821,  DOI: 10.1021/acs.jctc.0c00972
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    21
    Sensitivity of binding free energy calculations to initial protein crystal structure
    Suruzhon, Miroslav; Bodnarchuk, Michael S.; Ciancetta, Antonella; Viner, Russell; Wall, Ian D.; Essex, Jonathan W.
    Journal of Chemical Theory and Computation (2021), 17 (3), 1806-1821CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
    Binding free energy calcns. using alchem. free energy (AFE) methods are widely considered to be the most rigorous tool in the computational drug discovery arsenal. Despite this, the calcns. suffer from accuracy, precision, and reproducibility issues. In this publication, the authors perform a high-throughput study of more than a thousand AFE calcns., utilizing over 220μs of total sampling time, on three different protein systems to investigate the impact of the initial crystal structure on the resulting binding free energy values. The authors also consider the influence of equilibration time and discover that the initial crystal structure can have a significant effect on free energy values obtained at short timescales that can manifest itself as a free energy difference of more than 1 kcal/mol. At longer timescales, these differences are largely overtaken by important rare events, such as torsional ligand motions, typically resulting in a much higher uncertainty in the obtained values. This work emphasizes the importance of rare event sampling and long-timescale dynamics in free energy calcns. even for routinely performed alchem. perturbations. The authors conclude that an optimal protocol should not only conc. computational resources on achieving convergence in the alchem. coupling parameter (λ) space but also on longer simulations and multiple repeats.
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  22. 22
    Pérez-Benito, L.; Keränen, H.; van Vlijmen, H.; Tresadern, G. Predicting Binding Free Energies of PDE2 Inhibitors. The Difficulties of Protein Conformation. Sci. Rep. 2018, 8, 4883,  DOI: 10.1038/s41598-018-23039-5
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    22
    Predicting Binding Free Energies of PDE2 Inhibitors. The Difficulties of Protein Conformation
    Perez-Benito Laura; Keranen Henrik; van Vlijmen Herman; Tresadern Gary; Keranen Henrik
    Scientific reports (2018), 8 (1), 4883 ISSN:.
    A congeneric series of 21 phosphodiesterase 2 (PDE2) inhibitors are reported. Crystal structures show how the molecules can occupy a 'top-pocket' of the active site. Molecules with small substituents do not enter the pocket, a critical leucine (Leu770) is closed and water molecules are present. Large substituents enter the pocket, opening the Leu770 conformation and displacing the waters. We also report an X-ray structure revealing a new conformation of the PDE2 active site domain. The relative binding affinities of these compounds were studied with free energy perturbation (FEP) methods and it represents an attractive real-world test case. In general, the calculations could predict the energy of small-to-small, or large-to-large molecule perturbations. However, accurately capturing the transition from small-to-large proved challenging. Only when using alternative protein conformations did results improve. The new X-ray structure, along with a modelled dimer, conferred stability to the catalytic domain during the FEP molecular dynamics (MD) simulations, increasing the convergence and thereby improving the prediction of ΔΔG of binding for some small-to-large transitions. In summary, we found the most significant improvement in results when using different protein structures, and this data set is useful for future free energy validation studies.
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  23. 23
    Friesner, R. A.; Murphy, R. B.; Repasky, M. P.; Frye, L. L.; Greenwood, J. R.; Halgren, T. A.; Sanschagrin, P. C.; Mainz, D. T. Extra Precision Glide: Docking and Scoring Incorporating a Model of Hydrophobic Enclosure for Protein-Ligand Complexes. J. Med. Chem. 2006, 49, 6177– 6196,  DOI: 10.1021/jm051256o
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    23
    Extra Precision Glide: Docking and Scoring Incorporating a Model of Hydrophobic Enclosure for Protein-Ligand Complexes
    Friesner, Richard A.; Murphy, Robert B.; Repasky, Matthew P.; Frye, Leah L.; Greenwood, Jeremy R.; Halgren, Thomas A.; Sanschagrin, Paul C.; Mainz, Daniel T.
    Journal of Medicinal Chemistry (2006), 49 (21), 6177-6196CODEN: JMCMAR; ISSN:0022-2623. (American Chemical Society)
    A novel scoring function to est. protein-ligand binding affinities has been developed and implemented as the Glide 4.0 XP scoring function and docking protocol. In addn. to unique water desolvation energy terms, protein-ligand structural motifs leading to enhanced binding affinity are included:(1) hydrophobic enclosure where groups of lipophilic ligand atoms are enclosed on opposite faces by lipophilic protein atoms, (2) neutral-neutral single or correlated hydrogen bonds in a hydrophobically enclosed environment, and (3) five categories of charged-charged hydrogen bonds. The XP scoring function and docking protocol have been developed to reproduce exptl. binding affinities for a set of 198 complexes (RMSDs of 2.26 and 1.73 kcal/mol over all and well-docked ligands, resp.) and to yield quality enrichments for a set of fifteen screens of pharmaceutical importance. Enrichment results demonstrate the importance of the novel XP mol. recognition and water scoring in sepg. active and inactive ligands and avoiding false positives.
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  24. 24
    Case, D. A.; Cheatham, T. E., 3rd; Darden, T.; Gohlke, H.; Luo, R.; Merz, K. M., Jr.; Onufriev, A.; Simmerling, C.; Wang, B.; Woods, R. J. The Amber Biomolecular Simulation Programs. J. Comput. Chem. 2005, 26, 1668– 1688,  DOI: 10.1002/jcc.20290
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    The amber biomolecular simulation programs
    Case, David A.; Cheatham, Thomas E., III; Darden, Tom; Gohlke, Holger; Luo, Ray; Merz, Kenneth M., Jr.; Onufriev, Alexey; Simmerling, Carlos; Wang, Bing; Woods, Robert J.
    Journal of Computational Chemistry (2005), 26 (16), 1668-1688CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
    The authors describe the development, current features, and some directions for future development of the Amber package of computer programs. This package evolved from a program that was constructed in the late 1970s to do Assisted Model Building with Energy Refinement, and now contains a group of programs embodying a no. of powerful tools of modern computational chem., focused on mol. dynamics and free energy calcns. of proteins, nucleic acids, and carbohydrates.
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    Zhang, X.; Perez-Sanchez, H.; Lightstone, F. C. A Comprehensive Docking and MM/GBSA Rescoring Study of Ligand Recognition Upon Binding Antithrombin. Curr. Top. Med. Chem. 2017, 17, 1631– 1639,  DOI: 10.2174/1568026616666161117112604
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    25
    A Comprehensive Docking and MM/GBSA Rescoring Study of Ligand Recognition upon Binding Antithrombin
    Zhang, Xiaohua; Perez-Sanchez, Horacio; Lightstone, Felice C.
    Current Topics in Medicinal Chemistry (Sharjah, United Arab Emirates) (2017), 17 (14), 1631-1639CODEN: CTMCCL; ISSN:1568-0266. (Bentham Science Publishers Ltd.)
    Background: A high-throughput virtual screening pipeline has been extended from single energetically minimized structure Mol. Mechanics/Generalized Born Surface Area (MM/GBSA) rescoring to ensemble-av. MM/GBSA rescoring. The correlation coeff. (R2) of calcd. and exptl. binding free energies for a series of antithrombin ligands has been improved from 0.36 to 0.69 when switching from the single-structure MM/GBSA rescoring to ensemble-av. one. The electrostatic interactions in both solute and solvent are identified to play an important role in detg. the binding free energy after the decompn. of the calcd. binding free energy. The increasing neg. charge of the compds. provides a more favorable electrostatic energy change but creates a higher penalty for the solvation free energy. Such a penalty is compensated by the electrostatic energy change, which results in a better binding affinity. A highly hydrophobic ligand is detd. by the docking program to be a non-specific binder. Results: Our results have demonstrated that it is very important to keep a few top poses for rescoring, if the binding is non-specific or the binding mode is not well detd. by the docking calcn.
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  26. 26
    Wright, D. W.; Husseini, F.; Wan, S.; Meyer, C.; van Vlijmen, H.; Tresadern, G.; Coveney, P. V. Application of the ESMACS Binding Free Energy Protocol to a Multi-Binding Site Lactate Dehydogenase a Ligand Dataset. Adv. Theory Simul. 2019, 3, 1900194  DOI: 10.1002/adts.201900194
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    Wright, D. W.; Wan, S.; Meyer, C.; van Vlijmen, H.; Tresadern, G.; Coveney, P. V. Application of ESMACS Binding Free Energy Protocols to Diverse Datasets: Bromodomain-Containing Protein 4. Sci. Rep. 2019, 9, 6017,  DOI: 10.1038/s41598-019-41758-1
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    27
    Application of ESMACS binding free energy protocols to diverse datasets: Bromodomain-containing protein 4
    Wright David W; Wan Shunzhou; Coveney Peter V; Meyer Christophe; van Vlijmen Herman; Tresadern Gary
    Scientific reports (2019), 9 (1), 6017 ISSN:.
    As the application of computational methods in drug discovery pipelines becomes more widespread it is increasingly important to understand how reproducible their results are and how sensitive they are to choices made in simulation setup and analysis. Here we use ensemble simulation protocols, termed ESMACS (enhanced sampling of molecular dynamics with approximation of continuum solvent), to investigate the sensitivity of the popular molecular mechanics Poisson-Boltzmann surface area (MMPBSA) methodology. Using the bromodomain-containing protein 4 (BRD4) system bound to a diverse set of ligands as our target, we show that robust rankings can be produced only through combining ensemble sampling with multiple trajectories and enhanced solvation via an explicit ligand hydration shell.
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  28. 28
    Wan, S.; Potterton, A.; Husseini, F. S.; Wright, D. W.; Heifetz, A.; Malawski, M.; Townsend-Nicholson, A.; Coveney, P. V. Hit-to-Lead and Lead Optimization Binding Free Energy Calculations for G Protein-Coupled Receptors. Interface Focus 2020, 10, 20190128  DOI: 10.1098/rsfs.2019.0128
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    28
    Hit-to-lead and lead optimization binding free energy calculations for G protein-coupled receptors
    Wan Shunzhou; Husseini Fouad S; Wright David W; Coveney Peter V; Potterton Andrew; Heifetz Alexander; Townsend-Nicholson Andrea; Heifetz Alexander; Malawski Maciej; Coveney Peter V
    Interface focus (2020), 10 (6), 20190128 ISSN:2042-8898.
    We apply the hit-to-lead ESMACS (enhanced sampling of molecular dynamics with approximation of continuum solvent) and lead-optimization TIES (thermodynamic integration with enhanced sampling) methods to compute the binding free energies of a series of ligands at the A1 and A2A adenosine receptors, members of a subclass of the GPCR (G protein-coupled receptor) superfamily. Our predicted binding free energies, calculated using ESMACS, show a good correlation with previously reported experimental values of the ligands studied. Relative binding free energies, calculated using TIES, accurately predict experimentally determined values within a mean absolute error of approximately 1 kcal mol(-1). Our methodology may be applied widely within the GPCR superfamily and to other small molecule-receptor protein systems.
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    Wright, D. W.; Hall, B. A.; Kenway, O. A.; Jha, S.; Coveney, P. V. Computing Clinically Relevant Binding Free Energies of HIV-1 Protease Inhibitors. J. Chem. Theory Comput. 2014, 10, 1228– 1241,  DOI: 10.1021/ct4007037
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    29
    Computing Clinically Relevant Binding Free Energies of HIV-1 Protease Inhibitors
    Wright, David W.; Hall, Benjamin A.; Kenway, Owain A.; Jha, Shantenu; Coveney, Peter V.
    Journal of Chemical Theory and Computation (2014), 10 (3), 1228-1241CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
    The use of mol. simulation to est. the strength of macromol. binding free energies is becoming increasingly widespread, with goals ranging from lead optimization and enrichment in drug discovery to personalizing or stratifying treatment regimes. To realize the potential of such approaches to predict new results, not merely to explain previous exptl. findings, it is necessary that the methods used are reliable and accurate, and that their limitations are thoroughly understood. However, the computational cost of atomistic simulation techniques such as mol. dynamics (MD) has meant that until recently little work has focused on validating and verifying the available free energy methodologies, with the consequence that many of the results published in the literature are not reproducible. Here, we present a detailed anal. of two of the most popular approx. methods for calcg. binding free energies from mol. simulations, mol. mechanics Poisson-Boltzmann surface area (MMPBSA) and mol. mechanics generalized Born surface area (MMGBSA), applied to the nine FDA-approved HIV-1 protease inhibitors. Our results show that the values obtained from replica simulations of the same protease-drug complex, differing only in initially assigned atom velocities, can vary by as much as 10 kcal mol-1, which is greater than the difference between the best and worst binding inhibitors under investigation. Despite this, anal. of ensembles of simulations producing 50 trajectories of 4 ns duration leads to well converged free energy ests. For seven inhibitors, we find that with correctly converged normal mode ests. of the configurational entropy, we can correctly distinguish inhibitors in agreement with exptl. data for both the MMPBSA and MMGBSA methods and thus have the ability to rank the efficacy of binding of this selection of drugs to the protease (no account is made for free energy penalties assocd. with protein distortion leading to the over estn. of the binding strength of the two largest inhibitors ritonavir and atazanavir). We obtain improved rankings and ests. of the relative binding strengths of the drugs by using a novel combination of MMPBSA/MMGBSA with normal mode entropy ests. and the free energy of assocn. calcd. directly from simulation trajectories. Our work provides a thorough assessment of what is required to produce converged and hence reliable free energies for protein-ligand binding.
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    Accurate calcn. of important thermodn. properties, such as macromol. binding free energies, is one of the principal goals of mol. dynamics simulations. However, single long simulation frequently produces incorrectly converged quant. results due to inadequate sampling of conformational space in a feasible wall-clock time. Multiple short (ensemble) simulations have been shown to explore conformational space more effectively than single long simulations, but the two methods have not yet been thermodynamically compared. Here we show that, for end-state binding free energy detn. methods, ensemble simulations exhibit significantly enhanced thermodn. sampling over single long simulations and result in accurate and converged relative binding free energies that are reproducible to within 0.5 kcal/mol. Completely correct ranking is obtained for six HIV-1 protease variants bound to lopinavir with a correlation coeff. of 0.89 and a mean relative deviation from expt. of 0.9 kcal/mol. Multidrug resistance to lopinavir is enthalpically driven and increases through a decrease in the protein-ligand van der Waals interaction, principally due to the V82A/I84V mutation, and an increase in net electrostatic repulsion due to water-mediated disruption of protein-ligand interactions in the catalytic region. Furthermore, we correctly rank, to within 1 kcal/mol of expt., the substantially increased chem. potency of lopinavir binding to the wild-type protease compared to saquinavir and show that lopinavir takes advantage of a decreased net electrostatic repulsion to confer enhanced binding. Our approach is dependent on the combined use of petascale computing resources and on an automated simulation workflow to attain the required level of sampling and turn around time to obtain the results, which can be as little as three days. This level of performance promotes integration of such methodol. with clin. decision support systems for the optimization of patient-specific therapy.
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    Journal of Chemical Information and Modeling (2017), 57 (4), 897-909CODEN: JCISD8; ISSN:1549-9596. (American Chemical Society)
    Optimization of ligand binding affinity to the target protein of interest is a primary objective in small-mol. drug discovery. Until now, the prediction of binding affinities by computational methods has not been widely applied in the drug discovery process, mainly due to its lack of accuracy and reproducibility, as well as the long turnaround times required to obtain results. Herein, the authors report on a collaborative study that compares tropomyosin receptor kinase A (TrkA) binding affinity predictions using two recently formulated fast computational approaches - namely ESMACS (Enhanced Sampling of Mol. dynamics with Approxn. of Continuum Solvent) and TIES (Thermodn. Integration with Enhanced Sampling) - to exptl. derived TrkA binding affinities for a set of Pfizer pan-Trk compds. ESMACS gives precise and reproducible results and is applicable to highly diverse sets of compds. It also provides detailed chem. insight into the nature of ligand-protein binding. TIES can predict and thus optimize more subtle changes in binding affinities between compds. of similar structure. Individual binding affinities were calcd. in a few hours, exhibiting good correlations with the exptl. data of 0.79 and 0.88 from ESMACS and TIES approaches resp. The speed, level of accuracy and precision of the calcns. are such that the affinity predictions can be used to rapidly explain the effects of compd. modifications on TrkA binding affinity. The methods could therefore be used as tools to guide lead optimization efforts across multiple prospective structurally-enabled programs in the drug discovery setting for a wide range of compds. and targets.
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    Journal of Chemical Theory and Computation (2017), 13 (2), 784-795CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
    Binding free energies of bromodomain inhibitors are calcd. with recently formulated approaches, namely ESMACS (enhanced sampling of mol. dynamics with approxn. of continuum solvent) and TIES (thermodn. integration with enhanced sampling). A set of compds. is provided by GlaxoSmithKline, which represents a range of chem. functionality and binding affinities. The predicted binding free energies exhibit a good Spearman correlation of 0.78 with the exptl. data from the 3-trajectory ESMACS, and an excellent correlation of 0.92 from the TIES approach where applicable. Given access to suitable high end computing resources and a high degree of automation, the authors can compute individual binding affinities in a few hours with precisions no greater than 0.2 kcal/mol for TIES, and no larger than 0.34 kcal/mol and 1.71 kcal/mol for the 1- and 3-trajectory ESMACS approaches.
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Cited By

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This article is cited by 5 publications.

  1. Hannes H. Loeffler, Shunzhou Wan, Marco Klähn, Agastya P. Bhati, Peter V. Coveney. Optimal Molecular Design: Generative Active Learning Combining REINVENT with Precise Binding Free Energy Ranking Simulations. Journal of Chemical Theory and Computation 2024, 20 (18) , 8308-8328. https://doi.org/10.1021/acs.jctc.4c00576
  2. Shunzhou Wan, Agastya P. Bhati, Alexander D. Wade, Peter V. Coveney. Ensemble-Based Approaches Ensure Reliability and Reproducibility. Journal of Chemical Information and Modeling 2023, 63 (22) , 6959-6963. https://doi.org/10.1021/acs.jcim.3c01654
  3. Shunzhou Wan, Agastya P. Bhati, Peter V. Coveney. Comparison of Equilibrium and Nonequilibrium Approaches for Relative Binding Free Energy Predictions. Journal of Chemical Theory and Computation 2023, 19 (21) , 7846-7860. https://doi.org/10.1021/acs.jctc.3c00842
  4. Alexander D. Wade, Agastya P. Bhati, Shunzhou Wan, Peter V. Coveney. Alchemical Free Energy Estimators and Molecular Dynamics Engines: Accuracy, Precision, and Reproducibility. Journal of Chemical Theory and Computation 2022, 18 (6) , 3972-3987. https://doi.org/10.1021/acs.jctc.2c00114
  5. Shunzhou Wan, Agastya P. Bhati, David W. Wright, Alexander D. Wade, Gary Tresadern, Herman van Vlijmen, Peter V. Coveney. The performance of ensemble-based free energy protocols in computing binding affinities to ROS1 kinase. Scientific Reports 2022, 12 (1) https://doi.org/10.1038/s41598-022-13319-6
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  • Abstract

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    Figure 1

    Figure 1. Structure of SMYD3, complexed with one of the compounds in this study. The N-terminal SET domain, the MYND domain, the post-SET domain, and the C-terminal region are colored in orange, yellow, pink, and white, respectively. The cofactor SAH is shown with a bond representation and the ligand (S01) in a ball-and-stick model. The Zn2+ ions are shown with sphere models and colored green.

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    Figure 2

    Figure 2. Comparison of calculated binding free energies from two independent studies of the ligand-SMYD3 models performed on Blue Waters (bw, horizontal axis) and DNAnexus (DNA, vertical axis). The dashed line shows an ideal y = x regression. The standard errors are calculated using a bootstrapping method.

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    Figure 3

    Figure 3. Comparison of calculated binding free energies and experimental binding affinity data from 1-traj ESMACS approach. The dotted line shows a linear regression. A correlation coefficient of 0.84 [CI: 0.65–0.93] is obtained for the entire set of compounds. The +1e charged compounds are shown in blue and electrostatically neutral ones in black.

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    Figure 4

    Figure 4. Electrostatic interactions between the R2 group and the protein. The negatively charged residues GLU192, ASP241, and GLU294, and positively charged R2 group, along with positively charged LYS 329, form favorable electrostatic interactions.

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    Figure 5

    Figure 5. Comparison between TIES-predicted relative binding affinities and experimental data for a total of 19 compound pairs. The long dashed line represents y = x, whereas dashed and dotted lines represent 1 kcal/mol and 2 kcal/mol ranges, respectively. The pairs involving S08 are highlighted in blue.

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    Figure 6

    Figure 6. Distributions of experimental pIC50 values shown as histogram and kernel density curve. Four compounds from the current project (a–d) are used, which have been tested more than 100 times. A bin size of 0.05 is used. The dashed lines indicate the means of the experimental measurements.

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  • References

    This article references 39 other publications.

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      Deregulation of lysine methylation signaling has emerged as a common etiol. factor in cancer pathogenesis, with inhibitors of several histone lysine methyltransferases (KMTs) being developed as chemotherapeutics. The largely cytoplasmic KMT SMYD3 (SET and MYND domain contg. protein 3) is overexpressed in numerous human tumors. However, the mol. mechanism by which SMYD3 regulates cancer pathways and its relationship to tumorigenesis in vivo are largely unknown. Here we show that methylation of MAP3K2 by SMYD3 increases MAP kinase signaling and promotes the formation of Ras-driven carcinomas. Using mouse models for pancreatic ductal adenocarcinoma and lung adenocarcinoma, we found that abrogating SMYD3 catalytic activity inhibits tumor development in response to oncogenic Ras. We used protein array technol. to identify the MAP3K2 kinase as a target of SMYD3. In cancer cell lines, SMYD3-mediated methylation of MAP3K2 at lysine 260 potentiates activation of the Ras/Raf/MEK/ERK signaling module and SMYD3 depletion synergizes with a MEK inhibitor to block Ras-driven tumorigenesis. Finally, the PP2A phosphatase complex, a key neg. regulator of the MAP kinase pathway, binds to MAP3K2 and this interaction is blocked by methylation. Together, our results elucidate a new role for lysine methylation in integrating cytoplasmic kinase-signaling cascades and establish a pivotal role for SMYD3 in the regulation of oncogenic Ras signaling.
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      SMYD3: an oncogenic driver targeting epigenetic regulation and signaling pathways
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      Cancers (2020), 12 (1), 142CODEN: CANCCT; ISSN:2072-6694. (MDPI AG)
      SMYD3 is a member of the SMYD lysine methylase family and plays an important role in the methylation of various histone and non-histone targets. Aberrant SMYD3 expression contributes to carcinogenesis and SMYD3 upregulation was proposed as a prognostic marker in various solid cancers. Here we summarize SMYD3-mediated regulatory mechanisms, which are implicated in the pathophysiol. of cancer, as drivers of distinct oncogenic pathways. We describe SMYD3-dependent mechanisms affecting cancer progression, highlighting SMYD3 interplay with proteins and RNAs involved in the regulation of cancer cell proliferation, migration and invasion. We also address the effectiveness and mechanisms of action for the currently available SMYD3 inhibitors. The findings analyzed herein demonstrate that a complex network of SMYD3-mediated cytoplasmic and nuclear interactions promote oncogenesis across different cancer types. These evidences depict SMYD3 as a modulator of the transcriptional response and of key signaling pathways, orchestrating multiple oncogenic inputs and ultimately, promoting transcriptional reprogramming and tumor transformation. Further insights into the oncogenic role of SMYD3 and its targeting of different synergistic oncogenic signals may be beneficial for effective cancer treatment.
      >> More from SciFinder ®
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      Van Aller, G. S.; Graves, A. P.; Elkins, P. A.; Bonnette, W. G.; McDevitt, P. J.; Zappacosta, F.; Annan, R. S.; Dean, T. W.; Su, D. S.; Carpenter, C. L.; Mohammad, H. P.; Kruger, R. G. Structure-Based Design of a Novel SMYD3 Inhibitor That Bridges the Sam-and Mekk2-Binding Pockets. Structure 2016, 24, 774– 781,  DOI: 10.1016/j.str.2016.03.010
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      Structure-Based Design of a Novel SMYD3 Inhibitor that Bridges the SAM-and MEKK2-Binding Pockets
      Van Aller, Glenn S.; Graves, Alan P.; Elkins, Patricia A.; Bonnette, William G.; McDevitt, Patrick J.; Zappacosta, Francesca; Annan, Roland S.; Dean, Tony W.; Su, Dai-Shi; Carpenter, Christopher L.; Mohammad, Helai P.; Kruger, Ryan G.
      Structure (Oxford, United Kingdom) (2016), 24 (5), 774-781CODEN: STRUE6; ISSN:0969-2126. (Elsevier Ltd.)
      SMYD3 is a lysine methyltransferase overexpressed in colorectal, breast, prostate, and hepatocellular tumors, and has been implicated as an oncogene in human malignancies. Methylation of MEKK2 by SMYD3 is important for regulation of the MEK/ERK pathway, suggesting the possibility of selectively targeting SMYD3 in RAS-driven cancers. Structural and kinetic characterization of SMYD3 was undertaken leading to a co-crystal structure of SMYD3 with a MEKK2-peptide substrate bound, and the observation that SMYD3 follows a partially processive mechanism. These insights allowed for the design of GSK2807, a potent and selective, SAM-competitive inhibitor of SMYD3 (Ki = 14 nM). A high-resoln. crystal structure reveals that GSK2807 bridges the gap between the SAM-binding pocket and the substrate lysine tunnel of SMYD3. Taken together, our data demonstrate that small-mol. inhibitors of SMYD3 can be designed to prevent methylation of MEKK2 and these could have potential use as anticancer therapeutics.
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    4. 4
      Su, D. S.; Qu, J.; Schulz, M.; Blackledge, C. W.; Yu, H.; Zeng, J.; Burgess, J.; Reif, A.; Stern, M.; Nagarajan, R.; Pappalardi, M. B.; Wong, K.; Graves, A. P.; Bonnette, W.; Wang, L.; Elkins, P.; Knapp-Reed, B.; Carson, J. D.; McHugh, C.; Mohammad, H.; Kruger, R.; Luengo, J.; Heerding, D. A.; Creasy, C. L. Discovery of Isoxazole Amides as Potent and Selective SMYD3 Inhibitors. ACS Med. Chem. Lett. 2020, 11, 133– 140,  DOI: 10.1021/acsmedchemlett.9b00493
      4
      Discovery of Isoxazole Amides as Potent and Selective SMYD3 Inhibitors
      Su, Dai-Shi; Qu, Junya; Schulz, Mark; Blackledge, Chuck W.; Yu, Hongyi; Zeng, Jenny; Burgess, Joelle; Reif, Alexander; Stern, Melissa; Nagarajan, Raman; Pappalardi, Melissa Baker; Wong, Kristen; Graves, Alan P.; Bonnette, William; Wang, Liping; Elkins, Patricia; Knapp-Reed, Beth; Carson, Jeffrey D.; McHugh, Charles; Mohammad, Helai; Kruger, Ryan; Luengo, Juan; Heerding, Dirk A.; Creasy, Caretha L.
      ACS Medicinal Chemistry Letters (2020), 11 (2), 133-140CODEN: AMCLCT; ISSN:1948-5875. (American Chemical Society)
      We report herein the discovery of isoxazole amides as potent and selective SET and MYND Domain-Contg. Protein 3 (SMYD3) inhibitors. Elucidation of the structure-activity relationship of the high-throughput screening (HTS) lead compd. 1 provided potent and selective SMYD3 inhibitors. The SAR optimization, cocrystal structures of small mols. with SMYD3, and mode of inhibition (MOI) characterization of compds. are described. The synthesis and biol. and pharmacokinetic profiles of compds. are also presented.
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    5. 5
      Schindler, C. E. M.; Baumann, H.; Blum, A.; Bose, D.; Buchstaller, H. P.; Burgdorf, L.; Cappel, D.; Chekler, E.; Czodrowski, P.; Dorsch, D.; Eguida, M. K. I.; Follows, B.; Fuchss, T.; Gradler, U.; Gunera, J.; Johnson, T.; Jorand Lebrun, C.; Karra, S.; Klein, M.; Knehans, T.; Koetzner, L.; Krier, M.; Leiendecker, M.; Leuthner, B.; Li, L.; Mochalkin, I.; Musil, D.; Neagu, C.; Rippmann, F.; Schiemann, K.; Schulz, R.; Steinbrecher, T.; Tanzer, E. M.; Unzue Lopez, A.; Viacava Follis, A.; Wegener, A.; Kuhn, D. Large-Scale Assessment of Binding Free Energy Calculations in Active Drug Discovery Projects. J. Chem. Inf. Model. 2020, 60, 5457– 5474,  DOI: 10.1021/acs.jcim.0c00900
      5
      Large-Scale Assessment of Binding Free Energy Calculations in Active Drug Discovery Projects
      Schindler, Christina E. M.; Baumann, Hannah; Blum, Andreas; Boese, Dietrich; Buchstaller, Hans-Peter; Burgdorf, Lars; Cappel, Daniel; Chekler, Eugene; Czodrowski, Paul; Dorsch, Dieter; Eguida, Merveille K. I.; Follows, Bruce; Fuchss, Thomas; Graedler, Ulrich; Gunera, Jakub; Johnson, Theresa; Jorand Lebrun, Catherine; Karra, Srinivasa; Klein, Markus; Knehans, Tim; Koetzner, Lisa; Krier, Mireille; Leiendecker, Matthias; Leuthner, Birgitta; Li, Liwei; Mochalkin, Igor; Musil, Djordje; Neagu, Constantin; Rippmann, Friedrich; Schiemann, Kai; Schulz, Robert; Steinbrecher, Thomas; Tanzer, Eva-Maria; Unzue Lopez, Andrea; Viacava Follis, Ariele; Wegener, Ansgar; Kuhn, Daniel
      Journal of Chemical Information and Modeling (2020), 60 (11), 5457-5474CODEN: JCISD8; ISSN:1549-9596. (American Chemical Society)
      Accurate ranking of compds. with regards to their binding affinity to a protein using computational methods is of great interest to pharmaceutical research. Physics-based free energy calcns. are regarded as the most rigorous way to est. binding affinity. In recent years, many retrospective studies carried out both in academia and industry have demonstrated its potential. Here, we present the results of large-scale prospective application of the FEP+ method in active drug discovery projects in an industry setting at Merck KGaA, Darmstadt, Germany. We compare these prospective data to results obtained on a new diverse, public benchmark of eight pharmaceutically relevant targets. Our results offer insights into the challenges faced when using free energy calcns. in real-life drug discovery projects and identify limitations that could be tackled by future method development. The new public data set we provide to the community can support further method development and comparative benchmarking of free energy calcns.
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    6. 6
      Ciordia, M.; Pérez-Benito, L.; Delgado, F.; Trabanco, A. A.; Tresadern, G. Application of Free Energy Perturbation for the Design of Bace1 Inhibitors. J. Chem. Inf. Model. 2016, 56, 1856– 1871,  DOI: 10.1021/acs.jcim.6b00220
      6
      Application of Free Energy Perturbation for the Design of BACE1 Inhibitors
      Ciordia, Myriam; Perez-Benito, Laura; Delgado, Francisca; Trabanco, Andres A.; Tresadern, Gary
      Journal of Chemical Information and Modeling (2016), 56 (9), 1856-1871CODEN: JCISD8; ISSN:1549-9596. (American Chemical Society)
      Novel spiroaminodihydropyrroles probing for optimized interactions at the P3 pocket of β-secretase 1 (BACE1) were designed with the use of free energy perturbation (FEP) calcns. The resulting mols. showed pIC50 potencies in enzymic BACE1 inhibition assays ranging from approx. 5 to 7. Good correlation was obsd. between the predicted activity from the FEP calcns. and exptl. activity. Simulations run with a default 5 ns approach delivered a mean unsigned error (MUE) between prediction and expt. of 0.58 and 0.91 kcal/mol for retrospective and prospective applications, resp. With longer simulations of 10 and 20 ns, the MUE was in both cases 0.57 kcal/mol for the retrospective application, and 0.69 and 0.59 kcal/mol for the prospective application. Other considerations that impact the quality of the calcns. are discussed. This work provides an example of the value of FEP as a computational tool for drug discovery.
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    7. 7
      Wang, L.; Wu, Y.; Deng, Y.; Kim, B.; Pierce, L.; Krilov, G.; Lupyan, D.; Robinson, S.; Dahlgren, M. K.; Greenwood, J.; Romero, D. L.; Masse, C.; Knight, J. L.; Steinbrecher, T.; Beuming, T.; Damm, W.; Harder, E.; Sherman, W.; Brewer, M.; Wester, R.; Murcko, M.; Frye, L.; Farid, R.; Lin, T.; Mobley, D. L.; Jorgensen, W. L.; Berne, B. J.; Friesner, R. A.; Abel, R. Accurate and Reliable Prediction of Relative Ligand Binding Potency in Prospective Drug Discovery by Way of a Modern Free-Energy Calculation Protocol and Force Field. J. Am. Chem. Soc. 2015, 137, 2695– 2703,  DOI: 10.1021/ja512751q
      7
      Accurate and Reliable Prediction of Relative Ligand Binding Potency in Prospective Drug Discovery by Way of a Modern Free-Energy Calculation Protocol and Force Field
      Wang, Lingle; Wu, Yujie; Deng, Yuqing; Kim, Byungchan; Pierce, Levi; Krilov, Goran; Lupyan, Dmitry; Robinson, Shaughnessy; Dahlgren, Markus K.; Greenwood, Jeremy; Romero, Donna L.; Masse, Craig; Knight, Jennifer L.; Steinbrecher, Thomas; Beuming, Thijs; Damm, Wolfgang; Harder, Ed; Sherman, Woody; Brewer, Mark; Wester, Ron; Murcko, Mark; Frye, Leah; Farid, Ramy; Lin, Teng; Mobley, David L.; Jorgensen, William L.; Berne, Bruce J.; Friesner, Richard A.; Abel, Robert
      Journal of the American Chemical Society (2015), 137 (7), 2695-2703CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
      Designing tight-binding ligands is a primary objective of small-mol. drug discovery. Over the past few decades, free-energy calcns. have benefited from improved force fields and sampling algorithms, as well as the advent of low-cost parallel computing. However, it has proven to be challenging to reliably achieve the level of accuracy that would be needed to guide lead optimization (∼5× in binding affinity) for a wide range of ligands and protein targets. Not surprisingly, widespread com. application of free-energy simulations has been limited due to the lack of large-scale validation coupled with the tech. challenges traditionally assocd. with running these types of calcns. Here, we report an approach that achieves an unprecedented level of accuracy across a broad range of target classes and ligands, with retrospective results encompassing 200 ligands and a wide variety of chem. perturbations, many of which involve significant changes in ligand chem. structures. In addn., we have applied the method in prospective drug discovery projects and found a significant improvement in the quality of the compds. synthesized that have been predicted to be potent. Compds. predicted to be potent by this approach have a substantial redn. in false positives relative to compds. synthesized on the basis of other computational or medicinal chem. approaches. Furthermore, the results are consistent with those obtained from our retrospective studies, demonstrating the robustness and broad range of applicability of this approach, which can be used to drive decisions in lead optimization.
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    8. 8
      Wan, S.; Bhati, A. P.; Zasada, S. J.; Coveney, P. V. Rapid, Accurate, Precise and Reproducible Ligand-Protein Binding Free Energy Prediction. Interface Focus 2020, 10, 20200007  DOI: 10.1098/rsfs.2020.0007
      8
      Rapid, accurate, precise and reproducible ligand-protein binding free energy prediction
      Wan Shunzhou; Bhati Agastya P; Zasada Stefan J; Coveney Peter V; Coveney Peter V
      Interface focus (2020), 10 (6), 20200007 ISSN:2042-8898.
      A central quantity of interest in molecular biology and medicine is the free energy of binding of a molecule to a target biomacromolecule. Until recently, the accurate prediction of binding affinity had been widely regarded as out of reach of theoretical methods owing to the lack of reproducibility of the available methods, not to mention their complexity, computational cost and time-consuming procedures. The lack of reproducibility stems primarily from the chaotic nature of classical molecular dynamics (MD) and the associated extreme sensitivity of trajectories to their initial conditions. Here, we review computational approaches for both relative and absolute binding free energy calculations, and illustrate their application to a diverse set of ligands bound to a range of proteins with immediate relevance in a number of medical domains. We focus on ensemble-based methods which are essential in order to compute statistically robust results, including two we have recently developed, namely thermodynamic integration with enhanced sampling and enhanced sampling of MD with an approximation of continuum solvent. Together, these form a set of rapid, accurate, precise and reproducible free energy methods. They can be used in real-world problems such as hit-to-lead and lead optimization stages in drug discovery, and in personalized medicine. These applications show that individual binding affinities equipped with uncertainty quantification may be computed in a few hours on a massive scale given access to suitable high-end computing resources and workflow automation. A high level of accuracy can be achieved using these approaches.
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    9. 9
      Wan, S.; Tresadern, G.; Pérez-Benito, L.; Vlijmen, H.; Coveney, P. V. Accuracy and Precision of Alchemical Relative Free Energy Predictions with and without Replica-Exchange. Adv. Theory Simul. 2019, 3, 1900195  DOI: 10.1002/adts.201900195
      There is no corresponding record for this reference.
    10. 10
      Wan, S.; Knapp, B.; Wright, D. W.; Deane, C. M.; Coveney, P. V. Rapid, Precise, and Reproducible Prediction of Peptide-MHC Binding Affinities from Molecular Dynamics That Correlate Well with Experiment. J. Chem. Theory Comput. 2015, 11, 3346– 3356,  DOI: 10.1021/acs.jctc.5b00179
      10
      Rapid, precise, and reproducible prediction of peptide-MHC binding affinities from molecular dynamics that correlate well with experiment
      Wan, Shunzhou; Knapp, Bernhard; Wright, David W.; Deane, Charlotte M.; Coveney, Peter V.
      Journal of Chemical Theory and Computation (2015), 11 (7), 3346-3356CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
      The presentation of potentially pathogenic peptides by major histocompatibility complex (MHC) mols. is one of the most important processes in adaptive immune defense. Prediction of peptide-MHC (pMHC) binding affinities is therefore a principal objective of theor. immunol. Machine learning techniques achieve good results if substantial exptl. training data are available. Approaches based on structural information become necessary if sufficiently similar training data are unavailable for a specific MHC allele, although they have often been deemed to lack accuracy. In this study, we use a free energy method to rank the binding affinities of 12 diverse peptides bound by a class I MHC mol. HLA-A*02:01. The method is based on enhanced sampling of mol. dynamics calcns. in combination with a continuum solvent approxn. and includes ests. of the configurational entropy based on either a one or a three trajectory protocol. It produces precise and reproducible free energy ests. which correlate well with exptl. measurements. If the results are combined with an amino acid hydrophobicity scale, then an extremely good ranking of peptide binding affinities emerges. Our approach is rapid, robust, and applicable to a wide range of ligand-receptor interactions without further adjustment.
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    11. 11
      Bhati, A. P.; Wan, S.; Wright, D. W.; Coveney, P. V. Rapid, Accurate, Precise, and Reliable Relative Free Energy Prediction Using Ensemble Based Thermodynamic Integration. J. Chem. Theory Comput. 2017, 13, 210– 222,  DOI: 10.1021/acs.jctc.6b00979
      11
      Rapid, Accurate, Precise, and Reliable Relative Free Energy Prediction Using Ensemble Based Thermodynamic Integration
      Bhati, Agastya P.; Wan, Shunzhou; Wright, David W.; Coveney, Peter V.
      Journal of Chemical Theory and Computation (2017), 13 (1), 210-222CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
      The accurate prediction of the binding affinities of ligands to proteins is a major goal in drug discovery and personalized medicine. The time taken to make such predictions is of similar importance to their accuracy, precision and reliability. In the last few years, an ensemble based mol. dynamics approach has been proposed that provides a route to reliable predictions of free energies based on the mol. mechanics Poisson-Boltzmann surface area method which meets the requirements of accuracy, precision and reliability. Here, we describe an equiv. methodol. based on thermodn. integration to substantially improve the accuracy, precision and reliability of calcd. relative binding free energies. We report the performance of the method when applied to a diverse set of protein targets and ligands. The results are in very good agreement with exptl. data (90% of calcns. agree to within 1 kcal/mol) while the method is reproducible by construction. Statistical uncertainties of the order of 0.5 kcal/mol or less are achieved. We present a systematic account of how the uncertainty in the predictions may be estd.
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    12. 12
      Kollman, P. A.; Massova, I.; Reyes, C.; Kuhn, B.; Huo, S.; Chong, L.; Lee, M.; Lee, T.; Duan, Y.; Wang, W.; Donini, O.; Cieplak, P.; Srinivasan, J.; Case, D. A.; Cheatham, T. E., 3rd Calculating Structures and Free Energies of Complex Molecules: Combining Molecular Mechanics and Continuum Models. Acc. Chem. Res. 2000, 33, 889– 897,  DOI: 10.1021/ar000033j
      12
      Calculating Structures and Free Energies of Complex Molecules: Combining Molecular Mechanics and Continuum Models
      Kollman, Peter A.; Massova, Irina; Reyes, Carolina; Kuhn, Bernd; Huo, Shuanghong; Chong, Lillian; Lee, Matthew; Lee, Taisung; Duan, Yong; Wang, Wei; Donini, Oreola; Cieplak, Piotr; Srinivasan, Jaysharee; Case, David A.; Cheatham, Thomas E., III
      Accounts of Chemical Research (2000), 33 (12), 889-897CODEN: ACHRE4; ISSN:0001-4842. (American Chemical Society)
      A review, with 63 refs. A historical perspective on the application of mol. dynamics (MD) to biol. macromols. is presented. Recent developments combining state-of-the-art force fields with continuum solvation calcns. have allowed us to reach the fourth era of MD applications in which one can often derive both accurate structure and accurate relative free energies from mol. dynamics trajectories. We illustrate such applications on nucleic acid duplexes, RNA hairpins, protein folding trajectories, and protein-ligand, protein-protein, and protein-nucleic acid interactions.
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    13. 13
      Coveney, P. V.; Wan, S. On the Calculation of Equilibrium Thermodynamic Properties from Molecular Dynamics. Phys. Chem. Chem. Phys. 2016, 18, 30236– 30240,  DOI: 10.1039/C6CP02349E
      13
      On the calculation of equilibrium thermodynamic properties from molecular dynamics
      Coveney, Peter V.; Wan, Shunzhou
      Physical Chemistry Chemical Physics (2016), 18 (44), 30236-30240CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
      The purpose of statistical mechanics is to provide a route to the calcn. of macroscopic properties of matter from their constituent microscopic components. It is well known that the macrostates emerge as ensemble avs. of microstates. However, this is more often stated than implemented in computer simulation studies. Here we consider foundational aspects of statistical mechanics which are overlooked in most textbooks and research articles that purport to compute macroscopic behavior from microscopic descriptions based on classical mechanics and show how due attention to these issues leads in directions which have not been widely appreciated in the field of mol. dynamics simulation.
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    14. 14
      Vassaux, M.; Wan, S.; Edeling, W.; Coveney, P. V. Ensembles Are Required to Handle Aleatoric and Parametric Uncertainty in Molecular Dynamics Simulation. J. Chem. Theory Comput. 2021, 17, 5187– 5197,  DOI: 10.1021/acs.jctc.1c00526
      14
      Aleatoric and parametric uncertainty in molecular dynamics simulation
      Vassaux, Maxime; Wan, Shunzhou; Edeling, Wouter; Coveney, Peter V.
      Journal of Chemical Theory and Computation (2021), 17 (8), 5187-5197CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
      Classical mol. dynamics is a computer simulation technique that is in widespread use across many areas of science, from physics and chem. to materials, biol. and medicine. The method continues to attract criticism due its oft-reported lack of reproducibility which is in part due to a failure to submit it to reliable uncertainty quantification (UQ). Here we show that the uncertainty arises from a combination of (i) the input parameters and (ii) the intrinsic stochasticity of the method controlled by the random seeds. To illustrate the situation, we make a systematic UQ anal. of a widely used mol. dynamics code (NAMD), applied to est. binding free energy of a ligand-bound to a protein. In particular, we replace the usually fixed input parameters with random variables, systematically distributed about their mean values, and study the resulting distribution of the simulation output. We also perform a sensitivity anal., which reveals that, out of a total of 175 parameters, just six dominate the variance in the code output. Furthermore, we show that binding energy calcn. damps the input uncertainty, in the sense that the variation around the mean output free energy is less than the variation around the mean of the assumed input distributions, if the output is ensemble-averaged over the random seeds. Without such ensemble averaging, the predicted free energy is five times more uncertain. The distribution of the predicted properties is thus strongly dependent upon the random seed. Owing to this substantial uncertainty, robust statistical measures of uncertainty in mol. dynamics simulation require the use of ensembles in all contexts.
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    15. 15
      Wade, A.; Bhati, A. P.; Wan, S.; Coveney, P. V. Alchemical Free Energy Estimators and Molecular Dynamics Engines: Accuracy Precision and Reproducibility. ChemRxiv 2021,  DOI: 10.26434/chemrxiv-2021-nqp8r .
      There is no corresponding record for this reference.
    16. 16
      Bhati, A. P.; Coveney, P. V. Large Scale Study of Ligand-Protein Relative Binding Free Energy Calculations: Actionable Predictions from Statistically Robust Protocols. J. Chem. Theory Comput. 2022, 18, 2687– 2702,  DOI: 10.1021/acs.jctc.1c01288
      16
      Large Scale Study of Ligand-Protein Relative Binding Free Energy Calculations: Actionable Predictions from Statistically Robust Protocols
      Bhati, Agastya P.; Coveney, Peter V.
      Journal of Chemical Theory and Computation (2022), 18 (4), 2687-2702CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
      The accurate and reliable prediction of protein-ligand binding affinities can play a central role in the drug discovery process as well as in personalized medicine. Of considerable importance during lead optimization are the alchem. free energy methods that furnish an estn. of relative binding free energies (RBFE) of similar mols. Recent advances in these methods have increased their speed, accuracy, and precision. This is evident from the increasing no. of retrospective as well as prospective studies employing them. However, such methods still have limited applicability in real-world scenarios due to a no. of important yet unresolved issues. Here, we report the findings from a large data set comprising over 500 ligand transformations spanning over 300 ligands binding to a diverse set of 14 different protein targets which furnish statistically robust results on the accuracy, precision, and reproducibility of RBFE calcns. We use ensemble-based methods which are the only way to provide reliable uncertainty quantification given that the underlying mol. dynamics is chaotic. These are implemented using TIES (Thermodn. Integration with Enhanced Sampling). Results achieve chem. accuracy in all cases. Ensemble simulations also furnish information on the statistical distributions of the free energy calcns. which exhibit non-normal behavior. We find that the "enhanced sampling" method known as replica exchange with solute tempering degrades RBFE predictions. We also report definitively on numerous assocd. alchem. factors including the choice of ligand charge method, flexibility in ligand structure, and the size of the alchem. region including the no. of atoms involved in transforming one ligand into another. Our findings provide a key set of recommendations that should be adopted for the reliable application of RBFE methods.
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    17. 17
      Knapp, B.; Ospina, L.; Deane, C. M. Avoiding False Positive Conclusions in Molecular Simulation: The Importance of Replicas. J. Chem. Theory Comput. 2018, 14, 6127– 6138,  DOI: 10.1021/acs.jctc.8b00391
      17
      Avoiding False Positive Conclusions in Molecular Simulation: The Importance of Replicas
      Knapp, Bernhard; Ospina, Luis; Deane, Charlotte M.
      Journal of Chemical Theory and Computation (2018), 14 (12), 6127-6138CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
      Mol. simulations are a computational technique used to investigate the dynamics of proteins and other mols. The free energy landscape of these simulations is often rugged, and minor differences in the initial velocities, floating-point precision, or underlying hardware can cause identical simulations (replicas) to take different paths in the landscape. In this study the authors investigated the magnitude of these effects based on 310 000 ns of simulation time. The authors performed 100 identically parametrized replicas of 3000 ns each for a small 10 amino acid system as well as 100 identically parametrized replicas of 100 ns each for an 827 residue T-cell receptor/MHC system. Comparing randomly chosen subgroups within these replica sets, the authors estd. the reproducibility and reliability that can be achieved by a given no. of replicas at a given simulation time. These results demonstrate that conclusions drawn from single simulations are often not reproducible and that conclusions drawn from multiple shorter replicas are more reliable than those from a single longer simulation. The actual no. of replicas needed will always depend on the question asked and the level of reliability sought. On the basis of the data, it appears that a good rule of thumb is to perform a min. of five to 10 replicas.
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    18. 18
      Wan, S.; Sinclair, R. C.; Coveney, P. V. Uncertainty Quantification in Classical Molecular Dynamics. Philos. Trans. R. Soc., A 2021, 379, 20200082  DOI: 10.1098/rsta.2020.0082
      18
      Uncertainty quantification in classical molecular dynamics
      Wan, Shunzhou; Sinclair, Robert C.; Coveney, Peter V.
      Philosophical Transactions of the Royal Society, A: Mathematical, Physical & Engineering Sciences (2021), 379 (2197), 20200082CODEN: PTRMAD; ISSN:1364-503X. (Royal Society)
      Mol. dynamics simulation is now a widespread approach for understanding complex systems on the atomistic scale. It finds applications from physics and chem. to engineering, life and medical science. In the last decade, the approach has begun to advance from being a computer-based means of rationalizing exptl. observations to producing apparently credible predictions for a no. of real-world applications within industrial sectors such as advanced materials and drug discovery. However, key aspects concerning the reproducibility of the method have not kept pace with the speed of its uptake in the scientific community. Here, we present a discussion of uncertainty quantification for mol. dynamics simulation designed to endow the method with better error ests. that will enable it to be used to report actionable results. The approach adopted is a std. one in the field of uncertainty quantification, namely using ensemble methods, in which a sufficiently large no. of replicas are run concurrently, from which reliable statistics can be extd. Indeed, because mol. dynamics is intrinsically chaotic, the need to use ensemble methods is fundamental and holds regardless of the duration of the simulations performed. We discuss the approach and illustrate it in a range of applications from materials science to ligand-protein binding free energy estn.
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    19. 19
      Bieniek, M. K.; Bhati, A. P.; Wan, S.; Coveney, P. V. TIES 20: Relative Binding Free Energy with a Flexible Superimposition Algorithm and Partial Ring Morphing. J. Chem. Theory Comput. 2021, 17, 1250– 1265,  DOI: 10.1021/acs.jctc.0c01179
      19
      TIES 20: Relative Binding Free Energy with a Flexible Superimposition Algorithm and Partial Ring Morphing
      Bieniek, Matuesz K.; Bhati, Agastya P.; Wan, Shunzhou; Coveney, Peter V.
      Journal of Chemical Theory and Computation (2021), 17 (2), 1250-1265CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
      The TIES (Thermodn. Integration with Enhanced Sampling) protocol is a formally exact alchem. approach in computational chem. to the calcn. of relative binding free energies. The validity of TIES relies on the correctness of matching atoms across compared pairs of ligands, laying the foundation for the transformation along an alchem. pathway. We implement a flexible topol. superimposition algorithm which uses an exhaustive joint-traversal for computing the largest common component(s). The algorithm is employed to enable matching and morphing of partial rings in the TIES protocol along with a validation study using 55 transformations and five different proteins from our previous work. We find that TIES 20 with the RESP charge system, using the new superimposition algorithm, reproduces the previous results with mean unsigned error of 0.75 kcal/mol with respect to the exptl. data. Enabling the morphing of partial rings decreases the size of the alchem. region in the dual-topol. transformations resulting in a significant improvement in the prediction precision. We find that increasing the ensemble size from 5 to 20 replicas per λ window only has a minimal impact on the accuracy. However, the non-normal nature of the relative free energy distributions underscores the importance of ensemble simulation. We further compare the results with the AM1-BCC charge system and show that it improves agreement with the exptl. data by slightly over 10%. This improvement is partly due to AM1-BCC affecting only the charges of the atoms local to the mutation, which translates to even fewer morphed atoms, consequently reducing issues with sampling and therefore ensemble averaging. TIES 20, in conjunction with the enablement of ring morphing, reduces the size of the alchem. region and significantly improves the precision of the predicted free energies.
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    20. 20
      Sadiq, S. K.; Wright, D.; Watson, S. J.; Zasada, S. J.; Stoica, I.; Coveney, P. V. Automated Molecular Simulation Based Binding Affinity Calculator for Ligand-Bound HIV-1 Proteases. J. Chem. Inf. Model. 2008, 48, 1909– 1919,  DOI: 10.1021/ci8000937
      20
      Automated Molecular Simulation Based Binding Affinity Calculator for Ligand-Bound HIV-1 Proteases
      Sadiq, S. Kashif; Wright, David; Watson, Simon J.; Zasada, Stefan J.; Stoica, Ileana; Coveney, Peter V.
      Journal of Chemical Information and Modeling (2008), 48 (9), 1909-1919CODEN: JCISD8; ISSN:1549-9596. (American Chemical Society)
      The successful application of high throughput mol. simulations to det. biochem. properties would be of great importance to the biomedical community if such simulations could be turned around in a clin. relevant timescale. An important example is the detn. of antiretroviral inhibitor efficacy against varying strains of HIV through calcn. of drug-protein binding affinities. We describe the Binding Affinity Calculator (BAC), a tool for the automated calcn. of HIV-1 protease-ligand binding affinities. The tool employs fully atomistic mol. simulations alongside the well established mol. mechanics Poisson-Boltzmann solvent accessible surface area (MMPBSA) free energy methodol. to enable the calcn. of the binding free energy of several ligand-protease complexes, including all nine FDA approved inhibitors of HIV-1 protease and seven of the natural substrates cleaved by the protease. This enables the efficacy of these inhibitors to be ranked across several mutant strains of the protease relative to the wildtype. BAC is a tool that utilizes the power provided by a computational grid to automate all of the stages required to compute free energies of binding: model prepn., equilibration, simulation, postprocessing, and data-marshaling around the generally widely distributed compute resources utilized. Such automation enables the mol. dynamics methodol. to be used in a high throughput manner not achievable by manual methods. This paper describes the architecture and workflow management of BAC and the function of each of its components. Given adequate compute resources, BAC can yield quant. information regarding drug resistance at the mol. level within 96 h. Such a timescale is of direct clin. relevance and can assist in decision support for the assessment of patient-specific optimal drug treatment and the subsequent response to therapy for any given genotype.
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    21. 21
      Suruzhon, M.; Bodnarchuk, M. S.; Ciancetta, A.; Viner, R.; Wall, I. D.; Essex, J. W. Sensitivity of Binding Free Energy Calculations to Initial Protein Crystal Structure. J. Chem. Theory Comput. 2021, 17, 1806– 1821,  DOI: 10.1021/acs.jctc.0c00972
      21
      Sensitivity of binding free energy calculations to initial protein crystal structure
      Suruzhon, Miroslav; Bodnarchuk, Michael S.; Ciancetta, Antonella; Viner, Russell; Wall, Ian D.; Essex, Jonathan W.
      Journal of Chemical Theory and Computation (2021), 17 (3), 1806-1821CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
      Binding free energy calcns. using alchem. free energy (AFE) methods are widely considered to be the most rigorous tool in the computational drug discovery arsenal. Despite this, the calcns. suffer from accuracy, precision, and reproducibility issues. In this publication, the authors perform a high-throughput study of more than a thousand AFE calcns., utilizing over 220μs of total sampling time, on three different protein systems to investigate the impact of the initial crystal structure on the resulting binding free energy values. The authors also consider the influence of equilibration time and discover that the initial crystal structure can have a significant effect on free energy values obtained at short timescales that can manifest itself as a free energy difference of more than 1 kcal/mol. At longer timescales, these differences are largely overtaken by important rare events, such as torsional ligand motions, typically resulting in a much higher uncertainty in the obtained values. This work emphasizes the importance of rare event sampling and long-timescale dynamics in free energy calcns. even for routinely performed alchem. perturbations. The authors conclude that an optimal protocol should not only conc. computational resources on achieving convergence in the alchem. coupling parameter (λ) space but also on longer simulations and multiple repeats.
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    22. 22
      Pérez-Benito, L.; Keränen, H.; van Vlijmen, H.; Tresadern, G. Predicting Binding Free Energies of PDE2 Inhibitors. The Difficulties of Protein Conformation. Sci. Rep. 2018, 8, 4883,  DOI: 10.1038/s41598-018-23039-5
      22
      Predicting Binding Free Energies of PDE2 Inhibitors. The Difficulties of Protein Conformation
      Perez-Benito Laura; Keranen Henrik; van Vlijmen Herman; Tresadern Gary; Keranen Henrik
      Scientific reports (2018), 8 (1), 4883 ISSN:.
      A congeneric series of 21 phosphodiesterase 2 (PDE2) inhibitors are reported. Crystal structures show how the molecules can occupy a 'top-pocket' of the active site. Molecules with small substituents do not enter the pocket, a critical leucine (Leu770) is closed and water molecules are present. Large substituents enter the pocket, opening the Leu770 conformation and displacing the waters. We also report an X-ray structure revealing a new conformation of the PDE2 active site domain. The relative binding affinities of these compounds were studied with free energy perturbation (FEP) methods and it represents an attractive real-world test case. In general, the calculations could predict the energy of small-to-small, or large-to-large molecule perturbations. However, accurately capturing the transition from small-to-large proved challenging. Only when using alternative protein conformations did results improve. The new X-ray structure, along with a modelled dimer, conferred stability to the catalytic domain during the FEP molecular dynamics (MD) simulations, increasing the convergence and thereby improving the prediction of ΔΔG of binding for some small-to-large transitions. In summary, we found the most significant improvement in results when using different protein structures, and this data set is useful for future free energy validation studies.
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    23. 23
      Friesner, R. A.; Murphy, R. B.; Repasky, M. P.; Frye, L. L.; Greenwood, J. R.; Halgren, T. A.; Sanschagrin, P. C.; Mainz, D. T. Extra Precision Glide: Docking and Scoring Incorporating a Model of Hydrophobic Enclosure for Protein-Ligand Complexes. J. Med. Chem. 2006, 49, 6177– 6196,  DOI: 10.1021/jm051256o
      23
      Extra Precision Glide: Docking and Scoring Incorporating a Model of Hydrophobic Enclosure for Protein-Ligand Complexes
      Friesner, Richard A.; Murphy, Robert B.; Repasky, Matthew P.; Frye, Leah L.; Greenwood, Jeremy R.; Halgren, Thomas A.; Sanschagrin, Paul C.; Mainz, Daniel T.
      Journal of Medicinal Chemistry (2006), 49 (21), 6177-6196CODEN: JMCMAR; ISSN:0022-2623. (American Chemical Society)
      A novel scoring function to est. protein-ligand binding affinities has been developed and implemented as the Glide 4.0 XP scoring function and docking protocol. In addn. to unique water desolvation energy terms, protein-ligand structural motifs leading to enhanced binding affinity are included:(1) hydrophobic enclosure where groups of lipophilic ligand atoms are enclosed on opposite faces by lipophilic protein atoms, (2) neutral-neutral single or correlated hydrogen bonds in a hydrophobically enclosed environment, and (3) five categories of charged-charged hydrogen bonds. The XP scoring function and docking protocol have been developed to reproduce exptl. binding affinities for a set of 198 complexes (RMSDs of 2.26 and 1.73 kcal/mol over all and well-docked ligands, resp.) and to yield quality enrichments for a set of fifteen screens of pharmaceutical importance. Enrichment results demonstrate the importance of the novel XP mol. recognition and water scoring in sepg. active and inactive ligands and avoiding false positives.
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    24. 24
      Case, D. A.; Cheatham, T. E., 3rd; Darden, T.; Gohlke, H.; Luo, R.; Merz, K. M., Jr.; Onufriev, A.; Simmerling, C.; Wang, B.; Woods, R. J. The Amber Biomolecular Simulation Programs. J. Comput. Chem. 2005, 26, 1668– 1688,  DOI: 10.1002/jcc.20290
      24
      The amber biomolecular simulation programs
      Case, David A.; Cheatham, Thomas E., III; Darden, Tom; Gohlke, Holger; Luo, Ray; Merz, Kenneth M., Jr.; Onufriev, Alexey; Simmerling, Carlos; Wang, Bing; Woods, Robert J.
      Journal of Computational Chemistry (2005), 26 (16), 1668-1688CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
      The authors describe the development, current features, and some directions for future development of the Amber package of computer programs. This package evolved from a program that was constructed in the late 1970s to do Assisted Model Building with Energy Refinement, and now contains a group of programs embodying a no. of powerful tools of modern computational chem., focused on mol. dynamics and free energy calcns. of proteins, nucleic acids, and carbohydrates.
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    25. 25
      Zhang, X.; Perez-Sanchez, H.; Lightstone, F. C. A Comprehensive Docking and MM/GBSA Rescoring Study of Ligand Recognition Upon Binding Antithrombin. Curr. Top. Med. Chem. 2017, 17, 1631– 1639,  DOI: 10.2174/1568026616666161117112604
      25
      A Comprehensive Docking and MM/GBSA Rescoring Study of Ligand Recognition upon Binding Antithrombin
      Zhang, Xiaohua; Perez-Sanchez, Horacio; Lightstone, Felice C.
      Current Topics in Medicinal Chemistry (Sharjah, United Arab Emirates) (2017), 17 (14), 1631-1639CODEN: CTMCCL; ISSN:1568-0266. (Bentham Science Publishers Ltd.)
      Background: A high-throughput virtual screening pipeline has been extended from single energetically minimized structure Mol. Mechanics/Generalized Born Surface Area (MM/GBSA) rescoring to ensemble-av. MM/GBSA rescoring. The correlation coeff. (R2) of calcd. and exptl. binding free energies for a series of antithrombin ligands has been improved from 0.36 to 0.69 when switching from the single-structure MM/GBSA rescoring to ensemble-av. one. The electrostatic interactions in both solute and solvent are identified to play an important role in detg. the binding free energy after the decompn. of the calcd. binding free energy. The increasing neg. charge of the compds. provides a more favorable electrostatic energy change but creates a higher penalty for the solvation free energy. Such a penalty is compensated by the electrostatic energy change, which results in a better binding affinity. A highly hydrophobic ligand is detd. by the docking program to be a non-specific binder. Results: Our results have demonstrated that it is very important to keep a few top poses for rescoring, if the binding is non-specific or the binding mode is not well detd. by the docking calcn.
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    26. 26
      Wright, D. W.; Husseini, F.; Wan, S.; Meyer, C.; van Vlijmen, H.; Tresadern, G.; Coveney, P. V. Application of the ESMACS Binding Free Energy Protocol to a Multi-Binding Site Lactate Dehydogenase a Ligand Dataset. Adv. Theory Simul. 2019, 3, 1900194  DOI: 10.1002/adts.201900194
      There is no corresponding record for this reference.
    27. 27
      Wright, D. W.; Wan, S.; Meyer, C.; van Vlijmen, H.; Tresadern, G.; Coveney, P. V. Application of ESMACS Binding Free Energy Protocols to Diverse Datasets: Bromodomain-Containing Protein 4. Sci. Rep. 2019, 9, 6017,  DOI: 10.1038/s41598-019-41758-1
      27
      Application of ESMACS binding free energy protocols to diverse datasets: Bromodomain-containing protein 4
      Wright David W; Wan Shunzhou; Coveney Peter V; Meyer Christophe; van Vlijmen Herman; Tresadern Gary
      Scientific reports (2019), 9 (1), 6017 ISSN:.
      As the application of computational methods in drug discovery pipelines becomes more widespread it is increasingly important to understand how reproducible their results are and how sensitive they are to choices made in simulation setup and analysis. Here we use ensemble simulation protocols, termed ESMACS (enhanced sampling of molecular dynamics with approximation of continuum solvent), to investigate the sensitivity of the popular molecular mechanics Poisson-Boltzmann surface area (MMPBSA) methodology. Using the bromodomain-containing protein 4 (BRD4) system bound to a diverse set of ligands as our target, we show that robust rankings can be produced only through combining ensemble sampling with multiple trajectories and enhanced solvation via an explicit ligand hydration shell.
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    28. 28
      Wan, S.; Potterton, A.; Husseini, F. S.; Wright, D. W.; Heifetz, A.; Malawski, M.; Townsend-Nicholson, A.; Coveney, P. V. Hit-to-Lead and Lead Optimization Binding Free Energy Calculations for G Protein-Coupled Receptors. Interface Focus 2020, 10, 20190128  DOI: 10.1098/rsfs.2019.0128
      28
      Hit-to-lead and lead optimization binding free energy calculations for G protein-coupled receptors
      Wan Shunzhou; Husseini Fouad S; Wright David W; Coveney Peter V; Potterton Andrew; Heifetz Alexander; Townsend-Nicholson Andrea; Heifetz Alexander; Malawski Maciej; Coveney Peter V
      Interface focus (2020), 10 (6), 20190128 ISSN:2042-8898.
      We apply the hit-to-lead ESMACS (enhanced sampling of molecular dynamics with approximation of continuum solvent) and lead-optimization TIES (thermodynamic integration with enhanced sampling) methods to compute the binding free energies of a series of ligands at the A1 and A2A adenosine receptors, members of a subclass of the GPCR (G protein-coupled receptor) superfamily. Our predicted binding free energies, calculated using ESMACS, show a good correlation with previously reported experimental values of the ligands studied. Relative binding free energies, calculated using TIES, accurately predict experimentally determined values within a mean absolute error of approximately 1 kcal mol(-1). Our methodology may be applied widely within the GPCR superfamily and to other small molecule-receptor protein systems.
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    29. 29
      Wright, D. W.; Hall, B. A.; Kenway, O. A.; Jha, S.; Coveney, P. V. Computing Clinically Relevant Binding Free Energies of HIV-1 Protease Inhibitors. J. Chem. Theory Comput. 2014, 10, 1228– 1241,  DOI: 10.1021/ct4007037
      29
      Computing Clinically Relevant Binding Free Energies of HIV-1 Protease Inhibitors
      Wright, David W.; Hall, Benjamin A.; Kenway, Owain A.; Jha, Shantenu; Coveney, Peter V.
      Journal of Chemical Theory and Computation (2014), 10 (3), 1228-1241CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
      The use of mol. simulation to est. the strength of macromol. binding free energies is becoming increasingly widespread, with goals ranging from lead optimization and enrichment in drug discovery to personalizing or stratifying treatment regimes. To realize the potential of such approaches to predict new results, not merely to explain previous exptl. findings, it is necessary that the methods used are reliable and accurate, and that their limitations are thoroughly understood. However, the computational cost of atomistic simulation techniques such as mol. dynamics (MD) has meant that until recently little work has focused on validating and verifying the available free energy methodologies, with the consequence that many of the results published in the literature are not reproducible. Here, we present a detailed anal. of two of the most popular approx. methods for calcg. binding free energies from mol. simulations, mol. mechanics Poisson-Boltzmann surface area (MMPBSA) and mol. mechanics generalized Born surface area (MMGBSA), applied to the nine FDA-approved HIV-1 protease inhibitors. Our results show that the values obtained from replica simulations of the same protease-drug complex, differing only in initially assigned atom velocities, can vary by as much as 10 kcal mol-1, which is greater than the difference between the best and worst binding inhibitors under investigation. Despite this, anal. of ensembles of simulations producing 50 trajectories of 4 ns duration leads to well converged free energy ests. For seven inhibitors, we find that with correctly converged normal mode ests. of the configurational entropy, we can correctly distinguish inhibitors in agreement with exptl. data for both the MMPBSA and MMGBSA methods and thus have the ability to rank the efficacy of binding of this selection of drugs to the protease (no account is made for free energy penalties assocd. with protein distortion leading to the over estn. of the binding strength of the two largest inhibitors ritonavir and atazanavir). We obtain improved rankings and ests. of the relative binding strengths of the drugs by using a novel combination of MMPBSA/MMGBSA with normal mode entropy ests. and the free energy of assocn. calcd. directly from simulation trajectories. Our work provides a thorough assessment of what is required to produce converged and hence reliable free energies for protein-ligand binding.
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    30. 30
      Phillips, J. C.; Braun, R.; Wang, W.; Gumbart, J.; Tajkhorshid, E.; Villa, E.; Chipot, C.; Skeel, R. D.; Kale, L.; Schulten, K. Scalable Molecular Dynamics with NAMD. J. Comput. Chem. 2005, 26, 1781– 1802,  DOI: 10.1002/jcc.20289
      30
      Scalable molecular dynamics with NAMD
      Phillips, James C.; Braun, Rosemary; Wang, Wei; Gumbart, James; Tajkhorshid, Emad; Villa, Elizabeth; Chipot, Christophe; Skeel, Robert D.; Kale, Laxmikant; Schulten, Klaus
      Journal of Computational Chemistry (2005), 26 (16), 1781-1802CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
      NAMD is a parallel mol. dynamics code designed for high-performance simulation of large biomol. systems. NAMD scales to hundreds of processors on high-end parallel platforms, as well as tens of processors on low-cost commodity clusters, and also runs on individual desktop and laptop computers. NAMD works with AMBER and CHARMM potential functions, parameters, and file formats. This article, directed to novices as well as experts, first introduces concepts and methods used in the NAMD program, describing the classical mol. dynamics force field, equations of motion, and integration methods along with the efficient electrostatics evaluation algorithms employed and temp. and pressure controls used. Features for steering the simulation across barriers and for calcg. both alchem. and conformational free energy differences are presented. The motivations for and a roadmap to the internal design of NAMD, implemented in C++ and based on Charm++ parallel objects, are outlined. The factors affecting the serial and parallel performance of a simulation are discussed. Finally, typical NAMD use is illustrated with representative applications to a small, a medium, and a large biomol. system, highlighting particular features of NAMD, for example, the Tcl scripting language. The article also provides a list of the key features of NAMD and discusses the benefits of combining NAMD with the mol. graphics/sequence anal. software VMD and the grid computing/collab. software BioCoRE. NAMD is distributed free of charge with source code at www.ks.uiuc.edu.
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    31. 31
      Beveridge, D. L.; Dicapua, F. M. Free-Energy Via Molecular Simulation - Applications to Chemical and Biomolecular Systems. Annu. Rev. Biophys. Bioeng. 1989, 18, 431– 492,  DOI: 10.1146/annurev.bb.18.060189.002243
      31
      Free energy via molecular simulation: applications to chemical and biomolecular systems
      Beveridge, D. L.; DiCapua, F. M.
      Annual Review of Biophysics and Biophysical Chemistry (1989), 18 (), 431-92CODEN: ARBCEY; ISSN:0883-9182.
      A review with over 250 refs. General approaches to free energy detns. by mol. simulation are formulated theor. and the practical uses are discussed. In general, the agreement between calcd. and exptl. data is good when some exptl. data are used in parametrization of the intermol. potentials. The applications of the methods are also discussed.
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    32. 32
      Genheden, S.; Ryde, U. How to Obtain Statistically Converged MM/GBSA Results. J. Comput. Chem. 2010, 31, 837– 846,  DOI: 10.1002/jcc.21366
      32
      How to obtain statistically converged MM/GBSA results
      Genheden, Samuel; Ryde, Ulf
      Journal of Computational Chemistry (2010), 31 (4), 837-846CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
      The mol. mechanics/generalized Born surface area (MM/GBSA) method has been investigated with the aim of achieving a statistical precision of 1 kJ/mol for the results. The authors studied the binding of seven biotin analogs to avidin, taking advantage of the fact that the protein is a tetramer with four independent binding sites, which should give the same estd. binding affinities. The authors show that it is not enough to use a single long simulation (10 ns), because the std. error of such a calcn. underestimates the difference between the four binding sites. Instead, it is better to run several independent simulations and av. the results. With such an approach, the authors obtain the same results for the four binding sites, and any desired precision can be obtained by running a proper no. of simulations. The authors discuss how the simulations should be performed to optimize the use of computer time. The correlation time between the MM/GBSA energies is ∼5 ps and an equilibration time of 100 ps is needed. For MM/GBSA, the authors recommend a sampling time of 20-200 ps for each sep. simulation, depending on the protein. With 200 ps prodn. time, 5-50 sep. simulations are required to reach a statistical precision of 1 kJ/mol (800-8000 energy calcns. or 1.5-15 ns total simulation time per ligand) for the seven avidin ligands. This is an order of magnitude more than what is normally used, but such a no. of simulations is needed to obtain statistically valid results for the MM/GBSA method. © 2009 Wiley Periodicals, Inc. J Comput Chem 2010.
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    33. 33
      Sadiq, S. K.; Wright, D. W.; Kenway, O. A.; Coveney, P. V. Accurate Ensemble Molecular Dynamics Binding Free Energy Ranking of Multidrug-Resistant HIV-1 Proteases. J. Chem. Inf. Model. 2010, 50, 890– 905,  DOI: 10.1021/ci100007w
      33
      Accurate Ensemble Molecular Dynamics Binding Free Energy Ranking of Multidrug-Resistant HIV-1 Proteases
      Sadiq, S. Kashif; Wright, David W.; Kenway, Owain A.; Coveney, Peter V.
      Journal of Chemical Information and Modeling (2010), 50 (5), 890-905CODEN: JCISD8; ISSN:1549-9596. (American Chemical Society)
      Accurate calcn. of important thermodn. properties, such as macromol. binding free energies, is one of the principal goals of mol. dynamics simulations. However, single long simulation frequently produces incorrectly converged quant. results due to inadequate sampling of conformational space in a feasible wall-clock time. Multiple short (ensemble) simulations have been shown to explore conformational space more effectively than single long simulations, but the two methods have not yet been thermodynamically compared. Here we show that, for end-state binding free energy detn. methods, ensemble simulations exhibit significantly enhanced thermodn. sampling over single long simulations and result in accurate and converged relative binding free energies that are reproducible to within 0.5 kcal/mol. Completely correct ranking is obtained for six HIV-1 protease variants bound to lopinavir with a correlation coeff. of 0.89 and a mean relative deviation from expt. of 0.9 kcal/mol. Multidrug resistance to lopinavir is enthalpically driven and increases through a decrease in the protein-ligand van der Waals interaction, principally due to the V82A/I84V mutation, and an increase in net electrostatic repulsion due to water-mediated disruption of protein-ligand interactions in the catalytic region. Furthermore, we correctly rank, to within 1 kcal/mol of expt., the substantially increased chem. potency of lopinavir binding to the wild-type protease compared to saquinavir and show that lopinavir takes advantage of a decreased net electrostatic repulsion to confer enhanced binding. Our approach is dependent on the combined use of petascale computing resources and on an automated simulation workflow to attain the required level of sampling and turn around time to obtain the results, which can be as little as three days. This level of performance promotes integration of such methodol. with clin. decision support systems for the optimization of patient-specific therapy.
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    34. 34
      Wan, S.; Bhati, A. P.; Skerratt, S.; Omoto, K.; Shanmugasundaram, V.; Bagal, S. K.; Coveney, P. V. Evaluation and Characterization of Trk Kinase Inhibitors for the Treatment of Pain: Reliable Binding Affinity Predictions from Theory and Computation. J. Chem. Inf. Model. 2017, 57, 897– 909,  DOI: 10.1021/acs.jcim.6b00780
      34
      Evaluation and Characterization of Trk Kinase Inhibitors for the Treatment of Pain: Reliable Binding Affinity Predictions from Theory and Computation
      Wan, Shunzhou; Bhati, Agastya P.; Skerratt, Sarah; Omoto, Kiyoyuki; Shanmugasundaram, Veerabahu; Bagal, Sharan K.; Coveney, Peter V.
      Journal of Chemical Information and Modeling (2017), 57 (4), 897-909CODEN: JCISD8; ISSN:1549-9596. (American Chemical Society)
      Optimization of ligand binding affinity to the target protein of interest is a primary objective in small-mol. drug discovery. Until now, the prediction of binding affinities by computational methods has not been widely applied in the drug discovery process, mainly due to its lack of accuracy and reproducibility, as well as the long turnaround times required to obtain results. Herein, the authors report on a collaborative study that compares tropomyosin receptor kinase A (TrkA) binding affinity predictions using two recently formulated fast computational approaches - namely ESMACS (Enhanced Sampling of Mol. dynamics with Approxn. of Continuum Solvent) and TIES (Thermodn. Integration with Enhanced Sampling) - to exptl. derived TrkA binding affinities for a set of Pfizer pan-Trk compds. ESMACS gives precise and reproducible results and is applicable to highly diverse sets of compds. It also provides detailed chem. insight into the nature of ligand-protein binding. TIES can predict and thus optimize more subtle changes in binding affinities between compds. of similar structure. Individual binding affinities were calcd. in a few hours, exhibiting good correlations with the exptl. data of 0.79 and 0.88 from ESMACS and TIES approaches resp. The speed, level of accuracy and precision of the calcns. are such that the affinity predictions can be used to rapidly explain the effects of compd. modifications on TrkA binding affinity. The methods could therefore be used as tools to guide lead optimization efforts across multiple prospective structurally-enabled programs in the drug discovery setting for a wide range of compds. and targets.
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    35. 35
      Wan, S.; Bhati, A. P.; Zasada, S. J.; Wall, I.; Green, D.; Bamborough, P.; Coveney, P. V. Rapid and Reliable Binding Affinity Prediction of Bromodomain Inhibitors: A Computational Study. J. Chem. Theory Comput. 2017, 13, 784– 795,  DOI: 10.1021/acs.jctc.6b00794
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      Rapid and Reliable Binding Affinity Prediction of Bromodomain Inhibitors: A Computational Study
      Wan, Shunzhou; Bhati, Agastya P.; Zasada, Stefan J.; Wall, Ian; Green, Darren; Bamborough, Paul; Coveney, Peter V.
      Journal of Chemical Theory and Computation (2017), 13 (2), 784-795CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
      Binding free energies of bromodomain inhibitors are calcd. with recently formulated approaches, namely ESMACS (enhanced sampling of mol. dynamics with approxn. of continuum solvent) and TIES (thermodn. integration with enhanced sampling). A set of compds. is provided by GlaxoSmithKline, which represents a range of chem. functionality and binding affinities. The predicted binding free energies exhibit a good Spearman correlation of 0.78 with the exptl. data from the 3-trajectory ESMACS, and an excellent correlation of 0.92 from the TIES approach where applicable. Given access to suitable high end computing resources and a high degree of automation, the authors can compute individual binding affinities in a few hours with precisions no greater than 0.2 kcal/mol for TIES, and no larger than 0.34 kcal/mol and 1.71 kcal/mol for the 1- and 3-trajectory ESMACS approaches.
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    36. 36
      Scheen, J.; Wu, W.; Mey, A.; Tosco, P.; Mackey, M.; Michel, J. Hybrid Alchemical Free Energy/Machine-Learning Methodology for the Computation of Hydration Free Energies. J. Chem. Inf. Model. 2020, 60, 5331– 5339,  DOI: 10.1021/acs.jcim.0c00600
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      Hybrid Alchemical Free Energy/Machine-Learning Methodology for the Computation of Hydration Free Energies
      Scheen, Jenke; Wu, Wilson; Mey, Antonia S. J. S.; Tosco, Paolo; Mackey, Mark; Michel, Julien
      Journal of Chemical Information and Modeling (2020), 60 (11), 5331-5339CODEN: JCISD8; ISSN:1549-9596. (American Chemical Society)
      A methodol. that combines alchem. free energy calcns. (FEP) with machine learning (ML) has been developed to compute accurate abs. hydration free energies. The hybrid FEP/ML methodol. was trained on a subset of the FreeSolv database, and retrospectively shown to outperform most submissions from the SAMPL4 competition. Compared to pure machine-learning approaches, FEP/ML yields more precise ests. of free energies of hydration, and requires a fraction of the training set size to outperform standalone FEP calcns. The ML-derived correction terms are further shown to be transferable to a range of related FEP simulation protocols. The approach may be used to inexpensively improve the accuracy of FEP calcns., and to flag mols. which will benefit the most from bespoke forcefield parameterization efforts.
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    37. 37
      Frost, C.; Thompson, S. G. Correcting for Regression Dilution Bias: Comparison of Methods for a Single Predictor Variable. J. R. Stat. Soc. 2000, 163, 173– 189,  DOI: 10.1111/1467-985X.00164
      There is no corresponding record for this reference.
    38. 38
      Ruff, T. W.; Neelin, J. D. Long Tails in Regional Surface Temperature Probability Distributions with Implications for Extremes under Global Warming. Geophys. Res. Lett. 2012, 39, L04704,  DOI: 10.1029/2011GL050610
      There is no corresponding record for this reference.
    39. 39
      Weitzman, M. L. Fat-Tailed Uncertainty in the Economics of Catastrophic Climate Change. Rev. Environ. Econ. Policy 2011, 5, 275– 292,  DOI: 10.1093/reep/rer006
      There is no corresponding record for this reference.