Predicting Relative Binding Affinity Using Nonequilibrium QM/MM Simulations

Wang, Meiting; Ye, Mei; Ryde, Ulf

doi:10.1021/acs.jctc.8b00685

Cited by 20 publications

(43 citation statements)

References 72 publications

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“…This gave even better results with a precision of 0.5-0.9 kJ/mol, a MAD of 4.7 ± 0.2 and a R 2 correlation of 0.86 ± 0.04. Recently, we have shown that similar results can be obtained with approximately a fourth of the computational effort using multiple short QM/MM simulations [23] or by using non-equilibrium simulations and Jarzynski's equality [32][33][34].…”

Section: Introductionsupporting

confidence: 58%

Binding free energies in the SAMPL6 octa-acid host–guest challenge calculated with MM and QM methods

Caldararu

Olsson

Ignjatović

et al. 2018

J Comput Aided Mol Des

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We have estimated free energies for the binding of eight carboxylate ligands to two variants of the octa-acid deep-cavity host in the SAMPL6 blind-test challenge (with or without endo methyl groups on the four upper-rim benzoate groups, OAM and OAH, respectively). We employed free-energy perturbation (FEP) for relative binding energies at the molecular mechanics (MM) and the combined quantum mechanical (QM) and MM (QM/MM) levels, the latter obtained with the reference-potential approach with QM/MM sampling for the MM → QM/MM FEP. The semiempirical QM method PM6-DH+ was employed for the ligand in the latter calculations. Moreover, binding free energies were also estimated from QM/MM optimised structures, combined with COSMO-RS estimates of the solvation energy and thermostatistical corrections from MM frequencies. They were performed at the PM6-DH+ level of theory with the full host and guest molecule in the QM system (and also four water molecules in the geometry optimisations) for 10-20 snapshots from molecular dynamics simulations of the complex. Finally, the structure with the lowest free energy was recalculated using the dispersion-corrected density-functional theory method TPSS-D3, for both the structure and the energy. The two FEP approaches gave similar results (PM6-DH+/MM slightly better for OAM), which were among the five submissions with the best performance in the challenge and gave the best results without any fit to data from the SAMPL5 challenge, with mean absolute deviations (MAD) of 2.4-5.2 kJ/mol and a correlation coefficient (R) of 0.77-0.93. This is the first time QM/MM approaches give binding free energies that are competitive to those obtained with MM for the octa-acid host. The QM/MM-optimised structures gave somewhat worse performance (MAD = 3-8 kJ/mol and R = 0.1-0.9), but the results were improved compared to previous studies of this system with similar methods.

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Section: Introductionsupporting

confidence: 58%

Binding free energies in the SAMPL6 octa-acid host–guest challenge calculated with MM and QM methods

Caldararu

Olsson

Ignjatović

et al. 2018

J Comput Aided Mol Des

Self Cite

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“…This is suggestive that computational resources could be better utilized by repeating many, short simulations from different starting positions rather than performing extended sampling of a single simulation, as is done here. 61,62…”

Section: Resultsmentioning

confidence: 99%

“…The accuracy of all methods often did not significantly improve upon extending the simulation sampling from 50 ps to 200 ps, which suggests that computational resources could be better utilized by reperforming short simulations several times and averaging the results. 61,62…”

Section: Discussionmentioning

confidence: 99%

Development of a Robust Indirect Approach for MM → QM Free Energy Calculations That Combines Force-Matched Reference Potential and Bennett’s Acceptance Ratio Methods

Giese

York

2019

J. Chem. Theory Comput.

110

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We use the PBE0/6-31G* density functional method to perform ab initio quantum mechanical/molecular mechanical (QM/MM) molecular dynamics (MD) simulations under periodic boundary conditions with rigorous electrostatics using the ambient potential composite Ewald method in order to test the convergence of MM→QM/MM free energy corrections for the prediction of 17 small-molecule solvation free energies and 8 ligand binding free energies to T4 lysozyme. The “indirect” thermodynamic cycle for calculating free energies is used to explore whether a series of reference potentials improve the statistical quality of the predictions. Specifically, we construct a series of reference potentials that optimizes a molecular mechanical (MM) force field’s parameters to reproduce the ab initio QM/MM forces from a QM/MM simulation. The optimizations form a systematic progression of successively expanded parameters that include bond, angle, dihedral and charge parameters. For each reference potential, we calculate benchmark quality reference values for the MM→QM/MM correction by performing the mixed MM and QM/MM Hamiltonians at 11 intermediate states, each for 200 ps. We then compare forward and reverse application of Zwanzig’s relation, thermodynamic integration, and Bennett’s acceptance ratio (BAR) methods as a function of reference potential, simulation time, and the number of simulated intermediate states. We find that Zwanzig’s equation is inadequate unless a large number of intermediate states are explicitly simulated. The TI and BAR mean signed errors are very small even when only the end-state simulations are considered, and the standard deviation of the TI and BAR errors are decreased by choosing a reference potential that optimizes the bond and angle parameters. We find a robust approach for the data sets of fairly rigid molecules considered here is to use bond+angle reference potential together with the end-state-only BAR analysis. This requires a QM/MM simulations to be performed in order to generate reference data to parameterize the bond+angle reference potential, and then this same simulation serves a dual purpose as the full QM/MM end-state. The convergence of the results with respect to time suggests that computational resources may be used more efficiently by running multiple simulations for no more than 50 ps, rather than running one long simulation.

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“…25 We have also developed two approaches to speed up the RPQS approach using either multiple short equilibrium or non-equilibrium MD simulations. 26,27 It is well-known that SQM methods are less reliable than DFT methods for intermolecular interactions and binding affinities. 28,29 Therefore, it is of great interest to develop methods to obtain relative binding free energies at the DFT level of theory.…”

Section: Introductionmentioning

confidence: 99%

Host–Guest Relative Binding Affinities at Density-Functional Theory Level from Semiempirical Molecular Dynamics Simulations

Wang

Ryde

2019

J. Chem. Theory Comput.

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Relative free energies for the binding of nine cyclic carboxylate ligands to the octaacid deep-cavity host were calculated at the combined density-functional theory and molecular mechanics (DFT/MM) level of theory. The DFT calculations employed the BLYP functional and the 6-31G* basis set for the ligand. We employed free-energy perturbations (FEP) with the reference-potential approach and used molecular dynamics (MD) simulations with the semiempirical quantum mechanical (SQM) PM6-DH+ method for the ligand as an intermediate level between MM and DFT/MM to improve the convergence. Thus, the relative binding free energy of two ligands was first calculated at the MM level by an alchemical transformation from one ligand to another in both the bound and unbound states. Then, for each ligand the free-energy correction for going from the MM to the SQM/MM potentials was calculated using explicit SQM/MM MD simulations. Finally, the free-energy correction for going from the SQM/MM to the DFT/MM potentials was estimated with FEP without running any DFT/MM simulations. Instead, the free energy was calculated by single-step exponential averaging (ssEA) or employing the cumulant approximation to the second order (CA). The results show that CA converges much better than ssEA and with 500-4500 DFT/MM single-point energy calculations, converged free energies with a precision of 0.3 kJ/mol can be obtained. These free energies reproduce the experimental binding free energy differences with a mean absolute deviation of 3.4 kJ/mol, a correlation (R 2) of 0.97 and correct signs for all of the eight free-energy differences. This is appreciably better than the results obtained at the SQM/MM level of theory and also slightly better than those obtained with MM. We show that the convergence of the SQM/MM→DFT/MM perturbations can be monitored by the use of Wu and Kofke's bias metric Π and by the standard deviation of the difference between the SQM/MM and DFT/MM energies. Finally, we show that the use of the intermediate SQM/MM MD simulations improves the convergence of the free energies by a factor of at least two, compared to doing direct MM→DFT/MM perturbations.

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Predicting Relative Binding Affinity Using Nonequilibrium QM/MM Simulations

Cited by 20 publications

References 72 publications

Binding free energies in the SAMPL6 octa-acid host–guest challenge calculated with MM and QM methods

Binding free energies in the SAMPL6 octa-acid host–guest challenge calculated with MM and QM methods

Development of a Robust Indirect Approach for MM → QM Free Energy Calculations That Combines Force-Matched Reference Potential and Bennett’s Acceptance Ratio Methods

Host–Guest Relative Binding Affinities at Density-Functional Theory Level from Semiempirical Molecular Dynamics Simulations

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