| 1. |
- Verteramo, Maria Luisa, et al.
(författare)
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Interplay between Conformational Entropy and Solvation Entropy in Protein-Ligand Binding
- 2019
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Ingår i: Journal of the American Chemical Society. - : American Chemical Society (ACS). - 0002-7863 .- 1520-5126. ; 141:5, s. 2012-2026
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Tidskriftsartikel (refereegranskat)abstract
- Understanding the driving forces underlying molecular recognition is of fundamental importance in chemistry and biology. The challenge is to unravel the binding thermodynamics into separate contributions and to interpret these in molecular terms. Entropic contributions to the free energy of binding are particularly difficult to assess in this regard. Here we pinpoint the molecular determinants underlying differences in ligand affinity to the carbohydrate recognition domain of galectin-3, using a combination of isothermal titration calorimetry, X-ray crystallography, NMR relaxation, and molecular dynamics simulations followed by conformational entropy and grid inhomogeneous solvation theory (GIST) analyses. Using a pair of diastereomeric ligands that have essentially identical chemical potential in the unbound state, we reduced the problem of dissecting the thermodynamics to a comparison of the two protein-ligand complexes. While the free energies of binding are nearly equal for the R and S diastereomers, greater differences are observed for the enthalpy and entropy, which consequently exhibit compensatory behavior, Δ ΔH°(R - S) = -5 ± 1 kJ/mol and -T Δ ΔS°(R - S) = 3 ± 1 kJ/mol. NMR relaxation experiments and molecular dynamics simulations indicate that the protein in complex with the S-stereoisomer has greater conformational entropy than in the R-complex. GIST calculations reveal additional, but smaller, contributions from solvation entropy, again in favor of the S-complex. Thus, conformational entropy apparently dominates over solvation entropy in dictating the difference in the overall entropy of binding. This case highlights an interplay between conformational entropy and solvation entropy, pointing to both opportunities and challenges in drug design.
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| 2. |
- Caldararu, Octav, et al.
(författare)
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Binding free energies in the SAMPL5 octa-acid host–guest challenge calculated with DFT-D3 and CCSD(T)
- 2017
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Ingår i: Journal of Computer-Aided Molecular Design. - : Springer Science and Business Media LLC. - 0920-654X .- 1573-4951. ; 31:1, s. 87-106
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Tidskriftsartikel (refereegranskat)abstract
- We have tried to calculate the free energy for the binding of six small ligands to two variants of the octa-acid deep cavitand host in the SAMPL5 blind challenge. We employed structures minimised with dispersion-corrected density-functional theory with small basis sets and energies were calculated using large basis sets. Solvation energies were calculated with continuum methods and thermostatistical corrections were obtained from frequencies calculated at the HF-3c level. Care was taken to minimise the effects of the flexibility of the host by keeping the complexes as symmetric and similar as possible. In some calculations, the large net charge of the host was reduced by removing the propionate and benzoate groups. In addition, the effect of a restricted molecular dynamics sampling of structures was tested. Finally, we tried to improve the energies by using the DLPNO–CCSD(T) approach. Unfortunately, results of quite poor quality were obtained, with no correlation to the experimental data, systematically too positive affinities (by ~50 kJ/mol) and a mean absolute error (after removal of the systematic error) of 11–16 kJ/mol. DLPNO–CCSD(T) did not improve the results, so the accuracy is not limited by the energy function. Instead, four likely sources of errors were identified: first, the minimised structures were often incorrect, owing to the omission of explicit solvent. They could be partly improved by performing the minimisations in a continuum solvent with four water molecules around the charged groups of the ligands. Second, some ligands could bind in several different conformations, requiring sampling of reasonable structures. Third, there is an indication the continuum-solvation model has problems to accurately describe the binding of both the negatively and positively charged guest molecules. Fourth, different methods to calculate the thermostatistical corrections gave results that differed by up to 30 kJ/mol and there is an indication that HF-3c overestimates the entropy term. In conclusion, it is a challenge to calculate binding affinities for this octa-acid system with quantum–mechanical methods.
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| 3. |
- Caldararu, Octav, et al.
(författare)
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Binding free energies in the SAMPL6 octa-acid host–guest challenge calculated with MM and QM methods
- 2018
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Ingår i: Journal of Computer-Aided Molecular Design. - : Springer Science and Business Media LLC. - 0920-654X .- 1573-4951. ; 32:10, s. 1027-1046
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Tidskriftsartikel (refereegranskat)abstract
- 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 (R2) 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 R2 = 0.1–0.9), but the results were improved compared to previous studies of this system with similar methods.
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| 4. |
- Olsson, Martin A., et al.
(författare)
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Binding affinities of the farnesoid X receptor in the D3R Grand Challenge 2 estimated by free-energy perturbation and docking
- 2018
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Ingår i: Journal of Computer-Aided Molecular Design. - : Springer Science and Business Media LLC. - 0920-654X .- 1573-4951. ; 32:1, s. 211-224
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Tidskriftsartikel (refereegranskat)abstract
- We have studied the binding of 102 ligands to the farnesoid X receptor within the D3R Grand Challenge 2016 blind-prediction competition. First, we employed docking with five different docking software and scoring functions. The selected docked poses gave an average root-mean-squared deviation of 4.2 Å. Consensus scoring gave decent results with a Kendall’s τ of 0.26 ± 0.06 and a Spearman’s ρ of 0.41 ± 0.08. For a subset of 33 ligands, we calculated relative binding free energies with free-energy perturbation. Five transformations between the ligands involved a change of the net charge and we implemented and benchmarked a semi-analytic correction (Rocklin et al., J Chem Phys 139:184103, 2013) for artifacts caused by the periodic boundary conditions and Ewald summation. The results gave a mean absolute deviation of 7.5 kJ/mol compared to the experimental estimates and a correlation coefficient of R2 = 0.1. These results were among the four best in this competition out of 22 submissions. The charge corrections were significant (7–8 kJ/mol) and always improved the results. By employing 23 intermediate states in the free-energy perturbation, there was a proper overlap between all states and the precision was 0.1–0.7 kJ/mol. However, thermodynamic cycles indicate that the sampling was insufficient in some of the perturbations.
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| 5. |
- Olsson, Martin A., et al.
(författare)
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Comparison of QM/MM Methods To Obtain Ligand-Binding Free Energies
- 2017
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Ingår i: Journal of Chemical Theory and Computation. - : American Chemical Society (ACS). - 1549-9618 .- 1549-9626. ; 13:5, s. 2245-2253
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Tidskriftsartikel (refereegranskat)abstract
- We have compared two approaches to calculate relative binding free energies employing molecular dynamics simulations at the combined quantum-mechanical/molecular mechanics (QM/MM) level. As a test case, we study the binding of nine cyclic carboxylate ligands to the octa-acid deep-cavitand host system. The ligand is treated with the semiempirical PM6-DH+ QM method. In the first approach, we perform direct alchemical QM/MM free energy perturbation (FEP). In the second, reference-potential approach, we convert the ligands with FEP at the molecular mechanics (MM) level and then perform also MM → QM/MM FEP for each ligand. We show that the two approaches give identical results within statistical uncertainty. For the reference-potential approach, the MM → QM/MM perturbation converges in terms of energies, uncertainties, and overlap measures with two intermediate states, giving a precision of 0.5-0.9 kJ/mol for all eight transformations considered. On the other hand, the QM/MM-FEP approach requires 17-18 intermediate states, showing that the reference-potential approach is more effective. Previous calculations with single-step exponential averaging (i.e., entirely avoiding QM/MM simulations) required fewer QM/MM energy calculations, but they gave worse precision and involved approximations with an unclear effect on the results.
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| 6. |
- Olsson, Martin A., et al.
(författare)
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Converging ligand-binding free energies obtained with free-energy perturbations at the quantum mechanical level
- 2016
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Ingår i: Journal of Computational Chemistry. - : Wiley. - 0192-8651 .- 1096-987X. ; 37:17, s. 1589-1600
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Tidskriftsartikel (refereegranskat)abstract
- In this article, the convergence of quantum mechanical (QM) free-energy simulations based on molecular dynamics simulations at the molecular mechanics (MM) level has been investigated. We have estimated relative free energies for the binding of nine cyclic carboxylate ligands to the octa-acid deep-cavity host, including the host, the ligand, and all water molecules within 4.5 Å of the ligand in the QM calculations (158-224 atoms). We use single-step exponential averaging (ssEA) and the non-Boltzmann Bennett acceptance ratio (NBB) methods to estimate QM/MM free energy with the semi-empirical PM6-DH2X method, both based on interaction energies. We show that ssEA with cumulant expansion gives a better convergence and uses half as many QM calculations as NBB, although the two methods give consistent results. With 720,000 QM calculations per transformation, QM/MM free-energy estimates with a precision of 1 kJ/mol can be obtained for all eight relative energies with ssEA, showing that this approach can be used to calculate converged QM/MM binding free energies for realistic systems and large QM partitions.
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