| 1. |
- Andrejic, Milica, et al.
(författare)
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Coupled-Cluster Interaction Energies for 200-Atom Host-Guest Systems
- 2014
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Ingår i: ChemPhysChem. - : Wiley. - 1439-7641 .- 1439-4235. ; 15:15, s. 3270-3281
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Tidskriftsartikel (refereegranskat)abstract
- We have developed a method to calculate interaction energies of large systems (such as host-guest or even protein-ligand systems) at the local coupled-cluster with singles, doubles, and perturbative triples level, and with extrapolation to the limit of a complete basis set. The method is based on the polarizable multipole interactions with supermolecular pairs molecular fractionation approach, which combines a pairwise quantum-mechanical evaluation of the short-range interactions with a polarizable multipole treatment of many-body effects. The method is tested for nine guest molecules binding to an octa-acid host (in total 198-207 atoms), as part of the SAMPL4 blind challenge. From the test calculations, the accuracy of the approach is found to be 10 kJ mol(-1) or better. Comparison with dispersion-corrected density functional theory reveals that the latter underestimates the dispersion contribution for this type of system, which leads to a difference in the ranking of the ligands.
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| 2. |
- Genheden, Samuel, et al.
(författare)
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Accurate Predictions of Nonpolar Solvation Free Energies Require Explicit Consideration of Binding-Site Hydration
- 2011
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Ingår i: Journal of the American Chemical Society. - : American Chemical Society (ACS). - 1520-5126 .- 0002-7863. ; 133:33, s. 13081-13092
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Tidskriftsartikel (refereegranskat)abstract
- Continuum solvation methods are frequently used to increase the efficiency of computational methods to estimate free energies. In this paper, we have evaluated how well such methods estimate the nonpolar solvation free-energy change when a ligand binds to a protein. Three different continuum methods at various levels of approximation were considered, viz., the polarized continuum model (PCM), a method based on cavity and dispersion terms (CD), and a method based on a linear relation to the solvent-accessible surface area (SASA). Formally rigorous double-decoupling thermodynamic integration was used as a benchmark for the continuum methods. We have studied four protein-ligand complexes with binding sites of varying solvent exposure, namely the binding of phenol to ferritin, a biotin analogue to avidin, 2-aminobenzimidazole to trypsin, and a substituted galactoside to galectin-3. For ferritin and avidin, which have relatively hidden binding sites, rather accurate nonpolar solvation free energies could be obtained with the continuum methods if the binding site is prohibited to be filled by continuum water in the unbound state, even though the simulations and experiments show that the ligand replaces several water molecules upon binding. For the more solvent exposed binding sites of trypsin and galectin-3, no accurate continuum estimates could be obtained, even if the binding site was allowed or prohibited to be filled by continuum water. This shows that continuum methods fail to give accurate free energies on a wide range of systems with varying solvent exposure because they lack a microscopic picture of binding-site hydration as well as information about the entropy of water molecules that are in the binding site before the ligand binds. Consequently, binding affinity estimates based upon continuum solvation methods will give absolute binding energies that may differ by up to 200 kJ/mol depending on the method used. Moreover, even relative energies between ligands with the same scaffold may differ by up to 75 kJ/mol. We have tried to improve the continuum solvation methods by adding information about the solvent exposure of the binding site or the hydration of the binding site, and the results are promising at least for this small set of complexes.
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| 3. |
- Genheden, Samuel, et al.
(författare)
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Binding affinities by alchemical perturbation using QM/MM with a large QM system and polarizable MM model.
- 2015
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Ingår i: Journal of Computational Chemistry. - : Wiley. - 1096-987X .- 0192-8651. ; 36:28, s. 2114-2124
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Tidskriftsartikel (refereegranskat)abstract
- The most general way to improve the accuracy of binding-affinity calculations for protein-ligand systems is to use quantum-mechanical (QM) methods together with rigorous alchemical-perturbation (AP) methods. We explore this approach by calculating the relative binding free energy of two synthetic disaccharides binding to galectin-3 at a reasonably high QM level (dispersion-corrected density functional theory with a triple-zeta basis set) and with a sufficiently large QM system to include all short-range interactions with the ligand (744-748 atoms). The rest of the protein is treated as a collection of atomic multipoles (up to quadrupoles) and polarizabilities. Several methods for evaluating the binding free energy from the 3600 QM calculations are investigated in terms of stability and accuracy. In particular, methods using QM calculations only at the endpoints of the transformation are compared with the recently proposed non-Boltzmann Bennett acceptance ratio (NBB) method that uses QM calculations at several stages of the transformation. Unfortunately, none of the rigorous approaches give sufficient statistical precision. However, a novel approximate method, involving the direct use of QM energies in the Bennett acceptance ratio method, gives similar results as NBB but with better precision, ∼3 kJ/mol. The statistical error can be further reduced by performing a greater number of QM calculations. © 2015 Wiley Periodicals, Inc.
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| 4. |
- Genheden, Samuel, et al.
(författare)
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Nonpolar Solvation Free Energies of Protein-Ligand Complexes
- 2010
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Ingår i: Journal of Chemical Theory and Computation. - : American Chemical Society (ACS). - 1549-9618 .- 1549-9626. ; 6:11, s. 3558-3568
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Tidskriftsartikel (refereegranskat)abstract
- Recent investigations have indicated that different solvation methods give qualitatively different results for the nonpolar solvation contribution to ligand-binding affinities. Therefore, we have calculated the nonpolar solvation contribution to the free energy of benzene binding to the T4 lysozyme Leu99Ala mutant using thermodynamic integration (TI) and three approximate methods. The total binding free energy was calculated with TI and then decomposed into contributions from the solvent and the solute. The nonpolar contribution from the solute was compared to approximate methods within the framework of the molecular-mechanics and generalized Born with surface area method (MM/GBSA). First, the nonpolar solvation energy was calculated with a linear relation to the solvent-accessible surface area (SASA). Second, a recent approach that divides the nonpolar solvation energy into cavity and dispersion parts was used, and third, the nonpolar solvation energy was calculated with the polarized continuum model (PCM). Surprisingly, the simple SASA estimate reproduces the TI results best. However, the reason for this is that all continuum methods assume that the benzene cavity is filled with water for the free protein, contrary to both experimental and simulation results. We present a method to avoid this assumption and then, PCM provides results that are closest to the results obtained with TI.
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| 5. |
- Genheden, Samuel, et al.
(författare)
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Transferability of conformational dependent charges from protein simulations
- 2012
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Ingår i: International Journal of Quantum Chemistry. - : Wiley. - 0020-7608. ; 112:7, s. 1768-1785
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Tidskriftsartikel (refereegranskat)abstract
- We have studied the transferability of atomic charges for proteins, fitted to the quantum mechanical electrostatic potential and extensively averaged over a set of structures sampled by molecular dynamics (MD) and over all residues of the same kind in the protein sequence (xAvESP). Previously, such charges were obtained for one single protein (avidin). In this study, we use five additional proteins. The aim of this study is fourfold. First, we provide xAvESP charges for all amino acids, including amino- and carboxy-terminal variants of all, as well as alternative protonation states of His, Asp, Glu, Lys, Arg, Cys, and Tyr. Second, we show that the xAvESP charges averaged over the five new proteins are similar to charges obtained in the same way for avidin, with a correlation coefficient of 0.997. This shows that the charges are transferable and system-independent. Electrostatic proteinligand interaction energies calculated with charges obtained from different proteins differ by only 13 kJ/mol on average. The xAvESP charges correlate rather well with Amber charges (except for the N atom of amino-terminal residues that are erroneous in Amber), although they are obtained in a more general way. Third, the conformational dependence of the charges is significant and gives rise to quite large differences in energies. However, these differences are to a large extent screened by solvation effects. For example, the solvent-screened electrostatic interaction energy between the protein galectin-3 and five different ligands varies with the charge sets by less than 3 kJ/mol on average. Finally, we show that the xAvESP charges give a comparable root-mean-squared deviation as the Amber charges for the MD simulations of 18 proteinligand complexes, they give comparable or slightly worse backbone N?H order parameters for two galectin-3 complexes, but they give a better correlation between calculated and experimental affinities for the binding of seven biotin analogues to avidin and for nine inhibitors of factor Xa. (c) 2011 Wiley Periodicals, Inc. Int J Quantum Chem 112:17681785, 2012
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| 6. |
- Godschalk, Frithjof, et al.
(författare)
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Comparison of MM/GBSA calculations based on explicit and implicit solvent simulations.
- 2013
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Ingår i: Physical Chemistry Chemical Physics. - : Royal Society of Chemistry (RSC). - 1463-9084 .- 1463-9076. ; 15:20, s. 7731-7739
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Tidskriftsartikel (refereegranskat)abstract
- Molecular mechanics with generalised Born and surface area solvation (MM/GBSA) is a popular method to calculate the free energy of the binding of ligands to proteins. It involves molecular dynamics (MD) simulations with an explicit solvent of the protein-ligand complex to give a set of snapshots for which energies are calculated with an implicit solvent. This change in the solvation method (explicit → implicit) would strictly require that the energies are reweighted with the implicit-solvent energies, which is normally not done. In this paper we calculate MM/GBSA energies with two generalised Born models for snapshots generated by the same methods or by explicit-solvent simulations for five synthetic N-acetyllactosamine derivatives binding to galectin-3. We show that the resulting energies are very different both in absolute and relative terms, showing that the change in the solvent model is far from innocent and that standard MM/GBSA is not a consistent method. The ensembles generated with the various solvent models are quite different with root-mean-square deviations of 1.2-1.4 Å. The ensembles can be converted to each other by performing short MD simulations with the new method, but the convergence is slow, showing mean absolute differences in the calculated energies of 6-7 kJ mol(-1) after 2 ps simulations. Minimisations show even slower convergence and there are strong indications that the energies obtained from minimised structures are different from those obtained by MD.
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| 7. |
- Hu, LiHong, et al.
(författare)
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Accurate reaction energies in proteins obtained by combining QM/MM and large QM calculations
- 2013
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Ingår i: Journal of Chemical Theory and Computation. - : American Chemical Society (ACS). - 1549-9618 .- 1549-9626. ; 9, s. 640-649
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Tidskriftsartikel (refereegranskat)abstract
- We here suggest and test a new method to obtain stable energies in proteins for charge-neutral reactions by running large quantum mechanical (QM) calculations on structures obtained by combined QM and molecular mechanics (QM/MM) geometry optimisation on several snapshots from molecular dynamics simulations. As a test case, we use a proton transfer between a metal-bound cysteine residue and a second-sphere histidine residue in the active site of [Ni,Fe] hydrogenase, which has been shown to be very sensitive to the surroundings. We include in the QM calculations all residues within 4.5 Å of the active site, two capped residues on each side of the active-site residues, as well as all charged groups that are buried inside the protein, which for this enzyme includes three iron–sulphur clusters, in total 930 atoms. These calculations are performed at the BP86/def2-SV(P) level, but the energies are then extrapolated to the B3LYP/def2-TZVP level with a smaller QM system and zero-point energy, entropy, and thermal effects are added. We test three approaches to model the remaining atoms of the protein solvent, viz. by standard QM/MM approaches using either mechanical or electrostatic embedding, or by using a continuum solvation model for the large QM systems. Quite encouragingly, the three approaches give the same results within 13 kJ/mol and variations in the size of the QM system do not change the energies by more than 8 kJ/mol, provided that the QM/MM junctions are not moved closer to the QM system. The statistical precision for the average over ten snapshots is 1–3 kJ/mol.
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| 8. |
- Kaukonen, Markus, et al.
(författare)
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Proton transfer at metal sites in proteins studied by quantum mechanical free-energy perturbations
- 2008
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Ingår i: Journal of Chemical Theory and Computation. - : American Chemical Society (ACS). - 1549-9618 .- 1549-9626. ; 4:6, s. 985-1001
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Tidskriftsartikel (refereegranskat)abstract
- Catalytic metal sites in enzymes frequently have second-sphere carboxylate groups that neutralize the charge of the site and share protons with first-sphere ligands. This gives rise to an ambiguity concerning the position of this proton, which has turned out to be hard to settle with experimental, as well as theoretical, methods. We study three such proton-transfer reactions in two proteins and show that, in [Ni,Fe] hydrogenase, the bridging Cys-546 ligand is deprotonated by His-79, whereas in oxidized copper nitrite reductase, the His-100 ligand is neutral and the copper-bound water molecule is deprotonated by Asp-98. We show that these reactions strongly depend on the electrostatic interactions with the surrounding protein and solvent, because there is a large change in the dipole moment of the active site (2-6 D). Neither vacuum quantum mechanical (QM) calculations with large models, a continuum solvent, or a Poisson-Boltzmann treatment of the surroundings, nor combined QM and molecular mechanics (QM/MM) optimizations give reliable estimates of the proton-transfer energies (mean absolute deviations of over 20 kJ/mol). Instead, QM/MM free-energy perturbations are needed to obtain reliable estimates of the reaction energies. These calculations also indicate what interactions and residues are important for the energy, showing how the quantum system may be systematically enlarged. With such a procedure, results with an uncertainty of similar to 10 kJ/mol can be obtained, provided that a proper QM method is used.
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| 9. |
- Kaukonen, Markus, et al.
(författare)
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QM/MM-PBSA method to estimate free energies for reactions in proteins
- 2008
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Ingår i: The Journal of Physical Chemistry Part B. - : American Chemical Society (ACS). - 1520-5207 .- 1520-6106. ; 112:39, s. 12537-12548
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Tidskriftsartikel (refereegranskat)abstract
- We have developed a method to estimate free energies of reactions in proteins, called QM/MM-PBSA. It estimates the internal energy of the reactive site by quantum mechanical (QM) calculations, whereas bonded, electrostatic, and van der Waals interactions with the surrounding protein are calculated at the molecular mechanics (MM) level. The electrostatic part of the solvation energy of the reactant and the product is estimated by solving the Poisson-Boltzmann (PB) equation, and the nonpolar part of the solvation energy is estimated from the change in solvent-accessible surface area (SA). Finally, the change in entropy is estimated from the vibrational frequencies. We test this method for five proton-transfer reactions in the active sites of [Ni,Fe] hydrogenase and copper nitrite. reductase. We show that QM/MM-PBSA reproduces the results of a strict QM/MM free-energy perturbation method with a mean absolute deviation (MAD) of 8-10 kJ/mol if snapshots from molecular dynamics simulations are used and 4-14 kJ/mol if a single QM/MM structure is used. This is appreciably better than the original QM/MM results or if the QM energies are supplemented with a point-charge model, a self-consistent reaction field, or a PB model of the protein and the solvent, which give MADs of 22-36 kJ/mol for the same test set.
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| 10. |
- Kongsted, Jacob, et al.
(författare)
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How accurate are continuum solvation models for drug-like molecules?
- 2009
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Ingår i: Journal of Computer-Aided Molecular Design. - : Springer Science and Business Media LLC. - 1573-4951 .- 0920-654X. ; 23:7, s. 395-409
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Tidskriftsartikel (refereegranskat)abstract
- We have estimated the hydration free energy for 20 neutral drug-like molecules, as well as for three series of 6-11 inhibitors to avidin, factor Xa, and galectin-3 with four different continuum solvent approaches (the polarised continuum method the Langevin dipole method, the finite-difference solution of the Poisson equation, and the generalised Born method), and several variants of each, giving in total 24 different methods. All four types of methods have been thoroughly calibrated for a number of experimentally known small organic molecules with a mean absolute deviation (MAD) of 1-6 kJ/mol for neutral molecules and 4-30 kJ/mol for ions. However, for the drug-like molecules, the accuracy seems to be appreciably worse. The reason for this is that drug-like molecules are more polar than small organic molecules and that the uncertainty of the methods is proportional to the size of the solvation energy. Therefore, the accuracy of continuum solvation methods should be discussed in relative, rather than absolute, terms. In fact, the mean unsigned relative deviations of the best solvation methods, 0.09 for neutral and 0.05 for ionic molecules, correspond to 2-20 kJ/mol absolute error for the drug-like molecules in this investigation, or 2-3,000 in terms of binding constants. Fortunately, the accuracy of all methods can be improved if only relative energies within a series of inhibitors are considered, especially if all of them have the same net charge. Then, all except two methods give MADs of 2-5 kJ/mol (corresponding to an uncertainty of a factor of 2-7 in the binding constant). Interestingly, the generalised Born methods typically give better results than the Poison-Boltzmann methods.
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