Inner-sphere reorganization energy of iron-sulfur clusters studied with theoretical methods

Models of several types of iron-sulfur clusters (e.g., Fe(4)S(4)(SCH(3))(4)(2-/3-/4-)) have been studied with the density functional B3LYP method and medium-sized basis sets. In a vacuum, the inner-sphere reorganization energies are 40, 76, 40, 62, 43, and 42 kJ/mol for the rubredoxin, [2Fe-2S] ferredoxin, Rieske, [4Fe-4S] ferredoxin, high-potential iron protein, and desulfoferrodoxin models, respectively. The first two types of clusters were also studied in the protein, where the reorganization energy was approximately halved. This change is caused by the numerous NH.S(Cys) hydrogen bonds to the negatively charged iron-sulfur cluster, giving rise to a polar local environment. The reorganization energy of the iron-sulfur clusters is low because the iron ions retain the same geometry and coordination number in both oxidation states. Cysteine ligands give approximately the same reorganization energy as imidazole, but they have the advantage of stabilizing a lower coordination number and giving more covalent bonds and therefore more effective electron-transfer paths.     

Can Water Act as a Nucleophile in CO Oxidation Catalysed by Mo/Cu CO-Dehydrogenase? Answers from Theory

The aerobic CO dehydrogenase from Oligotropha carboxidovorans is an environmentally crucial bacterial enzyme for maintenance of subtoxic concentration of CO in the lower atmosphere, as it allows for the oxidation of CO to CO₂ which takes place at its Mo−Cu heterobimetallic active site. Despite extensive experimental and theoretical efforts, significant uncertainties still concern the reaction mechanism for the CO oxidation. In this work, we used the hybrid quantum mechanical/molecular mechanical approach to evaluate whether a water molecule present in the active site might act as a nucleophile upon formation of the new C−O bond, a hypothesis recently suggested in the literature. Our study shows that activation of H₂O can be favoured by the presence of the Mo=O_eq group. However, overall our results suggest that mechanisms other than the nucleophilic attack by Mo=O_eq to the activated carbon of the CO substrate are not likely to constitute reactive channels for the oxidation of CO by the enzyme.     

Accurate metal-site structures in proteins obtained by combining experimental data and quantum chemistry

The use of molecular mechanics calculations to supplement experimental data in standard X-ray crystallography and NMR refinements is discussed and it is shown that structures can be locally improved by the use of quantum chemical calculations. Such calculations can also be used to interpret the structures, e.g. to decide the protonation state of metal-bound ligands. They have shown that metal sites in crystal structures are frequently photoreduced or disordered, which makes the interpretation of the structures hard. Similar methods can be used for EXAFS refinements to obtain a full atomic structure, rather than a set of metal-ligand distances.     

Binding affinities by alchemical perturbation using QM/MM with a large QM system and polarizable MM model

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.     

Structure,strain, and reorganization energy of blue copper models in the protein

The copper coordination geometry in the blue copper proteins plastocyanin, nitrite reductase, cucumber basic protein, and azurin has been studied by combined density functional (B3LYP) and molecular mechanical methods. Compared to quantum chemical vacuum calculations, a significant improvement of the geometry is seen (toward the experimental structures) not only for the dihedral angles of the ligands but also for the bond lengths and angles around the copper ion. The flexible Cu–S_Met bond is well reproduced in the oxidized structures, whereas it is too long in some of the reduced complexes (too short in vacuum). The change in the geometry compared to the vacuum state costs 33–66 kJ/mol. If the covalent bonds between the ligands and the protein are broken, this energy decreases by ∼25 kJ/mol, which is an estimate of the covalent strain. This is similar to what is found for other proteins, so the blue copper proteins are not more strained than other metalloproteins. The inner‐sphere self‐exchange reorganization energy of all four proteins are ∼30 kJ/mol. This is 30–50 kJ/mol lower than in vacuum. The decrease is caused by dielectric and electrostatic effects in the protein, especially the hydrogen bond(s) to the cysteine copper ligands and not by covalent strain. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 81: 335–347, 2001     

Quantum Refinement Does Not Support Dinuclear Copper Sites in Crystal Structures of Particulate Methane Monooxygenase

Particulate methane monooxygenase (pMMO) is one of the few enzymes that can activate methane. The metal content of this enzyme has been highly controversial, with suggestions of a dinuclear Fe site or mono‐, di‐, or trinuclear Cu sites. Crystal structures have shown a mono‐ or dinuclear Cu site, but the resolution was low and the geometry of the dinuclear site unusual. We have employed quantum refinement (crystallographic refinement enhanced with quantum‐mechanical calculations) to improve the structure of the active site. We compared a number of different mono‐ and dinuclear geometries, in some cases enhanced with more protein ligands or one or two water molecules, to determine which structure fits two sets of crystallographic raw data best. In all cases, the best results were obtained with mononuclear Cu sites, occasionally with an extra water molecule. Thus, we conclude that there is no crystallographic support for a dinuclear Cu site in pMMO.     

QM/MM-PBSA method to estimate free energies for reactions in proteins

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.     

An improved method to predict the entropy term with the MM/PBSA approach

A method is suggested to calculate improved entropies within the MM/PBSA approach (molecular mechanics combined with Poisson-Boltzmann and surface area calculations) to estimate protein-ligand binding affinities. In the conventional approach, the protein is truncated outside ~8 A from the ligand. This system is freely minimised using a distance-dependent dielectric constant (to simulate the removed protein and solvent). However, this can lead to extensive changes in the molecular geometry, giving rise to a large standard deviation in this term. In our new approach, we introduce a buffer region approximately 4 A outside the truncated protein (including solvent molecules) and keep it fixed during the minimisation. Thereby, we reduce the standard deviation by a factor of 2-4, ensuring that the entropy term no longer limits the precision of the MM/PBSA predictions. The new method is tested for the binding of seven biotin analogues to avidin, eight amidinobenzyl-indole-carboxamide inhibitors to factor Xa, and two substrates to cytochrome P450 3A4 and 2C9. It is shown that it gives more stable results and often improved predictions of the relative binding affinities.     

Conformational dependence of charges in protein simulations

We have studied the conformational dependence of molecular mechanics atomic charges for proteins by calculating the charges fitted to the quantum mechanical (QM) electrostatic potential (ESP) for all atoms in complexes between avidin and seven biotin analogues for 20 snapshots from molecular dynamics simulations. We have studied how various other charge sets reproduce those charges. The QM charges, even if averaged over all snapshots or all residues, in general have a larger magnitude than standard Amber charges, indicating that the restraint toward zero in the restrained ESP method is too strong. This has a significant influence on the electrostatic conformational energies and the interaction energy between the biotin ligand and the protein, giving a difference between the QM and Amber charges of 43 and 8 kJ/mol for the negatively charged and neutral biotin analogues, respectively (3-4%). However, this energy difference is strongly reduced if the solvation energy (calculated by the Poisson-Boltzmann or Generalized Born methods) is added, viz., to 7 kJ/mol for charged and 3 kJ/mol for uncharged ligand. In fact, charges need to be recalculated with a QM method only for residues within 7 or 4 A of the ligand, if the error should be less than 4 kJ/mol. Unfortunately, the QM charges do not give significantly better MM/PBSA estimates of ligand-binding affinities than standard Amber charges.