Benchmark Study of Redox Potential Calculations for Iron-Sulfur Clusters in Proteins.

Redox potentials have been calculated for 12 different iron-sulfur sites of 6 different types with 1-4 iron ions. Structures were optimized with combined quantum mechanical and molecular mechanical (QM/MM) methods, and the redox potentials were calculated using the QM/MM energies, single-point QM methods in a continuum solvent or by QM/MM thermodynamic cycle perturbations. We show that the best results are obtained with a large QM system (∼300 atoms, but a smaller QM system, ∼150 atoms, can be used for the QM/MM geometry optimization) and a large value of the dielectric constant (80). For absolute redox potentials, the B3LYP density functional method gives better results than TPSS, and the results are improved with a larger basis set. However, for relative redox potentials, the opposite is true. The results are insensitive to the force field (charges of the surroundings) used for the QM/MM calculations or whether the protein and solvent outside the QM system are relaxed or kept fixed at the crystal structure. With the best approach for relative potentials, mean absolute and maximum deviations of 0.17 and 0.44 V, respectively, are obtained after removing a systematic error of -0.55 V. Such an approach can be used to identify the correct oxidation states involved in a certain redox reaction.

Critical evaluation of a crystal structure of nitrogenase with bound N2 ligands.

Recently, a 1.83 Å crystallographic structure of nitrogenase was suggested to show N2-derived ligands at three sites in the catalytic FeMo cluster, replacing the three [Formula: see text] bridging sulfide ligands (two in one subunit and the third in the other subunit) (Kang et al. in Science 368: 1381-1385, 2020). Naturally, such a structure is sensational, having strong bearings on the reaction mechanism of the enzyme. Therefore, it is highly important to ensure that the interpretation of the structure is correct. Here, we use standard crystallographic refinement and quantum refinement to evaluate the structure. We show that the original crystallographic raw data are strongly anisotropic, with a much lower resolution in certain directions than others. This, together with the questionable use of anisotropic B factors, give atoms an elongated shape, which may look like diatomic atoms. In terms of standard electron-density maps and real-space Z scores, a resting-state structure with no dissociated sulfide ligands fits the raw data better than the interpretation suggested by the crystallographers. The anomalous electron density at 7100 eV is weaker for the putative N2 ligands, but not lower than for several of the [Formula: see text] bridging sulfide ions and not lower than what can be expected from a statistical analysis of the densities. Therefore, we find no convincing evidence for any N2 binding to the FeMo cluster. Instead, a standard resting state without any dissociated ligands seems to be the most likely interpretation of the structure. Likewise, we find no support that the homocitrate ligand should show monodentate binding.

Geometry and Electronic Structure of the P-Cluster in Nitrogenase Studied by Combined Quantum Mechanical and Molecular Mechanical Calculations and Quantum Refinement.

We have studied the geometry and electronic structure of the P-cluster in nitrogenase in four oxidation states: PN, P1+, P2+, and P3+. We have employed combined quantum mechanical and molecular mechanical (QM/MM) calculations, using two different density-functional theory methods, TPSS and B3LYP. The calculations confirm that the side chain of Ser-188 is most likely deprotonated in the partly oxidized P1+ state, thereby forming a bond to Fe6. Likewise, the backbone amide group of Cys-88 is deprotonated in the doubly oxidized P2+ state, forming a bond to Fe5. The calculations also confirm the two conformations of the P-cluster in the atomic-resolution crystal structure of the enzyme, representing the PN and P2+ states, but show that the finer differences between the two structures are not fully reflected in the crystal structure, because the coordinates of only two atoms differ between the two conformations. However, the recent crystal structure of the P1+ state seems to be of lower quality with many dubious Fe-Fe and Fe-S distances. Quantum refinement of this structure indicates that it is a mixture of the P1+ and P2+ states but confirms that the side chain of Ser-188 is most likely deprotonated in both states. TPSS gives structures that are appreciably closer to the crystal structures than does B3LYP. In addition, we have studied all 16-48 possible broken-symmetry states of the four oxidation states of the P-cluster with DFT in the one or two observed spin states. For the reduced PN state, we can settle the most likely state from the calculated energies and geometries. However, for the more oxidized states there are large differences in the predictions obtained with the two DFT methods.

Combining crystallography with quantum mechanics.

In standard crystallographic refinement of biomacromolecules, the crystallographic raw data are supplemented by empirical restraints that ensure that the structure makes chemical sense. These restraints are typically accurate for amino acids and nucleic acids, but less so for cofactors, substrates, inhibitors, ligands and metal sites. In quantum refinement, this potential is replaced by more accurate quantum mechanical (QM) calculations. Several implementations have been presented, differing in the level of QM and whether it is used for the entire structure or only for a site of particular interest. It has been shown that the method can improve and correct errors in crystal structures and that it can be used to determine protonation and tautomeric states of various ligands and to decide what is really seen in the structure by refining different interpretations and using standard crystallographic and QM quality measures to decide which fits the structure best.

Computationally enhanced X-ray diffraction analysis of a gold(III) complex interacting with the human telomeric DNA G-quadruplex. Unravelling non-unique ligand positioning.

The crystal structure of the human telomeric DNA Tel24 G-quadruplex (Tel24 = TAG3(T2AG3)3T) in complex with the novel [AuL] species (with L = 2,4,6-tris(2-pyrimidyl)-1,3,5-triazine - TPymT-α) was solved by a novel joint molecular mechanical (MM)/quantum mechanical (QM) innovative approach. The quantum-refinement crystallographic method (crystallographic refinement enhanced with quantum mechanical calculation) was adapted to treat the [AuL]/G-quadruplex structure, where each gold complex in the binding site was found spread over four equally occupied positions. The four positions were first determined by docking restrained to the crystallographically determined metal ions' coordinates. Then, the quantum refinement method was used to resolve the poorly defined density around the ligands and improve the crystallographic determination, revealing that the binding preferences of this metallodrug toward Tel24 G-quadruplex arise from a combined effect of pyrimidine stacking, metal-guanine interactions and charge-charge neutralizing action of the π-acid triazine. The occurrence of interaction in solution with the Tel24 G-quadruplex DNA was further proved through DNA melting experiments, which showed a slight destabilisation of the quadruplex upon adduct formation.

Quantum-refinement studies of the bidentate ligand of V­nitrogenase and the protonation state of CO-inhibited Mo­nitrogenase.

Nitrogenase is the only enzyme that can cleave the triple bond in N2, making nitrogen available to plants (although the enzyme itself is strictly microbial). It has been studied extensively with both experimental and computational methods, but many details of the reaction mechanism are still unclear. X-ray crystallography is the main source of structural information for biomacromolecules, but it has problems to discern hydrogen atoms or to distinguish between elements with the same number of electrons. These problems can sometimes be alleviated by introducing quantum chemical calculations in the refinement, providing information about the ideal structure (in the same way as the empirical restraints used in standard crystallographic refinement) and comparing different interpretations of the structure with normal crystallographic and quantum mechanical quality measures. We have performed such quantum-refinement calculations to address two important issues for nitrogenase. First, we show that the bidentate ligand of the active-site FeV cluster in V­nitrogenase is carbonate, rather than bicarbonate or nitrate. Second, we study the CO-inhibited structure of Mo­nitrogenase. CO binds to a reduced and protonated state of the enzyme by replacing one of the sulfide ions (S2B) in the active-site FeMo cluster. We examined if it is possible to deduce from the crystal structure the location of the protons. Our results indicates that the crystal structure is best modelled as fully deprotonated.

fragHAR: towards ab initio quantum-crystallographic X-ray structure refinement for polypeptides and proteins.

The first ab initio aspherical structure refinement against experimental X-ray structure factors for polypeptides and proteins using a fragmentation approach to break up the protein into residues and solvent, thereby speeding up quantum-crystallographic Hirshfeld atom refinement (HAR) calculations, is described. It it found that the geometric and atomic displacement parameters from the new fragHAR method are essentially unchanged from a HAR on the complete unfragmented system when tested on dipeptides, tripeptides and hexapeptides. The largest changes are for the parameters describing H atoms involved in hydrogen-bond interactions, but it is shown that these discrepancies can be removed by including the interacting fragments as a single larger fragment in the fragmentation scheme. Significant speed-ups are observed for the larger systems. Using this approach, it is possible to perform a highly parallelized HAR in reasonable times for large systems. The method has been implemented in the TONTO software.

Fast and Accurate Quantum Crystallography: From Small to Large, from Light to Heavy.

The coupling of the crystallographic refinement technique Hirshfeld atom refinement (HAR) with the recently constructed libraries of extremely localized molecular orbitals (ELMOs) gives rise to the new quantum-crystallographic method HAR-ELMO. This method is significantly faster than HAR but as accurate and precise, especially concerning the free refinement of hydrogen atoms from X-ray diffraction data, so that the first fully quantum-crystallographic refinement of a protein is presented here. However, the promise of HAR-ELMO exceeds large molecules and protein crystallography. In fact, it also renders possible electron-density investigations of heavy elements in small molecules and facilitates the detection and isolation of systematic errors from physical effects.