Computational protocol: A combined computational and experimental investigation of the [2Fe–2S] cluster in biotin synthase

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[…] The quantum mechanical (QM)/molecular mechanical (MM) calculations were performed with the ComQum software program [, ] utilising Turbomole 5.9 [] for the QM calculations and Amber 9 [] for the MM calculations. The QM calculations were performed using the BP86 functional [, ] and the def2-SV(P) basis sets [], which have given reasonable results for [2Fe–2S] clusters in previous calculations [, ]. For the MM calculations, we used the Amber-99 force field [, ]. For the [4Fe–4S] cluster and the dethiobiotin and S-adenosylmethionine ligands, we used force-field parameters previously determined in our group [–].In the QM/MM approach, the protein and solvent are split into three subsystems. The QM region (system 1) contains the most interesting atoms and is relaxed by QM methods. System 2 consists of the residues closest to the QM system and is optimised by MM calculations. The remaining part of the protein and the surrounding solvent molecules (system 3) are kept fixed at the crystallographic coordinates. In the QM calculations, system 1 is represented by a wavefunction, whereas all the other atoms are represented by an array of partial point charges, one for each atom, taken from MM libraries. Thereby, the polarisation of the quantum chemical system by the surroundings is included in a self-consistent manner. When there is a bond between systems 1 and 2 (a junction), the quantum region is truncated by hydrogen atoms, the positions of which are linearly related to the corresponding carbon atoms in the full system (the hydrogen-link-atom approach) []. To eliminate the non-physical effect of placing point charges on atoms in the MM region bound to junction atoms (i.e. the closest neighbours of the QM system), those charges are zeroed, and the resulting residual charges are smoothly distributed [].The total energy is calculated aswhere EQM1+ptch is the QM energy of system 1 truncated by the hydrogen atoms and embedded in the set of point charges (but excluding the self-energy of the point charges). EMM1 is the MM energy of system 1, still truncated by hydrogen atoms, but without any electrostatic interactions. Finally, EMM123 is the classical energy of all atoms with normal atoms at the junctions and with the charges of the quantum system set to zero (to avoid double-counting of the electrostatic interactions). By this approach, which is similar to the one used in the ONIOM method [], errors caused by the truncation of the quantum system should cancel.The calculations were based on the crystal structure (Protein Data Bank code 1R30) []. As the enzyme was crystallised as a homodimer with little difference in atom positions (less than 0.1 Å differences within the [2Fe–2S] cluster), only the A subunit was used for the investigations and only this subunit is discussed. Hydrogen atoms were added to the crystal structure and the protein was solvated in a sphere of water molecules with a radius of 36 Å using the Leap module in the Amber software suite. The protonation status of all residues was checked by the PROPKA program [] and it was concluded that no residues have strongly perturbed pKa values (thus, all arginine and lysine residues, except Arg260, see below, were considered in their protonated state, whereas all aspartate and glutamate residues were considered in their deprotonated state). For the histidine residues, the protonation was decided from a detailed study of the solvent exposure and hydrogen-bond pattern. This procedure led to the following assignment: His34 and His107 were protonated on both nitrogen atoms, whereas His31 was protonated on Nε2 only and His152 was protonated on Nδ1 only. The cysteine residues coordinating the Fe/S clusters were assumed to be deprotonated. The [4Fe–4S] cluster, S-adenosylmethionine and the dethiobiotin molecule found in the crystal structure were all included in the calculations. The total charge of the simulated system was −8 (neutral arginine) or −7 (protonated arginine). The positions of the atoms added were optimised by a 90-ps simulated-annealing molecular dynamics simulation, followed by 10,000 steps of conjugate gradient energy minimisation. All bond lengths involving hydrogen atoms were constrained by the SHAKE algorithm []. The water solvent was described explicitly using the TIP3P model []. The temperature was kept constant at 300 K using the Berendsen weak-coupling algorithm [] with a time constant of 1 ps. The molecular dynamics time step was 2 fs. The non-bonded cut-off was 15 Å and the pair list was updated every 50 fs. In the QM/MM calculations, an infinite cut-off was used instead.The entire system was then divided into three subsystems. System 1 contained the [2Fe–2S] cluster and the relevant atoms of the four coordinating amino acids (Cys97, Cys128, Cys188 and Arg260) and was treated with QM methods. The side chains were included as far as Cβ for the cysteine residues (replacing Cα by a hydrogen atom) and as far as Cδ for the arginine residue (replacing Cγ by a hydrogen atom). Thus, it consisted of [(CH3S)3(CH3NHCH(NH)NH2)Fe2S2]− for the calculations with neutral arginine and [(CH3S)3(CH3NHCH(NH2)NH2)Fe2S2] for the calculations with protonated arginine. System 2 included all residues with any atom within 6 Å of any atom in system 1 and was relaxed with MM methods. System 3 included the remaining protein atoms as well as the water molecules and was kept fixed at the crystallographic coordinates.As both iron atoms of the oxidised [2Fe–2S] cluster are in the FeIII high-spin state (S = 5/2), two spin states are possible (the ferromagnetically coupled, F, state, S = 5, and the antiferromagnetically coupled, AF, state, S = 0). The AF state always had a lower energy than the F state and it is also the one observed experimentally. Therefore, all results presented are AF energies. To ensure that the QM/MM energy differences are stable, the calculations were in general run forth and back between the relevant states until the energies were stable within 4 kJ/mol.Similar calculations were also performed on one-electron-reduced clusters, i.e. clusters containing one FeII and one FeIII ion (net charge of the QM system −1 or −2, depending on the protonation of the arginine model), on two-electron-reduced clusters (net charge −2 or −3) and on clusters with one of the bridging sulphur atoms removed (the one closest to dethiobiotin; net charge 0 or −1, so this is equivalent to removing an S2− ion and reducing both iron ions to FeII), in all cases in the AF (S = 1/2 or S = 0) state.For convenience, all geometry optimisations discussed were started from an initial optimisation with structure 2 (Structure ). To verify that this is acceptable, we tested to what extent the optimised geometry depends on the starting geometry. In addition, the influence of the spin and oxidation states of the [2Fe–2S] cluster on structural properties was investigated. These explorative calculations were performed in a vacuum (i.e. system 1 only), starting from the crystal geometry. Geometry optimisations for structure 2 in different oxidation states (FeII/FeII, FeII/FeIII or FeIII/FeIII) and spin states (AF or F) showed that the final geometries of the intact clusters, especially the Fe···Fe distances and the orientation of the arginine residue, do not depend on the starting geometries. The oxidised AF and F states were also tested for the other protonation states (structures 1, 3 and 4), with similar results. In all calculations, the AF state was energetically favoured (by 18–118 kJ/mol). Short Fe···Fe distances were found in all cases, although they were slightly longer for the F states (AF: 2.57–2.65 Å, F: 2.42–2.89 Å); no additional electronic states with larger Fe···Fe distances were detected. To verify this observation, the Fe···Fe distance was fixed to values between 2.5 and 3.5 Å (structure 2, oxidised, AF state) and the rest of the geometry was optimised. Only one energy minimum was found, at approximately 2.6 Å (61 kJ/mol more stable than the distance in the crystal structure) and no evidence for a second minimum close to the crystal structure distance was found.Structure 1Similar explorative calculations were performed with the hybrid B3LYP functional [, ] (to examine the effect of another functional with exact exchange), giving similar results [EAF − EF = −20 to −55 kJ/mol, d(Fe···Fe) = 2.55–2.72 (AF) and 2.70–2.96 Å (F) and an energy minimum at 2.8 Å, 36 kJ/mol lower than the crystal structure].Quadrupole splittings were calculated according towhere Q = 0.16 b (1.6 × 10−29 m2) for 57Fe, η = (Vxx − Vyy)/Vzz, with |Vxx| < |Vyy| < |Vzz|, and 1 mm/s is equivalent to 4.8075 × 10−18 eV. [...] We also performed a set of quantum-refinement calculations, using the software program ComQum-X []. They can be seen as QM/MM calculations in which the structures are restrained towards crystallographic raw data. In ComQum-X, the MM program is replaced by the crystallographic refinement program Crystallography & NMR System (CNS) []. In crystallographic refinement, the coordinates, B factors, occupancies, etc. are improved by optimising the fit of the observed and calculated structure-factor amplitudes, typically estimated by the residual disagreement, the R factor. Because of the limited resolution normally obtained with X-ray diffraction of biomolecules, a MM force field is used to supplement the data for the whole protein []. This force field ensures that the bond lengths and angles make chemical sense. In ComQum-X, this force field is replaced by more accurate QM calculations for a small, but interesting, part of the protein (system 1), in a manner completely analogous to the use of quantum mechanics in QM/MM calculations. The junctions are handled in the same way as in ComQum.Thus, the ComQum-X refinement takes the form of a minimisation using an energy function of the formHere, EMM1 and EMM123 have the same meaning as in Eq. , whereas EQM1 is the energy of the QM system, without any point-charge model of the surroundings. EX-ray is a penalty function, describing how well the model agrees with the experimental X-ray data. We have used the default maximum likelihood refinement target using amplitudes (MLF) in CNS []. wA is a weight factor, which is necessary because EX-ray is in arbitrary units whereas the other terms are in energy units. It should be emphasised that the wA factor is nothing special for quantum refinement. On the contrary, it also has to be set in standard crystallographic refinement (which is obtained from Eq.  with EQM1 = EMM1 = 0), although it is rarely discussed. The default behaviour of CNS is to determine wA so that the EX-ray and EMM123 forces have the same magnitude during a short molecular dynamics simulation [], i.e. that the crystallographic raw data and the MM force field have a similar influence on the structure. We tested nine different values for the wA factor between 0 and 30. Unfortunately, we encountered convergence problems if we used the default value of wA (4.87) for some of the structures (because the crystallographically preferred structure of the [2Fe–2S] cluster is so poor at this low resolution that it becomes incompatible with the QM calculations). Therefore, we present results only for the largest value of the wA factor that gave converged structures for all models, viz. wA = 1. The results are qualitatively the same if other values are used, regarding the preferred model and coordination mode of the arginine ligand.Following crystallographic custom, no hydrogen atoms were included in the MM region of the ComQum-X calculations, because hydrogen atoms are not discernible in the crystal structure. Therefore, polarisation of the quantum system by the surrounding protein is not included in ComQum-X.Finally, it should be noted that the MM force field used in CNS (protein_rep.param, dna-rna_rep.param, water.param and ion.param) is based on a statistical survey of crystal structures [], rather than the energy-based force field in Amber and in the QM calculations. Therefore, the CNS energy has to be weighted by a factor of 1/3 to be comparable with the QM and Amber MM energies [].The quantum-refinement calculations were based on the same crystal structure as the QM/MM calculations (but both subunits were considered) [] and the corresponding structure factors were downloaded from the Protein Data Bank. Calculations were performed with the same QM system as with QM/MM [(CH3S)3(CH3NHCH(NH1–2)NH2)Fe2S2], as well as a QM system enlarged with a CH3OH model of Ser43 and a CH3NHCH(NH2)2 model of Arg95 (for both the intact oxidised cluster, as well as the one-electron-reduced cluster without one of the bridging sulphide ions). The QM method and basis sets were the same as in the QM/MM calculations. […]

Pipeline specifications

Software tools PROPKA, CNS, AMBER
Applications Small-angle scattering, Protein structure analysis
Chemicals Biotin, Cysteine, Iron, S-Adenosylmethionine, Guanidine