Mechanistic insights into the reductive dehydroxylation pathway for the biosynthesis of isoprenoids promoted by the IspH enzyme

We report an integrated QM/MM study of the bio-organometallic reaction pathway of the reductive dehydroxylation of (E)-4-hydroxy-3-methylbut-2-enyl pyrophosphate (HMBPP).

: Relaxed scan of Fe--O and C--O to simulate the dissociation of the two bonds for the de--protonated Glu126 using model M1 and ONIOM--MM(B3LYP/TZVP:Amber). 3. Figure S4: Relaxed scan of Fe--O and C--O to simulate the dissociation of the two bonds for the protonated Glu126 using model M1 and ONIOM--MM(B3LYP/TZVP:Amber). 4. Figure S5: Relaxed scan of C--O to simulate the dissociation of the 4--OH group using protonated phosphate group and model M1. 5. Figure S6: ONIOM(B3LYP:TZVP/Amber)--EE reaction profile of the rotation and dehydroxylation step using different QM models calculated for the deprotonated Glu126. 6. Figure S7: ONIOM(B3LYP:TZVP/Amber)--EE reaction profile of the rotation and dehydroxylation step using different QM models calculated for the protonated Glu126. 7. Figure S8: Reaction profile of the 4--OH rotation and elimination calculated using ONIOM(B3LYP/TZVP:Amber)--ME level of theory and model M1 and M2 for the protonated and deprotonated Glu126. 8. Figure  S9: Reaction profile of the 4--OH Rotation and elimination step calculated at ONIOM (B3LYP/TZVP:Amber)--EE using M2. 9. Figure S10: HMBPP substrate with the atom numbering reported in the following tables 10. Figure S11: Balls and sticks representation of the reaction profile stationary points for the reduced state [Fe4S4] + and deprotonated Glu126 11. Figure  S12: Balls and sticks representation of the dehydroxylation reaction profile stationary points for the oxidized state [Fe 4 S 4 ] +2 and protonated Glu126. 12. Figure  S13: Reaction profile of the 4--OH Rotation and elimination step calculated at ONIOM (B3LYP/TZVP:Amber)--EE using M2 (red) and DFT+U (blue) using M3. 13. Figure  S14: Relaxed scans of the C--H bond distance to simulate the protonation at C2 (blue) and at C4 (red). Relaxed scans are calculated using model M1 and ONIOM--MM (B3LYP/TZVP:Amber) level of theory. 14. Figure   18. Table  S4: Natural Population Analysis charges and spin densities calculated for the QM region using model M2 (160 atoms) using B3LYP/TZVP calculated for the reduced state and the protonated Glu126. 19. Table  S5: Natural Population Analysis charges and spin densities calculated for the QM region using model M2 (160 atoms) using B3LYP/TZVP calculated for the reduced state and the deprotonated Glu126. 20. Table  S6: Natural Population Analysis charges and spin densities calculated for the QM region using model M2 (160 atoms) using B3LYP/TZVP calculated for the oxidized state and the protonated Glu126. 21. Table S7: Frontier molecular orbitals of EH126 in the reduced state. 22. Table S8: Frontier molecular orbitals of EH126 in the oxidized state. 23. Table S9: Frontier molecular orbitals of E126 in the reduced state. 24. Table S10: Frontier molecular orbitals of EH126 second step reaction step. 25. Table S11: NPA charges and spin densities of the stationary points of the e --/H + coupled reaction calculated for the QM region and the protonated Glu126 using model M2 and optimized at ONIOM(B3LYP/TZVP:Amber) level of theory for the reduced state. 26. Table S12: Reported the topological analysis of the electron density of selected bonds on the local minima of the rotation and elimination of 4--OH group using NBO analysis. 27. 28. Appendix: Gas phase and water solution calculations 29. Table S14: DFT/TZVP optimized parameters of the IspH active site model depicted in figure 2 for R and I1 30. Table S15: Optimized parameters of R and I using the simple active site model in figure 2 depicted in the main text. 31. Table S16: NPA charges and spin densities of the reaction profile calculated the oxidized state and the reduced states of the cluster using QM gas phase model depicted in figure 2 of the main text. 32. ONIOM--optimized coordinates of the QM region (M2) of the reaction profile stationary points for the protonated glutamate.
Computational details.
Active site calculations. The initial coordinates of IspH were taken from the crystallographic structure solved to 1.7 Å (PDB code 3KE8). 1 Initial calculations were performed on a simple small model of the active site missing the pyrophosphate group (see Figure 2). This model includes the iron--sulfur cluster, its coordinating thiolates ( Cys 12,96 and 197) and the substrate represented by 2--methylbut--2--enyl alcohol. Cysteines side chains are truncated at the Cβ, and the broken Cα--Cβ bond is capped by a H atom. In the case of the IspH [Fe 4 S 4 ] cluster, the antiferromagnetic (AF) coupled state has parallel spin on two iron atoms aligned opposite to the spin on the other two irons. In practice, BS-DFT 2,3 states were obtained by partitioning the system into the appropriate fragments to generate a specific AF state. The four iron atoms (Fe1--4) were divided into four separate fragments and the remaining part of the system into a separate fragment. Six AF states were generated, corresponding to the following spin combinations on the Fe atoms: ααββ, αβαβ, αββα, βααβ, βαβα, and ββαα. All the calculations were carried out with the B3LYP functional 4--7 and the all--electron triple--ζ TZVP 8,9 basis set using the G09 program. 10 Two oxidation state of the cluster were considered, corresponding to the reduced [Fe 4 S 4 ] + and the oxidized [Fe 4 S 4 ] +2 states. All the broken symmetry states were generated using the fragment guess approach using Gaussview 5. 11 Figure S1: Representation of the [Fe 4 S 4 ] cluster with the carbon skeleton of the substrate, and the numbering used in the discussion.
Since Greco et al 12 have shown that the Mulliken charges of the [Fe 4 S 4 ] clusters are scarcely sensitive to the coupling pattern between the iron sites, we have calculated the restrained electrostatic potential (RESP) charges (necessary for the ONIOM calculations) for the cluster, the coordinated cysteines and the complete HMBPP substrate using the most stable BS wavefunction. Geometry optimizations were performed for all the generated BS states and the most stable state was selected for the reactivity study. Frequency calculations were performed in order to characterize the located stationary points as minimum energy or first order saddle point structures. All the reported energies are the electronic energy of the system. ONIOM Calculations. Starting from the IspH coordinates (PDB code 3KE8), protons were added using the HBUILD facility implemented in CHARMM 13 with the AMBER force field. 14 Parameters for the HMBPP substrate were constructed using ACPYPE (AnteChamber PYthon Parser interfacE), 15 the General Amber Force Field (GAFF) 16,17 and the RESP 17 charges calculated with the Antechamber program, 17 based on the ESP charges calculated at DFT/TZVP level using G09. Molecular mechanics (MM) relaxation of the whole system with fixing the substrate and the iron--cluster was performed to remove clashes between atoms. The MM optimized structure was used as the initial structure for the ONIOM calculations. All lysines and arginines were considered positively charged, while aspartate and glutamate were considered negatively charged, except for glutamate 126 that was considered in two states, namely protonated (neutral) and deprotonated (negatively charged). All the cysteines coordinated to the iron--cluster were considered as deprotonated. In the Quantum Mechanics/Molecular Mechanics (QM/MM) method, the enzyme is divided into two parts: an inner part treated at QM level and an outer part treated at MM level. In our case the inner part or QM region is described at B3LYP/TZVP level of theory and the surrounding protein residues (MM region) is described using the empirical AMBER force field. The QM region is consisting of the iron--sulfur cluster, the substrate HMBPP, the three cysteines coordinating the cluster (Cys 12, 96 and 197), Thr167, Glu126 and 8 crystal waters inside the active site found important for the geometrical optimization from initial trials. The valence of the cutting bonds at the interface between the QM and the MM regions is completed by adding hydrogen link atom. The cutting was done between the Cα--Cβ bonds. Geometry optimization of the enzyme was carried out at the ONIOM (B3LYP/TZVP: AMBER) with a mechanical embedding of the MM charges (ME) level of calculations without any constrains using model 1 (92 atoms) (see figure  3). ONIOM--electronic embedding (EE) single--point energy calculations were then performed to refine the energetics at the same level and at more extended QM model 2 (160 atoms) (see Figure 3) For these calculations we used the M1 optimized geometry and we partitioned differently the system into QM and MM parts, to have a larger QM part. The approach used to generate the broken symmetry spin states in the gas phase was kept. Thus, different BS states were generated and the most stable spin state was used to model reactivity (see Table S1--3). We have investigated the reaction mechanism of IspH with two different state of Glu126 (protonated and deprotonated). Frequency calculations were performed in order to verify the located stationary points to be minimum (free of imaginary frequencies) or maximum (only one imaginary frequency corresponding to the reaction coordinates) only for the QM region. Natural Population Analysis (NPA) was carried out using Natural Bond Orbital 6 (NBO) program. 18 DFT+U plan wave calculations. Finally, we have rescored the stationary points localized with the ONIOM model with a DFT+U method using the larger QM model M3 (456 atoms). This larger model allowed to check for the effect of the partitioning of the system into QM and MM regions, and to have a better control of the effect of the surrounding residues on the [Fe 4 S 4 ] cluster along the reaction profile. In the plane wave calculations we performed spin--polarized periodic calculations based on DFT in the generalized gradient approximation (using the PW91 exchange--correlation functional) as implemented in the VASP 19--22 code. For the DFT+U calculations, the Hubbard potential was applied to the d orbital of Fe atoms and taken as U eff =U--J=3.2 -1.0 = 2.2 eV. 23 A plane-wave basis set (with a kinetic energy cutoff of 400 eV) describes the valence electrons: 1 electron for H, four electrons for C, five electrons for N and P, six electrons for O and S, and eight electrons for Fe, to include the 4s and 3d electrons. The core electrons were replaced by projector augmented wave (PAW) pseudo--potentials. 24,25 Geometry optimization of key intermediates was performed by constraining the position of the Cα atoms at the boundaries of the cluster. The relaxation of the atomic positions in the supercell took place until energy differences are smaller than 0.001 eV. The clusters are placed in a repeating cubic box with an edge length of 32 Å, large enough to prevent interaction between the cluster with its image. Figure S2: Representation of the different QM models (M1--M3) used in this work. Model M1 (92 atoms) is used for the ONIOM--ME geometry optimizations. Model M2 (160 atoms) is used in the ONIOM--EE calculations to refine the energy of the M1 optimized geometries. Model M3 is used for the DFT+U calculations (456 atoms).                Table S12. Reported the electron density (ρ(r)) in a.u. and its laplacian (s 2 ρ(r)) at CPs located at the interatomic distance of selected atoms. ρ(r) and s 2 ρ(r) are reported as the sum of the alpha and beta contributions.

Appendix: Gas phase and water solution calculations.
In the gas phase calculations, the model depicted in figure 2 was used to study the 4-OH group rotation and elimination. We have removed the diphosphate group as we loose the hairpin structure of the substrate upon optimization in vacuum. This shows the importance of the enzyme environment to keep the diphosphate in hairpin fold which is necessary for the catalysis. The idea behind the active site calculations is to check the electronic structures of some key intermediates expected to be involved in the reaction mechanism. So the active site calculations are not to conclude on the IspH catalysis rather than to have a general idea about these intermediates. First, we tried to optimize the protonated initial state (the alkoxide state) in which we added one proton to the 4-OH group coordinated to the apical iron atom of the cluster. Upon optimization the proton was migrated to one of the sulfur atoms bound to the cluster and the dehydration of the substrate did not occur.
Using the oxidized state [Fe 4 S 4 ] +2 , the rotation of the 4-OH group is easy to happen with small barrier of only 4.3 kcal/mol in vacuum and 4.9 kcal/mol in solution. Overall solvent effect has no considerable effect on the energetics of the reaction profile except for the rotation of 4-OH group which decreases the stability of I2. For the dehydroxylation we tried to test the two proposed mechanism pathways; the organometallic and the Birch-like pathway. First, we simulated the organometallic pathway by the dissociation of the C-O bond and the formation of η 3 -complex between the allylic moiety and the apical iron atom of the cluster. The dehydroxylation step is rather difficult with considerable high barrier of 63.8 kcal/mol and the reaction is endothermic (37.2 kcal/mol). Second, we simulated Birch-like by the dissociation of the hydroxyl group which then is bound to the cluster and formation of the free radical on the substrate. This step has lower barrier than the organometallic pathway and the reaction is less endothermic.
Concerning the electronic structures depicted in scheme 2, Table S16 reported the NPA charges and spin densities of the reaction profile stationary points. There are no any significant spin densities localized on the substrate from R to I2. Limited spin densities are located on C2 (-0.2e) and C4 (-0.2e). I2 and I3 are η 3 -complexes and are agreeing well with the organometallic pathway though which reaction is kinetically unfavorable. This finding evidences the importance of the protein environment on the dehydroxylation step and its role in the stabilization of the reaction intermediates and transition state. I2' has significant spin density (-1.0e) transferred from the cluster located mainly on C2 (0.2e), C3 (-0.6e) and C4 (-0.6e). I2' is the free radical via which the Birch-like reduction of the substrate occurs using the cluster.
Scheme S1. reaction profile of the IspH catalysis using active site model depicted in figure 2. In A) the reaction profile used the oxidized state [Fe 4 S 4 ] +2 , the first value in parenthesis is ΔE and second value is ΔE in solution of water. In B) is the reaction profile using the reduced state [Fe 4 S 4 ] + . All reported calculations are carried out using B3LYP/TZVP level of theory.
Using the reduced state [Fe 4 S 4 ] + , the situation does not change a lot the same relative tendency between the organometallic and Birch-like pathways is again applied. Also, limited spin densities are localized on the substrate in INT1, INT2, and INT3 complexes (see Table S5). In the same way the free radical formation on I2' is evidenced by the important spin densities localized on C2 and C4 of the substrate (see Table S17).
Further, we considered state [Fe 4 S 4 ] 0 in which all the iron atoms have Fe (II) oxidation state. On optimization of R using this state, does not provoke any rotation or elimination of the 4-OH group. So, the hypothesis stated that the electron transfer triggers the rotation or dehydroxylation of 4-OH group is ruled out. On conclusion of the simple model calculations; using the oxidized and the reduced states of the cluster, we could not observe any evidence of rupture of C-O bond initiated by the electronic transfer to the substrate. The reaction is easier on the surface of the reduced state than on the oxidized state, notably the rotation of the 4-OH group which is much more favorable using the reduced state.