Spin-orbit coupling effectS in o 2 activation by cofactor-independent 2 , 4-dioxygenaSe

The O2 (dioxygen) is paramagnetic molecule with two non-paired electron spins and triplet ground state (S = 1) while majority of organic molecules are diamagnetic species; they have all electron spins paired and the singlet ground state with the total spin S = 0. Oxygenases catalyze a concerted insertion of the triplet dioxygen into organic (diamagnetic) molecules in a strictly spin-forbidden process and this puzzle is not solved so far in modern enzymology. Many oxidases and oxygenases utilize the π-conjugated organic cofactor (like flavins, pterins) in a singlet ground state and reaction of cofactor with O2 is still spin-forbidden. It is clear that the protein environment in the enzyme active-site “helps” in some way to overcome spin prohibition, but this environment is definitely diamagnetic and the spin-puzzle still exists. Some oxidases and oxygenases use paramagnetic metal ions as a cofactor; in this case the spin prohibition is formally reduced. In recent years, a numbers of oxidative enzymes are discovered which do not contain any cofactor. In the present work, we considered a rather popular cofactor-free bacterial 2,4-dioxygenase and its oxygenolytic reactions with 2-nalkyl-3-hydroxy-4(1H)-quinolones (aHQ’s). We presented results of quantum-chemical calculations of intermediate diradical proposed recently for direct reaction of dioxygen with aHQ substrate and made conclusion about the mechanism of spin-catalysis.


D
ioxygen (O 2 ) possesses the triplet ground state X 3 Σ g -, which implies strong quantum restrictions on its spectra and biochemical reactivity [1][2][3][4][5][6][7][8][9][10].The whole aerobic life strongly depends on the kinetic barriers to dioxygen reactions; O 2 is used as an oxidant in respiration of mammals reducing food to water and carbon dioxide and in many oxidative metabolic processes distributed from bacteria to human.Typically dioxygen in its ground triplet state is chemically non-reactive to organic substrates, because O 2 reaction with the singlet-state organic molecule to form diamagnetic products is strictly spin-forbidden [1][2][3][4].This is due to quantumchemical reasons determined by pure quantum nature of the spin notion [10].In this sense oxidative enzymology is a pure quantum-chemical science, though experimentalists do not like to discuss spins [3,4].Oxygenase enzymes can effectively catalyze O 2 reactions which appear to the normal chemical intuition as very strange and exotic [4].At least, they seem impossible in synthetic chemical laboratory.
The present work is devoted to the spin-selection rule analysis for some particular dioxygenases which were recently discovered in bacteria [11][12][13][14][15][16][17][18].Dioxygenases catalyze incorporation of two oxygen atoms from O 2 into their organic substrates as a reme dy to initiate metabolism [12].These enzymes provide key functions for human health and were used in development of antitumor therapy [13].They are also important for plants participating in signaling functions [11,13].Bacterial dioxygenases are interesting for biotechnology being involved in harmful substances biodegradation [13].Thus, the problem to overcome spin prohibition in O 2 activation by these enzymes is of very general importance for biology.
Typically, oxygenases use cofactor in the form of transition metal or highly unsaturated dyes (like flavins, folates or pterins) with particular redox proper ties.The reduced cofactor is a prerequisite for efficient oxygenolysis.During last two decades seve ral oxygenases have been discovered which do not contain any cofactor [11][12][13][14][15][16][17][18][19][20][21].This stresses the problem of spin prohibition overcoming and raises the general question of how such enzymes do activate dioxygen.
Cofactor-free oxygenases.One of the first cofactorindependent enzymes was identified by Shen et al. [20].It was the tetracenomycin F1 monooxygenase (TcmF1) being involved in biosynthesis of aromatic polyketides [20].Shen et al. also proposed the first mechanism of cofactorfree oxygenation for the TcmF1 example [20].It assumes the substrate and protein radicals formation before O 2 activation [20].This mechanism seems to be unreliable because of high activation energy barrier.
The structure of HOD has been studied by X-ray crystallography analysis in the native state as well as in the complex with its natural MHQ substrate [15].The structures of HOD complex with the NAA reaction product, and with chloride as dioxygen mimic, have also been studied.All these structures have been used in DFT simulations of the catalytic reaction path [12][13][14].We also use these structures in our DFT geometry optimizations.
Detailed DFT calculations [13] show the role of the nearest protein environment of HOD enzyme in catalysis of reaction (1).The most important is hystidine residue, His 102 , in the active-site acidic dyad His 102 , Asp 126 [15].At the first stage of reaction (not shown in Scheme 1) a proton from O 3 H group of MHQ substrate (1) is transferred to hystidine residue (His 102 ) of enzyme [11][12][13][14][15].Thus, the substrate SH (denoted MHQ) became S -anion and this is the starting point in the reaction mechanism (Scheme 1).
At the same time the O 4 atom is additionally stabilized by interaction with OH group of the Ser 101 residue [13].In the HOD protein scaffold the first acidic dyad His 102 , Asp 126 together with Ser 101 residue form an important catalytic triad which plays a crucial role in stabilization and activation of substrate [13,15].In Scheme 1 the resting state ( 3 r) of catalysis is shown as the first step when dioxygen enters the active site of HOD.Deprotonated MHQ (S -singlet anion) can provide electron transfer to O 2 and from this point we have two different opportunities.Only one of them is shown in Scheme 1, being established by DFT calculations [13].
According to [13] a direct O 2 attack on substrate S -anion leads to a covalently-bound 3 i 1 triplet intermediate through a large barrier of 17.4 kcal/mol.The spin inversion between 3 i 1 and 1 i 1 would occurs at the minimum energy crossing point (MECP) [13].The authors [13] did not achieved the MECP optimization and did not conclude about the driving force for TS transition.But they insist on the direct oxygen attack mechanism shown in Scheme 1.
The other mechanism proposed by Fetzner et al. [15][16][17][18] includes electron transfer from reduced substrate S -to O 2 and the triplet radical pair formation between subatrate radical (S • ) and superoxide (O 2

•
) initially formed in the triplet state (not shown in Scheme 1) undergoes the tripletsinglet (TS) transition by analogy with the well-known mechanism of Massey [22] for flavincontaining oxygenases and then recombines into the proposed peroxide intermediate 1 i 1 [18].
Here the spinflip mechanism in the radical pair between flavin semiquinone radical and superoxide ion was postulated, probably, on the ground of radical pair theory (RPT) [23].Though Eq. ( 2) was proposed for free flavins initially reduced in solvents it was thought to be applied for all O 2 -activating enzymes which contain flavin cofactor [22].
The weak point here is connected with the nature of driving force for the spin flip in Eq. ( 2).Massey made no comments about this.One can propose logically that Massey has taken into account the ideas of RPT [23] which were popular that time.The square brackets in Eq. ( 2) denote the solvent cage for radical pair which is really big and embraces a micro-part of solvent volume [23].It means that two radicals can be far separated before their secondary collision and spin evolution proceeds during free diffusion of radicals inside solvent cage between two collisions.According to RPT the driving force for spin inversion in such radical pair is represented by very weak electron-nuclear spin-spin interaction (hyperfine coupling, 10 -4 cal/mol) inside each radical [23] being additional reason for external magne tic field effects [24].By no means RPT can be applied neither to flavoenzymes no cofactorfree oxygeanses, since the enzyme active cite is very limited in space.Of course, some limited diffusion is possible (other wise O 2 would never penetrate the enzyme active cite) but secondary collisions in the flavoprotein cage are not likely.Thus, the RPT arguments with their driving force for spin inversion can not be accepted for enzymes.This could be an additional argument against the "substrate-assisted" mechanism and electron-transfer concept of Fetzner et al. [1618] being in favour of direct dioxygen attack proposed by Hernandez-Ortega et al. [13].
Contrary to these arguments, in the present paper we want to discard conclusions of Ref. [13] and support the electron-transfer concept of Fetzner et al. [16] on the ground of the MECP calculation and magnetic forces responsible for TS transition.

Method of calculations
We have started with the optimized geometry of the 3 i 1 triplet intermediate (Scheme 1) published in supplementary [13].We have recalculated 3 i 1 structure by the density functional theory (DFT) with the B3LYP functional [25,26] and 631 G(d,p) basis set [26] by spinunrestricted DFT method for the triplet state.The minimum energy crossing point has been found using method of Harvey et al. [27].It means that the complete active space selfconsistent field (CAS SCF) method was applied to find MECP geometry using various active spaces.The best conical intersection was obtained with the (16,11) CAS, which includes 16 electrons in 11 orbitals (8 occupied and 3 unoccupied MO's).This choice is reasonab le since only 3 MOs, discussed below, are the most important in the CAS wavefunctions.
The MECP was optimized using a steepest-descent approach [27] with the difference of the energy gradients derived from stateaveraged CAS SCF calculations.These gradients were minimized for both T and S states first.The MECP was characterized as a minimum on the crossing seam between T and S potential energy surfaces by diagonalization of the projected effective Hessian matrix [27].On the found MECP geometry we also made a single-point CASPT2 calculation with better account of dynamic correlation effects [28].CASPT2 was realized in the form of extended multiconfiguration quasidegenera te method at the second order of perturbation theory (XMC-QDPT2) [30].
The SOC matrix elements between the singlet state wave-function and each spin sub-level of the triplet state were calculated using the CASSCF and XMCQDPT2 wavefunctions.We used an effective singleelectron approximation for SOC operator with specially calibrated nuclear charges for spin-other orbit interaction account as it was implemented in the GAMESS (US) program [29].All calculations were done with the Firefly quantum chemistry code made in MGU by Granovsky [28].Firefly package is partially based on the GAMESS program [29] but includes modern versions of CASPT2 (XMC QDPT2) method for open shell calculations.

results and discussions
The new mechanism of HOD catalysis for oxygenolytic breakdown of the quinolone substrates (Scheme 1), proposed by HernandezOrtega et al. [13], considers a direct O 2 attack on substrate S -anion ( 3 r step) leading to a covalently-bound 3 i 1 triplet intermediate which undergoes TS transition into its singlet 1 i 1 counterpat.The authors did not succeed in optimization of the minimum energy crossing point (MECP) between T and S hypersurfaces and did not calculate the driving force for TS spin inversion [13].They rejected the electron-transfer mechanism of Fetzner et al. [16,18], which is analogous to dioxygen activation by flavoenzymes, Eq. ( 2) [22], where the radical pair (S • … O 2

•
) is formed in the HOD cavity and the TS transition occurs inside this RP.Both theories [13] and [18] say nothing about the magnetic force nature responsible for the spin flip.
Hernandez-Ortega et al. [13] refused from the electrontransfer mechanism [16] because they did not succeed in calculation of radical pair (S • … O 2

•
) inside the studied models of the HOD cavity.Diffe rent number of amino-acid residues were simulated based on the X-ray analysis of HOD (all include the important catalytic triad His 102 , Asp 126 and Ser 101 and other residues in vicinity of substrate S -) [12,13], but the reaction (3) was not supported by DFT calculations [13].
The UB3LYP optimization converges to the ground state that is better assigned as 3 r in Scheme 1.But some spin transfer was still observed; spin density of 1.6 on dioxygen moiety and 0.4 on the substrate were fixed for 3 r model in enzyme [13].This means that with better protein arrangement and more correlated wave-functions the larger spin density transfer, close to Eq. ( 3) could be achieved.
The selfconsistent field methods are known [14] to meet convergence problems when they attempt to reproduce radical pair structure (3) lying at higher energy than the simple 3 r alternative (with singlet closedshell S -substrate and the clear triplet O 2 wavefunctions).The difficulty with convergence achievement is not an indication of the intrinsic instability of the (S • … O 2

•
) radical pair in the HOD cavity.Thus, P. Silva has analyzed the kinetic and thermodynamic parameters of reactions (3) using the Marcus theory [14], which is based on separate calculations of the donor and acceptor energies.Silva has calculated radical pairs for various quinolones (R=F, COH, NO, CN, NO 2 , NH 2 , COO -, CH 3 in Scheme 1) with superoxide at 212 nm distances [14].The calculated rate constants for electron transfer (ET) reactions (3) exceed 0.1 s -1 .Comparison of these reaction and activation energies to the energy of MECP (or the 3 i 1 intermediate energy [13]) indicates that ET reaction with the MHQ substrate is favored over reaction through MECP by more than 8 kcal/mol [14].Thus, Silva comes to conclusion that generation of the The driving force for the spin flip in cofactor independent enzymes was considered [14,21] to be spinorbit coupling (SOC) as it was proposed for the first time for oxidases containing flavin cofactor [1,7].The SOC mechanism was also proved to be correct for explanations of many optical and chemical properties of dioxygen [1][2][3][4][5][6][7][8][9][10] and its application for O 2 activation by cofactor-free dioxygenases will be considered later at the final conclusions of this paper.
Now we want to check applicability of the whole mechanism (Scheme 1) proposed by [13] and to calculate MECP for SOC estimation at the 3 i 1 → 1 i 1 transition.Direct dioxygen attack on C 2 atom of substrate MHQ leads to a C-O bond formation and TS transition has to occur at this stage (Scheme 1) [13].
The minimum energy crossing point between the 3 i 1 and 1 i 1 potential energy surfaces optimized by the Harvey algorithm [27] with the CASSCF (16,11)/631G(d,p) method is presented in Fig. 1.The state-averaged molecular orbitals which determine mostly the openshell wavefunctions of the T and S states are shown in Fig. 2. One should note that the MECP energy and the structure of the intersecting T and S states wavefunctions strongly depend on the active space choice, but geometry of nuclear displacement is more-or-less constant and corresponds to peroxo compounds in T and S states shown in Scheme 1.Even the covalent structure of 3 i 1 peroxydiradical is rather different from the closedshell singlet state of peroxide intermediate 1 i 1 .The MECP structure is rather similar to the local minimum of the 3 i 1 state.The triplet 3 i 1 looks like diradical with one non-paired electron on the peroxo -O-O group (local radical center on the terminal atom with spin density 0.7 and spin 0.3 at the distal atom) and the second non-paired electron being delocalized in the ring (spin density on carbon atoms C 4 and C 3 is equal 0.24 and 0.15, on O 4 and O 3 oxygen atoms -0.21 and 0.29, respectively).Thus, the shown 3 i 1 structure in Scheme 1 does not fully correspond to the calculated spin density distribution.
The MECP structure (Fig. 1) is rather similar to the 3 i 1 diradical intermediate calculated [13,14].The substrate-oxygen bond (1.499 Å) is the same; the O-O bond is shorter in MECP (1.35 Å) than in diradical (1.38 Å) [13] being more close to free superoxide (1.334 Å).In the singlet state 1 i 1 some electron transfer from the O 3 atom occurs to the terminal oxygen of peroxo-group in agreement with the simplified covalent structures of Scheme 1.In the triplet state the π p -π 1 configuration dominates with small admixture of the π p -π 2 configuration wave function.The CAS structure of the singlet state is more complicated and includes some contributions from the closed shells.
At the CASSCF optimized geometry of the minimum energy crossing point we have recalculated the wave-functions and energies of a number of states with the extended multiconfiguration XMC  31G(d,p) method QDPT2 method [30] in order to obtain the most accurate account of electronic correlation effects for quasidegenerate states.Now the lowest S and T states have different energies (Table ), but their ener gy gap is only 630 cm -1 (0.078 eV), which is practically negligible at the energy scale of Table.Thus, we have calculated the SOC matrix elements with this CASSCF and XMCQDPT2 methods.
At the MECP geometry the orbital structures of the S and T states are only partly different which leads to a relatively small SOC integral for the M s = 0 spin sublevel w 0 = <T 0 |H so |S> = 2.2 cm -1 .The other spin sublevels have even smaller SOC constants: 1.45 cm -1 (M s = 1) and 0.67 cm -1 (M s = 1).This leads to the total SOC constant |w| 2 = 7.39 cm -2 , which can be used in the rate constant calculation [1][2][3].With account of Landau-Zener theory for non-adiabatic TS transition [7] at the minimum energy crossing point and the activation energy to reach MECP [14] we have estimated the rate constant (3.6×10 1 s -1 ), which could be the upper limit for observed reaction.But this rate is too low for experimentally measured kinetics [13,18].
In order to have a large SOC matrix element between T and S states their orbital structures should be different by symmetry elements which correspond to rotation around axes.The π p orbital (Fig. 2) is mostly localized on dioxygen, but π 1 and π 2 MO's are delocalized as π-conjugations in the rings.Onecenter SOC contribution on dioxygen moiety which include orbital rotation is rather small (Fig. 2), thus the MECP structure (Fig. 1) is not favored for strong magnetic perturbation and can not provide an efficient spin flip.
Electron transfer step and formation of radical pair with superoxide ion was proved by direct DFT calculations of glucose oxidase (GO) enzyme during its oxidative half-reaction [7].The maximum large SOC in such radical pair of the type (2) was explained by specific orbital structure of the superoxide ion and its rotation upon TS transition [1].The T and S states in this radical pair can be denoted by the following orbital structures [7] T The curly brackets here denote the cage cavity of the enzyme active site and the square brackets denote MOs.The first square bracket corresponds to the highest occupied MO of reduced flavin adenine dinucleotide and two square brackets of dioxygen represent the doubly degenerate π g,x and π g,y orbitals oriented in the mutually perpendicular directions [2].The TS transition in Eq. ( 4) corresponds to  States energy (cm -1 ) obtained at the MeCP geometry with the CaSPT2 (XMC-QDPT2) method one-electron jump between these MOs which means a rotation of "electron cloud" around dioxygen molecu lar axis z.Such rotation creates a large orbital angular momentum which interacts with spin moment and induces the spin flip [2,3].The SOC matrix element between T and S states in Eq. ( 4) is equal to the maxi mum possible SOC value w = iς O /2 [1][2][3], where ς O is a SOC constant for oxygen atom determined from atomic spectra (ς O = 154 cm -1 ) [2].
With such SOC estimation (w 2 = 5929 cm -2 ) the rate constant of TS transition (10 4 -10 6 s -1 ) is quite competitive with other possible processes in the cage of enzyme [5][6][7] and the electron transfer theory seems highly likely.The same type of spinflip mechanism can be reali zed in the studied HOD 2,4-dioxygenase with the MHQ substrate cleavage to CO and N-acetyl-anthranilate products, Eq. ( 1), if we accept the Fetzner's scheme of electron transfer from deprotonated substrate anion (S -) to dioxygen, Eq.
(3).This scheme is supported by DFT studies [14] and by our multiconfigurational calculations of the minimum energy crossing point at the stage of .The SOC between T and S states in Eq. ( 4) does not depend on the spin of flavin cofactor and can be applied for cofactor-independent oxygenases (FAD cofactor can be equally substituted by substrate).After the TS transition at the electrontransfer stage, Eq.
(3), and generation of the 1 i 1 peroxy-intermediate the reaction follows the path shown in Scheme 1 [13].

1 i 1 2 •
intermediate can proceed through the triplet state ET reaction (3) with subsequent TS transition at the (S • … O ) radical pair stage and recombination of radicals in agreement with Fetzner mechanism [1618].

Fig. 2 .
Fig. 2. The most important molecular orbitals for the S and T states description at the MeCP geometry