Magnetc Torque in Superoxide Ion is the Main Driving Force of Dioxygen Activation in Aerobic Life

paired; therefore reactions catalysed by oxidases and oxygenases have to involve intersystem crossing (ISC), that is a total spin change in the state multiplicity during bio oxidation. These reactions are strictly forbidden in the ordinary non-relativistic quantum chemistry. In order to overcome this severe quantum prohibition and sovereign limitation of dioxygen-induced metabolism, oxygenation enzymes require usually a redox cofactor or paramagnetic metal cofactor for effective catalysis. The spin-containing metal ions have no formal spin prohibition for reactions with dioxygen. But many oxidative enzymes include the metal-free flavin or pterin cofactors; their catalytic activity in respect to O 2 still remains mysterious in modern biochemistry and medicine. Last decades have shown, that some oxygenases can catalyse dioxygen incorporation into organic substrates even in the absence of any enzymatic cofactor. The intriguing mechanism followed by those cofactor-free enzymes which enable to provide ISC and overcome spin prohibition has been unraveled recently on the ground of common idea about specific magnetic properties of dioxygen open shell. Similar spin-orbit coupling effects are typical for O 2 molecule and for some reactive oxygen species (ROS). These spin-orbit torques are vitally decisive forces for all aerobic life.

Dioxygen (O 2 molecule) is a biradical with two unpaired electron spins, while most of organic substances have all electron spins paired; therefore reactions catalysed by oxidases and oxygenases have to involve intersystem crossing (ISC), that is a total spin change in the state multiplicity during bio oxidation. These reactions are strictly forbidden in the ordinary non-relativistic quantum chemistry. In order to overcome this severe quantum prohibition and sovereign limitation of dioxygen-induced metabolism, oxygenation enzymes require usually a redox cofactor or paramagnetic metal cofactor for effective catalysis. The spin-containing metal ions have no formal spin prohibition for reactions with dioxygen. But many oxidative enzymes include the metal-free flavin or pterin cofactors; their catalytic activity in respect to O 2 still remains mysterious in modern biochemistry and medicine. Last decades have shown, that some oxygenases can catalyse dioxygen incorporation into organic substrates even in the absence of any enzymatic cofactor. The intriguing mechanism followed by those cofactor-free enzymes which enable to provide ISC and overcome spin prohibition has been unraveled recently on the ground of common idea about specific magnetic properties of dioxygen open shell. Similar spin-orbit coupling effects are typical for O 2 molecule and for some reactive oxygen species (ROS). These spin-orbit torques are vitally decisive forces for all aerobic life.
the first radicals, which can initiate a radical-chain process thereby removing the spin-forbidden character of O 2 reaction with organic substances. Such type of dioxygen activation is impossible in-side the living cell since the radicals would burn the cell.
Aerobic organisms use special enzymes, which involve magnetic perturbations affording to induce ISC and brake the severe spin selection rule for two unpaired electrons of dioxygen during bio-oxidation of organic matter; that is to overcome spin selection and sever quantum prohibition for triplet O 2 biradical to react with diamagnetic organic substances. Magnetic spin catalysis of concerted reactions of molecular oxygen in the enzyme active center does not correspond to the classical chemical concepts and common organic reaction rules. One has to stress that only magnetic They are important for all aerobic evolution, photo-synthesis, appearance of reactive oxygen species and superoxide dismutase, oxi-dative stress and signalling functions in plants.
The problem of molecular oxygen activation is a longstanding task in bio-chemistry [1][2][3][4][5][6]. In contrast to the majority of stable organic substances, M in Eq. (1), which usually are dia magnetics, since their electron spins are paired and the total spin quantum number (S) is zero, the molecular oxygen (dioxygen) is a paramagnetic gas. That is, the O 2 molecule has a ground triplet state X 3 Σ g with a nonzero electron spin (S=1) produced by two nonpaired electrons at the degenerate highest occupied molecular orbital (HOMO) πg [1]. The presence of spin in the ground state of O 2 leads to a strict quantum prohibition on oxidation of organic substrates by dioxygen, since the reaction products (P = CO 2 , H 2 O, N 2 ) are also diamagnetic species.
The M molecule has a singlet ground state (S=0) and the total spin of reactants is triplet (S=1), while the product has a singlet state again. Thus, combustion of organic matter is strictly spinforbidden if no special initiation by additional radical R, which is responsible for ignition.
The total spin (S=1/2) and its projection on z-axis (Ms=+1/2) are the same in the left and right part of Eq. (2). Thus, the radical-initiated combustion proceeds as radical-chain reaction until the whole fuel M would be exhausted or the chain-transfer radical would be saturated and removed by a scavenger [1]. In the absence of radicals the direct oxidation by dioxygen is spin-forbidden, Eq.
(1); this is the reason why our world had not been burnt when O ∆ oxygen (known as one of the most reactive oxygen species in the oxidative stress) is monitored now in tissues by its NIR luminescence at 1.27μm [9][10][11][12]. Analysis of dioxygen wave-functions and transition moments in the electronic O 2 spectrum sheds light on the role of internal magnetic forces, which make it possible to overcome spin restrictions in both enigmatic phenomena -in light emission and in biological oxidation by dioxygen [1,12].

Oxidizing Power of Dioxygen and its Slaggish Reactivity without Enzymes
We used to take our respiration for granted and do not care much about spin of dioxygen; although, we have to care. The high reduction potential of dioxygen causes its great oxidizing power [3].
Using only thermodynamic backgrounds one can predict that O 2 is one of the best oxidizing agent [7]. But the triplet spin in the ground state of dioxygen prevents spontaneous oxidation of organic matter and its full combustion into puf of smoke and soot. Respiration of aerobic creatures consumes almost 90% of all dioxygen produced by photosynthesis and utilized in the Earth's biosphere [6,19].
In aerobic organisms about 80% of the consumed dioxygen is by cytochrome c oxidase in most aerobic organisms [5,18]. This terminal step of respiration represents the four-electron reduction of dioxygen in order to produce two water molecules, Eq. 3 [5,6]: The overall resulting reduction potential of reaction (3) is equal +0.815 V versus NHE (normal hydrogen electrode); this means that such reduction is highly favored in terms of thermodynamics [5,[13][14][15][16][17][18][19][20]. Much of the rest of the consumed dioxygen besides respiration, Eq. 3, is utilized during metabolism for biosynthesis of proteins and other useful molecular substrates. This biosynthesis is catalyzed by monooxygenases or dioxygenases. With these enzymes one or two oxygen atoms from dioxygen molecule are incorporated into the final products, respectively [17,18]. The overall reduction, Eq.
(3), usually proceeds through a series of one and two electron transfer steps [2][3][4][5]. These reactions are strongly favored by reduction potentials expecting the one-electron reduction of O 2 to produce anion-radical superoxide 2 O •− [5,19]. The late process has a reduction potential equals -0.33V versus NHE; this relatively low reduction potential for one-electron transfer to dioxygen is an important factors which limits the kinetic reactivity of O 2 [5].
But this is not the most important factor! The point is that the high oxidizing power stored up in O 2 molecule cannot be realized until the first one-electron jump and reduction to O 2 •will be produced.
And the following reaction step in the enzyme active center has to proceed in a concerted manner with the same reducing agent E, which is responsible for electron transfer to O 2 . This means that the  [5,6]. Glycolysis still exists and takes place in the cytosol of modern eukariots in some emergency cases.
But it was the only source of energy until the GOE time when O 2 gas became widespread available on the Earth in air and oceans.
The tricarboxylic acid (Krebs) cycle using dioxyen provides 32 ATP molecules, instead of two. Thus, much more free energy of adenosine triphosphate (ATP) became available to plants and animals and provided a breakthrough in evolution [5]. The advent of triplet dioxygen increased aerobic metabolism dramatically and made global impacts on all environment. What was the role of O 2 electron spin in this Great Oxidation Event? Let us try to collect first the well-known facts.
One can consider mitochondria created and evolved after the GOE [5]. These mitochondria gave to aerobic cells much more energy exploiting oxidative phosphorilation with new and more complex morphology of inner membranes [5]. These are the places of the tricarboxylic acid cycle and the OP realization by which a large number of ATP molecules are produced from organic fuel. This is done through the electrochemical proton gradient, which is generated across the inner membranes by the high-energy electrons, which are passing along the electron transport chain [6]. But the role of mitochondria in living organisms extends far beyond oxidation of glucose via oxidative phosphorilation; it includes synthesis of haem, hormones, amino acids and many other molecules used for metabolism [7,18]. The recently discovered new role of mitochondria is their involvement in apoptosis and ion homeostasis through the signaling functions of ROS [8]. During the OP process mitochondria utilize dioxygen to generate ATP, but conjugation of this process with the electron transport chain can lead to O 2 partial reduction and to superoxide anion generation. This is the most important reactive oxygen species being the ancestor of other ROS, which are partly reduced forms of dioxygen: the hydrogen peroxide (H 2 O 2 ), very reactive hydroxyl (OH • ), peroxyl radicals (ROO • ) and the singlet Highly likely, that ROS appeared on the Earth during GOE together with the first photosynthetic dioxygen and ROS have been a permanent companion of aerobic evolution ever since [8].
In addition, one can take into account the highly-reducing milleu and high lev-el of reduced iron in the ancient oceans which provide efficient conversion of the first photosynthetic dioxygen  3,14]. This type of spin catalysis is rather simple and determined by exchange interactions [3]. Formally, catalysis by metal cofactor is allowed by spin-selection rules and its efficiency depends on the differences in exchange integrals for different electron pairs in the transition state region Otherwise, the evolved metal-free cofactors are more complicated in terms of their spin dynamic mechanisms.
These spin transformations are met in numerous flavoenzymes [2,19]. Flavins and related pterins are extremely miscellaneous and versatile cofactors, which capable to activate O 2 [18]. trends stress the great importance of the late role especially for plants [8,18]. Physical, chemical and biological principles by which flavoenzymes realize catalytic action upon dioxygen have been the subject of intense studies during last sixty years [5][6][7]18].

Oxidases and Monooxygenases with Flavin Cofactors
Current understanding of these rules is based mostly on seminal works of Vincent Massey [7,19]. A wealth of kinetic, mechanistic, computational and spectroscopy data [7] represent his consistent view on the functional and structural properties of flavin-containing oxidases and oxygenases. However, not all aspects of flavoproteincatalyzed bioreactions have been solved yet [18]. The major area of the flavoenzyme research still concentrates on elucidation of the electronic mechanisms and molecular basis for the dioxygen spin activation [1,22].
Similar spin flip occurs when one oxygen atoms from O 2 molecule is incorporating into the products; in this way monooxygenases activate dioxygen through spin catalysis by forming the C(4a) peroxyflavin intermediate, which then reacts with substrate and inserts one oxygen atom into substrate by ordinary chemical rearrangement [18,22]. Free reduced flavins also react with dioxygen in solvents quite efficiently, forming oxidized flavin and hydrogen peroxide faster than in one second [19]. Stopped-flow spectra, EPR and rapid quenching techniques were used for such rapid reactions in order to understand their high rate in spite of the spin prohibition [7]. The oxidized flavin (Flox) was monitored by its strong absorption increase with a maximum at 450nm (Figure 1).
The short delay in the beginning indicated a reaction intermediate  proposed the following reaction scheme [19]: EPR spectra of semiquinones (Flsq) show a large spin density on C(4a) atom [7]. The product was identified as the C(4a)-flavin hydroperoxide ( Figure 2) by detection of the 450 and 370nm absorption bands (Figure 1). In aqueous media this rather unstable product transforms heterolytically to the oxidized flavin (Flox) and  [19], was generalized for flavoenzymes ( Figure 2) and postulates the following scenario. As in the solvent case, the electron transfer to O 2 produces the caged triplet radical pair in the active cite of enzyme, which is capable (by unknown rea-sons) to undergo the T→S transition [18,19]. After such intersystem crossing, de-noted  Massey [19] and all his ancestors [20] accept the spin flip at the radical pair stage in Eq. (3) for granted (without any comments or explanations). One can propose that Massey has conceived the arguments of the well-known radical pair theory (RPT) based on the cage effect in solvent and account for hyperfine coupling with nuclear spins. RTP has been proposed 50 years ago [33] being very popular in nineties [19]. But, the RTP ideas cannot be applied to enzyme active center, where the radical pair is not separated in two radicals by a long distance (> 10nm like in the solvent cage) [21].

Spin-Orbit Coupling in Dioxygen Open Shell
Now we have to consider O 2 structure in more details. The dioxygen molecule in the triplet ground state characterized by the following electronic configuration (1σ g ) 2 (1σ u ) 2 (2σ g ) 2 (2σ u ) 2 (3σ g ) 2 (1π u ) 4 (1π g ) 3 [9]. The first 14 electrons  of L z operator with eigenvalues 0, ±2ћ, 0. Exchange interaction stabilizes the triplet state |3Sg-> as the lowest one; the degenerate singlet states |1Δg> are higher in energy by 22kcal/mol, while the |1Σg+> state is the highest one with a total energy 36kcal/mol [9].
Wave functions of these states in the form of Slater determinants are: Some symbols are omitted here and only two-electronic parts of wave functions are shown [1]. Spin orbit coupling (SOC) between S and L angular momenta is known to be responsible for magnetic spitting of orbitally degenerate spin multiplets in atoms and diatomic molecules [9]. For diatomics such splitting is possible for states with the wave functions being eigenfunctions of the L z operator (L z Ψ= Λћ Ψ), for which Λ≠0 [9]. Naturally, magnetic spitting indused by SOC is possible only for states with spin quantum number S≠0 [9]. In such case the spin and orbital angular momenta projections on the molecular axis are observable values and their coupling depends on mutual orientation of both magnetic moments. This provides a well-seen SOC-induced splitting of the molecular Π, Δ, Φ multiplets (typically of the order 0.01eV in light molecules) [36]. In this work we use a simple semiempirical approximation for spin-orbit coupling (SOC) operator [10] , . .
Here ζ А -is a spin-orbit coupling constant for the valence shell of atom A, deter-mined from atomic splitting, -are the orbital and spin angular momenta operators (in ћ units) for the i-th electron [1]. Expectation value of this operator is equal zero for the ground triplet state X 3 Σ g -of the O 2 molecule, since it has Λ=0. But the S z =0 component of the triplet state, shown in Eq. (5), is still slightly split from the upper S z = ±ћ components in the second order of perturbation theory, ΔE(2), since the triplet and singlet states in Eq.
(5) are mixed by spin-orbit coupling matrix element [11]: This integral is reduced to the spin-orbit coupling constant for the atomic oxygen O(3P) ground state and this is the largest possible energy of magnetic internal interaction in all oxygen all atrops. In the absence of external magnetic field the spitting between spin sublevels ms =0 and ms =±1 of the ground triplet state X 3 Σ g -of the O 2 molecule, produced by SOC contribution from Eq. (7) [10] is equal to: Here the S-T energy gap is equal 1.63 eV (from experiment [9]). The calculated ΔE(2) spitting is equivalent to 2.42cm -1 , which provides 61% of the total observed zero-field splitting (ZFS=3.98 cm -1 ) [10]. The rest is determined by direct spin-spin coupling of two electrons [45][46][47]. This rather small measure of internal magnetic forces in the dioxygen ground triplet state have no direct connection with the origin of O 2 activation by enzymes. However, it is important for the singlet dioxygen excitation and quenching in solvents [11][12][13]. Account of Eq. (7) in the first order of perturbation theory provides a mixture of two states from Eq. (5).
With account of spin-orbit coupling, Eq. (6), in the first order of perturbation theory these four configurations will be spit in two sublevels: . This is in a good agreement with experimental result for O 2 -• ion: E( 2 Π 1/2 ) -E( 2 Π 3/2 ) = 160 cm -1 (0.02 eV) [48]. Such energy is relatively large for SOC in light molecule [49,50] and is determined by the observable orbital angular momentum of the 2 Π state (L z =ћ). It is million times larger than a typical hyperfine coupling used in the radical pair theory to induce T-S flip [33]. The same type of orbital rotation around z axis, as in Eq. (7), determines this internal magnetic energy. The splitting is inverted (Ω=3/2 is lower than Ω=1/2 sublevel), since the (1πg) 3 open shell is more-than-half occupied [14]. Here Ω is the total angular momentum projection Ω=|Λ+ Sz| [9]. Now we can apply this result to the Massey's mechanism of Eq. (3) [19], including our quantum cell notation [] for molecular orbitals and the curly brackets for the enzyme active center: The triplet→singlet quantum transition in the enzyme active that tends to cause spin rotation in the mechanism described by Eq.
(11) is unusually strong for such light molecule as dioxygen. That is why the Massey's mechanism is so efficient in many enzymes [22][23][24][25][26][27][28][29][30]. The T-S matrix element of SOC operator in enzyme active center described by Eq. (11) is equal to i(½)ζ O = i0.01 eV being imaginary value [2]. Calculation of the T→S transition rate constant includes the square of this absolute value [4]; thus, the imaginary unit (i=√-1) does not matter for the measurement of rate constant and can be omitted. The SOC energy of 10 -2 eV realized inside small O 2 -• species (about 0.2nm diameter) corresponds to magnetic force of about 10 -6 dyne. This is relatively strong force for quantum microparticles. We mean the force exerted between spin magnet and orbital movement (πg,x → πg,y rotation) of electrically charged particle (electron). Such force is much stronger than those magnetic forces, which deter-mine rate of T-S transitions in phosphorescence of organic molecules [50]. p-hydroxyphenyl acetate hydroxylase [7,19]. The measured rate constants demonstrate pseudo-first-order character being linear in dioxygen concentration with effective bimolecular rate constant of the order 10 6 -10 7 mole-1 s -1 [18,19]. These reactions are much faster than O 2 reactions with free flavins reduced in solvents with rate constants about 250 mole -1 s -1 [5,18]. This means that protein environment of enzyme not only as-sists in the electron transfer to O 2 [4], but also enhances vibrational maintenance of intersystem crossing process [39].