12th International Symposium for Bioluminescence

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The non-radical pathway to luminol luminescence requires dioxygenation, but ... Reducing O2 by two equivalents generates hydrogen peroxide (H2O2). The.
MOLECULAR OXYGEN ( O2 ): REACTIVITY AND LUMINESCENCE ROBERT C. ALLEN Dept of Pathology and Laboratory Medicine, Emory University School of Medicine, Grady Memorial Hospital Clinical Laboratory, 80 Jesse Hill Jr Dr SE, Atlanta, GA 30303 USA. Email: [email protected] INTRODUCTION Luminescence occurs when an electron relaxes from an excited state by photon emission. Electronic excitations require relatively high energies. Emission of a blue photon requires about 60 kcal.mol-1 of energy. This quantity of energy is significantly greater than the energies liberated in most biochemical reactions. For example, hydrolysis of ATP to ADP yields about 7 kcal.mol-1. Essentially all chemiluminescence (CL) and bioluminescence (BL) phenomena result from O2-dependent reactions, i.e., dioxygenations and mixed function oxygenations.1-2 These reactions are combustions and O2 is incorporated into the final product. The great electronegativity of oxygen promises reaction exergonicities sufficient for electronic excitation. Compare the reaction of O2 and chlorine (Cl2) with an organic substrate such as ethylene. Reaction with chlorine (Cl2) yields about -51 kcal.mol-1 of free energy while reaction with O2 yields about -87 kcal.mol-1. Cl2 is a potent reactive agent that is biologically lethal in very low concentration, yet we live in an environment that is about 21 % O2. Chlorination reactions are highly exergonic, yet oxygenation reactions are significantly more exergonic. Chlorine reactivity is spontaneous, but direct oxygenation is not. What protects against spontaneous combustion? Although O2 is required for CL and BL, the pathway to oxygenation is indirect. The non-radical pathway to luminol luminescence requires dioxygenation, but reaction with O2 is not direct. Luminol is first dehydrogenated to its diazaquinone by removal of two reducing equivalents, i.e., two electrons (2e-) and two protons (2H+). Dehydrogenation is a type of oxidation that does not require the direct participation of O2. Reducing O2 by two equivalents generates hydrogen peroxide (H2O2). The luminol diazaquinone reacts with H2O2 to yield a dioxygenated product that rearranges to electronically excited aminophthalate, and this excited state relaxes by photon (hν) emission. The net reaction is a simply dioxygenation, luminol + O2 → aminophthalate + N2 + hν, but luminol reaction with O2 is indirect. Why are exchanges of reducing equivalents required to ultimately achieve dioxygenation? What limits the direct reactivity of O2? The answers to these questions can be found in boson-fermion symmetry considerations. The symmetry-based approach described herein is straightforward and consistent with the law of parsimony. Where necessary, fundamental quantum mechanical principles are developed to provide appropriate background material.

PARTICLES AND SYMMETRY Exchange Principle Particles are the stuff that makes up our universe. Particles make up chemistry and biology. All particles belong to one of two symmetry types. They are either bosons (Bose-Einstein particles) or fermions (Fermi-Dirac particles).3-7 According to the exchange principle, a pair of particles, a and b, can be described by a wavefunction, Ψ (a, b), representing the space and spin coordinates of the particles. Exchanging the particles generates a new wavefunction Ψ (b, a). Even if the particles are indistinguishable (e.g., electrons), the particle sites are distinguishable. Each site has a unique spin-state, i.e., spin up (↑) or spin-down (↓). Each combination is distinct. For indistinguishable particles, the result of exchange can differ by no more than a quantum phase factor. The initial state Ψ (a, b) is recovered by a second exchange. There are only two symmetry possibilities. Exchange can be symmetric, Ψ (a, b) = Ψ (b, a), or exchange can be antisymmetric, Ψ (a, b) = -Ψ (b, a).6 Bosons Bosons yield wavefunctions that are symmetric to exchange of a pair of particles; i.e., Ψ (a, b) = Ψ (b, a). Bosons obey ordinary commutation; a x b = b x a. Rotating a boson through 360 degrees, Ψ 360°→ Ψ, returns it to its original state. Bosons are symmetric particles with integral spin. Photons, the force carrier particles of electromagnetic energy, are bosons with zero mass and integer spin. Photons are described by Planck’s equation, E = hν, where E is energy, h is Planck’s constant, and ν is frequency. Bosons can be generated from fermions. Two antisymmetric fermions can couple to produce a symmetric boson. Such products include large bosons with mass. Examples are alpha particles, atoms, e.g., helium (He), and molecules, e.g., hydrogen (H2) and nitrogen (N2). Complex particles composed of an even number of fermions are typically bosons. Most organic molecules are bosons. Fermions Fermions yield wavefunctions that are antisymmetric to exchange of particles; i.e., Ψ (a, b) = -Ψ (b, a). Fermions are antisymmetric particles with half-integer spin. Spin is quantized and is intrinsic to the particle. It appears as multiples of the basic unit ½ħ, where ħ (h-bar) equals Planck’s constant (h) divided by 2π. Fermions anti-commute; a x b ≠ b x a. Rotating a fermion through 360 degrees, Ψ 360°→ -Ψ, changes the sign (the phase) of the fermion but does not return the fermion to its original state. An additional 360 degrees rotation (for a total of 720 degrees), -Ψ 360°→Ψ, is required to return the antisymmetric particle to its original state. Fermions are the solid stuff of the universe and include electrons, protons and neutrons. Large complex systems such as paramagnetic (radical) atoms, e.g., atomic hydrogen (H), and paramagnetic (radical) molecules, e.g., superoxide anion (O2-), are also fermions.

Fermion symmetry requires that any state Ψ must also have a state -Ψ. Only one fermion can populate a specific state. However, two phase-opposite fermions can populate a specific state. In the latter case the two antisymmetric fermions couple generating a symmetric boson. Complex particles composed of an even number of fermions are typically bosons, whereas complex particles composed of an odd number of fermions are fermions. Principal, Radial and Angular Quantum Numbers Atomic hydrogen (H) is composed of a positively charged nuclear proton (H+) and a negatively charged electron (e-). Both H+ and e- are fermions. Since H+ is a thousand-fold more massive than e-, the kinetic and potential energies of e- are described as its “orbit” about the massive nucleus. The orbital wavefunction describes the energy possibilities. Using polar coordinates, the position of e- can be described as its distance, r, from its nucleus, and two angles, θ and φ. The total wavefunction is isolated into 3 separate contributions, Ψ (r,θ,φ) = R(r)Θ(θ)Φ(φ), where R(r) is the radial component, and Θ(θ) and Φ(φ) are the angular components. Solution of each component yields a quantum number. The radial component yields the principal quantum number, n. The angular components yield the azimuthal quantum number, l, and the magnetic quantum number, ml. The principal quantum, n, describes the energy of the orbital. The degree of orbital degeneracy is the square of the principal quantum number, n2. When n = 1, the degeneracy is 12 = 1, yielding the 1s orbital. When n = 2, the degeneracy is 22 = 4, yielding the 2s, 2px, 2py, 2pz orbitals.3 The azimuthal quantum number, l, describes the shape of the orbit and the orbital angular momentum of e-. The magnetic quantum number, ml., describes the number of orbitals with a given value of l. The value of the total orbital angular momentum, L, is L = √[l(l + 1)]ħ. Spin Quantum Number Electrons and other fermions possess intrinsic angular momentum that is independent of orbital motion. This quantum mechanical property is spin, and is described by the spin quantum number, s. Spin is quantized and the magnitude of s is restricted to a value of ½. The total spin angular momentum, S, of a system is expressed by the equation S = √[s(s + 1)]ħ. Intrinsic spin with its value of ½ħ (abbreviated to ½) is a quality of fermions without analogy in classical physics.7 Just as l gives rise to ml, s gives rise to the quantum number ms. Only two values for ms are allowed. When ms = ½, the e- is described as spin up (↑); when ms = –½, the e- is described as spin down (↓). Pauli Exclusion Principle Every e- in an atom is defined by its five quantum numbers: n, l, ml, s, ms. The Pauli exclusion principle states that no two electrons of a given atom can have identical quantum numbers. For an orbit to accommodate two electrons, the

LUMO

Energy

(1s)

σu*

1s

SOAO 2

|2(½)| + 1 = 2 H, doublet multiplicity

1s (1s)

HOMO 1

σg

|2(½ - ½)| + 1 = 1 H2, singlet multiplicity

2

|2(½)| + 1 = 2 H, doublet multiplicity

Figure 1. Electronic configurations of atomic (H) and molecular hydrogen (H2).

Differences between energy levels are not to scale in this or following figures.

electrons must have opposite spins. If one e- has an ms = ½ ( ↑ ), the other orbital emust have an ms = –½ ( ↓ ). As such, the total spin quantum number, S, for the orbital electron-couple is ½ – ½ = 0 ( ↑↓ ). Coupling the fermionic electrons brings about spin-neutralization. In effect, the antisymmetric fermions combine to make a symmetric boson. This concept is illustrated by the reaction of two atomic H’s to generate molecular H2. In Fig 1. two atomic H’s (indicated by the symbols 2H) are shown to the left and right of center in the diagram. The superscript ( 2 ) preceding H represents its multiplicity, defined as |2(S)| + 1, where S is the total spin number. For atomic 2H the value of S is ½ or -½; the multiplicity is doublet. For molecular 1H2 (center of the diagram) the value of S is 0; the multiplicity is singlet. In ground (lowest energy) electronic state, atomic H has a single e- in the 1s orbital (where 1 = n, the principal quantum number, and s is l, the azimuthal quantum number). Each orbital is depicted as a horizontal bar (_____), and the spin quantum number of each e- is represented by a spin-up (ms = ½ = ↑) or spin-down (ms = -½ = ↓) arrow. Orbital overlap of the two atomic H’s can be constructive or destructive. Constructive interaction results in chemical bonding; i.e., there is an increased probability of finding an e- in the internuclear region of the two H’s. In effect, the two atomic 1s orbitals combine to form a bonding sigma molecular orbital, σ. Bonding lowers the energy of the system. In contrast, destructive interference decreases the probability of finding an electron in the internuclear region, and the orbital so formed is an antibonding sigma orbital, σ* (* indicates antibonding). Frontier orbital theory focuses on the initial orbital conditions of the reactants and on reactive transition with special emphasis on the highest occupied and lowest unoccupied orbitals.8-9 In the present case each 2H is a radical and the frontier orbital is a singly occupied atomic orbital (SOAO). When the spins of each e- are opposite, frontier orbital overlap is constructive resulting in doublet-doublet annihilation and generation of singlet multiplicity molecular hydrogen (1H2). The radical SOAO’s of the two H’s combine to produce the σ molecular orbital of H2, the highest occupied molecular orbital (HOMO). In Fig. 1 the (1s) notation before σ indicates the atomic source orbitals. The circle surrounding the orbital electron-

couple of the HOMO symbolizes bosonic character. The σ* orbital is the lowest unoccupied molecular orbital (LUMO) of H2. Boson-Fermion Symmetry and Spin Conservation An alternative perception of reactivity and bonding is realized by considering the fermion and boson symmetry of the reactant and product states. Tab. 1 presents the Wigner spin conservation rules expanded to include boson or fermion symmetry. As depicted in Fig. 1, combining the 1s orbitals of two doublet multiplicity atomic 2H’s generates the σ bond of singlet multiplicity molecular 1H2. Accordingly, the reaction of two fermions produces a boson. Table I: Multiplicity and related fermion or boson character of reactants and products relative to Wigner spin conservation.10-11 Multiplicity and Fermion-Boson Character Reactants

Products

Singlet (Boson) + Singlet (Boson)

Singlet (Boson)

Singlet (Boson) + Doublet (Fermion)

Doublet (Fermion)

Singlet (Boson) + Triplet (Complex Fermion)

Triplet (Complex Fermion)

Doublet (Fermion) + Doublet (Fermion)

Singlet (Boson)

Doublet (Fermion) + Triplet (Complex Fermion)

Doublet (Fermion)

Triplet (Complex Fermion) + Triplet (Complex Fermion)

Singlet (Boson)

Triplet (Complex Fermion) + Quartet (Complex Fermion)

Doublet (Fermion)

Quartet (Complex Fermion) + Quartet (Complex Fermion)

Singlet (Boson)

The Pauli principle requires the total wavefunction for any system of electrons to be antisymmetric to exchange of an orbital pair of electrons. Only phase-opposite fermions can occupy a given orbital state. Orbital electron coupling imposes a composite bosonic state. The transfer of a composite orbital electron-couple in a HOMO-LUMO frontier orbital reaction is also bosonic and symmetric. Hund’s Maximum Multiplicity Rule The same approach can be applied to reactions involving more complex elements. Fig. 2 depicts reaction of two nitrogen atoms (N) to yield molecular nitrogen (N2). Ground state N is a paramagnetic triradical with one e- in each of its three degenerate (same energy) 2p orbitals. According to Hund’s maximum multiplicity rule, the configuration with highest multiplicity has the lowest energy. Atomic N has quartet multiplicity, i.e., |2(3(½))| + 1 = 4. The orbitals of higher multiplicity states are more contracted than those of lower multiplicity. Higher multiplicity states produce greater nuclear-electron attraction and are of lower energy.12-13 Combining the 1s and 2s orbitals of the two 4N’s generates the (1s) and (2s) σ and σ* orbitals of 1N2. Constructive overlap of the phase-opposite electrons of the

(2pz)σu* (2px)πg*

2px

2py

(2py)πg*

2px

2pz (2px)πu

2py

2pz

(2py)πu

SOAO

Energy

(2pz)σg (2s) σu*

2s

2s (2s) σg

(1s) σu*

1s

1s (1s) σg

4

|2(3(½))| + 1 = 4 N, quartet multiplicity

1

|2(0)| + 1 = 1 N2, singlet multiplicity

4

|2(3(-½))| + 1 = 4 N, quartet multiplicity

Figure 2. The electronic configurations of atomic (N) and molecular nitrogen (N2). three 2p SOAO’s of the two 4N’s generates the one σ and the two π bonds of triplebonded 1N2. The two radical 4N’s combine to yield one non-radical 1N2. From the fermion-boson perspective, each atomic N is a complex fermion; i.e., each atomic 4N includes three fermionic SOAO’s. Coupling a 4N in state Ψ (i.e., S = ½ + ½ + ½ = 3(½)) with a 4N in state -Ψ (i.e., S = -½ - ½ - ½ = 3(-½)) yields molecular 1N2, a boson (i.e., S = 0). As described in Tab. 1, reaction of two quartet multiplicity complex fermions generates a singlet multiplicity boson. OXYGEN CHEMISTRY Fig. 3 depicts the reaction of two oxygen atoms (O) to produce molecular O2. Only the frontier orbitals, i.e., the 2p orbitals of O and their resulting σ, π, π*, and σ* orbitals of O2 are shown. The diagram show the combination of two paramagnetic triplet atomic 3O’s to yield singlet molecular 1O2. Note that the product 1O2 does not obey Hund’s maximum multiplicity rule, and as such, 1O2 is electronically excited with energy of about 22.5 kcal.mol-1 greater than that of the ground state 3O2 we breath.14 Relaxation of 1O2 to 3O2 with emission of an infrared photon requires change in spin multiplicity. Changing spin multiplicity is a low probability event. Thus, 1O2 is metastable, i.e., relatively long-lived for an excited state. The lifetime of 1O2 is sufficient to allow it to participate as a reactive electrophile in chemical reactions.

Highest Occupied Molecular Orbital

(2p)

Lowest Unoccupied Molecular Orbital

σ* u

Energy

HOMO

LUMO (2p)

2px

2py

π*

(2p)

g

π* g

2pz

2px (2p)

π

(2p)

u

2pz

2py

π

u

SOAO (2p)

|2(2(½))| + 1 = 3

Single Occupied Atomic Orbital

σ

g

|2(0)| + 1 = 1

3

|2(2(-½))| + 1 = 3

1

O, triplet multiplicity

3

O2, singlet multiplicity

O, triplet multiplicity

Figure 3. Electronic configurations depicting the SOAO’s of 2 atomic oxygens (O’s) and the HOMO and LUMO of singlet molecular oxygen (1O2). Ground state 3O2 is depicted in Fig.4. In its triplet state O2 is a diradical with one e in each of its two π* singly occupied molecular orbitals (SOMO). As such, 3 O2 is a complex fermion; 3O2 can be in either the Ψ (i.e., S = ½ + ½ = 2(½) = 1) state or the -Ψ (i.e., S = -½ - ½ = 2(-½) = -1) state. The vast majority of molecules that comprise organic and biochemistry are singlet multiplicity S = 0 bosons. For these molecules, reactions involve bosonic HOMO-LUMO exchange of a composite orbital electron-couple. Radical reactions (SOMO reactions) are relatively uncommon in biological chemistry. Radicals tend to react with radicals. Bonding is favored by the ease of radical electronic interaction in SOMO-SOMO reactions. Fermions preferentially react with fermions to yield bosons. Conversely, reaction of a triplet (complex fermion) molecule such as 3O2 with a singlet (boson) organic molecule is symmetry-restricted. -

2HO2

3O2

Energy

(2p)

(2p)

σ*

(2p)

u

π*

(2p)

g

π* g

(2p)

e-

1H2O2

σ*

(2p)

u

π*

(2p)

g

π* g

H+ (2p)

π

(2p)

u

(2p)

π

(2p)

u

σ

π

(2p)

u

(2p)

g

O2, triplet multiplicity

u

(2p) πg

(2p)

π*

π

(2p)

π

*

e-

g

H+

|2(2(½))| + 1 = 3 3

σ*

π

(2p)

u

σ

(2p)

g

|2(½))| + 1 = 2 2

HO2, doublet multiplicity

u

σ

g

|2(0)| + 1 = 1 1

H2O2, triplet multiplicity

Figure 4. Molecular configurations of oxygen relative to state of reduction.

u

Phagocyte Microbicidal Activity Blood leukocytes generate luminescence as an energy product of microbicidal activity.15-17 Phagocyte luminescence was discovered in experiments designed to test the hypothesis that blood leukocytes change the spin quantum number of O2 in order to realize its broad reactive potential as a microbicidal agent. Phagocytes employ metabolically generated reducing equivalents to change the multiplicity and fermionic character of O2. Fig. 4 depicts the effect of equivalent reduction of oxygen on its symmetry. Addition of a reducing equivalent (a fermion) changes the multiplicity from triplet (3O2, a complex fermion) to doublet (a fermion). This reaction involves flavoprotein-catalysed reduction of O2 to 2HO2 and its conjugate base superoxide (2O2-). The SOMO-SOMO reaction of 2HO2 with phaseopposite 2O2- generates singlet multiplicity H2O2 and 1O2.18 Reactive annihilation of two doublets (fermions) yields two singlets (bosons). Myeloperoxidase catalyses the reaction: H2O2 + Cl- → H2O + HOCl. The reactants and products are exclusively singlet multiplicity (bosons). Hypochlorous acid (HOCl) and H2O2 participate in bosonic HOMO-LUMO reactions with singlet biochemical substrates (bosons) yielding singlet multiplicity dioxygenated products (bosons). The 1O2, produced in the reaction: H2O2 + HOCl → H2O + 1O2 + Cl-, can directly react with bosonic substrates yielding bosonic dioxygenated products. The Luminescence Event The endoperoxide and dioxetane products of dioxygenation reactions are of relatively high energy, and disintegrate yielding electronically excited products such as the n-π π* excited carbonyl function depicted in Fig. 5. The absorbance or emission of a hν (boson) reflects e- (fermion) orbital transition; the difference between the initial and final quantum state of the e- is the . R2 C -. O R2 C = O

Energy

(2p)

π*

(2p)

2px

π*

2px

C

C n (2py)

(2p)

π

O

2px



n (2py)

(2p)

O

2px

π

nπ* excited state singlet carbonyl ground state singlet carbonyl Figure 5. Singlet (n-π π*) electronically excited and singlet ground state carbonyl functions. The σ bonding and σ* antibonding orbitals are not shown.

energy of the absorbed or emitted hν. An hν is a symmetric boson; its absorbance or emission does not affect the fermionic character of the e-. However, hν absorption by one e- of an orbital electron-couple causes its excitation to a higher energy orbital. Separating the electrons of the bosonic orbital couple to different orbitals regenerates the fermionic character of each individual e-. In Fig. 5 the excited carbonyl is a complex singlet. The single electron populating the n (non-bonding) orbital of O and the single electron of the π* orbital of the carbonyl have opposite spins. Although the overall state remains singlet and is relatively short-lived, both n orbital and π* orbital are radical SOMO’s with internal fermionic orbital character. The excited carbonyl relaxes by hν emission with etransition from the π* orbital of the carbonyl to the n orbital of O re-establishing the n orbital electron-couple and bosonic character.

Energy

BOSONIC ELECTRON TRANSFER REACTIONS A HOMO-LUMO reaction involves molecular interchange of an orbital electroncouple. The reactants and products are uniformly bosonic. Pre-flavoprotein biochemical redox reactions are essentially non-radical and bosonic. Radical (SOMO) mechanisms are atypical. The bosonic nature of biological reactions imposes a symmetry barrier that protects against direct reaction with fermionic 3O2. Changing the fermionic character of O2 allows phagocytes to realize the electronegative reactive potential of oxygen and direct it against target microbes. The bosonic nature of the orbital electron-couple may also be essential for efficient redox transfer in biologic systems. According to Heisenberg’s uncertainty principle the uncertainty of momentum (∆p) multiplied by the uncertainty of position (∆x) is always greater than ħ; i.e., ∆p∆x ≥ ½ħ.3,4 Since the spin momentum of the bosonic orbital electron-couple is known, i.e., zero, the positional uncertainty of the couple must be relatively large. This opens the possibility that intermolecular transfer of a symmetric orbital electron-couple in a biological redox reaction might proceed by a quantum tunnelling mechanism analogous to the escape of a bosonic alpha particle from an atomic nucleus in alpha decay. This possibility is depicted in Fig. 6.

Molecule A

Bosonic Quantum Tunneling

Molecule B

Figure 6. Bosonic electron-couple redox transfer by quantum tunnelling.

ACKNOWLEDGEMENT Dedicated to my mentor Richard H. Steele. REFERENCES 1. Seliger HH. The origin of bioluminescence. Photochem Photobiol 1975; 21:355-61. 2. Adam W, Cilento G. eds. Chemical and biological generation of excited states. New York: Academic Press, 1982. 3. Matthews PSC. Quantum chemistry of atoms and molecules. Cambridge: Cambridge University Press, 1986. 4. Sudbery A. Quantum mechanics and the particles of nature. Cambridge: Cambridge University Press, 1986. 5. Feynman RP, Leighton RB, Sands M. The Feynman lectures on physics. Quantum mechanics. Reading: Addison-Wesley Publ Co, 1965. 6. Waldram JR. The theory of thermodynamics. Cambridge: Cambridge University Press, 1985. 7. Dirac PAM. The principles of quantum mechanics. 4th Ed. Oxford: Oxford Press, 1958. 8. Fukui K. Recognition of stereochemical paths by orbital interaction. Accts Chem Res 1971; 4:57-64. 9. Fleming I. Frontier orbitals and organic chemical reactions. Chichester: John Wiley & Sons, 1978. 10. Wigner E, Witmer EE. Über die struktur der zweiatomigen molekelspektren nach der quantenmechanik. Z Physik 1928; 51:859-86. 11. Herzberg G. Molecular spectra and molecular structure. Spectra of diatomic molecules. New York; Van Nostrand Reinhold, 1950. 12. Katriel J, Pauncz R. Theoretical interpretation of Hund’s rule. Adv Quantum Chem 1977; 10:143-85. 13. Salem L. Electrons in chemical reactions: First principles. Chichester: John Wiley & Sons, 1982. 14. Kasha M, Khan AH. The physics, chemistry, and biology of singlet molecular oxygen. Ann New York Acad Sci 1970; 171:1-33. 15. Allen RC, Stjernholm RL, Steele. Evidence for the generation of an electronic excitation state(s) in human polymorphonuclear leukocytes and its participat-ion in bactericidal activity. Biochem Biophys Res Commun 1972; 47:679-84. 16. Allen RC. Phagocytic leukocyte oxygenation activities and chemilumin-escence: a kinetic approach to analysis. Meth Enzymol 1986; 133: 449-93. 17. Allen RC. Oxygen-dependent microbe killing by phagocytic leukocytes: spin conservation and reaction rate. Stud Org Chem 1988; 33: 425-34. 18. Khan AH. Singlet molecular oxygen from superoxide and sensitised fluorescence of organic molecules. Science 1970; 168:476-7.