**2.** *Ab initi***o: Magnetic-isotope catalysis in chemistry and biochemistry**

Apart from the energy control (the law of conservation of energy), any chemical reaction as electron-nuclear rearrangement of reactants into products is controlled by angular momentum, spin, of reactants. Namely, the total spin of reaction products must be identical to the total spin of reactants. This law of spin conservation immediately follows from quantum mechanics, from the fundamental and universal Pauli principle: no two electrons may occupy the same quantum state simultaneously (see, e.g., Brocklenhurst, 2002; Buchachenko, 2009).

Figure 1 illustrates how the law of conservation of spin gives control over reactivity of free radicals, R•. For example, a pair of free radicals, each with electron spin *S*=1/2, may form a chemical bond and the resultant diamagnetic molecule, the total electron spin of which *S*=0 (Fig. 1a). However, from the law of conservation of spin, it follows that the chemical bond between these two radicals may happen only if the spin state of the pair at collision is singlet, i.e., spins of two electrons are subtracted to give the net *S*=0 (spin multiplicity, 2*S*+1=1). If the spin state of the radical pair is triplet, i.e., if the electron spins are added up to give the net *S*=1 (spin multiplicity, 2*S*+1=3), then the radicals cannot react immediately.

Fig. 1. Spin control in the chemical reactions of free-radical pairs.

In gas or liquid phase, with the time allotted for any collisions of radicals of order of 1 ns or less, neither spin-spin relaxation (in order of 10 ns) nor spin-lattice relaxation (in order of 100 ns) has time to fit the spin orientation. As a result, only one-quarter of encounters, with the radical pair in the singlet state, gives the recombination product while three-quarters of the initial radical pairs are inhibited from the reaction. Another example is presented on Fig. 1b. Namely, it is the reaction of free radical R• with oxygen, molecules of which are normally in the triplet spin state. The total spin, *S*, of this reagent pair can be 1/2 when the individual spins are subtracted (2*S*+1=1) or 3/2 when the individual spins are added up (2*S*+1=4). Meanwhile, for the product of the reaction RO2 •, peroxyl radical, *S*=1/2. Hence, from six possible spin states of the reactants only two states do not require a change in the total electron spin of the reactants and, therefore, are permitted for formation of RO2 •; other four states are forbidden for the reaction. A well-known reaction of mitochondrial ubisemiquinone with oxygen, in which O2 •– is produced, exhibits a similar case (see, e.g., (Chance, 1979; Nohl et al., 1993). This reaction is permitted only from the doublet state of the

Apart from the energy control (the law of conservation of energy), any chemical reaction as electron-nuclear rearrangement of reactants into products is controlled by angular momentum, spin, of reactants. Namely, the total spin of reaction products must be identical to the total spin of reactants. This law of spin conservation immediately follows from quantum mechanics, from the fundamental and universal Pauli principle: no two electrons may occupy the same quantum state simultaneously (see, e.g., Brocklenhurst, 2002;

Figure 1 illustrates how the law of conservation of spin gives control over reactivity of free radicals, R•. For example, a pair of free radicals, each with electron spin *S*=1/2, may form a chemical bond and the resultant diamagnetic molecule, the total electron spin of which *S*=0 (Fig. 1a). However, from the law of conservation of spin, it follows that the chemical bond between these two radicals may happen only if the spin state of the pair at collision is singlet, i.e., spins of two electrons are subtracted to give the net *S*=0 (spin multiplicity, 2*S*+1=1). If the spin state of the radical pair is triplet, i.e., if the electron spins are added up to give the net *S*=1 (spin multiplicity, 2*S*+1=3), then the radicals cannot react immediately.

In gas or liquid phase, with the time allotted for any collisions of radicals of order of 1 ns or less, neither spin-spin relaxation (in order of 10 ns) nor spin-lattice relaxation (in order of 100 ns) has time to fit the spin orientation. As a result, only one-quarter of encounters, with the radical pair in the singlet state, gives the recombination product while three-quarters of the initial radical pairs are inhibited from the reaction. Another example is presented on Fig. 1b. Namely, it is the reaction of free radical R• with oxygen, molecules of which are normally in the triplet spin state. The total spin, *S*, of this reagent pair can be 1/2 when the individual spins are subtracted (2*S*+1=1) or 3/2 when the individual spins are added up

from six possible spin states of the reactants only two states do not require a change in the total electron spin of the reactants and, therefore, are permitted for formation of RO2•; other four states are forbidden for the reaction. A well-known reaction of mitochondrial

(Chance, 1979; Nohl et al., 1993). This reaction is permitted only from the doublet state of the

•, peroxyl radical, *S*=1/2. Hence,

•– is produced, exhibits a similar case (see, e.g.,

Fig. 1. Spin control in the chemical reactions of free-radical pairs.

(2*S*+1=4). Meanwhile, for the product of the reaction RO2

ubisemiquinone with oxygen, in which O2

**2.** *Ab initi***o: Magnetic-isotope catalysis in chemistry and biochemistry** 

Buchachenko, 2009).

reactants. Four quartet "channels" are forbidden by the law of the spin conservation (Fig. 1c).

To lift the ban on reactions forced by the law of spin conservation, spins of the reactants must be changed. Inasmuch as spin-orbital coupling is negligibly small in organic free radicals, magnetic fields are the only means which are able to change the spin states and, thereby, switch the reaction over spin-forbidden and spin-allowed channels. The probability of chemical reaction is a function of the parameters of magnetic interactions (Brocklenhurst, 2002; Buchachenko, 2009):

#### *P=f(H; ; H1; J; a; I; mI; n)*

In this equation *H* is external magnetic field (Zeeman interaction), and *H*1 are frequency and amplitude of microwave magnetic fields. Correspondingly, acceleration of the freeradical reaction can be achieved through changes in the total electron spin of reactants by interaction with an applied external magnetic field. The parameter *J* is energy of the exchange interaction. Correspondingly, the reactions of organic free radicals or ion-radicals can be catalyzed via interaction of partners of the radical pair with a foreign, third spin carrier, like nitroxide radical. It is called "electron spin catalysis".

The above mentioned equation also contains parameters of hyperfine coupling *a*, nuclear spin *I*, nuclear spin projection *m*I, and nuclear magnetic moment n, i.e., the parameters of interactions of electron spins with magnetic nuclei which are known as the cause of the hyperfine splitting in EPR spectra of free radicals. Correspondingly, acceleration of the freeradical reactions can be achieved through changes in the total electron spin of reactants by interaction with magnetic fields of magnetic nuclei. This is known as "magnetic-isotope effect" (MIE): the reaction shows different reaction rates and different yields of products according to whether the reagents contain magnetic or nonmagnetic isotopes (Brocklenhurst, 2002; Buchachenko, 2009). While classical isotope mass effect selects isotopic nuclei in accordance with their masses, MIE selects isotopes by spin and magnetic moment. In action, MIE is a purely kinetic phenomenon and manifests itself as the dependence of the reaction rate on the nuclear spins of the reactants. Within recent years, MIE in chemistry has been discovered for a number of magnetic isotopes, among them H–D, 13C, 17O, 29Si, 33S, 73Ge, 117,119Sn, 199,201Hg, and 235U (Buchachenko, 2009). By analogy with "electron spin catalysis", the enhancement of the reaction rate by the nuclear spins of the reactants can be denoted as the "nuclear spin catalysis" (Koltover, 2007, 2008).

In biochemistry, MIE has been recently discovered for magnetic isotope of magnesium, 25Mg, by A.L. Buchachenko and his group. It is generally known that energetic demands of every operation in living systems are met by molecules of ATP, be it eukaryotic cells of animals and plants or prokaryotic cells of bacteria. In aerobic organisms, most of ATP is produced in the so-called "oxidative phosphorylation". There are specific enzymes, "biomolecular nanoreactors", organized in the respiratory electron transport chains (ETC). Normal function of the ETC enzymes, be it mitochondrial nanoreactors in eukaryotic cells of animals or similar nanoreactors of bacteria cells, is in the transport of electrons, one by one, from the electron donor molecules to the end enzyme, cytochrome oxidase, from which the electrons are transferred to molecules of oxygen with two electron reduction of oxygen into water. Free energy released during the electron transport is used by the specific enzyme,

Stable Magnetic Isotopes as a New Trend in Biomedicine 109

Due to the hyperfine interaction of the unpaired electron with the nuclear spin of 25Mg, the state of this virtual pair is converted from the short-lived singlet (total electron spin of the pair, *S*=0) into the long-lived triplet (*S*=1) in which the yield of the reaction of the ATP synthesis correspondingly increases (Buchachenko et al., 2008). A similar spin-selective ionradical pair of Ca+ with the phosphate radical of adenosine has been suggested to explain

It should be mentioned that the hypothesis about a possible key-role of such virtual ionradical pairs in oxidative phosphorylation and energy transformation processes has long been stated (Blumenfeld & Koltover, 1972). Within the context of modern bioenergetics, which postulated a proton electrochemical gradient across the mitochondrial membrane as the energy-rich intermediate of oxidative phosphorylation in the "molecular motors" (see, e.g., Nelson & Cox, 2008), another plausible explanation for the MIE can be proposed. It is reasonably to suggest that the proton electrochemical gradient poses conformational pressure in the catalytic center of ATP-synthase, generating electronic-conformational excitation in the АDP-Mg2+ complex. This would essentially increase reactivity of the adenine base of ADP to phosphate (Koltover et al., 1971; Blumenfeld & Koltover, 1972). The nuclear spin of 25Mg (or 43Ca) can provoke the transition of the exited АDP-Mg2+ complex from the singlet state to the triplet state the lifespan of which is longer, thereby providing more time for the reaction of the ATP synthesis from ADP and Pi. Thus, the detailed

mechanism of the magnetic-isotope catalysis in bioenergetics remains to be cleared.

There is a great variety of chemical elements in biomolecular nanoreactors of living cells (see Table 1). Certain of them are only represented by magnetic isotopes, among them – hydrogen, nitrogen, sodium, phosphorus, potassium, manganese and so on. However, there are chemical elements which have both kinds of stable isotopes, nonmagnetic and magnetic ones, among them – carbon, oxygen, magnesium, calcium, iron, zinc and others (Table 1). Correspondingly, these are the elements which are required to search for magnetic-isotope

In this regard, magnesium is of particular interest. There are three stable isotopes of magnesium, 24Mg, 25Mg and 26Mg with natural abundance about 79, 10 and 11 %. Among them, only 25Mg has the nuclear spin (*I*=5/2) that produces the magnetic field. Two other isotopes are spinless (*I*=0) and, hence, produce no magnetic fields (Grant & Harris, 1996). As the most abundant intracellular divalent cation, Mg2+ is essential to regulate numerous cellular functions and enzymes. Ions of Mg2+ serve as obligatory cofactors in catalytic centers of many enzymes including ATP-synthase as the primary producer of ATP in mitochondria, chloroplasts, bacteria and archaea (Nelson & Cox, 2008). Moreover, a novel role for Mg2+ as an intracellular second messenger has been recently discovered (Li et al., 2011). Besides, the difference in masses between the isotopes of magnesium is much less, in percentage term, than that for the isotopes of carbon, for example, thereby minimizing the

Stable isotopes of magnesium, namely nutrient solutions highly enriched with 25Mg or 26Mg, have been used for many years as *in vivo* tracers to determine magnesium absorption in human subjects, animals and plants models (see., e.g., Coudray et al., 2006; Weatherall et al., 2006). It is reasonable that the problem of possible beneficial effects of the magnetic isotope

**3.** *In situ***: Magnetic-isotope catalysis in living cells** 

MIE of 43Ca (Buchachenko, 2011).

effects in living cells.

classical mass-isotope effect.

ATP-synthase, for synthesis of ATP from adenosine 5'-diphosphate (ADP) and inorganic phosphate (Nelson & Cox, 2008).

In the experiments with mitochondria isolated from the rat hearts, it has been revealed that the rate of oxidative phosphorylation with magnetic 25Mg was 2-3 times higher than that with nonmagnetic 24Mg and 26Mg while no difference was found between the nonmagnetic magnesium nuclei (Buchachenko et al., 2005). It was also revealed that activity of phosphocreatine kinase and phosphoglycerate kinase, for which ions of Mg2+ serve obligatory cofactors, was essentially higher with magnetic 25Mg than with 24Mg and 26Mg. Again, no difference in efficiency between the nonmagnetic magnesium nuclei was found in these experiments. Thus, there have been the very first evidences of MIE in biochemical reactions *in vitro*. Furthermore, the same research group has discovered MIE of calcium. The activity of phosphocreatine kinase with Ca2+ ions of magnetic nuclei 43Ca was found to be twice higher than with Ca2+ ions of nonmagnetic nuclei 40Ca (Buchachenko et al., 2011).

Factual evidence of MIE, on its own, indicates that there is a spin-selective "bottle-neck" of the process under investigation. The hypothetic mechanism of the acceleration of oxidative phosphorylation by the nuclear spin of 25Mg suggested by this group is as follows (Fig. 2). Namely, they suggested a reversible transfer of electron density in the active center of ATPsynthase from the terminal anion phosphate group of ADP to Mg2+-cation. It produces a virtual ion-radical pair, Mg+-adenosine phosphate radical in the singlet spin state.

Fig. 2. Reaction scheme for enzymatic phosphorylation (Buchachenko et al., 2008*).* 

ATP-synthase, for synthesis of ATP from adenosine 5'-diphosphate (ADP) and inorganic

In the experiments with mitochondria isolated from the rat hearts, it has been revealed that the rate of oxidative phosphorylation with magnetic 25Mg was 2-3 times higher than that with nonmagnetic 24Mg and 26Mg while no difference was found between the nonmagnetic magnesium nuclei (Buchachenko et al., 2005). It was also revealed that activity of phosphocreatine kinase and phosphoglycerate kinase, for which ions of Mg2+ serve obligatory cofactors, was essentially higher with magnetic 25Mg than with 24Mg and 26Mg. Again, no difference in efficiency between the nonmagnetic magnesium nuclei was found in these experiments. Thus, there have been the very first evidences of MIE in biochemical reactions *in vitro*. Furthermore, the same research group has discovered MIE of calcium. The activity of phosphocreatine kinase with Ca2+ ions of magnetic nuclei 43Ca was found to be twice higher than with Ca2+ ions of nonmagnetic nuclei 40Ca

Factual evidence of MIE, on its own, indicates that there is a spin-selective "bottle-neck" of the process under investigation. The hypothetic mechanism of the acceleration of oxidative phosphorylation by the nuclear spin of 25Mg suggested by this group is as follows (Fig. 2). Namely, they suggested a reversible transfer of electron density in the active center of ATPsynthase from the terminal anion phosphate group of ADP to Mg2+-cation. It produces a

virtual ion-radical pair, Mg+-adenosine phosphate radical in the singlet spin state.

Fig. 2. Reaction scheme for enzymatic phosphorylation (Buchachenko et al., 2008*).* 

phosphate (Nelson & Cox, 2008).

(Buchachenko et al., 2011).

Due to the hyperfine interaction of the unpaired electron with the nuclear spin of 25Mg, the state of this virtual pair is converted from the short-lived singlet (total electron spin of the pair, *S*=0) into the long-lived triplet (*S*=1) in which the yield of the reaction of the ATP synthesis correspondingly increases (Buchachenko et al., 2008). A similar spin-selective ionradical pair of Ca+ with the phosphate radical of adenosine has been suggested to explain MIE of 43Ca (Buchachenko, 2011).

It should be mentioned that the hypothesis about a possible key-role of such virtual ionradical pairs in oxidative phosphorylation and energy transformation processes has long been stated (Blumenfeld & Koltover, 1972). Within the context of modern bioenergetics, which postulated a proton electrochemical gradient across the mitochondrial membrane as the energy-rich intermediate of oxidative phosphorylation in the "molecular motors" (see, e.g., Nelson & Cox, 2008), another plausible explanation for the MIE can be proposed. It is reasonably to suggest that the proton electrochemical gradient poses conformational pressure in the catalytic center of ATP-synthase, generating electronic-conformational excitation in the АDP-Mg2+ complex. This would essentially increase reactivity of the adenine base of ADP to phosphate (Koltover et al., 1971; Blumenfeld & Koltover, 1972). The nuclear spin of 25Mg (or 43Ca) can provoke the transition of the exited АDP-Mg2+ complex from the singlet state to the triplet state the lifespan of which is longer, thereby providing more time for the reaction of the ATP synthesis from ADP and Pi. Thus, the detailed mechanism of the magnetic-isotope catalysis in bioenergetics remains to be cleared.
