Approaching magnetic field effects in biology using the radical pair mechanism

The goal of my graduate work has been to try to understand or explain some of the reported magnetic field effects in biology (see Chapter 1 for examples) using the radical pair mechanism, a quantum mechanical mechanism known for over 20 years that lets the yields of certain radical pair reactions depend on the applied magnetic field [1, 2, 3]. This goal seems reasonable considering the known roles of many biological free radicals in cancer, disease, aging, development, and cellular signaling, the constant reminders in the media to take anti-oxidant vitamins to protect against dangerous free radicals, and the success of the radical pair mechanism in explaining magnetic field effects in photosynthetic reaction centers. The radical pair mechanism (as detailed in Chapter 2) occurs when a pair of radicals forms a cage radical pair, a system composed of two unpaired electron spins whose spin motion is affected by nearby nuclear spins via the hyperfine interaction, by applied magnetic fields via the Zeeman effect, and by each other via the exchange and dipole interactions. The spin motion varies in singlet/triplet character, and if the chemical reaction is more (or less) favorable in a singlet/triplet state, the reaction rate can depend on applied magnetic fields, even ones very weak and near earth-strength. To approach the above goal, during my graduate work I have developed and published several new perturbation treatments for combinations of steady and oscillating magnetic fields in the radical pair mechanism: one based on the Schri::idinger Equation (see [4, 5] or Chapter 3), another based on the Liouville Equation (see [6] or Chapter 4), and two more mixed perturbation methods that bridge the gap between the Schri::idinger and Liouville formalisms (see Chapter 5). All of these iterative approaches can be used to calculate singlet-to-triplet yields when the strength of the oscillating magnetic field is weak compared to the other terms in the spin Hamiltonian. This range occurs both in the natural magnetic environment (where oscillating fields tend to be smaller than 0.03 G and steady fields tend to be near 0.5 G) and in many man-made environments. Thus, these perturbation treatments should be applicable both in studies of magnetic sensory mechanisms in animals and in studies of health effects of electromagnetic fields. These perturbation methods also allow much faster calculation of singlet-to-triplet yields than do numerical integration methods and are more generally applicable than the rotating frame treatment, allowing treatment of anisotropic spin Hamiltonians and treatment of multiple oscillating fields at any orientation with respect to the steady field. Finally, the different perturbation methods complement each other; that is, the Liouville Equation method yields a more efficient and reliable computer algorithm while the Schrodinger Equation method yields more insight into how effects of steady and oscillating magnetic fields occur and can more easily be used to generate analytical expressions for field and frequency dependences of singlet-to-triplet yields. Also, while the Liouville formalism allows one to calculate effects on steady and oscillating field sensitivity of different escape rates (ks and kr) for singlet and triplet pairs and can be generalized to include relaxation, the Schrodinger formalism lets one treat both exponential and Noyes time-dependences. Together these new methods can be quite useful for studying biological effects of oscillating magnetic fields, and their sample results show a number of behaviors in the singletto- triplet yields (such as saturation effects, oscillating field strength and frequency resonances, and steady field strength- and orientation- dependent frequency shifts) that, while typical in quantum mechanics or magnetic resonance, seem surprising in biology and may account for conflicts in the magnetic field bioeffects literature. Also during my graduate work I have used EPR (Electron Paramagnetic Resonance) data for the cage radical pairs formed by the homolytic cleavage of Co-C bonds in several coenzyme B12 dependent enzymes to calculate effects of earth-strength steady and oscillating magnetic fields on their singlet-to-triplet yields via the radical pair mechanism (see [7] or Chapter 6). Energy level repulsions and the state-mixing they induce are found to be very important for determining overall sizes of effects and lower bounds on oscillating-field frequencies that can cause effects in such systems. B12 and similar systems with nearly axial zero-field spin Hamiltonians, dominated by terms over 100 times larger than Zeeman terms due to earth-strength steady fields, if under relatively immobile conditions of long lifetime, slow molecular tumbling, and slow spin relaxation, may be useful as biological sensors of both steady and oscillating fields that occur in nature, since the yields calculated show sensitivity to steady field strength (even after powder averaging) and orientation, and undergo steadyfield- dependent shifts in the oscillating-field frequencies of maximal effect. Thus, since B12 is used by a number of enzymes (including ribonucleotide reductase, which converts RNA to DNA nucleotides; methyl malonyl CoA mutase, which controls the metabolism of certain fatty acids in mammals; and methionine synthase, which in mammals is used to regenerate active methyl groups on S-adenosyl methionine, which is involved in DNA methylation, melatonin and epinephrine synthesis, myelination, and methylation of chemotaxis proteins) and since some of these B12-dependent processes have been reported to be influenced by magnetic fields, coenzyme B12 may be an interesting candidate target for magnetic field effects in biology.U of I Onlydissertation/thesi