Green’s function calculation of electron spin polarization. II. Approximation schemes

Quantum mechanical model for the anticarcinogenic effect of extremely-low-frequency electromagnetic fields on early chemical hepatocarcinogenesis

Using the conventional Haberkorn approach, it is evaluated the recombination of the radical pair (RP) singlet spin state to study theoretically the cytoprotective effect of an extremely-low-frequency electromagnetic field (ELF-EMF) on early stages of hepatic cancer chemically induced in rats. The proposal is that ELF-EMF modulates the interconversion rate of singlet and triplet spin states of the RP populations modifying the products from the metabolization of carcinogens. Previously, we found that the daily treatment with ELF-EMF 120 Hz inhibited the number and area of preneoplastic lesions in chemical carcinogenesis. The singlet spin population is evaluated diagonalizing the spin density matrix through the Lanczos method in a radical pair mechanism (RPM). Using four values of the interchange energy, we have studied the variations over the singlet population. The low magnetic field effect as a test of the influence over the enzymatic chemical reaction is evaluated calculating the quantum yield. Through a bootstrap technique the range is found for the singlet decay rate for the process. Applying the quantum measurements concept, we addressed the impact toward hepatic cells. The result contributes to improving our understanding of the chemical carcinogenesis process affected by charged particles that damage the DNA.

Theoretical description of spin-selective reactions of radical pairs diffusing in spherical 2D and 3D microreactors

In this work, we treat spin-selective recombination of a geminate radical pair (RP) in a spherical "microreactor," i.e., of a RP confined in a micelle, vesicle, or liposome. We consider the microreactor model proposed earlier, in which one of the radicals is located at the center of the micelle and the other one undergoes three-dimensional diffusion inside the micelle. In addition, we suggest a two-dimensional model, in which one of the radicals is located at the "pole" of the sphere, while the other one diffuses on the spherical surface. For this model, we have obtained a general analytical expression for the RP recombination yield in terms of the free Green function of two-dimensional diffusion motion. In turn, this Green function is expressed via the Legendre functions and thus takes account of diffusion over a restricted spherical surface and its curvature. The obtained expression allows one to calculate the RP recombination efficiency at an arbitrary magnetic field strength. We performed a comparison of the two models taking the same geometric parameters (i.e., the microreactor radius and the closest approach distance of the radicals), chemical reactivity, magnetic interactions in the RP and diffusion coefficient. Significant difference between the predictions of the two models is found, which is thus originating solely from the dimensionality effect: for different dimensionality of space, the statistics of diffusional contacts of radicals becomes different altering the reaction yield. We have calculated the magnetic field dependence of the RP reaction yield and chemically induced dynamic nuclear polarization of the reaction products at different sizes of the microreactor, exchange interaction, and spin relaxation rates. Interestingly, due to the intricate interplay of diffusional contacts of reactants and spin dynamics, the dependence of the reaction yield on the microreactor radius is non-monotonous. Our results are of importance for (i) interpreting experimental data for magnetic field effects on RP recombination in confined space and (ii) for describing kinetics of chemical reactions, which occur predominantly on the surfaces of biomembranes, i.e., lipid peroxidation reactions.