Magnetic effects in biology: Crucial role of quantum coherence in the radical pair mechanism

The spin-chemical radical pair mechanism (RPM) has emerged as a leading theory for explaining the biological effects of low-intensity magnetic fields. These intriguing effects occur when the quantum system of radicals is well isolated from the disturbing influence of the environment. In other words, these effects are closely related to the spin coherence relaxation time τ, but an explicit relationship has not yet been established. In our study, we found an analytical solution to the Liouville-Neumann equation for an open system made up of two electrons and one nucleus, considering minimal interactions while concentrating on spin relaxation and chemical kinetics. This solution, supported by numerical integration, highlights the crucial role of quantum coherence. A straightforward expression is proposed that describes the RPM effect as a function of τ, within the ranges of magnetic field strength H and rate κ of chemical kinetics relevant to magnetobiology. Our findings reveal that RPM effects become significant only when fundamental relation γHτ>1+κτ holds: it controls the magnitude of the effects, and it is consistent with the principles of spin chemistry. Additionally, by comparing our results with existing experimental data, we estimate that the plausible spin decoherence times in magnetosensitive radical pairs within cryptochromelike proteins range from units to tens of nanoseconds. The effects of radio-frequency magnetic fields at the nT level were also examined, taking into account decoherence. These effects turned out to be negligible and incapable of disrupting the RPM patterns. The role of the quantum Zeno effect in magnetobiology is inspected from the perspective of the τ dependence of the RPM effect.