Magnetic resonances of ions in biological systems

A magnetic field transduction mechanism based on an ion oscillator model is derived from an explicit quantum mechanical description. The governing equation prescribes how the electric dipole moment of an ion oscillating in a symmetric potential well evolves under the influence of an arbitrary magnetic field. The resulting equation is an analog of the Bloch equation, a well-studied model for magnetic resonances in atomic and molecular spectroscopy. The differential equation for this ion oscillator model is solved numerically for a few illustrative magnetic field exposures, showing when those resonances occur with single frequency, linearly polarized fields. Our formulation makes explicit the conditions that must be present for magnetic fields to produce observable biological effects under the ion oscillator model. The ion's potential well must have symmetry sufficient to produce a degenerate excited state, e.g., octahedral or trigonal bipyramid potentials. The impulse that excites the ion must be spatially correlated with the orientation of the detector that reads off the final state of the oscillator. The orientation between the static and oscillating magnetic fields that produces resonance is a complicated function of the field magnitudes and frequency. We suggest several classes of experiments that could critically test the validity of the model presented here.