Numerous reports have indicated that some biological effects of relatively weak alternating magnetic fields depend upon the presence and magnitude of a parallel-directed static magnetic field. One explanation of these phenomena is parametric resonance mechanism , originally proposed by Lednev and also applied in modified form by Blackman and Blanchard. The mechanism, as formulated by Lednev, involves the Zeeman splitting of infrared vibration levels of Ca 2+ ions within proteins such as calmodulin. It is shown that this model can be formulated using mostly classical physics. In this formulation the linear vibration path of an oscillating ion is set into uniform rotation by the static magnetic field B dc at an angular velocity equal to one half of the ion cyclotron resonance frequency Ω. Application of the alternating magnetic field B ac = B 1 cos bt will make the angular velocity non-uniform. Rather than relying on transition between vibration levels, and thus implicitly on energy changes due to radiation, as in the original model, we propose that the non-uniform rotation will lead to time-varying changes in the electrostatic component of the binding forces between the ion and the surrounding ligands. The angular displacement Δ[straight phi] between "stagnation points", where the angular velocity of the vibration path is zero, is computed for applied angular frequencies, b = Ω, Ω/2 and 2 Ω at specified ratios α = (B 1 /B 0 ). The selected values of α are those where the Lednev model predicts maximum biological effects. The values of Δ[straight phi] are discussed in relation to published quantitative information about the structure of Ca 2+ binding sites within calmodulin. The double blind Jurkat cell experiments, conducted with B dc = [.707, .639, .566, .467, .231, .132, .059] Gauss and Bac = [.569, .572, .537, .538, .517] Gauss at f ac = [10, 20, 30, 40, 50] Hz, respectively, confirmed that our data were not inconsistent with the proposed mechanism. Based on our Jurkat data, when frequency index, n = ½, 1, 3/2, 2,...6, we tested resonance of 65 bio-ions for (1) the verification of the mechanism and (2) the comparison between the Lednev model and the Blackman and Blanchard model.
