New theoretical treatment of ion resonance phenomena

Despite experimental evidence supporting ICR-like interactions in biological systems, to date there is no reasonable theoretical explanation for this phenomenon. The parametric resonance approach introduced by Lednev has enjoyed limited success in predicting the response as a function of the ratio of AC magnetic intensity to that of the DC field, explaining the results in terms of magnetically induced changes in the transition probability of calcium binding states. In the present work, we derive an expression for the velocity of a damped ion with arbitrary q/m under the influence of the Lorentz force. Series solutions to the differential equations reveal transient responses as well as resonance-like terms. One fascinating result is that the expressions for ionic drift velocity include a somewhat similar Bessel function dependence as was previously obtained for the transition probability in parametric resonance. However, in the present work, not only is there an explicit effect due to damping, but the previous Bessel dependence now occurs as a subset of a more general solution, including not only the magnetic field AC/DC ratio as an independent variable, but also the ratio of the cyclotronic frequency Omega to the applied AC frequency omega. In effect, this removes the necessity to explain the ICR interaction as stemming from ion-protein binding sites. We hypothesize that the selectively enhanced drift velocity predicted in this model can explain ICR-like phenomena as resulting from increased interaction probabilities in the vicinity of ion channel gates.