Vincze G, Szasz A, Liboff A R
Biotechnics Department, Szent Istvan University, Budapest, Hungary.
Bioelectromagnetics. 2008 Jul;29(5):380-6. doi: 10.1002/bem.20406.
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.
尽管有实验证据支持生物系统中类似离子回旋共振（ICR）的相互作用，但迄今为止，对于这种现象尚无合理的理论解释。列德涅夫提出的参数共振方法在预测作为交流磁场强度与直流磁场强度之比的函数的响应方面取得的成功有限，该方法从钙结合态跃迁概率的磁诱导变化角度解释结果。在本工作中，我们推导了在洛伦兹力影响下具有任意荷质比的阻尼离子速度的表达式。微分方程的级数解揭示了瞬态响应以及类似共振的项。一个引人入胜的结果是，离子漂移速度的表达式包括一种与之前在参数共振中跃迁概率所得到的有点相似的贝塞尔函数依赖性。然而，在本工作中，不仅存在明确的阻尼效应，而且之前的贝塞尔依赖性现在作为一个更一般解的子集出现，该更一般解不仅包括作为自变量的磁场交流/直流比，还包括回旋频率Ω与外加交流频率ω之比。实际上，这消除了将ICR相互作用解释为源于离子 - 蛋白质结合位点的必要性。我们假设该模型中预测的选择性增强的漂移速度可以解释类似ICR的现象是由离子通道门附近相互作用概率增加导致的。
