EMF signals and ion/ligand binding kinetics: prediction of bioeffective waveform parameters.

The kinetics of an electromagnetic field (EMF) target pathway are used to estimate frequency windows for EMF bioeffects. Ion/ligand binding is characterized via first order kinetics from which a specific electrical impedance can be derived. The resistance/capacitance properties of the binding pathway impedance, determined by the kinetics of the rate-determining step, define the frequency range over which the target pathway is most sensitive to external EMF. Applied signals may thus be configured such that their spectral content closely matches that of the target, using evaluation of the signal to thermal noise ratio to optimize waveform parameters. Using the approach proposed in this study, a pulsed radio frequency (PRF) waveform, currently employed clinically for soft tissue repair, was returned by modulation of burst duration, producing significant bioeffects at substantially reduced signal amplitude. Application is made to Ca2+/Calmodulin-dependent myosin phosphorylation, for which the binding time constants may be estimated from reported kinetics, neurite outgrowth from embryonic chick dorsal root explants and bone repair in a fracture model. The results showed that the retuned signal produced increased phosphorylation rates, neurite outgrowth and biomechanical strength that were indistinguishable from those produced by the clinical signal, but with a tenfold reduction in peak signal amplitude, approximately 800-fold reduction in average amplitude and approximately 10(6)-fold reduction in average power.

The sensitivity of cells and tissues to exogenous fields: effects of target system initial state.

The effect of the initial biochemical or metabolic state of a cell membrane target pathway on its sensitivity to exogenous electromagnetic (EMF) fields is considered. It is shown that the resting or initial transmembrane voltage can affect the frequency response of the membrane pathway and substantially alter the signal to thermal noise threshold (SNR) of the target. EMF sensitivity is examined using a model which describes the response to applied fields of both single cells and cells in gap junction contact via a distributed parameter electrical circuit analog, wherein a voltage-dependent membrane impedance, relating to the initial biochemical state of the target cell(s), is considered. Application of the Hodgkin-Huxley K(+)-conduction pathway membrane to this model results, at a given transmembrane voltage, in a preferential array response to applied field frequencies in the 1-100 Hz range, centered at approximately 16 Hz for 1-10 mm array lengths. Extension of the model to consider the voltage dependence of the Hodgkin-Huxley K+ pathway results in a significant modulation of array frequency response with changing membrane resting potential. The result is EMF sensitivity (SNR) depends upon the initial state of the target tissue, providing a possible explanation of why, e.g., repairing, rather than resting, bone exhibits a physiologically relevant response to certain weak EMF signals.

Lorentz approach to static magnetic field effects on bound-ion dynamics and binding kinetics: thermal noise considerations.

The present study characterizes an ion-binding site, a molecular cleft in a signalling molecule such as calmodulin or troponin C, as a damped linear isotropic oscillator potential for small displacements about the origin. Quantitative assessments of the effects of thermal noise and exogenous static magnetic fields are made through a statistical mechanical treatment of the Lorentz-Langevin equation for an ion bound in a molecular cleft. Thermal noise causes a bound ion to be ejected from the site after a bound lifetime dependent upon the thermal noise spectral density. It is shown that the Lorentz-Langevin model requires values of the viscous damping parameter many orders of magnitude below those for bulk water in order to characterize the binding site and to obtain realistic lifetimes for a bound ion. The model predicts that milliTesla-range magnetic fields are required for static field effects on dissociation kinetics. The Lorentz equation also yields a classic coherent solution describing precession of the bound-ion oscillator orientation at the Larmor frequency. The bound-ion dynamics described by this coherent solution are sensitive to microTesla-range static magnetic fields in the presence of thermal noise. Numerical integration of the contribution of thermal noise forces to these dynamics is in good agreement with the results of statistical mechanical analysis, also producing realistic bound lifetimes for only very low viscous damping values. The mechanisms by which modulation of precessional motion might enable a signalling molecule such as calmodulin to detect an exogenous magnetic field are presently unclear.