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The influence of radiofrequency electromagnetic exposure on ligand binding to hydrophobic receptor proteins is a plausible early event of the interaction mechanism. A comprehensive quantum Zeeman-Stark model has been developed which takes into account the energy losses of the ligand ion due to its collisions inside the receptor crevice, the attracting nonlinear endogenous force due to the potential energy of the ion in the binding site, the out of equilibrium state of the ligand-receptor system due to the basal cell metabolism, and the thermal noise. The biophysical "output" is the change of the ligand binding probability that, in some instances, may be affected by a suitable low intensity exogenous electromagnetic "input" exposure, e.g., if the depth of the potential energy well of a putative receptor protein matches the energy of the radiofrequency photon. These results point toward both the possibility of the electromagnetic control of biochemical processes and the need for a new database of safety standards.

A quantum–mechanical model is proposed to evaluate the bioelectrochemical transduction of low-intensity acoustic exposure, with reference to the binding process of a ligand (messenger) ion to a receptor protein. The interaction of the acoustic exposure with the ligand–receptor chemical reaction is assumed to be mediated by the endogenous electric field of the receptor binding crevice. The displacement of the solvent (water) molecules surrounding the protein, when exposed to the acoustic field, induces the displacement of the receptor molecules from their initial thermal equilibrium position, so that the attractive endogenous force exerted by the receptor on the ligand becomes time-varying at the frequency of the acoustic exposure. A suitable perturbing Hamiltonian operator is evaluated, which transduces the exogenous acoustic exposure into a kind of Stark effect. The density operator method is utilized to statistically evaluate the binding probability in presence of thermal noise. The typical reference intensity (power density) of the incident acoustic wave is 0.1 mW cm −2 in the frequency range 0.5–5 MHz. Usual first-order approximation techniques are employed to evaluate in closed form the change in the binding probability, as compared as usual with its value at thermal equilibrium. By doing so, it is possible to identify a range of parameter values where resonant effects due to the acoustic exposure occur. Thus, a direct numerical integration of the equations is performed in order to validate these first-order findings. The resulting effects are very small, as compared with the binding probability under unperturbed conditions, i.e., at thermal equilibrium, which appears to be the limiting factor of the effectiveness of low-intensity acoustic exposure. These conclusions suggest future research directions, accounting for the out-of-equilibrium living state of a cell and its related basal metabolism, in order to explain those published experimental results which suggest that the binding probability may be significantly affected by a low-intensity exogenous acoustic field.

The statistical properties of the solution of the Langevin–Lorentz equation are analyzed by means of the Fokker–Planck approach. The equation describes the dynamics of an ion that is attracted by a central field and is interacting with a time-varying magnetic field and with the thermal bath. If the endogenous force is assumed to be elastic, then a closed-form expression for the probability density of the process can be obtained, in the case of constant magnetic exposure and, for the time-varying case, at least asymptotically. In the general case, a numerical integration of the resulting set of differential equations with periodically time-varying coefficients has been implemented. A framework for studying the possible effects of low-frequency, low-intensity electromagnetic fields on biological systems has been developed on the basis of the equation. The model assumes that an exogenous electromagnetic field may affect the binding of a messenger attracted by the endogenous force field of its receptor protein. The results are applicable to the analysis of experiments, e.g., exposing a Petri dish, containing a biological sample, to a periodically time-varying magnetic field generated by a pair of Helmholtz coils, most widely used in the scientific literature. The proposed model provides a theoretical mean for evaluating the biological effectiveness of low-frequency, low-intensity electromagnetic exposure.

This paper addresses the problem of evaluating theoretically the effects of electromagnetic (EM) exposure on biological systems. EM fields can affect the chemical activity of ions while they interact with the membrane receptors of a cell during a binding process. A coulombic three-state Zeeman model for the binding site is proposed, and the ion adsorption under low-frequency magnetic exposure is described by means of the density operator. The system interactions with the thermal bath are accounted for by a suitable set of lifetime parameters. The limits of a first-order perturbation approach, which allows us to find a closed-form expression for the ion-binding probability, are discussed. The biological effectiveness of a Helmholtz coil exposure system is rather small if computed according to the simplifying assumptions of the paper.

This paper attempts to elucidate the mechanism of action of electromagnetic exposure on ligand-receptor binding. The classical Langevin-Lorentz model, which can be used to describe the adsorption process of a messenger ion, is reviewed and discussed. We conclude that low intensity exposure does not affect appreciably the ion dynamics in the presence of background thermal white noise. A more realistic evaluation of the endogenous field present in a binding site leads to a quantum model based on weak Zeeman-Stark effects. The case of the Zeeman effect is studied in detail assuming a three-state binding site. The density operator method is used, introducing suitable lifetimes which model the thermal bath interaction. The closed form expression for the binding probability is found, as a function of the ligand-receptor parameters and of the electromagnetic sinusoidal exposure.

Non-invasive therapeutic treatment and/or quantitative evaluation of musculoskeletal tissue are performed in vivo by subjecting musculoskeletal tissue (11) to an ultrasonic acoustic signal pulse excitation, involving a composite sine wave signal consisting of plural discrete frequencies that are spaced in the ultrasonic region to approximately 2 MHZ, and repeated substantially in the range of 1 Hz to 1000 Hz. In a quantitative evaluation, the signal is supplied to one of two transducers (12, 13) on opposite sides of the tissue, and the signal received by the other transducer is processed (14): (a) to obtain an averaged per-pulse signal, and (b) to produce a Fourier transform of the averaged per-pulse tissue transmittal signal. In a separate operation, the same transducers are subjected to the same excitation, reception and processing, using a medium of known acoustic properties and path length to produce a reference Fourier transform. In a therapeutic treatment, the transducer (12) excited by the composite sine wave signal, is applied for a time period and magnitude.

The average behaviour of dipoles (water molecules) in the binding regions of charged ligands, where the local electric field may be high and nonuniform, is investigated. The model incorporates all the features of Clausius-Mossotti's, Debye's, Onsager's, and Kirkwood's approaches and assumes, as a novel feature, that the dielectrophoretic drift of dipoles is balanced by dipole diffusion. Our analysis shows that the current view of bound water near charged surfaces should be re-examined. A new relationship among local permittivity, electric field, and water density is found that could explain why water molecules are rejected by charged molecular crevices which can engineer ligand binding at very high rates as compared to bulk water.

The behaviour of electric dipoles (water molecules) under the action of a high and nonuniform electric field is investigated. The model incorporates all the features of Clausius-Mossotti’s Debye’s, Onsager’s and Kirkwood’s approaches, and assumes, as a novel feature, that the dielectrophoretic drift of dipoles is balanced by dipole diffusion. A new relationship among local permittivity, electric field and water density is found that could explain why water molecules are rejected by charged molecular crevices which can engineer the binding of ionized ligands at very high rates as compared to bulk water.

Low-intensity magnetic induction fields (