Elsa Moggia

Effect of lifetimes on ligand binding modelled by the density operator

Abstract 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.

Fokker–Planck analysis of the Langevin–Lorentz equation: Application to ligand-receptor binding under electromagnetic exposure

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 protei...

Interaction mechanism between electromagnetic fields and ion adsorption: endogenous forces and collision frequency

Abstract The adsorption of an ion messenger at a cell receptor is a potential target of electromagnetic exposure, which may affect the binding rate coefficient. The role of the endogenous field force experienced by an ion approaching the binding site is of paramount importance. In order to evaluate the effects of the exogenous field, the endogenous force obtained from the protein data bank has been approximated as a central field by means of a linear restoring force (“spring-like”) and by means of an inverse square field (“coulombic-like”). The first approximation is used in the classical Langevin-Lorentz model and the second in the quantum Zeeman-Stark model. The ion losses due to “collisions” near the binding site are modelled in the classical approach by a viscous collision frequency and in the quantum approach by a set of suitable inverse collision frequencies (lifetimes). In the case of collisions with solvent dipolar molecules (e.g. water), it is shown that the number of colliding solvent dipoles can be very small owing to the large gradients of the endogenous electric field. On the contrary, a binding site is, by definition, a spatial domain finite in size, where colliding molecules move in the Knudsen (ballistic) regime. As a consequence, the mean free path cannot exceed the domain dimension, irrespective of the low concentration of colliding molecules. It is concluded that the ion collision frequency (i.e. in classical terms, the effective viscosity of a binding site) can be many orders of magnitude lower than in the bulk solvent (lifetimes are longer in the quantum model), so that electromagnetic bioeffects may occur at low intensities of the exogenous fields.

Osmotic coefficients of electrolyte solutions.

In this paper, the osmotic coefficient, phi, of electrolyte solutions is considered. According to the Gibbs-Duhem equation, the calculation of phi follows from that of the mean activity coefficient, gamma, based on a pseudolattice approach recently proposed. For any given electrolyte, the whole range of concentrations providing gamma<or =1 is considered. The major feature of the pseudolattice approach is given by the fact that gamma can be calculated without using adjustable parameters where the (upper) concentration, clim, exists at which the electrolyte solution exhibits gamma=1. In the remaining cases, a unique parameter is required, that is, the value of clim that should ideally give gamma=1 for the electrolyte. Known values of clim from 1 up to 9 M (about) are available for several aqueous electrolytes at 25 degrees C. All formulas in this paper are applied for 1:1, 2:2, 1:2, and 2:1 aqueous electrolytes at 25 degrees C.

Enhancement of the interaction between low-intensity R.F. e.m. fields and ligand binding due to cell basal metabolism

Power absorption by biological tissues, due to low‐intensity electromagnetic exposure at radio frequencies, as those generated by personal telecommunication systems, is typically negligible. Nevertheless, the electromagnetic field is able to affect biological processes, like the binding of a messenger ion to a cell membrane receptor, if some specific conditions occur. The depth of the attracting potential energy well of the binding site must be comparable with the radio frequency photon energy. The dependance of the binding potential energy on the spatial coordinates must be highly non‐linear. The ion–receptor system, in absence of the exogenous electromagnetic exposure, must be biased out of thermodynamic equilibrium by the cell basal metabolism. When the above conditions concur a low‐intensity radio frequency sinusoidal field is able to induce a steady change of the ion binding probability, which overcomes thermal noise. The model incorporates the effects of both thermal noise and basal metabolism, so that it offers a plausible biophysical basis for potential bioeffects of electromagnetic fields, e.g., those generated by mobile communication systems.

Application of the quasi-random lattice model to rare-earth halide solutions for the computation of their osmotic and mean activity coefficients

This work dealt with the computation of the mean activity coefficients of rare-earth halide aqueous solutions at 25°C, by means of the Quasi Random Lattice (QRL) model. The osmotic coefficients were then calculated consistently, through the integration of the Gibbs-Duhem equation. Using of QRL was mainly motivated by its dependence on one parameter, given in the form of an electrolyte-dependent concentration, which was also the highest concentration at which the model could be applied. For all the electrolyte solutions here considered, this parameter was experimentally known and ranged from 1.5 to 2.2 mol/kg, at 25 °C. Accordingly, rare-earth halide concentrations from strong dilution up to 2 mol/kg about could be considered without need for best-fit treatment in order to compute their osmotic and mean activity coefficients. The experimental knowledge about the parameter was an advantageous feature of QRL compared to existing literature models. Following a trend already observed with low charge electrolytes, a satisfactory agreement was obtained with the experimental values for all the investigated rare-earth chlorides and bromides. For the sake of compactness, in this work the considered rare-earth halides were all belonging to the P63/m space group in their crystalline (anhydrous) form.

A Zeeman-Stark/Markov model approach to study the EM-RF exposure of a potassium channel

The extraordinary increase in the use of electromagnetic (EM) radiofrequency (RF) radiation has stimulated new researches concentrated on the study of the early steps of the EM interaction mechanisms. As most of the effects due to the exogenous exposure of biosystem has been associated with the cell membrane, these researches are mainly oriented toward the study of the molecular aspects of the interaction. Here, the authors introduce an integrated methodology of analysis, which involves cascading steps such as quantum modelling of the system constituted by a ligand ion (Ca/sup 2+/) and a protein receptor (Calmodulin) of the cell membrane and analysis of the protein channel activity by means of a stochastic model of the channel.

Ligand Binding under RF EM Exposure

The influence of electromagnetic exposure on ligand binding to receptor proteins is a putative early event of the interaction mechanism leading to biological effects. The most recent development of the quantum Zeeman-Stark model is reviewed, addressing the following points: losses due to the collisions of the ligand ion inside the hydrophobic binding crevice and thermal noise; evaluation of the attracting endogenous force of the binding site from the protein data base; out of equilibrium state of the ligand-receptor system due to the basal cell metabolism.

Influence of Mobile Telecommunication Fields on Ligand Binding to Hydrophobic Metallo-Proteins

With respect to the study of biological effects due to the exposure of living systems to electromagnetic fields, one of the most widely studied biochemical processes is the binding of light ligands (e.g. metal ions, like Cam) to receptor proteins. Two general models (though simplified to avoid any molecular dynamics simulation) of ion binding emerge from the literature: the classical Langevin-Lorentz (L-L) model and the quantum Zeeman-Stark (Z-S) model.

Validation of the quantum Z-S Model by Means of the Interaction Between MW Fields and Zn -Protoporphyrin System

The dynamics of the Zn-protoporphyrin IX has been assessed by means of molecular dynamics methods. The conformational rearrangements of the protoporphyrin atoms during the Zn2+ docking (sailing) into (from) the center of its binding site occurs in the picosecond scale, so that any microwave electromagnetic exposure can be considered as almost constant, with respect to the dynamics of the constituent atoms induced by the ion displacement. The computer simulation of the complexation process with and without a low-intensity electromagnetic field has demonstrated the inhibitory effect of the exposure on the complex formation.1 This result has been confirmed experimentally at 2.45 GHz.1,2 We have tested the predictive ability of the quantum Zeeman-Stark (Z-S) model3 of ligand binding against the Zn-protoporphyrin system.