A Lorentz model for weak magnetic field bioeffects: Part I—Thermal noise is an essential component of AC/DC effects on bound ion trajectory

Abstract

We have previously employed the Lorentz-Langevin model to describe the effects of weak exogenous magnetic fields via the classical Lorentz force on a charged ion bound in a harmonic oscillator potential, in the presence of thermal noise forces. Previous analyses predicted that microT-range fields give rise to a rotation of the oscillator orientation at the Larmor frequency and bioeffects were based upon the assumption that the classical trajectory of the bound charge itself could modulate a biochemical process. Here, it is shown that the thermal component of the motion follows the Larmor trajectory. The results show that the Larmor frequency is independent of the thermal noise strength, and the motion retains the form of a coherent oscillator throughout the binding lifetime, rather than devolving into a random walk. Thermal equilibration results in a continual increase in the vibrational amplitude of the rotating oscillator towards the steady-state amplitude, but does not affect the Larmor orbit. Thus, thermal noise contributes to, rather than inhibits, the effect of the magnetic field upon reactivity. Expressions are derived for the ensemble average of position and the velocity of the thermal component of the oscillator motion. The projection of position and velocity onto a Cartesian axis measures the nonuniformity of the Larmor trajectory and is illustrated for AC and combined AC/DC magnetic fields, suggesting a means of interpreting resonance phenomena. It is noted that the specific location and height of resonances are dependent upon binding lifetime and initial AC phase.

Primary human osteoblasts with reduced alkaline phosphatase and matrix mineralization baseline capacity are responsive to extremely low frequency pulsed electromagnetic field exposure — Clinical implication possible

“…Several theories are favored within the bioelectromagnetic society, e.g. the molecular gyroscope model (Binhi and Savin, 2002), Lorentz models (Muehsam and Pilla, 2009a, Muehsam and Pilla, 2009b), DNA antenna model (Blank and Goodman, 2011), radical pair model (Foley et al, 2011), and ion cyclotron resonance (Bawin et al, 1975). It might well be that effects triggered by the ELF-PEMFs described here can be explained by a combination of these theories.…”

Recovery Effects of a 180 mT Static Magnetic Field on Bone Mineral Density of Osteoporotic Lumbar Vertebrae in Ovariectomized Rats

“…Because our applied SMF at B max of 180 mT was much lower in the magnetic force compared with the SMF of several Tesla, different mechanisms might exist between them. Recently, Muehsam and Pilla [63, 64] proposed a Lorenz model for weak magnetic field bioeffects, suggesting that weak exogenous AC/DC magnetic fields can act on an ion/ligand bound in a molecular cleft, based upon the assumption that the receptor molecule is able to detect the Larmor trajectory of an ion or ligand within the binding site. To date, however, there is insufficient direct experimental evidence pertaining to this model.…”

Non-Thermal Radio Frequency and Static Magnetic Fields Increase Rate of Hemoglobin Deoxygenation in a Cell-Free Preparation

“…Although direct action on ferrous heme [28] or free radical lifetimes [29], [30] may account for the SMF effects observed here, several other models have been proposed for weak, μT-range magnetic field bioeffects [31]. We have previously shown using the Lorentz-Langevin model that μT-range magnetic fields may have an effect on the thermally activated orientation of ionic oscillators and waters bound at the protein surface [32], [33] and that the minimum magnetic field required to directly compete with thermal forces to affect dissociation of a bound ion or ligand from a protein binding site is in the 1–10 mT-range [34]. Thus, the effect of the mT-range magnetic field employed in this study could occur by the direct action of the Lorentz force on charges bound at the protein/water interface.…”