A hypothetical mathematical construct explaining the mechanism of biological amplification in an experimental model utilizing picoTesla (PT) electromagnetic fields.

We seek to answer the conundrum: What is the fundamental mechanism by which very weak, low frequency Electromagnetic fields influence biosystems? In considering the hydrophobicity of intramembranous protein (IMP) H-bonds which cross the phospholipid bilayer of plasma membranes, and the necessity for photonic recycling in cell surface interactions after dissipation of energetic states, present models lack structure and thermodynamic properties to maintain (DeltaE) sufficient energy sources necessary for amplifications by factors of 10(12). Even though one accepts that the ligand-receptor association alters the conformation of extracellular, extruding portions of IMP's at the cell surface, and that this change can be transmitted to the cytoplasm by the transmembranous helical segments by nonlinear vibrations of proteins with generation of soliton waves, one is still unable to account for repair and balanced function. Indeed, responses of critical molecules to certain magnetic field signals may include enhanced vibrational amplitudes, increased quanta of thermal energies and order inducing interactions. We may accept that microtrabecular reticulum-receptor is associated with actin filaments and ATP molecules which contribute to the activation of the cyclase enzyme system through piezoelectricity. Magnetic fields will pass through the membrane which sharply attenuates the electric field component of an EM field, due to its high impedance. Furthermore, EM oscillations are converted to mechanical vibrations; i.e., photon-phonon transduction, to induce molecular vibrations of frequencies specifically responsible for bioamplifications of weak triggers at the membrane surface, as well as GAP junctions. The hydrogen bonds of considerable importance are those in proteins (10(12)Hz) and DNA (10(11)Hz) and may be viewed as centers of EM radiation emission in the range from the mm microwaves to the far IR. However, classical electrodynamical theory does not yield a model for biomolecular resonant responses which are integrated over time and account for the connection between the phonon field and photons. Jacobson Resonance does supply an initial physical mechanism, as equivalencies in energy to that of Zeeman Resonance (i.e., zero-order magnetic resonance) and cyclotron resonance may be derived from the DeBroglie wave particle equation. For the first time, we view the introduction of Relativity Theory to biology in the expression, mc(2)=BvLq, where m is the mass of a particle in the 'box' or 'string' (molecule in a biosystem), c is the velocity of electromagnetic field in space, independent of its inertial frame of reference, B is the magnetic flux density,v is the velocity of the carrier or 'string' (a one or two dimensional 'box') in which the particle exists, L is its dimension (length) and q represents a unit charge q=1C, by defining electromotive force as energy per unit charge. Equivalencies suggest that qvBL is one of the fundamental expressions of energy of a charged wave-particle in magnetic fields, just as Zeeman and cyclotron resonance energy expressions, gbetaB and qhB/2pim, and is applicable to all charged particles (molecules in biological systems). There may exist spontaneous, independent and incessant interactions of magnetic vector B and particles in biosystems which exert Lorentz forces. Lorentz forces may be transmitted from EM field to gravitational field as a gravity wave which return to the phonon field as microgravitational fluctuations to therein produce quantum vibrational states that increase quanta of thermal energies integrated over time. This may account for the differential of 10(12) between photonic energy of ELF waves and the Boltzman energy kT. Recent data from in vivo controlled studies are included as empirical support for the various hypotheses presented.