Impact of mitochondrial electric field on modal occupancy in the Fröhlich model of cellular electromagnetism.

Fröhlich model describes emission of electromagnetic field in the interior of biological cells by oscillating polar units, now mostly identified with microtubule filaments. Central element of this theory is the system of rate equations for the quantum occupancy numbers n i of collective oscillation modes. These equations describe both linear and nonlinear properties of the system; presence of the latter can lead to condensation of the incoming energy into the lowest frequency mode - a phenomenon deemed to be of major importance for cell's biochemistry, because the excited mode can engage in chemical reactions while the major part of the system remains near the equilibrium, not exposed to energetic stress. This paper explores, using a simple model, the influence of strong static electric field created by mitochondria flanking the microtubules on nonlinear interactions and, in turn, on occupancy numbers. The computed results show that simultaneous presence of both sufficient metabolic pumping and adequately elevated static electric field is necessary for the full unfolding of the hallmark properties of the Fröhlich model. It is suggested that cancer-related mitochondrial dysfunction leading to metabolic transformation has additional adverse effect mediated by diminution of static fields which in turn reduces the nonlinear processes in the Fröhlich systems, essential for energy condensation in the fundamental mode.