Causal Structure of the Frohlich Model of Cellular Electromagnetic Activity

Abstract

The cellular membrane as well as some intracellular structures contain polar macromolecular units, which, especially when receiving energy from such sources as adenosine triphosphate (ATP) decomposition, can perform sustained vibrational motions and hence produce an electromagnetic field. Individual molecular oscillators within groups containing various numbers of them interact with each other and exchange energy with the surroundings. The phenomenon was modeled by H. Fröhlich using a system of coupled nonlinear rate equations for the occupancy numbers of the collective modes of oscillations. This article employs a special diagrammatic technique to represent causal relationships implicit in these equations for the case of two and three individual modes. In this way, better understanding of some known properties (such as energy condensation in the lowest order mode) is achieved, and some new features of the model are uncovered, in particular, the presence and attributes of the feedback loops in the representative diagrams.