Energy transfer and molecular switching. I. The nerve action potential

In previous papers (Barrett, 1977b, 1980), the concept of chemical paramemetric excitation was applied to a number of diverse chemical phenomena and contrasted with the concept of chemical resonance, which is a special case of parametric excitation. In the present paper, its status as the fundamental concept of energy transfer and molecular switching is indicated, providing a mechanically sound explanation of nerve excitation at a basic level.The mechanism addressed by the parametric excitation concept is intermediate between macroscopic models of membrane assymetry and molecular models. No assumptions are made concerning the related macroscopic processes, but a systematic approach to organizational aspects of the processes involved in energy transfer is proposed.The chemical analog of the Manley-Rowe relations, which are the power conservation relations for parametrically excited electrical networks, is also derived. The demonstration of such Manley-Rowe relations for chemical systems indicates, for the first time, an explanation for the directionality of flow of power, and thus designates a pumping role. The generalized Manley-Rowe relations translated into flow, reaction, as well as oscillatory system terms, are suggested to be a universal law. Non-linearity is due to the coupling of three systems—each separately describable by Onsager linear relations—by the generalized Manley-Rowe conditions relating flows/reactions/oscillations.All phenomena considered are treated in accordance with a principle of power transfer optimization (Odum & Pinkerton, 1955). Parametric excitation involves three-body interaction, with one system as energy donor, the pump, another as energy receiving, the idler, and a third as mediator of this energy flow, the signal. A conservation law is mandatory for flows/reactions/oscillations, ω_i so that ω_pump= ω_idler±ω_signal. The macroscopic structure, which sets up the conditions for this law to be in operation, may be of diverse kinds, e.g. membrane-bounded compartments, macromolecules capable of multiple conformations and bound cations, etc. All are non-linear.