Mechanisms for the interaction between nonstationary electric fields and biological systems II. Nonlinear dielectric theory and free-energy transduction

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Abstract
A discussion of nonlinear dielectric phenomena and their relationship to freeenergy transduction in biological systems is given. It transpires that the conditions required for observing the nonlinear dielectric behavior of biological membranes can be expected under easily realizable circumstances, and may potentially form the basis for powerful techniques for studying membrane and other proteins in their native environment. We develop a nonlinear dielectric theory, which generalizes the dielectric permittivity to include real and imaginary parts of harmonics of the fundamental frequency. An analytical relationship is derived between these permittivities and the kinetic constants of a model protein. Of special relevance is the occurrence of higher harmonics in the dielectric displacement even when the exciting electric field consists of a single sinusoidal frequency. This is manifested by the analytical result that the corresponding higher order permittivities are in general not equal to zero, as well as by the results of a calculation of the Fourier spectrum of the dielectric displacement of a membrane enzyme subjected to a sinusoidal electric field. Interestingly, the Fourier spectrum of the dielectric displacement betrays kinetic characteristics of the enzyme. In the nonlinear domain discussed here, additional free-energy transduction from the field to the reaction catalyzed by the enzyme is possible. A study of the nonlinear dielectric behavior of biological systems (“2-dimensional dielectric spectroscopy”) could serve to account for the fact that free energy may be harvested by enzymes (with a concomitant change in their activities) from energetically rather modest exogenous electrical fields.

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