Driven chemical kinetics: Optimalization of catalytic action of membrane proteins by rectangular alternating electric field

Abstract

The chemical kinetics driven by external force in the form of a train of alternating rectangular impulses is discussed. The model of the conformational transition of a membrane protein exposed to an ac electric field, proposed by R. D. Astumian and B. Robertson [J. Chem. Phys. 91, 4891 (1989)], is reconsidered. On the example of this model we show that the use of the driving field in the form of rectangular impulses has two distinct advantages over the usual sinusoidal driving. The first one is that the use of a rectangular driving field makes it possible to obtain the exact solution of the basic kinetic equation of the system. This in turn enables one to write down the simple and very good approximate solution for any form of the driving field, better than the harmonic expansion used by Astumian and Robertson. A more important advantage is the greater flexibility of the rectangular driving, which makes possible the better optimalization of the process of interest. Astumian and Robertson demonstrated that the movement of charge within the catalytic cycle provides a mechanism for the enzyme to absorb energy from an ac electric field and to use that energy to enhance the catalyzed process. In this paper we show that the use of the driving ac field in the form of alternating rectangular impulses of variable duration and amplitude (instead of the usual sinusoidal modulation) leads to further optimalization of the process. The efficiency of the energy transduction, for example, can be increased from about 25% for sinusoidal driving to about 37% for suitably chosen alternating rectangular pulses.