Dissipation in an oscillatory reaction mechanism with periodic input

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Abstract
We investigate dissipation in externally driven systems beyond marginal stability where, in the absence of external effects, the system has oscillations. The reaction mechanism we choose for study is that proposed by Higgins to describe the free oscillations in the phosphofructokinase reaction of the glycolytic pathway. Entrainment of that reaction is realized by imposing a periodic supply of fructose-6-phosphate. The condition of a periodic supply can be met in biological systems, for instance if transport occurs across a membrane with concentration dependent permeability. An essential reverse reaction is added on the input side of the mechanism, which then permits fructose-6-phosphate to interact with its own supply. A convenient definition of efficiency is introduced to measure the effect of a periodic source on the alteration of free energy dissipation. We go beyond a linear analysis in two respects : First, we integrate the kinetic equations numerically and second, we use the equivalent linearization method of Bogoluibov and Mitropolsky, which is not restricted to small amplitude motion. There is a large resonance effect on the dissipation in the fundamental entrainment band (much larger than for submarginal conditions) and smaller effects at higher harmonics and one subharmonic. A large change in efficiency, from positive to negative, occurs in a very narrow range of frequency of applied concentration variation, which provides the possibility of regulation of dissipation. The equivalent linearization method applied to the fundamental entrainment band gives qualitatively correct trends and results.

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