Experiments on the effects of external periodic variation of constraints on the thermodynamics of an oscillatory system

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Abstract
The first experiments are presented which show that an external periodic perturbation imposed on a nonlinear isothermal biochemical reaction far from equilibrium may change the dissipation and hence the efficiency of that reaction; the results confirm earlier theoretical and numerical predictions. The reaction is driven and maintained far from equilibrium, a process thermodynamically equivalent to the establishment and maintenance of a concentration gradient across a membrane, i.e., a biochemical pump. We study the highly nonlinear oxidation of NADH catalyzed by the enzyme horseradish peroxidase (HRP) under conditions of continuous oxygen influx. NAD+ is recycled to NADH by a second enzymatic reaction. Experimental conditions are set so that the (HRP) reaction is in a stable limit cycle (autonomous oscillations). We then apply a periodic perturbation to the oxygen influx such that the average influx during the perturbation equals the previous steady influx. We present data obtained for a variety of frequencies and amplitudes of sinusoidal variations in the oxygen influx. Upon imposition of the periodic perturbation, we find changes in the average steady-state concentration of NADH, the average ΔG of the (HRP) reaction, the average rate of the (HRP) reaction, the phase difference between ΔG and the rate, the response of the system to the perturbation, and the dissipation of the reaction. Changes in dissipation which occur upon the imposition of an external periodic perturbation are a result of a combination of changes which occur in the thermodynamic quantities listed. These results confirm the possibility of variable efficiency of biological pumps since the establishment and maintenance of a chemical potential difference across a membrane is thermodynamically equivalent to the establishment and maintenance of a nonequilibrium stationary state in a single phase, open, homogeneous system. Moreover, the results confirm the possibility of an alternating current chemistry of control and optimization of thermodynamic efficiency, dissipation, and yield by means of an external variation of constraints in nonlinear (bio)chemical reactions and biological pumps.