Proton pump thermodynamic efficiency

Consideration of relative proton affinities alone is not sufficient to explain the directionality of transport in proton pumps. For efficient proton pumping it is essential that the activated proton (state 2) cannot flow back to group A, which thermodynamically would be dictated by the fact that A has much higher proton affinity than C. To that effect, relative insulation to proton transport in state 2 is required either between B and A, or alternatively, between A and surface I. This requirement is often described in terms of an alternating access model [Jardetzky, 1966] and is now fairly well understood in bacteriorhodopsin [Lanyi, 1999]. Likewise, proton leakage from C to B must be prevented in step 4, where B has a much higher proton affinity than C. In the depicted scheme (Fig.2), the back flow of is hampered by the high proton activity of C relative to O, so that proton relay to B from A is rapid compared to alternative reprotonation from O via C. 

Fig. 2.3 also shows that the transfer of energy from the respiratory chain to the proton circuit can be extremely efficient, in that a slight thermodynamic disequilibrium results in a considerable energy flux. The actual disequilibrium between the respiratory chain and the proton electrochemical potential is even less than appears from the drop in the latter, since the redox span across the respiratory chain proton pumps also contracts [24],... 

Schell, M. Kundu, K. Ross, J. Dependence of thermodynamic efficiency of proton pumps on frequency of oscillatory concentration of ATR Proc. Natl. Acad. Sci. USA 1987, 84, 424-428. 

Protons are pumped in living systems to establish a proton gradient, and the energy necessary for this pumping is frequently provided by the hydrolysis of ATP, in which ADP and phosphate are formed [7]. In this section, we study a model of a proton pump found in the plasma membrane of plants [8-12] and include the coupling of potassium and calcium ion transport. As in prior examples, we calculate the thermodynamic efficiency [13] of the proton pump with a constant influx of ATP and compare that to the thermodynamic efficiency with an oscillatory influx of ATP, the average of which is the same as the constant concentration of ATP. 

The thermodynamic efficiency of the proton pump is defined by the equation... 

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