On the thermodynamic efficiency of Ca²⁺-ATPase molecular machines.

Experimental studies have shown that the activity of the reconstituted molecular pump Ca(2+)-ATPase strongly depends on the thickness of the supporting bilayer. It is thus expected that the bilayer structure will have an impact on the thermodynamic efficiency of this nanomachine. Here, we introduce a nonequilibrium-thermodynamics theoretical approach to estimate the thermodynamic efficiency of the Ca(2+)-ATPase from analysis of available experimental data about ATP hydrolysis and Ca(2+) transport. We find that the entropy production, i.e., the heat released to the surroundings under working conditions, is approximately constant for bilayers containing phospholipids with hydrocarbon chains of 18-22 carbon atoms. Our estimates for the heat released during the pump operation agree with results obtained from separate calorimetric experiments on the Ca(2+)-ATPase derived from sarcoplasmic reticulum. We show that the thermodynamic efficiency of the reconstituted Ca(2+)-ATPase reaches a maximum for bilayer thicknesses corresponding to maximum activity. Surprisingly, the estimated thermodynamic efficiency is very low, ∼12%. We discuss the significance of this result as representative of the efficiency of other nanomachines, and we address the influence of the experimental set-up on such a low efficiency. Overall, our approach provides a general route to estimate thermodynamic efficiencies and heat dissipation in experimental studies of nanomachines.