Thermodynamic marking of F_OF₁ ATP synthase

F_OF₁ ATP synthase is a ~100% efficient molecular machine for energy conversion in biology, and holds great lessons for man-made energy technology and nanotechnology. In light of formidable biocomplexity of the F_OF₁ machinery, its modeling from pure physical principles remains difficult and rare. Here we construct a thermodynamic model of F_OF₁ from experimentally accessible quantities plus a single entropy production that generally has vanishingly small values (<1k_B). Based on the physical inputs, this model captures F_OF₁ performance observed over an exhaustively wide range of proton-motive force and nucleotide concentrations. The model predicts a distinct 1/8k_BT slope for ATP synthesis rate versus proton-motive force, which is verified by experimental data and represents a profound thermodynamic marking of this amazingly efficient machine operating near a universal limit of the 2nd law of thermodynamics. The model further predicts two symmetries of heat productions, which are testable by available experimental techniques and offer quantitative constraints on F_OF₁'s possible mechanisms behind its ~100% efficiency.