Table 1.

Energetic consequences of catalytic activity determined according to the Rate Isotherm for a reaction proceeding at a fixed net rate of 10 mM s⁻¹.

				ATPase		ATP synthase
rf/rb	rf (mM s−1)	rb (mM s−1)	ΔGdiss= $\mathrm{RT}\ln (r_{\mathrm{f}}/r_{\mathrm{b}})$ (kJ mol−1)	PMFa (mV)	efficiency (%)	PMFb (mV)	efficiency (%)
1.01	1010	1000	0.026	155.38	99.95	155.54	99.95
1.1	110	100	0.246	154.70	99.51	156.23	99.51
11	11	1	6.177	136.25	87.65	174.67	89.00
101	10.1	0.1	11.889	118.50	76.22	192.43	80.79
103	10.01001	0.01001	17.795	100.13	64.41	210.79	73.75
104	10.001	0.001	23.727	81.69	52.55	229.24	67.82

^aThe PMF in this column shows that generated from ATP hydrolysis (assuming a free energy gradient of ΔG_ATP=−50 kJ mol⁻¹) in the face of the given free energy dissipation, ΔG_diss, determined according to the Rate Isotherm. It is calculated as PMF=(ΔG_ATP+ΔG_diss)/nF, where F is the Faraday constant and $n=3.\dot{3}\hspace{0.17em}{\mathrm{H}}^{+}/\mathrm{ATP}.$ The corresponding thermodynamic efficiency is calculated as (ΔG_ATP+ΔG_diss)/ΔG_ATP. ^bThe PMF in this column is that required to synthesize ATP against its free energy gradient of 50 kJ mol⁻¹ in the face of the given free energy dissipation, ΔG_diss, determined according to the Rate Isotherm. It is calculated as PMF=(ΔG_ATP−ΔG_diss)/nF. The corresponding thermodynamic efficiency is calculated as ΔG_ATP/(nF×PMF) or ΔG_ATP/(ΔG_ATP−ΔG_diss).