6.4.1 The proton-motive force

The proton concentration in the cytosol is approximately ten times higher than that in the mitochondrial matrix. How much free energy does it generate if protons travel downhill this concentration gradient? This can be determined from the following formula:

ΔG = RT ln(H⁺_in/H⁺_out)

With R = 8.31 J × K^-1× mole^-1, T = 310K, and H⁺_in/H⁺_out = 10 this comes to roughly 6 kJ/mole. While this is significant, the larger contribution to the proton-motive force actually comes from the electrostatic membrane potential across the inner mitochondrial membrane. Like the proton concentration gradient, this electrical potential is a direct consequence of the proton pumping: Each proton ejected leaves a deficit of a positive charge, or one negative charge, inside the mitochondrion. In a 'fully loaded' mitochondrion, the resulting potential amounts to 150 mV, negative inside.

The free energy contribution of the membrane potential can be calculated from this equation:

ΔG = –ΔE × n × F

With F = 96,500 Coulomb/mole, a potential ΔE = 0.15V, and the definition 1V = 1J/Coulomb, this gives us approximately 15 kJ/mole. In sum, the proton-motive force is caused to 3/4 by the membrane potential, and to 1/4 by the proton concentration gradient.