Question

Electron transport translocates protons across the mitochondrial membrane, establishing a pH gradient. During oxidative phosphorylation by a suspension of liver mitochondria in a medium of pH 7.4, the pH of the matrix was measured as 7.7 and the membrane potential as 0.17 V.

Calculate the [H+ ] in the external medium and in the matrix under these conditions. What is the outside : inside ratio of [H+ ]? Under the conditions listed, what is the free energy for the movement of a proton from the intermembrane space to the matrix at 37°C

Answer 1

a.

[H+] in the medium= 10^-7.4 = 4 * 10^-8 M

[H+] in the matrix =10^-7.7 = 2.0x10^-8 M

b.

[H+]_medium/[H+]_matrix

= 4.0x10^-8 / 2.0x10^-8

= 2

The free energy inherent in this concentration difference, ΔG^o

= -RT ln K

= -RT ln [H+]_medium/[H+]_matrix

= - 8.314 * 298 * ln 2

= -1.717 kJ

Concentration difference has free energy inherent in it. [H+] will tend to go from higher concentration to lower concentration and it will be a spontaneous process. For spontaneous processes, dG is negative.