Model proton pump

A simple proton pump curcuit to show elementary physico-chemical processes

The diagram shows a model proton pump, with elementary processes separated so that we can treat each as a partial reaction. We will consider the process at equilibrium, so that the pump operates against a proton gradient in equilibrium with the driving force from the overall electron transfer reaction from D₁ to A₂. Because the system is at equilibrium, each of the partial reactions must also be at equilibrium. To simplify the treatment, we have assumed that all electron transfers are 1-electron (or 1-electron, 1-H⁺) events.

For the electrogenic arm

E'_D1 = E'_C1
E'_A1 = E'_C2 But electron transfer across the membrane from C₁ to C₂ involves electrical work against the electrical component of the proton gradient (

):

G'_elect = znF

_(L-R)

The work available to drive this is the redox potential difference between C₁ and C₂, or from the equilibria above, between D₁ and A₁:

G'_chem = -znF

E'_{(A1 - D1)}

At equilibrium, the two work terms balance, and (since the electron carries a negative charge):

G'_elect =

G'_chem

E'_{(A1 - D1)} =

_(L-R) --------(1)

For the neutral arm, with hydrogen carrier C.H⁺/CH, the oxidized and reduced forms of the couple can both freely diffuse in the membrane phase, and so have the same activity on both sides of the membrane. However, the potential of the couple will be different on the left and right, because the protons with which the couple equilibrates will be at a different activities in left and right aqueous phases. From the condition of equilibrium,

On the right,

E'_A1 = E'_D2 = E'_C = E^o_C + 2.303.RT/zF.log₁₀ ([C][H⁺_R]/[CH])

On the left,

E'_A2 = E'_C = E^o_C + 2.303.RT/zF.log₁₀ ([C][H⁺_L]/[CH])

The pH gradient across the membrane will be maintained by the work term due to the difference in redox potential between couples A₁ and A₂, as shown by substitution between the equations above:

E'_A2 - E'_A1 = 2.303.RT/zF.log₁₀ [H⁺_L]/[H⁺_R] = -Z

pH_(L-R) ---------(2)

where Z = 2.303.RT/zF

Now, by substituting for E'_A1 from eq. (1) in eq. (2), we can find the balancing work terms from the redox drop between D₁ and A₂, and from the proton gradient.

E'_(A2-D1) = E'_A2 - E'_D1 =

_(L-R) - Z

pH_(L-R) =

p

Note that, because the redox potentials of couples at equilibrium in any phase have the same value, we would have reached the same equation if C₂ had donated electrons directly to the C/CH couple, or if the electron transfers between D₁ and C₁, and between CH and A₂, had occured at the membrane/water interface, with D₁ and A₂ in the membrane rather than in the water. This latter set of conditions is appropriate for many of the proton pumps of electron transfer chains.

©Copyright 1996, Antony Crofts, University of Illinois at Urbana-Champaign, a-crofts@uiuc.edu