Electrochemical potential difference oxidative phosphorylation

Here, the subscripts P, H, and O refer to phosphorylation, the H+ flow, and substrate oxidation, respectively, and A/uh is the electrochemical potential difference of protons. We consider only systems at steady state. The dissipation function can be transformed as... 

Two major ATP synthesizing reactions in living organisms are oxidative phosphorylation and photophosphorylation. Both reactions take place in H -ATPase (FqF,), which is driven by an electrochemical potential difference of protons across the biomembrane, as predicted by Mitchell [1]. In Racket s laboratory, ATPases related to oxidative phosphorylation were prepared, but their relationship to Mitchell s chemiosmotic hypothesis [1] was not described [2], Later, an insoluble ATPase (H -ATPase) was shown to translocate protons across the membrane when it was reconstituted into liposomes [3], H -ATPase was shown to be composed of a catalytic moiety called F, (coupling factor 1) [4], and a membrane moiety called Fq [5], which confers inhibitor sensitivity to F,. F was shown to be a proton channel, which translocates down an electrochemical potential gradient across the membrane when Fg is reconstituted into liposomes (Fig. 5.1) [6]. Thus, -ATPase was called FqFj or ATP synthetase. 

In the chemiosmotic theory for oxidative phosphorylation (Chap. 14), electron flow in the electron-transport chain is coupled to the generation of a proton concentration gradient across the inner mitochondrial membrane. Derive an expression for the difference in electrochemical potential for a proton across the membrane. 

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