I am reading oxidative phosphorylation and I can't understand why the protons that are pumped out must go again into the matrix and finally produce ATP.
Suppose initially that the inside (Matrix-M) and outside of the membrane (Intermembrane space-IMS) are neutral (for sake of simplicity). The exergonicity of the redox reactions powers the proton pumping. As the pumping goes on an electrochemical gradient arises because of the concentration gradient the pumping produces and due to the electrical gradient which is produced due to the unequal distribution of protons.
After the equilibrium of the redox reaction an electrochemical gradient has established. I can't understand why the protons have to flow back into the matrix. The redox reaction equilibrium means that the ratio $\ce{H_{M}}/\ce{H_{IMS}}$ has a specific value. Do they flow back because of the electrochemical gradient? I was thinking that the flow back is coupled to the pumping, is that correct? I mean we have the equilibrium: $$\ce{H_{M}} \rightleftharpoons \ce{H_{IMS}}$$ and by pumping we increase $\ce{H_{IMS}}$ so protons must flow back according to Le Chatelier principle. If that is the case then what is the purpose of ATP synthase? Why the protons must flow back through ATP synthase and not from any other region? Are respiratory chain and ATP synthase seperated and the only way for protons to flow back is throught ATP synthase?
I have read Biochemistry textbooks and still can't understand the importance of the so called proton motive force.
