Chemiosmosis couples transmembrane ion movement down an electrochemical gradient to a chemical transformation. For mitochondrial ATP synthesis, protons return from the intermembrane space to the mitochondrial matrix through ATP synthase.[ref]
Molecular Biology of the Cell, 4th edition by Bruce Alberts and others. Chapter 14, Electron-Transport Chains and Their Proton Pumps, Summary: inward proton flow driving ATP synthesis
An original thermodynamic example separates the electrical and chemical contributions. At fixed temperature , use ideal dilute thermodynamic activities and the electric potential on each side. The molar electrochemical potential difference for inward transfer of a singly charged proton isHere is the molar gas constant, the Faraday constant, and the natural logarithm. The sign convention is destination minus origin: a negative difference makes inward transfer favourable. Both lower proton activity and a more negative electric potential inside favour inward movement.
Stipulate , , , and . These illustrative inputs give approximately and for the chemical and electrical terms, hence per transferred proton. For a hypothetical device coupling three inward protons per ATP to an ATP-formation cost of ,The sign follows by adding changes in the state function Gibbs free energy. It establishes thermodynamic feasibility for this chosen model, not its reaction rate. Three is a stipulated coupling count, not a universal ATP synthase stoichiometry; transport costs and leaks can also consume the available free energy.
Downhill ion transport through ATP synthase can drive ATP formation from its substrates. The electrochemical free-energy drop per transported ion combines the membrane potential and concentration term. Reverse coupling can use ATP hydrolysis to maintain the ion gradient.
