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The chemiosmotic theory was first proposed by British biochemist Peter Mitchell in 1961.

The chemiosmotic theory is a model that explains how the movement of protons (H+) across a membrane can generate an electrochemical gradient, which in turn can be used to drive the synthesis of adenosine triphosphate (ATP).

According to the chemiosmotic theory, the proton-motive force is responsible for ATP synthesis in the following way: 1. In the process of cellular respiration, especially during the electron transport chain (ETC), protons (H+) are pumped across the inner mitochondrial membrane from the matrix to the intermembrane space. 2. As a result, a proton gradient is created, and an electrochemical proton gradient (proton-motive force) is established across the membrane. 3. The proton-motive force consists of two components: a transmembrane proton concentration difference (also called the chemical potential) and a transmembrane electric potential due to the charge difference. 4. The energy stored in the proton-motive force is used by the ATP synthase enzyme, which allows protons to flow back into the mitochondrial matrix through its F0 subunit. 5. The flow of protons (also called chemiosmosis) results in conformational changes in the ATP synthase enzyme's F1 subunit, promoting the synthesis of ATP from adenosine diphosphate (ADP) and inorganic phosphate (Pi). 6. Finally, ATP is released, and the energy derived from proton-motive force is utilized for cellular processes. Through these steps, the chemiosmotic theory explains the role of proton-motive force in ATP synthesis, linking the movement of protons and the generation of an electrochemical gradient to cellular energy production.