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Born at Mitcham in Surrey, Mitchell was educated at Cambridge University, where he obtained his PhD in 1950. He remained at Cambridge, teaching in the department of biochemistry until 1955, when he moved to Edinburgh University as director of the Chemical Biology Unit. In 1964 Mitchell made the unusual decision to set up his own private research institution, the Glynn Research Laboratory, in Bodmin, Cornwall.

It was well known that the cell obtains its energy from the adenosine triphosphate (ATP) molecule; it was also clear that ATP was made by coupling adenosine diphosphate (ADP) to an inorganic phosphate group by the process known to biochemists as oxidative phosphorylation. What was less clear was just how this happened and it was widely assumed that it was controlled by a number of enzymes. Despite considerable effort the proposed enzymes remained surprisingly elusive.

Beginning in 1961 Mitchell proposed a completely different and totally original model, without any obvious precursors and judged to be unorthodox to the point of eccentricity. He suggested a physical mechanism by which an electrochemical gradient is created across the cellular membrane; this, in turn, creates a proton current capable of controlling the phosphorylation.

For his account of such processes Mitchell was awarded the 1978 Nobel Prize for chemistry.