  We examine a simple model of proton pumping through the inner membrane of
mitochondria in the living cell. We demonstrate that the pumping process can be
described using approaches of condensed matter physics. In the framework of
this model, we show that the resonant F\"orster-type energy exchange due to
electron-proton Coulomb interaction can provide an unidirectional flow of
protons against an electrochemical proton gradient, thereby accomplishing
proton pumping. The dependence of this effect on temperature as well as
electron and proton voltage build-ups are obtained taking into account
electrostatic forces and noise in the environment. We find that the proton pump
works with maximum efficiency in the range of temperatures and transmembrane
electrochemical potentials which correspond to the parameters of living cells.
