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 Förster-type energy exchange due to electron-proton Coulomb interaction can provide a 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 buildups 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.