Cytochrome c oxidase (CcO) is the terminal enzyme of the cell respiratory chain in mitochondria and aerobic bacteria. It catalyzes the reduction of oxygen to water and utilizes the free energy of the reduction reaction for proton pumping across the inner-mitochondrial membrane, a process that results in a membrane electrochemical proton gradient. Although the structure of the enzyme has been solved for several organisms, the molecular mechanism of proton pumping remains unknown. In the present paper, continuum electrostatic calculations were employed to evaluate the electrostatic potential, energies, and protonation state of bovine heart cytochrome c oxidase for different redox states of the enzyme along its catalytic cycle. Three different computational models of the enzyme were employed to test the stability of the results. The energetics and pH dependence of the P-->F, F-->O, and O-->E steps of the cycle have been investigated. On the basis of electrostatic calculations, two possible schemes of redox-linked proton pumping are discussed. The first scheme involves His291 as a pump element, whereas the second scheme involves a group linked to propionate D of heme a(3). In both schemes, loading of the pump site is coupled to ET between the two hemes of the enzyme, while transfer of a chemical proton is accompanied by ejection of the pumped H+. The two models, as well as the energetics results are compared with recent experimental kinetic data. The proton pumping across the membrane is an endergonic process, which requires a sufficient amount of energy to be provided by the chemical reaction in the active site. In our calculations, the conversion of OH- to H2O provides 520 meV of energy to displace pump protons from a loading site and overall about 635 meV for each electron passing through the system. Assuming that the two charges are translocated per electron against the membrane potential of 200 meV, the model predicts an overall efficiency of 63%.