A brief description of the principal directions for searching and investigating the model of local coupling between respiration and phosphorylation proposed by R. Williams is given in this paper. We found conditions where it was possible to reveal typical functional special features of the mitochondrial phosphorylating system. According to the theory, such special features should be observed experimentally if the mitochondrial phosphorylating system operated in the state of a supercomplex. It was proved that the phosphorylating system is able to operate in two states: P. Mitchell state and R. Williams state. It was demonstrated that in the ATP synthesis reaction, ATP-synthase (F1F0) was able to use thermodynamic potential of Bronsted acids as a source of energy. It was shown using a double-inhibitor titration technique that when the phosphorylating system operated in the supercomplex state, the electron transfer system and ATP-synthesis system were docked rigidly. A model system of chemical synthesis of membrane-bound proton fraction (Bronsted acids), carrying a free energy excess, was developed on the model of bilayer lipid membrane. Catalysts selectively accelerating proton detachment of this fraction were also found. The formation of a Bronsted acids fraction carrying free energy excess was recorded during the operation of proton pumps on mitochondrial and mitoplastic membranes. In the experimental part of the work, a brief description is given of studies on new uncouplers that transfer the phosphorylation system from the local coupling state to the state of transmembrane proton transfer. Thus, they accelerated the respiration of mitochondria and decreased the ADP/O parameter.