Applications of permeabilized cell and skinned fiber techniques in combination with methods of mathematical modelling for studies of mitochondrial function in the cell are critically evaluated. Mathematical models may be useful tools for explaining biological phenomena, but only if they are selected by fitting the computing results with real experimental data. Confocal microscopy has been used in experiments with permeabilized cardiomyocytes and myocardial fibers to determine the maximal diffusion distance from medium to the core of cells, which is shown not to exceed 8-10 microm. This is a principal index for correctly explaining high apparent Km for exogenous ADP (200-300 microM) in regulation of mitochondrial respiration in oxidative muscle cells in situ. The best fitting of the results of in silico studies may be achieved by using of the compartmentalized energy transfer model. From these results, it may be concluded that in cardiac muscle cells the mitochondria and ATPases are organized into intracellular energetic units (ICEUs) separated from the bulk phase of cytoplasm by some barriers which limit the diffusion of adenine nucleotides. In contrast, alternative models based on the concept of the cell as homogenous system do not explain the observed experimental phenomena and have led to misleading conclusions. The various sources of experimental and conceptual errors are analyzed.