The fundamental principle of cardiac behaviour is described by the Frank-Starling law relating force of contraction during systole with end-diastolic volume. While both work and respiration rates increase linearly with imposed load, the basis of mechano-energetic coupling in heart muscle has remained a long-standing enigma. Here, we highlight advances made in understanding of complex cellular and molecular mechanisms that orchestrate coupling of mitochondrial oxidative phosphorylation with ATP utilization for muscle contraction. Cardiac system bioenergetics critically depends on an interrelated metabolic infrastructure regulating mitochondrial respiration and energy fluxes throughout cellular compartments. The data reviewed indicate the significance of two interrelated systems regulating mitochondrial respiration and energy fluxes in cells: (1) the creatine kinase, adenylate kinase and glycolytic pathways that communicate flux changes generated by cellular ATPases within structurally organized enzymatic modules and networks; and (2) a secondary system based on mitochondrial participation in cellular calcium cycle, which adjusts substrate oxidation and energy-transducing processes to meet increasing cellular energy demands. By conveying energetic signals to metabolic sensors, coupled phosphotransfer reactions provide a high-fidelity regulation of the excitation-contraction cycle. Such integration of energetics with calcium signalling systems provides the basis for 'metabolic pacing', synchronizing the cellular electrical and mechanical activities with energy supply processes.

The purpose of this study is to investigate theoretically which intracellular factors may be important for regulation of mitochondrial respiration in working heart cells in vivo. We have developed a model that describes quantitatively the published experimental data on dependence of the rate of oxygen consumption and metabolic state of working isolated perfused rat heart on workload over its physiological range (Williamson JR, Ford G, Illingworth J, Safer B. Circ Res 38, Suppl I, I39-I51, 1976). Analysis of this model shows that for phosphocreatine, creatine, and ATP the equilibrium assumption is an acceptable approximation with respect to their diffusion in the intracellular bulk water phase. However, the ADP concentration changes in the contraction cycle in a nonequilibrium workload-dependent manner, showing the existence of the intracellular concentration gradients. The model shows that workload-dependent alteration of ADP concentration in the compartmentalized creatine kinase system may be taken, together with the changes in P(i) concentration, to be among the major components of the metabolic feedback signal for regulation of respiration in muscle cells.

The aim of this work was to characterize quantitatively the arrangement of mitochondria in heart and skeletal muscles. We studied confocal images of mitochondria in nonfixed cardiomyocytes and fibers from soleus and white gastrocnemius muscles of adult rats. The arrangement of intermyofibrillar mitochondria was analyzed by estimating the densities of distribution of mitochondrial centers relative to each other (probability density function). In cardiomyocytes (1,820 mitochondrial centers marked), neighboring mitochondria are aligned along a rectangle, with distance between the centers equal to 1.97 Ϯ 0.43 and 1.43 Ϯ 0.43 m in the longitudinal and transverse directions, respectively. In soleus (1,659 mitochondrial centers marked) and white gastrocnemius (621 pairs of mitochondria marked), mitochondria are mainly organized in pairs at the I-band level. Because of this organization, there are two distances characterizing mitochondrial distribution in the longitudinal direction in these muscles. The distance between mitochondrial centers in the longitudinal direction within the same I band is 0.91 Ϯ 0.11 and 0.61 Ϯ 0.07 m in soleus and white gastrocnemius, respectively. The distance between mitochondrial centers in different I bands is ϳ3.7 and ϳ3.3 m in soleus and gastrocnemius, respectively. In the transverse direction, the mitochondria are packed considerably closer to each other in soleus than in white gastrocnemius, with the distance equal to 0.75 Ϯ 0.22 m in soleus and 1.09 Ϯ 0.41 m in gastrocnemius. Our results show that intermyofibrillar mitochondria are arranged in a highly ordered crystal-like pattern in a muscle-specific manner with relatively small deviation in the distances between neighboring mitochondria. This is consistent with the concept of the unitary nature of the organization of the muscle energy metabolism. confocal microscopy; quantitative analysis; cardiac and skeletal muscles; probability density function; unitary structure of cells RECENT STUDIES HAVE SHOWN the existence of multiple specific functional interactions among mitochondria, sarcoplasmic reticulum (SR), and myofibrils in permeabilized muscle fibers (5,14,30,34). Namely, endogenous ATP has been shown to be more efficient than exogenous ATP in maintaining calcium uptake into SR (14). In addition, kinetic studies have shown a direct supply of endogenous ADP from ATPases to mitochondria (30, 34). Such interaction can be explained by the existence of localized intracellular diffusion restrictions (28, 39). A mild treatment of the fibers with trypsin leads to the removal of these diffusion restrictions, and at the same time, distribution of mitochondria in the fiber is changed from regular arrangement in the control to random distribution after the treatment (28). Similarly, in ischemic hearts, various alterations in mitochondrial function such as the significant decrease in maximal respiration rate and half-saturation constant for ADP were observed in parallel with the changes in structural organization of the cardiac muscle cells (7,1...

The aim of this study was to investigate the influence of fiber orientation in the left ventricular (LV) wall on the ejection fraction, efficiency, and heterogeneity of the distributions of developed fiber stress, strain and ATP consumption. A finite element model of LV mechanics was used with active properties of the cardiac muscle described by the Huxley-type cross-bridge model. The computed variances of sarcomere length (SL(var)), developed stress (DS(var)), and ATP consumption (ATP(var)) have several minima at different transmural courses of helix fiber angle. We identified only one region in the used design space with high ejection fraction, high efficiency of the LV and relatively small SL(var), DS(var), and ATP(var). This region corresponds to the physiological distribution of the helix fiber angle in the LV wall. Transmural fiber angle can be predicted by minimizing SL(var) and DS(var), but not ATP(var). If ATP(var) was minimized, then the transverse fiber angle was considerably underestimated. The results suggest that ATP consumption distribution is not regulating the fiber orientation in the heart.

Heterogeneity of ADP diffusion and regulation of respiration were studied in permeabilized cardiomyocytes and cardiac fibers in situ and in silico. Regular arrangement of mitochondria in cells was altered by short-time treatment with trypsin and visualized by confocal microscopy. Manipulation of matrix volumes by changing K(+) and sucrose concentrations did not affect the affinity for ADP either in isolated heart mitochondria or in skinned fibers. Pyruvate kinase (PK)-phosphoenolpyruvate (PEP) were used to trap ADP generated in Ca,MgATPase reactions. Inhibition of respiration by PK-PEP increased 2-3 times after disorganization of regular mitochondrial arrangement in cells. ADP produced locally in the mitochondrial creatine kinase reaction was not accessible to PK-PEP in intact permeabilized fibers, but some part of it was released from mitochondria after short proteolysis due to increased permeability of outer mitochondrial membrane. In in silico studies we show by mathematical modeling that these results can be explained by heterogeneity of ADP diffusion due to its restrictions at the outer mitochondrial membrane and in close areas, which is changed after proteolysis. Localized restrictions and heterogeneity of ADP diffusion demonstrate the importance of mitochondrial functional complexes with sarcoplasmic reticulum and myofibrillar structures and creatine kinase in regulation of oxidative phosphorylation.

In this review we analyze the concepts and the experimental data on the mechanisms of the regulation of energy metabolism in muscle cells. Muscular energetics is based on the force-length relationship, which in the whole heart is expressed as a Frank-Starling law, by which the alterations of left ventricle diastolic volume change linearly both the cardiac work and oxygen consumption. The second basic characteristics of the heart is the metabolic stability--almost constant levels of high energy phosphates, ATP and phosphocreatine, which are practically independent of the workload and the rate of oxygen consumption, in contrast to the fast-twitch skeletal muscle with no metabolic stability and rapid fatigue. Analysis of the literature shows that an increase in the rate of oxygen consumption by order of magnitude, due to Frank-Starling law, is observed without any significant changes in the intracellular calcium transients. Therefore, parallel activation of contraction and mitochondrial respiration by calcium ions may play only a minor role in regulation of respiration in the cells. The effective regulation of the respiration under the effect of Frank-Starling law and metabolic stability of the heart are explained by the mechanisms of functional coupling within supramolecular complexes in mitochondria, and at the subcellular level within the intracellular energetic units. Such a complex structural and functional organisation of heart energy metabolism can be described quantitatively by mathematical models.

Recent studies have revealed the structural and functional interactions between mitochondria, myofibrils and sarcoplasmic reticulum in cardiac cells. Direct channeling of adenosine phosphates between organelles identified in the experiments indicates that diffusion of adenosine phosphates is limited in cardiac cells due to very specific intracellular structural organization. However, the mode of diffusion restrictions and nature of the intracellular structures in creating the diffusion barriers is still unclear, and, therefore, a subject of active research. The aim of this work is to analyze the possible role of two principally different modes of restriction distribution for adenosine phosphates (a) the uniform diffusion restriction and (b) the localized diffusion limitation in the vicinity of mitochondria, by fitting the experimental data with the mathematical model. The reaction-diffusion model of compartmentalized energy transfer was used to analyze the data obtained from the experiments with the skinned muscle fibers, which described the following processes: mitochondrial respiration rate dependency on exogenous ADP and ATP concentrations; inhibition of endogenous ADP-stimulated respiration by pyruvate kinase (PK) and phosphoenolpyruvate (PEP) system; kinetics of oxygen consumption stabilization after addition of 2 mM MgATP or MgADP; ATPase activity with inhibited mitochondrial respiration; and buildup of MgADP concentration in the medium after addition of MgATP. The analysis revealed that only the second mechanism considered--localization of diffusion restrictions--is able to account for the experimental data. In the case of uniform diffusion restrictions, the model solution was in agreement only with two measurements: the respiration rate as a function of ADP or ATP concentrations and inhibition of respiration by PK + PEP. It was concluded that intracellular diffusion restrictions for adenosine phosphates are not distributed uniformly, but rather are localized in certain compartments of the cardiac cells.

The mechanism of metabolic regulation of mitochondrial respiration in cardiac muscle cells was studied experimentally in the permeabilized heart fibres of mice and by computer modelling in silico. The experiments showed that the rate of mitochondrial respiration could be controlled by local production of ADP by mitochondrial creatine kinase in the intermembrane space of mitochondria. The spatially inhomogenous reaction-diffusion model of compartmentalized energy transfer was used to analyse which metabolite level in cytoplasm may be important for regulation of respiration. At low and moderate workloads, up to VO2 equal to 70 micromol min-1 g-1 dry weight, the only factor to which respiration responded was inorganic phosphate. At the values of VO2 higher than 70 micromol min-1 g-1 dry weight, the respiration rate responded mostly to changes in creatine, phosphocreatine and then time-averaged (over the contractile cycle) ADP concentrations in the cytoplasm. These results are taken to show that under conditions of moderate workloads, creatine kinase activity at given physiological creatine and phosphocreatine concentrations (apparent maximal activity achievable under these conditions) is in excess to oxidative phosphorylation rate, which is controlled by Pi concentration changes starting from very low values of the latter. At higher workloads mi-CK should be upregulated by increasing creatine and decreasing phosphocreatine concentrations, and only at very high workloads the ADP diffusion flux should be increased to upregulate oxidative phosphorylation. Thus, on the basis of the study in silico of compartmentalized energy transfer by phophocreatine/creatine system, the authors conclude that there exist multiple parallel regulatory factors controlling the rate of oxygen consumption in dependence of the workload. If creatine kinase is inhibited (and there is no myokinase activity), respiration requires high diffusive flux of ADP back into mitochondria, which is the sole regulator of respiration. This needs, however, increased ADP concentrations in the cytoplasm, which in turn result in inhibition of contraction.