Molecular System Bioenergics of the Heart: Experimental Studies of Metabolic Compartmentation and Energy Fluxes versus Computer Modeling †

In this review we analyze the recent important and remarkable advancements in studies of compartmentation of adenine nucleotides in muscle cells due to their binding to macromolecular complexes and cellular structures, which results in non-equilibrium steady state of the creatine kinase reaction. We discuss the problems of measuring the energy fluxes between different cellular compartments and their simulation by using different computer models. Energy flux determinations by 18O transfer method have shown that in heart about 80% of energy is carried out of mitochondrial intermembrane space into cytoplasm by phosphocreatine fluxes generated by mitochondrial creatine kinase from adenosine triphosphate (ATP), produced by ATP Synthasome. We have applied the mathematical model of compartmentalized energy transfer for analysis of experimental data on the dependence of oxygen consumption rate on heart workload in isolated working heart reported by Williamson et al. The analysis of these data show that even at the maximal workloads and respiration rates, equal to 174 μmol O2 per min per g dry weight, phosphocreatine flux, and not ATP, carries about 80–85% percent of energy needed out of mitochondria into the cytosol. We analyze also the reasons of failures of several computer models published in the literature to correctly describe the experimental data

[Analysis of mechanism of work of mitochondrial adenine nucleotide translocase using mathematical models]

International audienceThe kinetics of exchange of adenine nucleotides in a system with reconstituted mitochondrial adenine nucleotide translocase (ANT) was simulated mathematically to analyze the basic mechanisms of ANT functioning. Two known alternative kinetic schemes were analyzed, the ping-pong type scheme with single-center substrate binding and the scheme of sequential two-center substrate binding at opposite sides of ANT. According to our modeling, both schemes can explain the experimental data on the adenine nucleotide exchange in the reconstituted ANT system. However, the characteristic kinetic pattern of ADP exchanges in the mono exchange mode was reproduced only by the sequential binding scheme. This scheme is consistent with the data on the tetrameric structure of ANT. On the other hand, only the single-center binding scheme was compatible with recent data on possible translocation of ATP and ADP by the carrier that has no bound adenine nucleotide on its opposite side. Based on the analysis of the literature data on ANT properties, a compromise scheme of ANT operation was proposed. In the framework of this scheme, the ANT dimers function by the single-center binding mechanism: however, in tetramers they are integrated into a substructure with two oppositely oriented binding centers working by the mechanism of sequential substrate binding. Labile bonds between the ANT-forming dimers could allow conformational rearrangements of ANT induced by various influences on mitochondrial membrane structure, including those leading to the induction of permeability transition pores in apoptosis

Compartmentalized energy transfer in cardiomyocytes: use of mathematical modeling for analysis of in vivo regulation of respiration.

International audienceThe mathematical model of the compartmentalized energy transfer system in cardiac myocytes presented includes mitochondrial synthesis of ATP by ATP synthase, phosphocreatine production in the coupled mitochondrial creatine kinase reaction, the myofibrillar and cytoplasmic creatine kinase reactions, ATP utilization by actomyosin ATPase during the contraction cycle, and diffusional exchange of metabolites between different compartments. The model was used to calculate the changes in metabolite profiles during the cardiac cycle, metabolite and energy fluxes in different cellular compartments at high workload (corresponding to the rate of oxygen consumption of 46 mu atoms of O.(g wet mass)-1.min-1) under varying conditions of restricted ADP diffusion across mitochondrial outer membrane and creatine kinase isoenzyme "switchoff." In the complete system, restricted diffusion of ADP across the outer mitochondrial membrane stabilizes phosphocreatine production in cardiac mitochondria and increases the role of the phosphocreatine shuttle in energy transport and respiration regulation. Selective inhibition of myoplasmic or mitochondrial creatine kinase (modeling the experiments with transgenic animals) results in "takeover" of their function by another, active creatine kinase isoenzyme. This mathematical modeling also shows that assumption of the creatine kinase equilibrium in the cell may only be a very rough approximation to the reality at increased workload. The mathematical model developed can be used as a basis for further quantitative analyses of energy fluxes in the cell and their regulation, particularly by adding modules for adenylate kinase, the glycolytic system, and other reactions of energy metabolism of the cell

Is there the creatine kinase equilibrium in working heart cells?

International audienceThe mathematical model of the compartmentalised energy transfer system in cardiac myocytes, which includes mitochondrial synthesis of ATP by ATP-synthase, phosphocreatine production in the coupled mitochondrial creatine kinase reaction, the myofibrillar and cytoplasmic creatine kinase reactions, ATP utilisation by actomyosin ATPase during contraction cycle, and diffusional exchange of metabolites between different compartments, was used to calculate creatine kinase reaction rates (fluxes) in different cellular compartments at a workload corresponding to the rate of oxygen consumption of 46 micrograms-atom O2 *min-1 * (g wet mass)-1. The results of calculations showed that at this high workload all creatine kinase isoenzymes function most of their time in the cardiac cycle in the steady state far from equilibrium. This mathematical modelling shows that the validity of assumption of creatine kinase equilibrium is limited only to the diastolic phase of the contraction cycle in the working cardiac cells and only to the cytoplasmic compartment. In the systolic phase, due to rapid release of ADP at increased workloads, all creatine kinase isoenzymes are rapidly shifted out of the equilibrium. Cytoplasmic ADP concentration may increase up to 9 times in the systolic phase of the cardiac cycle, correspondingly changing all ADP-dependent parameters. Mitochondrial creatine kinase functions permanently in "metastable" steady state (Jurgen Daut, Biochim. Biophys. Acta 895, 41-62, 1987). It may be proposed that a more precise, in comparison to the equilibrium concept, way of calculating steady state cytoplasmic ADP concentrations at increased workloads is to use kinetic equations and mathematical models of energy metabolism

Mathematical modeling of intracellular transport processes and the creatine kinase systems: a probability approach.

International audienceA probability approach was used to describe mitochondrial respiration in the presence of substrates, ATP, ADP, Cr and PCr. Respiring mitochondria were considered as a three-component system, including: 1) oxidative phosphorylation reactions which provide stable ATP and ADP concentrations in the mitochondrial matrix; 2) adenine nucleotide translocase provides exchange transfer of matrix adenine nucleotides for those from outside, supplied from medium and by creatine kinase; 3) creatine kinase, starting these reactions when activated by the substrates from medium. The specific feature of this system is close proximity of creatine kinase and translocase molecules. This results in high probability of direct activation of translocase by creatine kinase-derived ADP or ATP without their leak into the medium. In turn, the activated translocase with the same high probability directly provides creatine kinase with matrix-derived ATP or ADP. The catalytic complexes of creatine kinase formed with ATP from matrix together with those formed from medium ATP provide activation of the forward creatine kinase reaction coupled to translocase activation. Simultaneously the catalytic complexes of creatine kinase formed with ADP from matrix together with those formed from medium ADP provide activation of the reverse creatine kinase reaction coupled to translocase activation. The considered probabilities were arranged into a mathematical model. The model satisfactorily simulates the available experimental data by several groups of investigators. The results allow to consider the observed kinetic and thermodynamic irregularities in behavior of structurally bound creatine kinase as a direct consequence of its tight coupling to translocase

Metabolic control and metabolic capacity: two aspects of creatine kinase functioning in the cells.

International audienceIn this short review, the merits and limits of three theoretical concepts explaining the functional role of the creatine kinase system in muscle and brain cells are analysed. In addition to the usual concept of an energy buffer system and the recently proposed metabolic capacity theory (Sweeney, H.L. (1994) Med. Sci. Sports Exerc. 26, 30-36), it is proposed that coupled creatine kinase systems are involved in effective metabolic regulation of energy fluxes and oxidative phosphorylation, beside their energy transfer function. This aspect of the system is considered on the basis of metabolic control analysis. It is shown by using the results of mathematical modelling that, due to amplification of ADP fluxes from the cytoplasm by the mechanism of metabolic channelling, coupled mitochondrial creatine kinase may exert a flux control coefficient significantly exceeding 1

Metabolic control and metabolic capacity: two aspects of creatine kinase functioning in the cells.

International audienceIn this short review, the merits and limits of three theoretical concepts explaining the functional role of the creatine kinase system in muscle and brain cells are analysed. In addition to the usual concept of an energy buffer system and the recently proposed metabolic capacity theory (Sweeney, H.L. (1994) Med. Sci. Sports Exerc. 26, 30-36), it is proposed that coupled creatine kinase systems are involved in effective metabolic regulation of energy fluxes and oxidative phosphorylation, beside their energy transfer function. This aspect of the system is considered on the basis of metabolic control analysis. It is shown by using the results of mathematical modelling that, due to amplification of ADP fluxes from the cytoplasm by the mechanism of metabolic channelling, coupled mitochondrial creatine kinase may exert a flux control coefficient significantly exceeding 1

Where have the fluxes gone?

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