[Analysis of mechanism of work of mitochondrial adenine nucleotide translocase using mathematical models]. / Analiz mekhanizma raboty mitokhondrial'noi adeninnukleotid-translokazy s pomoshch'iu matematicheskikh modelei.

The 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.

Tracer kinetics analysis of the extracellular spaces in saline perfused hearts.

BACKGROUND: Precise estimation of the cellular water content presupposes a correct definition of the water fraction in tissue extracellular space. Low molecular weight markers (LMM), such as sulphate ion and sucrose, are widely used to define extracellular space size despite indications that they penetrate the cell. In contrast, inulin, with molecular weight of about 5000, is commonly regarded as a cell impermeable extracellular marker. OBJECTIVES: To compare LMM with inulin as markers in determining extracellular space size. ANIMALS AND METHODS: The size of extracellular space in guinea pig hearts perfused with crystalloid solution (hydrated hearts) was determined morphometrically and by mathematical model analysis of washout kinetics of LMM ((35)SO(4), (14)C-sucrose) or (3)H-inulin. RESULTS: Morphometrically, the sizes of vascular and interstitial spaces in the hydrated hearts were estimated to be 102+/-8 mL/kg wet mass (wm) and 452+/-17 mL/kg wm, respectively. Comparable data were obtained from model simulation of tracer washout: 67 mL/kg wm for vascular space and 439 to 462 mL/kg wm for interstitial space. Tracer penetration into cellular water, as shown by model analysis, was 28% for LMM and, reported here for the first time, 18% for inulin. The observed edema was probably due entirely to fluid accumulation in the interstitial space. CONCLUSION: Intracellular penetration of LMM must be taken into account, especially in modern nuclear magnetic resonance spectroscopic methods of cellular water monitoring in isolated perfused hearts.

Metabolic control of contractile performance in isolated perfused rat heart. Analysis of experimental data by reaction:diffusion mathematical model.

The intracellular mechanisms of regulation of energy fluxes and respiration in contracting heart cells were studied. For this, we investigated the workload dependencies of the rate of oxygen consumption and metabolic parameters in Langendorff-perfused isolated rat hearts.(31)P NMR spectroscopy was used to study the metabolic changes during transition from perfusion with glucose to that with pyruvate with and without active creatine kinase system. The experimental results showed that transition from perfusion with glucose to that with pyruvate increased the phosphocreatine content and stability of its level at increased workloads. Inhibition of creatine kinase reaction by 15-min infusion of iodoacetamide decreased the maximal developed tension and respiration rates by a factor of two.(31)P NMR data were analyzed by a mathematical model of compartmentalized energy transfer, which is independent from the restrictions of the classical concept of creatine kinase equilibrium. The analysis of experimental data by this model shows that metabolic stability-constant levels of phosphocreatine, ATP and inorganic phosphate-at increased energy fluxes is an inherent property of the compartmentalized system. This explains the observed substrate specificity by changes in mitochondrial membrane potential. The decreased maximal respiration rate and maximal work output of the heart with inhibited creatine kinase is well explained by the rise in myoplasmic ADP concentration. This activates the adenylate kinase reaction in the myofibrillar space and in the mitochondria to fulfil the energy transfer and signal transmission functions, usually performed by creatine kinase. The activity of this system, however, is not sufficient to maintain high enough energy fluxes. Therefore, there is a kinetic explanation for the decreased maximal respiration rate of the heart with inhibited creatine kinase: i.e. a kinetically induced switch from an efficient energy transfer pathway (PCr-CK system) to a non-efficient one (myokinase pathway) within the energy transfer network of the cell under conditions of low apparent affinity of mitochondria to ADP in vivo. This may result in a significant decrease in the thermodynamic affinity of compartmentalized ATPase systems and finally in heart failure.

Mathematical model of compartmentalized energy transfer: its use for analysis and interpretation of 31P-NMR studies of isolated heart of creatine kinase deficient mice.

A mathematical model of the compartmentalized energy transfer in cardiac cells is described and used for interpretation of novel experimental data obtained by using phosphorus NMR for determination of the energy fluxes in the isolated hearts of transgenic mice with knocked out creatine kinase isoenzymes. These experiments were designed to study the meaning and importance of compartmentation of creatine kinase isoenzymes in the cells in vivo. The model was constructed to describe quantitatively the processes of energy production, transfer, utilization, and feedback between these processes. It describes the production of ATP in mitochondrial matrix space by ATP synthase, use of this ATP for phosphocreatine production in the mitochondrial creatine kinase reaction coupled to the adenine nucleotide translocation, diffusional exchange of metabolites in the cytoplasmic space, and use of phosphocreatine for resynthesis of ATP in the myoplasmic creatine kinase reaction. It accounts also for the recently discovered phenomenon of restricted diffusion of adenine nucleotides through mitochondrial outer membrane porin pores (VDAC). Practically all parameters of the model were determined experimentally. The analysis of energy fluxes between different cellular compartments shows that in all cellular compartments of working heart cells the creatine kinase reaction is far from equilibrium in the systolic phase of the contraction cycle and approaches equilibrium only in cytoplasm and only in the end-diastolic phase of the contraction cycle. Experimental determination of the relationship between energy fluxes by a 31P-NMR saturation transfer method and workload in isolated and perfused heart of transgenic mice deficient in MM isoenzyme of the creatine kinase, MM-/-showed that in the hearts from wild mice, containing all creatine kinase isoenzymes, the energy fluxes determined increased 3-4 times with elevation of the workload. By contrast, in the hearts in which only the mitochondrial creatine kinase was active, the energy fluxes became practically independent of the workload in spite of the preservation of 26% of normal creatine kinase activity. These results cannot be explained on the basis of the conventional near-equilibrium theory of creatine kinase in the cells, which excludes any difference between creatine kinase isoenzymes. However, these apparently paradoxical experimental results are quantitatively described by a mathematical model of the compartmentalized energy transfer based on the steady state kinetics of coupled creatine kinase reactions, compartmentation of creatine kinase isoenzymes in the cells, and the kinetics of ATP production and utilization reactions. The use of this model shows that: (1) in the wild type heart cells a major part of energy is transported out of mitochondria via phosphocreatine, which is used for complete regeneration of ATP locally in the myofibrils--this is the quantitative estimate for PCr pathway; (2) however, in the absence of MM-creatine kinase in the myofibrils in transgenic mice the contraction results in a very rapid rise of ADP in cytoplasmic space, that reverses the mitochondrial creatine kinase reaction in the direction of ATP production. In this way, because of increasing concentrations of cytoplasmic ADP, mitochondrial creatine kinase is switched off functionally due to the absence of its counterpart in PCr pathway, MM-creatine kinase. This may explain why the creatine kinase flux becomes practically independent from the workload in the hearts of transgenic mouse without MM-CK. Thus, the analysis of the results of studies of hearts of creatine kinase-deficient transgenic mice, based on the use of a mathematical model of compartmentalized energy transfer, show that in the PCr pathway of intracellular energy transport two isoenzymes of creatine kinase always function in a coordinated manner out of equilibrium, in the steady state, and disturbances in functioning of one of them inevitably result

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

The 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?

The 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.

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

In 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.

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

A 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.

Quantitative analysis of the 'phosphocreatine shuttle': I. A probability approach to the description of phosphocreatine production in the coupled creatine kinase-ATP/ADP translocase-oxidative phosphorylation reactions in heart mitochondria.

For the first time, a probability approach was used to describe heart mitochondrial respiration in the medium with ATP, Cr and PCr but without ADP. Respiring mitochondria were considered as a three-component system, including (1) oxidative phosphorylation reactions which provide stable ATP concentration in the mitochondrial matrix; (2) adenine nucleotide translocase, which provides exchange transfer of matrix ATP for outside creatine kinase-supplied ADP when both substrates are simultaneously bound to translocase and (3) creatine kinase, starting these reactions when activated by the substrates from medium. The specific feature of this system is a close proximity of creatine kinase and translocase molecules. This results in high probability of direct activation of translocase by creatine kinase-derived ADP without its leak into the medium. In turn, the activated translocase with the same high probability directly provides creatine kinase with matrix-derived ATP. The catalytic complexes of creatine kinase with ATP from matrix together with those formed from substrates from medium provide high activation of creatine kinase coupled to translocase activation. The considered probabilities were arranged into a mathematical model. The model satisfactorily simulates the experimental data by Jacobus, W.E. and Saks, V.A. ((1982) Arch. Biochem. Biophys. 219, 167-178), who investigated this system in all regimens of functioning. The results suggest the observed kinetic and thermodynamic irregularities in the behavior of structurally-bound creatine kinase as a direct consequence of its tight coupling to translocase.

The analysis of extracellular calcium exchange in perfused myocardium using mathematical modeling.

1. A mathematical model of diffusional Ca exchange in a continuously perfused heart has been formulated. Based on biochemical studies, sarcolemmal Ca binding on the extracellular surface of cardiomyocytes is taken into account. The changes in sarcolemmal Ca binding may affect the kinetics of Ca washout from the myocardium. The model is consistent with the real dynamics of 45Ca washout from rabbit heart septum reported by Philipson and Langer (F Mol Cell Cardiol 11, 857 (1979)). 2. The changes in the kinetics of Ca washout calculated according to the proposed model agree with the real changes in the kinetics of 45Ca washout from rabbit heart septum at two coronary flow rate values reported by Shine et al. (Am J Physiol 221, 1408 (1971)). 3. The calculated dynamics of the decrease in sarcolemmal Ca content is close to the real dynamics of the myocardial contractility decrease demonstrated by Philipson and Langer (1979). 4. The model offers an estimation of the contribution of different myocardial compartments to the kinetic components of Ca washout curves resolved by the method of Solomon (In: Mineral Metabolism 1A, p. 119, New York, Academic Press, (1960)). According to the results of the modeling, more than 80% of the fast exchanging pool 0 is composed of sarcolemmal Ca. 85 and 95% of the slowly exchanging pools 2 and 3 are composed of intracellular Ca; pool 1 is determined by both sarcolemmal and intracellular Ca.

[Fractionation of fragments of skeletal muscle sarcoplasmic reticulum according to their sensitivity to caffeine]. / Fraktsionirovanie fragmentov sarkoplazmaticheskogo retikuluma skeletnoi myshtsy po ikh chuvstvitel'nosti k kofeinu.

Sarcoplasmic reticulum fragments were fractionated according to the ability of caffeine to selectively block Ca2+ uptake in the population of caffeine-sensitive membranes. The membrane suspension was loaded with calcium in the presence of oxalate, Mg-ATP and caffeine, after which the Ca2+-loaded caffeine-sensitive fragments were separated by sucrose density gradient centrifugation. In Ca2+-unloaded fragments of the supernatant, the sensitivity to caffeine estimated by its ability to diminish the rate of Ca2+ uptake, Ca/ATP ratio and Ca-oxalate capacity amounted to 91-93%. The terms of protein composition, the caffeine-sensitive fragments were identified with terminal cystern membranes, while the caffeine-insensitive ones with the SR canalicular membranes. The sensitivity to caffeine may serve as a reliable criterion for estimating the relative content of terminal cystern fragments in different microsomal preparations.

Isolation of calcium pump system and purification of calcium ion-dependent ATPase from heart muscle.

The procedure for the isolation of the highly active fraction of sarcoplasmic reticulum from pigeon and dog hearts is described. The method is based on the partial loading of heart microsomes with calcium and oxalate ions and the precipitation of loaded vesicles in sucrose and potassium chloride concentration gradients. Preparations obtained possess high activity of Ca2+-dependent ATPase and are also able to accumulate up to 10 mumol Ca2+ per mg protein. Purification of sarcoplasmic reticulum membranes is accompanied by a decrease in concentration of cytochrome a+a3 and an increase in the content of [32P]phosphoenzyme. The basic components in "calcium-oxalate preparation" from hearts are proteins with molecular weights of about 100000 (Ca2+-dependent ATPase) and 55000 Calcium-oxalate preparation from pigeon hearts was used for subsequent purification of Ca2+-dependent ATPase. Specific activity of purified enzyme from pigeon hearts is 12-16 mumol Pi/min per mg protein. Enzyme activity of purified Ca2+-dependent ATPase is inhibited by EGTA and is not sensitive to azide, 2,4-dinitrophenol and ouabain. The data obtained demonstrate the similarity of calcium pump systems and Ca2+-dependent ATPases isolated from heart and skeletal muscles.

[Isolation of highly active preparations of sarcoplasmic reticulum and Ca2-dependent ATPase from cardiac muscle]. / Vydelenie vysokoaktivnykh preparatov sarkoplazmaticheskogo reticulum i Ca2-zavisimoi atpazy iz serdechnoi myshty

A microsomal preparation with a high ability for Ca2+ uptake has been isolated from pigeon heart. A method of further purification of Ca2+-accumulating system of heart, based on the ability of sarcoplasmic reticulum for the energy-dependent Ca2+ accumulation in the presence of oxalate, has been developed. Upon centrifugation in the gradient of sucrose and KCl concentration the fragments of sarcoplasmic reticulum, rendered "heavy" by calcium oxalate, can be separated from foreign cell membranes. The main component of heart "calcium pump" is Ca2+-dependent ATPase (making up to about 50% of all proteins of the purified reticulum), having a molecular weight of 100.000--105.000. Specific activity of heart Ca2+-ATPase as well as the ability of purified heart sarcoplasmic reticulum for Ca2+ uptake are only slightly less than those of the skeletal muscle reticulum. The data obtained suggest that heart sarcoplasmic reticulum may be efficient for providing heart muscle relaxation.

[Molecular mechanisms of cardiac insufficiency in myocardial ischemia]. / Molekuliarnye mekhanizmy serdechnoi nedostatochnosti pri ishemii miokarda

An analysis of the main concepts of the pathogenesis of heart muscle insufficiency under ischaemia was conducted. None of the hypotheses postulating the invariability of the energy supply to the myofibrills was shown to explain the fast reduction of the contractility of the ischaemic myocardium. These hypotheses are based on the experimental fact of the ATP level in the myocardium practically undergoing no reduction under ischaemia. At the same time, one of the earliest changes in the heart muscle under ichaemia consists in creatine phosphate concentration reduction that correlates with the decrease in the contractility. The recently obtained data indicate that the energy synthesized in the mitochondria of the cardiac muscle is carried away from them in the form of energy of creatine phosphate molecules that is later used for ATP synthesis in the myofibrill creatine phosphokinase reaction. A scheme is suggested that implies that under ischaemia severe changes in the energy supply consisting in creatine phosphate synthesis reduction are the leading factor in the pathogenesis resulting on the early stages of the process in a reduction of the contractility, and on the later ones--in irreversible damages of the membrane systems and cell destruction.