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Molecular and Cellular Biochemistry 184: 291–307, 1998.© 1998 Kluwer Academic Publishers. Printed in the Netherlands.

Quantitative studies of enzyme-substratecompartmentation, functional coupling andmetabolic channelling in muscle cells

Valdur Saks,1, 2 Pierre Dos Santos,3 Frank N. Gellerich4 and PhilippeDiolez5

1Laboratories of Bioenergetics, Joseph Fourier University, Grenoble, France; 2Institute of Chemical and BiologicalPhysics, Tallin, Estonia; 3INSERM Unite 441 - Atherosclerose: Determinisme Cellulaire et Moleculaire, ConséquencesFunctionnelles, Bordeaux, France; 4Muskel Laboratory, Martin Luther University, Halle, Germany; 5RésonanceMagnétique Nucléaire des Systèmes Biologiques, UMR 5536 CNRS/Université Bordeaux II, Bordeaux, France

Diversity of our opinions does not proceed from some men being more rationalthan others, but solely from the fact that our thoughts pass through

divers channels and the same objects are not considered by all.René Descartes, 1596–1650

Discours de la méthode

Abstract

Some historical aspects of development of the concepts of functional coupling, metabolic channelling, compartmentation andenergy transfer networks are reviewed. Different quantitative approaches, including kinetic and mathematical modeling of energymetabolism, intracellular energy transfer and metabolic regulation of energy production and fluxes in the cells in vivo are analyzed.As an example of the system with metabolic channelling, thermodynamic aspects of the functioning the mitochondrial creatinekinase functionally coupled to the oxidative phosphorylation are considered. The internal thermodynamics of the mitochondrialcreatine kinase reaction is similar to that for other isoenzymes of creatine kinase, and the oxidative phosphorylation processspecifically influences steps of association and dissociation of MgATP with the enzyme due to channelling of ATP from adeninenucleotide translocase. A new paradigm of muscle bioenergetics – the paradigm of energy transfer and feedback signaling networksbased on analysis of compartmentation phenomena and structural and functional interactions in the cell is described. Analysisof the results of mathematical modeling of the compartmentalized energy transfer leads to conclusion that both calcium andADP, which concentration changes synchronously in contraction cycle, may simultaneously activate oxidative phosphorylationin the muscle cells in vivo. The importance of the phosphocreatine circuit among other pathways of intracellular energy transfernetwork is discussed on the basis of the recent data published in the literature, with some experimental demonstration. The resultsof studies of perfused rat hearts with completely inhibited creatine kinase show significantly decreased work capacity andrespectively, energy fluxes, in these hearts in spite of significant activation of adenylate kinase system (Dzeja et al. this volume).These results, combined with those of mathematical analysis of the energy metabolism of hearts of transgenic mice with switchedoff creatine kinase isoenzymes confirm the importance of phosphocreatine pathway for energy transfer for cell function andenergetics in mature heart and many other types of cells, as one of major parts of intracellular energy transfer network andmetabolic regulation. (Mol Cell Biochem 184: 291–307, 1998)

Key words: creatine kinase, mitochondria, respiration, contraction, regulation, thermodynamics, compartmentation, functionalcoupling, metabolic channelling

Address for offprints: V.A. Saks, Laboratory of Bioenergetics, Joseph Fourier University, BP 53X - 38041 Grenoble Cedex, France

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Introduction

The best way to consider any problem in a general manneris to start with its history. The reason what makes this oftennecessary is an interesting phenomenon which many of usmay have observed after some decades of active scientificresearch. The observation is that very often scientific workis designed, performed with good results, sent for pub-lication, accepted, published – and after some time seemsto be totally forgotten. And then, usually after some 10–15years, similar work with similar results is made in anotherlaboratory by other people, who come to these ideasindependently, and again published. We may call thisphenomenon ‘resurrection of results and ideas’. Anyscientist above forty can find abundant evidence for thisphenomenon from its own practice. We give here our ownexamples of this experience.

In 1970 S. Nagle described facilitated diffusion of highenergy phosphates in the organized cytoplasm of musclecells [1]. In accordance with ‘the law of resurrection’, Meyeret al. gave independently, in 1984, a quantitative descriptionof this idea [2], and later Dzeja, Goldberg (see chapter 11 inthis volume) and we used it [3] as the basis of hypothesisof metabolic oscillations – a feedback signal betweencontraction and respiration.

Second example. In 1978 Sjostrand gave an excellentdescription of structural differences of mitochondria invivo and in vitro [4] – and only now these ideas are beginningto be used for explaining the experimental data (see thechapter 10 in this volume).

All scientists involved in the creatine kinase research mayalso confess that we have collectively ignored the paper byKlingengberg et al. [5], one of the first descriptions of theidea of the phosphocreatine pathway for energy transfer inthe muscle cells. One of the reasons of this may be that notmany of us were strong in German language in which thispaper was written.

The kinetics of the creatine kinase enzymes in all possibleversions was studied in many laboratories, including ours,in seventies and early eighties [6, 7]. And now our colleaguesfrom The Netherlands have successfully performed the sameexperiments with the same results [8], in good accordancewith the ‘low of resurrection’.

When reading very interesting chapters of the recent book‘Channelling in intermediary metabolism’ edited by Agius andSherratt (Portland Press, London and Miami 1997), anexperienced man in the area of research recalls withappreciation the paper by Sols and Marco ‘Concentrations ofmetabolites and binding sites. Implications in metabolicregulation.’ Published in 1970 [9], who already then discussedthe significance and meaning of macromolecular crowding,intracellular concentrations of enzymes and metabolites,thermodynamic activities, and compartmentation. Now

these ideas are finding increasingly rapid and importantdevelopment.

Probably, most important example: in 1979 P. Mitchellgave a Sir Hans Krebs Lecture in Dresden at the FEBSMeeting describing in details the idea of vectorial ligandtransduction [10]. It took again about 10–15 years (see thechapter 11 in this volume and ref. [3]) to recognize its valueand to start to use this profound concept of bioenergetics,based on the recognition of the importance of cellularorganization, for explanation of one particular problem – ofthe nature of intracellular feedback signal transduction forregulation of respiration.

Sometimes funny things happen: some good results pub-lished long time ago are excavated from journals and used,without critical analysis, to explain new data, forgetting,probably because of the lack of time, everything that happenedbetween, within decades of scientific research [11] (this is inmore details analyzed in chapter 6 of this volume).

And these are only few examples of the phenomenon of‘resurrection of ideas and results’.

In accordance with this general observation, the aim ofthis paper is to accelerate resurrection of some results andideas published earlier in the field of the creatine kinaseresearch and in muscle cell bioenergetics, to give somehistorical overview of the research in the field of metaboliccompartmentation to assist new generation of researchersand also to analyze some important new quantitativeapproaches, including mathematical modeling, in studiesof energy transfer networks in the cells. And finally we haveto explain why the studies of the energy transfer networksincluding creatine kinase systems are becoming increas-ingly important. For that, we analyze the function of theheart in which the creatine kinase system has been totallyinhibited.

Internal thermodynamics of mitochondrial creatinekinase, its functional coupling to the adeninenucleotide translocase and oxidative phosphorylation

In the chapters 9 and 10 of this volume by Schlattner et al.and by Stachoviak et al. from Theo Wallimanns laboratoryin Zuerich, the authors give fine analysis of the structure ofthe mitochondrial creatine kinase and discuss possible waysof its functional coupling with the adenine nucleotidetranslocase. The mitochondrial isoenzyme was the first ofcreatine kinases for which the molecular and spatial (X-ray) structure was solved [12]. In connection with theseachievements in structural analysis of creatine kinase, werecall our earlier studies on the kinetics and thermodynamicsof the coupled mitochondrial creatine kinase - they are verycomplementary to the structural data from Wallimann’slaboratory and may be useful in further studies of the

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Scheme 1. The schematic presentation of the mechanism of the creatine kinase reaction.

molecular physiology of mitochondrial creatine kinase andenergy channelling from mitochondria into cytoplasm.

We used the isolated rat heart mitochondria as a source ofthe bound mitochondrial creatine kinase [13]. The creatinekinase reaction rates were determined in the sucrose medium[14]. In the absence of oxidative phosphorylation, the reactionrate in the forward direction (phosphocreatine and ADPproduction) was measured by using the pyruvate kinase-lactatedehydrogenase coupled enzyme assay, and in the reversedirection (ATP production) by using the hexokinase – glucose-6-phosphate dehydrogenase coupled enzyme assay [14].

Under respiring conditions, the steady state rate of theforward creatine kinase reaction was calculated from therates of oxygen consumption in the presence of creatine asdescribed in details by Jacobus and Saks [14].

From these data, the dissociation constants of the enzyme-substrate complexes were calculated [14]. The creatinekinase reaction mechanism is known to be the randombinding quasi-equilibrium Bi-Bi type, according to Clelandsclassification (Scheme 1) [6, 7]. The reaction mechanismof the creatine kinase and the dissociation constants foreach step are shown in Scheme 1. The methods of thesecalculations are described earlier [14].

Since dissociation of the creatine kinase enzyme-substratecomplexes represent quasi-equilibrium processes, theyobey, in general, the rules of the classical thermodynamics:

∆Go = –2.303 RT log Kd (1)and:

log Kd = –∆Ho/2.303 RT + ∆So/2.303R (2)

The reaction rate determinations were made in the tem-perature range of 19–38°C. Figures 1 and 2 show the resultsof the complete kinetic analysis of the mitochondrial

creatine kinase in the membrane-bound state in the absenceand in the presence of oxidative phosphorylation. Thenequations (1) and (2) were used to construct the free energyprofile of the creatine kinase reaction and for generalpresentation of the data.

Figure 1A shows the experimental results for the forwardreaction (phosphocreatine production). The oxidativephosphorylation process does not influence the binding anddissociation of the creatine: its dissociation constants fromthe binary complex E.Cr, Kib, and from the ternary complexE.MgATP.Cr, Kb are the same in the presence and in theabsence of oxidative phosphorylation at any temperature.However, the situation with the second substrate, MgATP, isvery different. Depending on the temperature, the value ofKia, dissociation constant for the binary complex E.MgATP,is decreased two or three times under conditions of oxidativephosphorylation. However, Ka, the dissociation constant ofMgATP from the ternary complex E.MgATP.Cr is changedby order of magnitude. The V

max values are not changed by

the oxidative phosphorylation (Fig. 1B). Thus, the influenceof the oxidative phosphorylation on the creatine kinasereaction concerns only the effective concentration of thecommon intermediate, MgATP. Table 1 gives the empiricalequations for temperature dependencies of all of the constantsof dissociation of the enzyme-substrate complexes for theforward creatine kinase reaction in the absence and in thepresence of oxidative phosphorylation. These equations maybe used in future modelling of the coupling phenomena atany temperature in the given range (see chapters by Aliev etal. and Kemp et al. in this volume).

Finally, Fig. 2 shows the temperature dependencies of thekinetic constants of the reverse mitochondrial creatinekinase reaction (this reaction was not studied in the presenceof oxidative phosphorylation because of the experimental

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Fig. 1B. The temperature dependencies of the maximal reaction rate of theforward mitochondrial creatine kinase reaction; (–): in the absence of oxidativephosphorylation; (+): in the presence of oxidative phosphorylation.(Reproduced from ref. [13] with permission).

Table 1. Thermodynamic parameters of the forward and reversemitochondrial creatine kinase reactions in the membrane bound state ofenzyme in the absence of oxidative phosphorylation

Kinetic constant Empirical equation ∆G0

and of lgK = f (1/T) from kJ × mole–1

the reaction linear regression of data 25°C

I Forward reaction, Cr + MgATP → PCr + MgADP + H+

Kia 3.13 – 1019 × 1/T 1.65Ka 6.70 – 2241 × 1/T 4.7Kib 11.5 – 3066 × 1/T –6.9Kb 13.2 – 3739 × 1/T –3.7Vmax 14.62 – 4357 × 1/T Ea = 83.42*

II Reverse reaction, PCr + MgADP + H+ → MgATP + CrKic 4.04 – 1569 × 1/T 6.8Kc 6.6 – 2407 × 1/T 8.5Kid 3.09 – 909 × 1/T –0.24Kd 5.9 – 1854 × 1/T 1.83Vmax 14.66 – 4288 × 1/T Ea = 82.10*

*Ea – empirical activation energy determined according to the equation 5.Other thermodynamic values were calculated from the data of linearregression according to the equations 1–3.

difficulties concerning very high apparent affinity of themitochondrial oxidative phosphorylation for ADP). Theempirical equations for these constants are given in Table 1.

All data given in Table 1 were used to calculate the freeenergy profile for the membrane-bound mitochondrial creatinekinase reaction in the absence of oxidative phosphorylation.This free energy profile gives the internal thermodynamicsof the mitochondrial creatine kinase reaction and is shownin Fig. 3. The difference between free energy levels of E +PCr + MgADP and E + Cr + MgATP gives the standard freeenergy change of the creatine kinase reaction.

There are several remarkable peculiarities of this thermo-dynamic profile. First, the activation energies for theforward and reverse creatine kinase reactions calculatedfrom the Arrhenius equation are equal to each other (E

a = 82–

83 kJ/mole) and that conforms to the absence of free energychange at the step of phosphoryl transfer earlier discoveredby the NMR method [15]. The free energy profile shows thatthe free energy changes occur at the steps of the substratebinding and product dissociation. This is the common prop-erty of the phosphoryl or phosphate transfer enzymes, includingmany kinases and myosin ATPase [16, 17] acting as a kinetically

optimized enzymes, which, according to Albery and Knowles,have reached evolutionary perfection [17, 18]. The standard freeenergy change of the creatine kinase reaction (‘external thermo-dynamics’) calculated by this method is 10.5 kJ/mole and closeto other determinations [19].

Fig. 1A. The temperature dependencies of the kinetic constants for theforward creatine kinase reaction, catalyzed by the membrane-bound rat heartmitochondrial creatine kinase. The data for dissociation constants ofsubstrates in the absence of oxidative phosphorylation (–) and in thepresence of oxidative phosphorylation (+) are shown

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Since in the presence of oxidative phosphorylation theapparent kinetic constants of the mitochondrial creatinekinase do not represent any more parameters of quasi-equilibrium processes but are influenced by several coupledprocesses and need mathematical models for their analysis(see chapter by Aliev in this volume), it is not possible toconstruct the free energy profile for this case. However,the data shown in the Fig. 2 allow us to make some veryinteresting conclusions and predictions concerning themolecular physiology of the coupled mitochondrial creatinekinase reaction. The very significant decrease in only oneof the dissociation constant, Ka, at the background of theminor changes in the other one, Kia, means that formationof the ternary complex E.Cr.MgATP from E.Cr is mostfavored by direct channelling of the ATP molecules from theadenine nucleotide translocase to the mitochondrial creatinekinase under conditions of oxidative phosphorylation. WhenATP is channelled to the creatine kinase before binding ofcreatine (a process characterized by Kia), it may significantlydissociate from the E.MgATP complex before the formationof the productive ternary complex, E.Cr.MgATP. In general,this kind of mechanism of functional coupling whichincludes direct channelling of ATP from translocase tocreatine kinase and ADP back from creatine kinase to

translocase, is shown in Fig. 4. Quantitatively, this process hasbeen described by Aliev and Saks by a probability model ofthe functional coupling of creatine kinase and adeninenucleotide translocase in mitochondria [20]. And remarkably,after 15–20 years of these functional works, the conclusionsmade are now directly confirmed by structural studies (seechapters 9 and 10 in this volume). This mechanism offunctional (and structural) coupling is a good example ofmetabolic channelling phenomenon, and it is the basis of theaerobic phosphocreatine production in mitochondria in manycells in vivo, and probably a powerful amplifying mechanismfor the feedback regulation of respiration by creatine and bychanges (oscillations) of ADP concentrations [3].

The creatine kinases, compartmentation phenomena,intracellular energy transfer networks and the problemof respiration regulation in vivo

In spite of very advanced knowledge of particular problems,such as membrane bioenergetics in mitochondria, structureand function of actomyosin complexes, ion channels andpumps, all kind of membrane ATPases, different signaltransmission pathways (G-proteins etc.), the principles ofregulation of energy fluxes within the integrated cellularsystems in vivo are not yet well understood. There are verynumerous works and reviews on cellular regulation of energymetabolism in the cells, but the general agreement is not asyet achieved on the question in which way the feedback signalis given to cellular systems of ATP production to respondto increased cellular work-contraction, ion transport,biosynthesis etc. If there is some general agreementregarding this question, it is that in many cells the regulatorysignal is not simply the change in cytoplasmic ADP con-centration since it does not correlate with alteration of therespiration rate [23–30]. Intensive studies of the role ofcalcium ions in this process also did not give as yet anydecisive answer (see the chapters by Hansford and Zorov andMazat et al. in this volume). In fact, calcium alone cannotbe the solution of the problem since the energy transfer andfeedback signaling are associated with phosphoryl orphosphate group transfer, and the mass conservation lowrequires that the same amount of ADP as released inmyofibrils should be made available for rephosphorylationin the mitochondria under steady state conditions. Thatmeans that the signaling involves the group transfer, ormacroosmotic process, according to P. Mitchel [10]. Andit is important to note that diffusion of ADP seems to haveseveral serious obstacles in the cell, such as multiple bindingsites, macromolecular crowding [31, 32], problems of thecontrolled permeability through the outer mitochondrial porinpores [3] etc. Bereiter-Hahn and Voth studied morphologicalchanges of mitochondria, which acquire condensed form in

Fig. 2. The temperature dependencies of the kinetic constants for the reversecreatine kinase reaction catalyzed by the membrane-bound rat heartmitochondrial creatine kinase. The kinetic constants were determined underconditions of complete inhibition of mitochondrial oxidative phos-phorylation. (Reproduced from ref. [13] with permission).

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Fig. 3. The free energy profile of the mitochondrial creatine kinase reaction catalyzed by the rat heart mitochondrial creatine kinase in the absence of oxidativephosphorylation.

response to direct microinjection of ADP into the cells, andshowed that spreading of these mitochondrial responsesfrom tip of the injecting capillary to more peripheral zonesis in fact very slow indicating slow diffusion of ADP incytoplasm [33]. This observation is relevant to our data onthe increase of the apparent K

m for ADP in regulation of

oxidative phosphorylation in the cells in vivo by an orderof magnitude, in comparison with isolated mitochondria, dueto decreased permeability of outer mitochondrial membrane[3], and to the results by described Van Beek et al. inchapter 20 of this volume, showing that the response ofmitochondrial oxygen uptake to rapid work changes isdelayed with respect to rapid change of the level of PCr.Rapidly growing body of experimental evidence shows theunexpected importance of the porin pores, or VDAC, ofmitochondrial outer membrane for regulation of metabolicfluxes in the cells in vivo [3, 34– 41]. Marco Colombini’slaboratory has recently shown that this channel in ‘closed’configuration almost completely blocks ATP flux and also

decreases permeability for di- and trivalent anions whilemonovalent ions are still permeable [34, 35]. Some proteinsin cytoplasmic fraction have been found to increase thevoltage-dependence of this channel [36, 37], and we haveproposed that some of these proteins may be associated withcytoskeleton (see ref. [3] and chapter by Rappaport andSamuel in this volume). Also, there are evidences of possibleimportance of the complexes of mitochondrial porin withkinases and adenine nucleotide translocase for stimulationof mitochondrial oxidative phosphorylation and regulationof permeability transition pore in brain [38]. Because of thecontrolled permeability of porin channels for ADP, themitochondrial kinases connected to the outer membrane,outer surface of the inner membrane or in the intermembranespace become key enzymes in energy distribution betweendifferent networks and signal transmission for mitochondrialresponses to energetic demands [3, 38–42].

Therefore, one of the most important questions in cellularbioenergetics in vivo, an answer to which is in fact totally

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Fig. 4. The schematic explanation of the specific effect of oxidative phosphorylation on the kinetics of mitochondrial creatine kinase reaction. T-adeninenucleotide translocase. MgATP is directed by the translocase by the mechanism of direct channelling to the active side the mitochondrial creatine kinase. Inthe absence of creatine some dissociation of MgATP from the binary enzyme-substrate complex is possible. If MgATP is directed to the enzyme alreadysaturated with the creatine molecules the ternary complex is converted into the enzyme-product complex with the consequent dissociation of phosphocreatineand MgADP; the latter is taken back into the mitochondrial matrix by adenine nucleotide translocase for rephosphorylation in the mitochondrial oxidativephosphorylation to start new cycle of the coupled reactions. High turnover of these coupled reactions results in high steady-state concentration of theternary complex E.MgATP.creatine and this results in apparent decrease of the dissociation constant Ka value.

unknown, is the value of ADP diffusion coefficient in the cellcytoplasm. There are good experimental data for diffusioncoefficients for ATP, PCr and P

i in bulk water phase of cyto-

plasm determined by isotope or NMR pulse gradient methods[43, 44], but even these data are too general and do not takeinto account the complex, fine structural organization of thecell and existence of multiple compartments and micro-compartments, where the diffusion is significantly restricted[3, 31]. Also, one should take into account the structure ofthe intracellular water phases [45, 46]. For example, Walter andBrooks have described phase separation in cytoplasm due tomacromolecular crowding as the basis for formation of multiplemicrocompartments in the cells, and concluded that theinterface between these aqueous phases presents a barrierfor diffusion of molecules [45]. Further complications arise fordiffusion of ADP (and of any other substrate) if the activecenters of enzymes are fixed in multienzyme complexes (formore details on this topic see recent monograph by J. Ovaldi[31] and in several recent review [3, 32]). For example, this kindof fixation, probably with participation of the cytoskeletalsystem has been shown for glycolytic complexes and sarco-lemmal or other membrane ATPase and ATP-dependentpotassium channel in heart cells: exchange of ATP and ADPwithin these complexes (microcompartments) without therelease of adenine nucleotides into cytoplasm [47, 48]. Andbecause of diffusion problems for ADP and complex cellularstructural organization, simple calculations of diffusiondistances and transit times often used as arguments in dis-cussions on the basis of ADP diffusion constant in diluted

solutions may be taken only as entertaining exercise but nottoo convincing solution of this serious problem (see alsothe chapter 20 by Van Beek et al. in this volume).

Probably, there are numerous ways of transmission of thefeedback signal within the metabolic networks in the cell,depending on the type of the cell considered, and on themetabolic state of the given cell. For example, mechanismof regulation of respiration in the muscle cells seems to bevery tissue specific [49]. For fast twitch skeletal muscle theclassical paradigm based on homogeneous equilibrium meta-bolic system [50, 51] may be a reasonable approximation,especially in resting state. For other types of cells, notablyfor the working heart cells, and also for liver and brain cellsand probably many others it does not provide any reasonableexplanation of regulation of respiration [3, 23– 27]. In thesecells manifold changes in respiration rate is seen at minorchanges in metabolic state [3, 23–27, 30]. Many data areemerging now showing that the nature of this signal isinfluenced or even determined by the structural interactionsin the cell. This regulation most possibly includes functionalinteraction, or functional coupling between structurallyrelated enzyme systems in the compartments and micro-compartments of the cell, and finally, both calcium andmetabolic wave propagation between microcompartments.

Thus, the classical paradigm of muscle bioenergeticsbased on the concept of homogenous metabolic systems,which are in equilibrium, has to be changed and replaced bythe paradigm based on the concept of metabolic networks forenergy transfer and signal transduction, which basically

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function in non-equilibrium, metastable steady state. Thisconcept is developed in many chapters in this volume (Sakset al., Schlattner et al., Dzeja et al., Aliev et al., Van Beek et al.,Kholodenko et al., K Nicolay et al., Rappaport and Samuel,Ventura-Clapier et al.). According to this concept, not only freediffusion of metabolites but mostly enzymatic, vectorial grouptransfer (ligand conduction), due to fine structural organ-ization of the cell interior by cytoskeleton, with participationof different enzyme systems (creatine kinase, adenylate kinase,glycolytic systems etc.) carry out the energy transfer betweendifferent cellular compartments and feedback regulationprocesses in cellular bioenergetics. The contribution of diff-erent pathways in the process of energy transfer (total energyfluxes) may vary, depending of metabolic state or alteredexpression of enzymes (transgenic animals).

The concept of metabolic networks of energy transfer isdirectly related to the phenomenon of compartmentationof enzymes and metabolites. Two lines of experimentalresearch in the history of muscle biochemistry and physiologyled to the ideas of compartmentation of adenine nucleotidesin the cell: studies of the role of so-called peripheralkinases, as hexokinase, creatine kinase and adenylate kinasein the cells (peripheral – because in the mitochondria theyare associated with the outer surface of the inner membraneor to the outer membrane), and studies, or attempts, toestablish any connection, or correlation between heartmuscle contractile function and tissue high energy phosphatecontents, (more precisely, from discovery of the lack of thiscorrelation). The first line of ideas was pioneered byBessmann et al. [52], and the works of both Klingenberg [5]and Nagle [1] should be mentioned in connection to thisgroup. The second direction started to actively develop aftertwo publications – those by Gerken and Schlette, and byGudbjarnason et al. [53, 54]. This was the beginning. Furtherdevelopments in this area resulted in detailed description ofthe biochemistry and physiological roles of the coupledcreatine kinases reviewed in our first collective work [55].

The ideas of the metabolic channelling started to developon more general basis in cellular biochemistry in the worksof Kelety, Sols and Marco, as already mentioned, Srere,Kurganov and others, as reviewed in the ref. [3], and thecurrent state of studies of these problems is reviewed in therecent monograph by J. Ovaldi and in that edited by Agiusand Sherratt [31, 32]. In this volume, the reader can find manyreferences to earlier works and recent reviews in this areain the chapter by Kholodenko et al. in this volume.

In a rather unexpected way, the concept of metaboliccompartmentation and metabolic channelling (functionalcoupling) has recently found its most direct experimentalconfirmation in studies of excitation-contraction couplingand calcium metabolism due to serious advancements in theexperimental techniques, mostly due to the use of confocalmicroscopy [56–66]. The use of this technique allowed to

show that the calcium transients thought to representelevation of calcium concentration homogeneously incytoplasm during excitation-contraction coupling, in factrepresent summation of calcium sparks – triggered orspontaneous local increases of calcium concentration inmicrocompartments between cellular structures [57–60].Also, by using digital imaging microscopy, Isenberg et al.directly demonstrated the existence of deep calciumgradients and diffusion limitations within the sarcomere inventricular myocytes [63]. Local increase in calciumconcentration may propagate in cardiomyocytes as a wave[60, 61, 62]. References to these works are too numerousand too rapidly increasing to be given here exhaustively (seethe chapter by Mazat et al. in this volume). One interestingwork in this line was recently published by groups ofLewartowsky and Langer, showing direct channelling ofcalcium between sarcoplasmic reticulum and Na-Ca exchangerin sarcolemma in the process of calcium extrusion from thecells [66]. All that means that determination, or calculationof average cytoplasmic concentration of calcium is notenough to understand in quantitative terms the mechanismsof excitation-contraction coupling. In other words, allcellular processes of calcium metabolism and its regulationare now considered in terms of microcompartmentation.Some years ago, Carmeliet analyzed electrophysiologicaldata and concluded that also for sodium ions there is a‘fuzzy subsarcolemmal space’ where the ion concentrationis different from the average cytoplasmic one and itsdiffusion limited [67]. That means the existence of thecompartmentation phenomenon also for this small ion inthe cell.

And all that is exactly what we have been telling aboutenergy metabolism and adenine nucleotides in the cells formore than 25 years – that calculation of average cytoplasmicconcentrations of ATP and ADP does not help too much tounderstand the mechanisms of regulation of respiration andcellular energetics, and that functionally important pools ofadenine nucleotides are different from average concentrationsin the cell [3, 52–55, 68–71]. This conclusion has beendirectly confirmed by Lanoue’s group for the heart [72] andis consistent with many other experimental data which haveshown dissociation of muscle function from the totalcontent of ATP in the cells (see ref. [3] for discussion). Tosolve the problem of respiration regulation quantitatively,it is necessary to obtain some information of local ATP andADP concentrations in cellular compartments and micro-compartments. We clearly need some experimental methodsof direct determination of local concentrations of adeninenucleotides in the cellular microcompartments (analoguesto «calcium spark» detection). To the author’s knowledge,if this method exists, it is not openly described and notwidely used as yet. That makes it necessary to combine 31P-NMR flux determination with isotopic and other methods

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(see the chapters by Dzeja et al. and Klaas Nicolay et al. inthis volume) to collect quantitative information on themetabolic fluxes in the cell, and inevitably all conclusionsof the role of compartmentalization of adenine nucleotidesare still mostly indirect. One of interesting evidences forintracellular compartmentation of cyclic adenine nucleotideshas been recently reported by Jurevicius and Fischmeister:by using whole-cell patch-clamp recording and a doublecapillary for extracellular microperfusion, they studieddistant and local effects of drugs on L-type calcium currentand found higher cAMP concentration close to calciumchannel than in rest of the cell [73, 74].

Strong evidence for compartmentation phenomenoncomes from studies of the glycolytic pathway of free energyproduction: the glycolytically produced ATP (‘glycolyticATP’) has been found to be more effective than ATP producedin mitochondria, in prevention of ischemic contracture andmembrane damage [47, 48]. Also, the important consequenceof compartmentation of the adenine nucleotides in the cellis that the total contents of high energy phosphates aredissociated from the function [75, 76].

Awaiting for the future developments of experimentalmethods of direct determination of local concentrationsof adenine nucleotides in the cells, it is helpful to analyze theproblem of metabolic regulation of respiration quantitatively,by using kinetic and mathematical models and new achieve-ments in the Metabolic Control Analysis. And it seems tobe a very good idea to combine methods of mathematicalmodeling with some powerful experimental approach, suchas transgenic animal technology (see below and a chaptersby Klaas Nicolay et al. and Aliev et al. in this volume).

Mathematical models of the energy transfer networkbetween different cellular compartments

Mathematical modeling of the metabolic systems is not anew approach. Quantitative studies in muscle biochemistry,by using mathematical models, were pioneered some 25–30years ago by David Garfinkel in Philadelphia, USA. Thedifficulties he and his co-workers met in these studies ofthe whole metabolic systems – the large number of rateequations and parameters used that made the models verycomplicated for the analysis – promoted, in fact, the develop-ment of the Metabolic Control Analysis. In details, theseproblems and their historical aspects are well described byDavid Fell in his ‘Understanding the Control of Metabolism’,Portland Press, London and Miami 1997.

However, as it is mentioned by Korzenievski in thisvolume, there are some limits for the use of the MetabolicControl Analysis: it gives the methods of analysis ofregulation of a metabolic process in a given steady state,and usually is not related to and not very much interested

in its mechanism. It is the great value of the kinetic andmathematical models that they are based on the detailedmechanisms of the reactions and processes involved. Andhaving learned some interesting lessons from the MetabolicControl Analysis, we are now coming back to the math-ematical models of metabolic processes. We may call them‘focused mathematical models’. This volume gives fourexamples of these models: the kinetic model of interactionbetween electron carriers in the respiratory chain by Deminet al. the model of the oxidative phosphorylation reactionsin the muscle mitochondria by Korzenievski, the theoreticalmodel of the creatine kinase reactions in the spatial andtemporal energy buffering by Kemp et al. and the model ofcompartmentalized energy transfer with the analyze of theexperiments on the isolated hearts of the creatine kinasedeficient mice by Aliev et al. All these models give somereasonable results which can be experimentally proved, andthe model of the compartmentalized energy transfer explainswell the experimental results which look at first glanceparadoxical, and in this way increases or at least improvesour understanding of complicated intracellular situation. Thecommon property of all these models is that they are focusedon explaining quantitatively one or several processes whichare considered in details, while the others are generalizedand maximally simplified, or if possible, ignored. This isanalogous in some sense to the top-down analysis in whichthe complex system is also divided into parts to simplify theanalysis (see chapter 1 by M. Brand in this volume). Thefocused mathematical models require, however, that thecoefficients and constants included could be determinedexperimentally. Otherwise they rapidly loose they value asmethods of quantitative research.

In the literature we can find multiple good examples ofthis kind of focused models. One is the work by Meyer etal. on the analysis of the role of the equilibrium creatinekinase system in facilitated energy transfer [2], very goodexamples are the models of oxygen diffusion and energymetabolism by Michael Mahler [77], and the work by JurgenDaut on cellular energetics [78]. Thus, if the purposes ofmodeling are well defined and focused on analysis of a givenprocess with well determined boundary conditions, thesemathematical models prove to be very effective method ofthe research.

CK pathway for the energy transfer: the isoenzymecompartmentation, the problem of the creatine kinaseequilibrium and cytoplasmic ADP concentration

One of the rather surprising results of the use of mathematicalmodeling of the compartmentalized energy transfer incardiac muscle cells is the conclusion that the creatinekinase equilibrium concept has only a very limited value

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and application in muscle, particularly in the cardiac cellphysiology [21, 22]. This very simple and convenient conceptmay be well applied for the resting cell and in the diastolicphase but not in the contracting heart muscle. In fact, thisconclusion is not the unexpected one. Kent Sahlin hasquestioned the values of the estimation of the ADP con-centration in the cells [79]. Meyer found that in skeletal musclethe maximal activation of the contraction also causes thedisequilibrium of the creatine kinase reaction [80]. Calculationsmade on the basis of exact experimental data on creatine kinaseisoenzyme composition and accounting for compartmentationof its isoenzymes in different cellular compartments show thatfor mitochondrial creatine kinase this equilibrium never exists,and myofibrillar, or cytoplasmic creatine kinase may approachthe equilibrium state only in the systolic phase [21, 22]. Thus,all conclusions regarding the determination of the cytoplasmicADP concentration in the cells made on the basis of thecreatine kinase equilibrium may be considered critically andwith caution, if the muscle cell is performing significant workand the oxygen consumption significantly exceeds the restinglevel. Further, these calculations have also shown thateffective functioning of the phosphocreatine pathway insteady state requires co-expression of different creatine kinaseisoenzymes in the different compartments of the cell. Thismeans that in the cells in which the phosphocreatine pathwayis active, the components of this pathway – creatine kinaseisoenzymes function in coordinated manner out of equilibrium,in the metastable steady state (according to the terminologyintroduced by Jurgen Daut [78]), if the cell is not in the restingstate (see the chapter by Aliev et al. in this volume). The wayin which mitochondrial creatine kinase functions is sensitiveto the changes in the myofibrillar end of the phosphocreatineshuttle: in the MM-creatine kinase deficient mice mitochondrialcreatine kinase and aerobic phosphocreatine production arestrongly inhibited by high intracellular concentrations of ADP(see the chapter by Aliev et al. in this volume). This con-clusion is in concord with the results of the studies ofmolecular biology of creatine kinases (see the chapter by inthis volume) and with recent experimental results by Veksleret al. [81].

These calculations also show that if the compartmentalizedcreatine kinase system is out of equilibrium, in the metastablesteady state, one may observe very significant (by order ofmagnitude) variations of the myoplasmic ADP concentrationwithin the cardiac cycle under conditions when the totalcellular level of phosphorus metabolites, such as phospho-creatine or ATP change within the range of 4–5% [21]. That iswithin the range of experimental error of determination of thesemetabolites. And this may explain many experimental resultsfrom Balaban’s and other laboratories showing constant PCrlevels or PCr/ATP ratios during significant variations of therespiration rate [23–25], still leaving for ADP the leading rolein feedback regulation between contraction and respiration.

Many experimental data show variations of mitochondrialcalcium concentration within contraction cycle, synchron-ously with cytoplasmic calcium, favoring the theory ofcalcium regulation of mitochondrial oxidative phosphoryl-ation in details described in this volume by Hansford andZorov. This activation of oxidative phosphorylation bycalcium may coincide with changes in ADP concentrationin cytoplasm, and therefore these both potentially importantregulatory factors may exert their action on the oxidativephosphorylation in a well-coordinated manner. The result israpid and stable energy production exactly matching theenergy demand, and in this case the temporarily increasedADP signal may be rapidly quenched by calcium-activatedoxidative phosphorylation. As a result, we may have some-thing similar to ‘ADP sparks’ in cytoplasm, propagating asa wave, in complete analogy with modern concepts ofcalcium metabolism (see above). This is interestingpossibility of feedback regulation of respiration. Thisconclusion fits with several groups of experimental data.When calcium uptake into mitochondria is inhibited byruthenium red, the metabolic changes in response to alteredworkload are enhanced in comparison with non inhibitedhearts, this showing the ‘accumulation’ of ADP signalbecause of its decreased quenching [82]. However, therelationship between workload and oxygen consumptionstays unchanged.

Thus, it is most possible that both ADP and calciumsimultaneously participate in the feedback regulation ofoxidative phosphorylation in the intact heart cells.

Experimental verification of this conclusion requiresfurther experimental and theoretical studies.

What happens when the creatine kinase system isswitched off (inhibited) in the muscle cells?

The phosphocreatine shuttle, or circuit is classically con-sidered as a major energy transfer pathway in the cells withhigh energy fluctuations, such as heart, skeletal muscle, brainand many other types of the cells [3, 55, 68–71]. However,this is not a single pathway of energy transfer, since manytypes of cells such as liver etc. lack creatine kinase, and theexpression of the creatine kinase system is different indifferent types of cells (see the chapter by Ventura-Clapieret al. in this volume) and changes significantly during muscledevelopment [83]. The physiological importance of thissystem has been studied in very numerous works by usingthree different approaches: (1) inhibition of creatine kinasein the perfused heart [84–86]; (2) substitution of creatinein the cells by its analogs, such as guanidinopropionate orguanidinobutirate by feeding it experimental animal during2–3 weeks [87, 88]; (3) use of transgenic technology toswitch off different creatine kinase isoenzyme genes [89,

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Fig. 5. Left ventricular pressure of Langendorff perfused rat heart, glucose perfusion. (A): Heart before and after a transition from 1.25 mM to 3.5 free calciumperfusate concentration. Note the increase in left ventricular systolic pressure from 118–180 mmHg with almost no concomitant change in end diastolicpressure; (B): Left ventricular pressure of the same Langendorff glucose perfused heart before and after a transition from 3.5 to 0.5 free calcium perfusateconcentration. Note the decrease in left ventricular systolic pressure from 180 mmHg to 55 mmHg; (C): Left ventricular pressure of the same Langendorffglucose perfused heart switched back from 0.5 mm free calcium perfusate concentration to the initial concentration of 1.25 mM. Note the complete recoveryof the function and the absence of functional adverse effect of the protocol.

90]. In general, the results of all these approaches are inagreement with each other and may be summarized as itfollows: while the cells perfectly survive without the creatinekinase system due to activation of other metabolic systemsand adaptive changes (see the paper by Dzeja et al. andchapter 13 in this volume), the functional properties of thecell are impaired if the creatine kinase system is defectiveor inhibited. Thus, the physiological role of the creatinekinase system is related to the specific function of the cellbut not to its viability.

We illustrate this conclusion by the experimental results

shown in Figs 5–8. The isovolumic isolated rat heart wasperfused with solutions containing different concentrationsof calcium ranging from 0.5–3.5 mM. This resulted in 3fold increase of the developed tension, and this effect iscompletely reversible (Fig. 5). However, when the heartswere perfused with iodoacetamide which inhibits more than90 % of the creatine kinase activity [86], the inotropic effectof increasing calcium concentrations was completely lost(Figs 6 and 7) . In the hearts perfused with pyruvate as asubstrate, iodoacetamide itself had no effect on the contract-ility but eliminated the inotropic effect of increasing calcium

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Fig. 6. (A): Left ventricular pressure of Langendorff pyruvate perfused rat heart before and after a transition from 1.25 mM to 3.5 free calcium perfusateconcentration. Note the increase in systolic pressure from 100–180 mmHg; (B): Left ventricular pressure of the same heart before and after infusion ofiodoacetamide (120 µM over 15 min). Note the absence of increase in end diastolic pressure and again the abolition of contractile reserve when free calciumperfusate concentration is increased from 1.25–3.5 mM.

concentration (Fig. 6). In the case of glucose as a substrate,this inotropic effect disappeared simultaneously withelevation of the end diastolic pressure in the presence ofiodoacetamide (Fig. 7). The latter effect may be explainedby some inhibition of the enzymes of the glycolytic systemby iodoacetamide and decreased production of so calledglycolytic ATP which latter effect may be explained by someinhibition of the enzymes of the glycolytic system byiodoacetamide and decreased production of so calledglycolytic ATP which has been found to be important formaintaining heart muscle relaxation [48]. Figures 8A and8B summarize all these data in coordinates of oxygenconsumption rate (as a measure of energy fluxes) vs work-loads, represented, as usually for Langendorff perfusedhearts, by RPP, the rate-pressure product. The hearts withinhibited creatine kinase system are able to perform onlya limited amount of work and develop correspondinglylimited energy fluxes, independently of the substrate used(Fig. 8). Correspondingly, the maximal value of oxygen con-sumption in these hearts treated with iodoacetamide is 35µmole per min per gdw, in contrast with 65–70 µmole per minper gdw in the control hearts. Taking into the account that

Langendorff-perfused hearts usually perform decreasedlevels of work in comparison with working heart modelswhich develop oxygen consumption rates up to 120 µmolesper min per gdw [3], in the case of the latter models ofperfusion the differences may be expected to be even moresignificant. Thus, the hearts treated with iodoacetamide toinhibit the creatine kinase system have lost the contractilereserve. Dzeja et al. have directly shown more than 10-foldactivation of the flux through adenylate kinase system underthese conditions (see Fig. 3 in chapter 11 in this volume),which takes over the energy transfer function of the creatinekinase system. However, this is not enough to maintain themaximal contractile function. Thus, we may conclude thatunder normal conditions, in the intact heart, the creatinekinase system is indeed the major pathway of the energytransfer network in the cells.

These results are very similar to those reported recently byMatsumoto et al. and by Ingwalls group [84–86]. Very similarresults were obtained by Kapelko et al. in studies of rat heartsin which the creatine kinase was intact creatine was substitutedby guanidinopropionate [87], and by Zweier and Jacobus whoused guanidinobutyrate as an analog of creatine [88]. Both these

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Fig. 7. (A): Left ventricular pressure of glucose Langendorff perfused rat heart before and after a transition from 1.25–3.5 mM free calcium perfusateconcentration. Note the increase in left ventricular systolic pressure from 120–187 mmHg; (B): Left ventricular pressure of the same glucose Langendorffperfused rot heart before and after infusion of Iodoacetamide (120 µM in 15 min). Note the increase in diastolic pressure (from 8–30) and the complete abolitionof contractile reserve when perfusate free calcium concentration is increased from 1.25–3.5 mM.

types of hearts showed decreased contractile function.Similarly, the muscle contraction was significantly imp-

aired in transgenic mice with knocked out MM creatinekinase or both MM and mitochondrial creatine kinases (seechapters 13, 14 and refs [89, 90]). However, very significantadaptive changes observed in the cells of these transgenicanimals (see chapter 13) make it difficult to evaluate quantit-atively the importance of the phosphocreatine pathway forcontraction, since these strong adaptive changes give areason for a skepticism that these transgenic animal are infact new brand of animals. Nevertheless, this is a verypowerful technique which already has given us good lessons(see chapter by Klaas Nicolay et al. in this volume).

The situation may be more serious for the cell when thesestrong adaptive changes, for some reason, do not occur butthe creatine kinase system is impaired. This is a case of heartpathology [55, 91].

Acknowledgements

The authors thank Drs. Robert Balaban (Bethesda, USA),Jurgen Daut (Marburg, Germany) and Mais Aliev (Moscow,Russia) for active discussion of problems described in thisarticle. Technical assistance of Mrs. Lena Saareoja and Mr.Toomas Tiivel is gratefully acknowledged.

References

1 . Nagle S: Regelprobleme im Energiestoffwechel des Herzmuskels.Klin Wsch 48: 1075–1089, 1970

2 . Meyer RA, Sweeney HL, Kushmerick MJ: A simple analysis of the‘phosphocreatine shuttle’. Am J Physiol 246: C365–C377, 1984

3 . Saks VA, Khuchua ZA, Vasilyeva EV, Belikova Yu O, Kuzuetsov AV:Metabolic compartmentation and substrate channelling in musclecells. Role of coupled creatine kinases in in vivo regulation of cellular

304

Fig. 8. Myocardial oxygen consumption of Langendorff perfused rat hearts as a function of rate pressure product without (circles) and with (triangles)inhibition of creatine kineses by perfusion with iodoacetamide (120 µM for 15 min). Different levels of rate pressure product were obtained by changes of thefree calcium concentration from 0.5–3.5 mM. (A): Pyruvate as substrate; (B): Glucose as substrate.

A.

B.

305

respiration – a synthesis. Mol Cell Biochem 133/134: 155–192, 19944 . Sjostrand FS: The structure of mitochondrial membranes: A new

concept. J Ultrastruct Res 64: 217–245, 19785. Klingenberg M: Muskelmitochondrien. In: K Kramer, O Krayer, E

Lehnartz, A v Muralt, HH Weber (eds). Ergebnisse der Physiologic.Biologischen Chemie und Experimentellen Pharmakologie. Springer-Verlag, Berlin, 1964, pp 132–189

6. Morrison JF, Cleland WW: Isotope exchange studies of the mechanismof the reaction catalyzed by adenosine triphosphate: Creatinephosphotransferase. J Biol Chem 241: 637–683, 1966

7. Saks VA, Chernousova GB, Gukovsky DE, Smirnov VN, Chazov EI:Studies of energy transport in heart cells. Mitochondrial isoenzyme ofcreatine kinase: Kinetic properties and regulatory action of Mg ions.Eur J Biochem 57: 273– 290, 1975

8. van Dorsten FA, Furter R Bijkerk M, Wallimann T, Nicolay K: The in vitrokinetics of mitochondrial and cytosolic creatine kinase determined bysaturation transfer 31P-NMR Biochim Biophys Acta 1274: 59–66, 1996

9 . Sols A, Marco R: Concentrations of metabolites and binding sites.Implications in metabolic regulation. Curr Top Cell Reg 2: 227–273,1970

10. Mitchell P: Compartmentation and communication in living systems.Ligand conduction: A general catalytic principle in chemical, osmoticand chemiosmotic reaction systems. Eur J Biochem 95: 1–20, 1979

11. Wiseman RW, Jeneson JAL, Kushmerick MJ: Why is the sensitivity ofmitochondria to ADP over tenfold lower in permeabilized cells than invivo? Biothermokinetics of the Living Cell. Biothermokinetics Press,Amsterdam, 1996, pp 124–127

12. Fritz-Wolf K, Schnyder T, Wallimann T, Kabsch W: Structure ofmitochondrial creatine kinase. Nature 381: 341–345, 1996

13. Saks VA, Ventura-Clapier RJ: Biochemical organization of energymetabolism in muscle. J Biochem Org 1: 9–29, 1992

14. Jacobus WE, Saks VA: Creatine kinase of heart mitochondria:Changes in its kinetic properties induced by coupling to oxidativephosphorylation. Arch Biochem Biophys. 219: 167–178, 1982

15. Nageswara Rao BD, Cohn M: 31P-NMR of enzyme-bound substratesof rabbit muscle creatine kinase. Equilibrium constants, interconversionrates, and NMR parameters of enzyme-bound complexes. J Biol Chem256: 1716–1721, 1981

16. Burbaum JJ, Knowles JR: Internal thermodynamics of enzymesDetermined by equilibrium quench: Values of Kint for enolase andcreatine kinase. Biochemistry 28: 9306–9317, 1989

17. Albery WJ, Knowles JR: Evolution of enzyme function and thedevelopment of catalytic efficiency. Biochemistry 15: 5631–5640, 1976

18. Burbaum JJ, Raines RT, Albery J, Knowles JR: Evolutionary optimizationof the catalytic effectiveness of an enzyme. Biochemistry 28: 9293–9305, 1989

19. Lowson JWR, Veech RL: Effect of pH and free Mg2+ on the Keq of thecreatine kinase reaction and other phosphate hydrolases and phosphatetransfer reactions. J Biol Chem 254: 6528–6537, 1979

20. Aliev MK, Saks VA: Mathematical modelling of intracellular transportprocesses and the creatine kinase system: A probability approach.Mol Cell Biochem 133/134: 333–346, 1994

21. Aliev MK, Saks VA: Compartmentalized energy transfer in cardio-myocytes: Use of mathematical modelling for analysis of in vivoregulation of respiration. Biophys J 73: 428–445, 1997

22. Saks VA, Aliev MK: Is there the creatine kinase equilibrium inworking heart cells? Biochem Biophys Res Comm 227: 360–367, 1996

23. Balaban RS, Kantor HL, Katz LA, Briggs RW: Relation between workand phosphate metabolite in the in vivo paced mammalian heart.Science 232: 1121–1123, 1986

24. Balaban RS, Heneman FW: Control of mitochondrial respiration in theheart in vivo. Mol Cell Biochem 89: 191–197, 1989

25. Katz LA, Swain JA, Portman MA, Balaban RS: Relation between phosphatemetabolites and oxygen consumption of heart in vivo. Am J Physiol 256:H265–H274, 1989

26. Mootha VK, Arai AE, Balaban RS: Maximum oxidative phosphorylationcapacity of the mammalian heart. Am J Physiol 272: H769–H775, 1997

27. Hochachka PW, Matheson GO: Regulating ATP turnover rates overbroad dynamic work ranges in skeletal muscles. J Appl Physiol 73:1697–1703, 1992

28. Hochachka PW, McClelland GB: Cellular metabolic homeostasis duringlarge scale change in ATP turnover rates in muscles. J Exp Biol 200:381–386, 1997

29. Chance B, Leigh JS, Kent J, McCully K, Nioka S, Clark BJ, Maris JM,Graham T: Multiple controls of oxidative metabolism in living tissuesas studied by phosphorus magnetic resonance. Proc Natl Acad SciUSA 83: 9458–9462, 1986

30. Ammann H, Noël J, Tejedor A, Boulanger Y, Gougoux A, Vinay P:Could cytoplasmic concentration gradients for sodium and ATP existin intact renal cells? Can J Physiol Pharmacol 73: 421–435, 1995

31. Ovaldi J: Cell architecture and metabolic channelling. Springer Verlag,New York-Berlin-London-Paris, 1995, pp 1–250

32. Agius L, Sherratt HSA (eds).: Channelling in Intermediary Metabolism.Portland Press, London and Miami, 1997, pp 1–342

33. Bereiter-Hahn J, Voth M: Dynamics of mitochondria in living cells:Shape changes, dislocations, fusion and fission of mitochondria. MicroRes Tech 27: 198–219, 1994

34. Rostovtseva T, Colombini M: VDAC channels mediate and gate theflow of ATP: Implications for the regulation of mitochondrial function.Biophys J 72: 1954– 1962, 1997

35. Hodge T, Colombini M: Regulation of metabolic flux through voltage-gating of VDAC channels. J Membr Biol 157: 271–279, 1997

36. Heiden M, Hilschmann N, Thinnes FP, Kroll K: Proteins of cytosol andamniotic fluid increase the voltage dependence of human type-1 porin.J Bioenerg Biomembr 28: 171–180, 1996

37. Reymann S, Flörke H, Heiden M, Jakob C, Stadtmuller U, SteinackerP, Lalk VE, Pardowitz I, Thinnes FP: Further evidence for multi-topological localization of mammalian porin (VDAC) in the plasma-lemma forming part of a chloride channel complex affected in cysticfibrosis and encephalomyopathy. Biochem Mol Medicine 54: 75–87,1995

38. Beutner G, Ruck A, Riede B, Welte W, Brdiczka D: Complexes betweenkinases, mitochondrial porin and adenylate translocator in rat brainresemble the permeability transition pore. FEBS Lett 396: 189–195,1996

39. Clark JF, Kuznetsov AV, Radda GK: ADP regenerating enzyme systemsin mitochondria of guinea pig myometrium and heart. Am J Physiol272: C399–C404, 1997

40. McCabe ERB: Microcompartmentation of energy metabolism at theouter mitochondrial membrane: Role in diabetes mellitus and otherdiseases. J Bioenerg Biomembr 26: 317–325, 1994

41. Laterveer FD, Nicolay K, Gellerich FN: ADP delivery from adenylatekinase in the mitochondrial intermembrane space to oxidativephosphorylation increases in the presence of macromolecules. FEBSLett 386: 255–259, 1996

42. Brdiczka D, Wallimann T: The importance of outer mitochondrialcompartment in regulation of energy metabolism. Mol Cell Biochem133/134: 69–84, 1994

43. Kushmerick MJ, Podolsky RJ: Ion mobility in muscle cells. Science166: 1297–1298, 1969

44. Nicolay K, van der Toorn, Dijkhuizen RM: In vivo diffusion spectro-scopy. An overview. NMR Biomed 8: 365–374, 1995

45. Walter H, Brooks DE: Phase separation in cytoplasm, due to macro-molecular crowding, is the basis for microcompartmentation.FEBS Lett 361: 135–139, 1995

306

46. Oplatka A: The role of water in the mechanism of muscular contraction.FEBS Lett 355: 1–3, 1994

47. Weiss JN, Lamp ST: Glycolysis preferentially inhibits ATP-sensitiveK+ channels in isolated guinea pig cardiac myocytes. Science 238: 67–69, 1987

48. Opie LH: Cardiac metabolism – emergence, decline and resurgence.Cardiovasc Res 26: 721–733, 1992

49. Kuzuetsov AV, Tiivel T, Sikk P, Kaambre T, Kay L, Daneshrad Z, RossiA, Kadaja L, Peet N, Seppet EK, Saks VA: Striking differences betweenkinetics of regulation of respiration by ADP in slow-twitch and fast-twitch muscles in vivo. Eur J Biochem 241: 909–915, 1996

50. Veech RL, Lawson JWR, Cornell NW, Krebs HA: Cytosolic phos-phorylation potential. J Biol Chem 254: 6538–6547, 1979

51. Kushmerick MJ: Skeletal muscle: A paradigm for testing principles ofbioenergetics. J Bioenerg Biomembr 27: 555–569, 1995

52. Bessman SP, Geiger PJ: Transport of energy in muscle. The phosphoryl-creatine shuttle. Science 211: 448–452, 1981

53. Gercken G, Schlette U: Metabolite status of the heart in acuteinsufficiency due to 1-fluoro-2,4-dinitrobenzene. Experientia 24: 17–18, 1968

54. Gudbjarnason S, Mathes P, Ravens KG: Functional compartmentationof ATP and creatine phosphate in heart muscle. J Mol Cell Cardiol 1:325–339, 1970

55. Saks VA, Ventura-Clapier R (eds).: Cellular Bioenergetics: Role ofCoupled Creatine Kinase. Kluwer Academic Publishers, 1994, pp 1–346

56. Williams DA: Mechanisms of calcium release and propagation incardiac cells. Do studies with confocal microscopy add to ourunderstanding? Cell Calcium 14: 724–735, 1993

57. Rizzuto R, Bastianutto C, Brini M, Murgia M, Pozzan T: MitochondrialCa2+ homeostasis in intact cells. J Cell Biol 126: 1183–1194, 1994

58. Cheng H, Lederer WJ, Cannell MB: Calcium sparks: Elementary eventsunderlying excitation-contraction coupling in heart muscle. Science262: 740–744, 1993

59. Cannell MB, Cheng H, Lederer WJ: The control of calcium release inheart muscle. Science 268: 1045–1049, 1995

60. Lipp P, Niggli E: Modulation of calcium release in cultured neonatalcardiac myocytes. Insight from subcellular release patterns revealedby confocal microscopy. Circ Res 74: 979–990, 1994

61. Tanaka H, Kawanishi T, Matsuda T, Takahashi M, Shigenobu K:Intracellular free calcium movements in cultured cardiac myocytes asshown by rapid scanning confocal microscopy. J Cardiovasc Pharmacol27: 761–760, 1996

62. Minamikawa T, Cody SH, Williams DA: In situ visualization ofspontaneous calcium waves within perfused whole rat heart by confocalimaging. Am J Physiol 272: H236–H243, 1997

63. Isenberg G, Etter EF, Wendt-Gallitelli MF, Schiefer A, Carrington WA,Tuft RA, Fay FS: Intrasarcomere [Ca2+] gradients in ventricularmyocytes revealed by high speed digital imaging microscopy. ProcNatl Acad Sci USA 93: 5413–5418, 1996

64. Mironneau J, Amaudeau S, Macrez-Lepretre, Boittin FX: Ca2+ sparksand Ca2+ waves activate different Ca2+-dependent ion channels insingle myocytes from rat portal vein. Cell Calcium 20: 153–160, 1996

65. Fiolet JWT, Baartscheer A, Schumacher CA: Intracellular [Ca2+] and Vo2

after manipulation of the free-energy of the Na+/Ca2+-exchanger inisolated rat ventricular myocytes. J Mol Cell Cardiol 27: 1513–1525,1995

66. Janiak R, Lewartowsky B, Langer GA: Functional coupling betweensarcoplasmic reticulum and Na/Ca exchange in single myocytes ofguinea pig and rat heart. J Mol Cell Cardiol 28: 253–264, 1996

67. Carmeliet E: A fuzzy subsarcolemmal space for intracellular Na in cardiaccells? Cardiovasc Res 26: 433–442, 1992

68. Wallimann T: 31P-NMR-measured creatine kinase reaction flux in muscle:

A caveat! J Musc Res Cell Motil 17: 177–181, 199669. Wallimann T, Wyss M, Brdiczka D, Nicolay K, Eppenberger HM:

Intracellular compartmentation, structure and function of creatine kinaseisoenzymes in tissues with high and fluctuating energy demands: The‘phosphocreatine circuit’ for cellular energy homeostasis. Biochem J281: 31–40, 1992

70. Wallimann TW, Hemmer W: Creatine kinase in non -muscle tissuesand cells. Mol Cell Biochem 133/134: 193–220, 1994

71. Wyss M, Smeitnik J, Wever RA, Wallimann T: Mitochondrial creatinekinase: A key enzyme of aerobic energy metabolism. Biochim BiophysActa 1102: 119–166, 1992

72. Wan B, Dounen C, Duszyusky J, Salama G, Vary TC, Lanoue KF: Effectof cardiac work on electrical potential across mitochondrial membranein perfused heart. Am J Physiol 265: H453–H460, 1993

73. Jurevicius J, Fischmeister R: cAMP compartmentation is responsiblefor a local activation of cardiac Ca2+ channels by β-adrenergic agonists.Proc Natl Acad Sci USA 93: 295–299, 1996

74. Jurevicius J, Fischmeister R: Acetylcholine inhibits Ca2+ current byacting exclusively at a site proximal to adenylyl cyclase in frog cardiacmyocytes. J Physiol 491: 669–675, 1996

75. Hoerter JA, Lauer C, Vassort G, Gueron M: Sustained function ofnormoxic hearts depleted in ATP and phosphocreatine: A P-NMR study.Am J Physiol 255: C192–C201, 1988

76. Neely JR, Grotyohann LW: Role of glycolytic products in damage toischemic myocardium. Dissociation of adenosine triphosphate levelsand recovery of function of reperfused ischemic hearts. Circ Res 55:816–824, 1984

77. Mahler M: First-order kinetics of muscle oxygen consumption, and anequivalent proportionality between Qo2 and phosphorylcreatine level.J Gen Physiol 86: 135–165, 1985

78. Daut J: The living cell as energy-transducing machine. A minimalmodel of myocardial metabolism. Biochim Biophys Acta 895: 41–62,1987

79. Sahlin K: Control of energetic processes in contracting human skeletalmuscle. Biochem Exer 19: 353–358, 1991

80. Meyer RA, Foley JM: Cellular processes integrating the metabolicresponse to exercise. In: LB Rowell, JT Shepherd (eds). AmericanPhysiological Society Handbook of Physiology. Integration of Motor,Circulatory, Respiratory and Metabolic Control during Exercise. 1996,pp 841–868

81. Veksler VI, Kuznetsov AV, Anflous K, Mateo P, van Deursen J, WieringaB, Ventura-Clapier R: Muscle creatine kinase. Cardiac and skeletalmuscle exhibit tissue-specific adaptation of the mitochondrial function.J Biol Chem 270: 19921–19929, 1995

82. McCormack JG, England PJ: Ruthenium red inhibits the activation ofpyruvate dehydrogenase caused by positive inotropic agents in theperfused heart. Biochem J 214: 581–589, 1983

83. Hoerter JA, Ventura-Clapier R, Kuznetsov AV: Compartmentation ofcreatine kinases during perinatal development of mammalian heart.Mol Cell Biochem 133/134: 277–286, 1994

84. Matsumoto Y, Kaneko M, Kobayashi A, Fujise Y, Yamazaki N: Creatinekinase kinetics in diabetic cardiomyopathy. Am J Physiol 268: E1070–E1076, 1995

85. Hamman BL, Bittl JA, Jacobus WE, Allen PD, Spencer RS, Tian R, IngwallJS: Inhibition of the creatine kinase reaction decreases the contractilereserve of isolated rat hearts. Heart Circ Physiol 38: H1030–H1036, 1995

86. Tian R, Ingwall JS: Energetic basis for reduced contractile reserve inisolated rat hearts. Am J Physiol 270: H1207–H1216, 1996

87. Kapelko VI, Kupriyanov VV, Novikova NA, Lakomkin VL, SteinschneiderAY, Severina MY, Veksler VI, Saks VA: The cardiac contractile failureinduced by chronic creatine and phosphocreatine deficiency. JMol Cell Cardiol 20: 465–479, 1988

88. Zweier JL, Jacobus WE, Korecky B, Brandejs-Barry: Bioenergetic

307

consequences of cardiac phosphocreatine depletion induced by creatineanalog feeding. J Biol Chem 266: 20296–20304, 1991

89. van Deursen J, Heerschap A, Oerlemans F, Ruitenbeek W, Jap P, terLaak H, Wieringa B: Skeletal muscles of mice deficient in muscle creatinekinase lack burst activity. Cell 74: 621–631, 1993

90. Steeghs K, Benders A, Oerlemans F, de Haan A, Heerschap A, RuitenbeekW, Jost C, van Deursen J, Perrymann B, Pette D, Bruckwilder M,

Koudijs J, Jap P, Veerkamp Wieringa B: Altered Ca2+ responses in muscleswith combined mitochondrial and cytosolic creatine kinase deficiencies.Cell 89: 93–103, 1997

91. Neubauer S, Horn M, Naumann A, Tian R, Hu K, Laser M, Friedrich J,Gaudron, Schnackerz K, Ingwall JS, Ertl G: Impairment of energymetabolism in intact residual myocardium of rat hearts with chronicmyocardial infarction. J Clin Invest 95: 1092–1100, 1995

308