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Is There the Creatine Kinase Equilibrium in Working Heart Cells?
BIOCHEMICAL AND BIOPHYSICAL RESEARCH COMMUNICATIONS ARTICLE NO.
227, 360–367 (1996)
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Is There the Creatine Kinase Equilibrium in Working Heart Cells? Valdur A. Saks1 and Maiys K. Aliev* Laboratories of Bioenergetics, Joseph Fourier University, Grenoble, France, and Institute of Chemical and Biological Physics, Tallinn, Estonia; and *Laboratory of Experimental Cardiac Pathology, Cardiology Research Center, Moscow, Russia
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 mg-atom O2 * min01 * (g wet mass)01. 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 equlibrium concept, way of calculating steady state cytoplasmic ADP concentrations at increased workloads is to use kinetic equations q 1996 Academic Press, Inc. and mathematical models of energy metabolism.
It is hardly an exaggeration to say that the basis of muscle bioenergetics is an assumption of the equilibrium state of the creatine kinase reaction in cells. This assumption allows us to use the simple equilibrium equation of the CK reaction to calculate the free cytosolic ADP concentration and to calculate further all derived parameters such as the free energy change (affinity) of ATP hydrolysis, phosphorylation potential, etc. (1-9). Practically all experimental and theoretical studies of heart metabolism have been performed by using this very simple and clear approach (ref. 1-9 are just references to these works). However, there is not much direct experimental evidence for its validity under all possible conditions. The classical reference is the work by Veech et al. (1) which, however, was performed on resting muscle. Recently this problem has been reconsidered by Wiseman and Kushmerick (2) but also for resting muscle. To our knowledge, this problem has not been studied experimentally for working heart with elevated energy fluxes; therefore, this basic proposal is still an assumption a priori. This is why we used a mathematical model of compartmentalised energy transfer and experimentally determined values of the activity of creatine kinase and its compartmentalisation in the heart cells to reinvestigate the question of the state of the creatine kinase reaction in different cellular compartments. The results of this study shows that the assumption of the 1 Address for correspondence: Professor V.A. Saks, Laboratory of Bioenergetics, Institute of Chemical and Biological Physics, Akadeemia tee 23, EE 0026, Tallinn, Estonia. Fax: 372 6 398 382. E-mail: [email protected]. Abbreviations: Cr, creatine; PCr, phosphocreatine; Pi , inorganic phosphate; CK, creatine kinase (EC 2.7.3.2); CKmyo , myoplasmic isoenzyme of creatine kinase; CKmit , mitochondrial isoenzyme of creatine kinase; ANT, adenine nucleotide translocase; wm, mass of wet tissue.
360 0006-291X/96 $18.00 Copyright q 1996 by Academic Press, Inc. All rights of reproduction in any form reserved.
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FIG. 1. The general scheme of compartmentalised energy transfer in cardiac cell as a basis for mathematical modelling. For explanations see the text.
creatine kinase equilibrium is at best only a very rough approximation of the real situation in the cardiac cells at elevated energy fluxes and probably valid only for the diastolic phase of the contraction cycle. More precisely, cytoplasmic ADP concentrations in the ‘‘metastable steady state’’ at increased workloads can be calculated by using mathematical models of energy metabolism. METHODS Fig. 1 shows the general scheme of the compartmentalised energy exchange between mitochondrial and myofibrillar compartments. This scheme is based on the experimental evidence extensively reviewed in refs. 10-13. In mitochondria ATP is synthesised in matrix by ATP-synthase and after translocation across the inner mitochondrial membrane is used for PCr synthesis in the coupled mitochondrial CK reaction; in myofibrils CK is considered to be distributed homogeneously in the cytoplasmic and myofibrillar compartments. In the mathematical model used in this work differential equations for plane diffusion of ATP, ADP, Cr, PCr and Pi along the chosen diffusion path were solved numerically (14) with diffusion constants for myoplasm taken from Meyer et al. (3). The computations on the basis of Runge-Kutta-Nistrom algorithm (15) gave the metabolite concentrations for each of 13th segment of diffusion path at each 0.01 ms time step. The calculated concentrations of substrates along the diffusion pathway have been used for calculations of enzymatic rates at each segment of space and time to take into account the concentration changes due to enzymatic activities. Functional coupling of CKmit and ANT (10-13,16-20) was modelled by means of high local ATP concentration in the space between coupled CKmit and ANT using the experimental data of Fossel et al. (21) which showed that the phenomenon of functional coupling between enzymes appears if the distance between them is smaller than 10 nm. This was taken to be the maximal size of a gap (microcompartment) between CKmit and ANT in which the local ATP concentration is increased due to metabolic channelling. For calculations of local ATP concentration we used the experimental data obtained with isolated heart mitochondria when the creatine kinase reaction was studied under conditions of oxidative phosphorylation. The values of the coefficients of the diffusion restriction from this local compartment were estimated from the deviation of the mass action ratio of CKmit from CK equilibrium constant value observed experimentally by Saks et al. (16) and Soboll et al. (22,23) in coupled rat heart mitochondria under conditions of oxidative phosphorylation. We assumed that these definite changes are due to elevated local ATP concentrations in the gap between ANT and CKmit , which increases due to the activity of ANT and retarded diffusion of ATP out of this gap, due to its specific structure, and intermediate binding of ATP to the active or binding centres. Giving the values of the coefficients of the ATP diffusion restriction from the gap, we calculated the rates of mitochondrial 361
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creatine kinase reaction, comparing the calculated data with experimental results. The value of coefficient giving the best fit was used in the calculations. The kinetics of ATP hydrolysis by myofibrils during contraction was predicted from dynamics of dP/dt change in isovolumic rat hearts: linear increase in ATP hydrolysis rate up to 30th ms (t1), followed by its linear decrease to zero at 60th ms (t2) at heart rate of 333 beats*min01. This kinetic scheme has a simple analytic solution: ATPh Å Acl 1 t21 1 0.5 / Dcl 1 (t2-t1)2 1 0.5 where ATPh is total amount of hydrolysed ATP per cardiac cycle; Acl is the coefficient of acceleration in ATP hydrolysis rate at 0 - t1 time period; Dcl is the coefficient of deceleration in ATP hydrolysis rate at t1 - t2 time period. The taken amount of ATPh Å 0.414 mmol*(kg wm)01 *(cycle)01 corresponds to oxygen consumption of 23 mmol*min01 *(kg wm)01 at a heart rate of 333 beats*min01. CKmit CKmyo and vnet , respectively, were calculated from steady state equation The rates of CKmyo and CKmit reactions, vnet 13 of Saks et al. (19) using the diffusion provided substrate concentrations in each space segment. For CKmit the kinetic constants were taken from (20), the ATP concentrations were local ones, while ADP, Cr and PCr concentrations were those in the mitochondrial intermembrane space (jÅ13, Fig. 1). ATP export by ANT was taken equal to ATP production by ATP-synthase ; for this case the maximal ATP production by ATP-synthase was assumed to be equal to the maximum of ANT activity. Thus, as a first approximation, it was assumed that ANT functions in a rapid equilibrium state, providing a constant ATP/ADP ratio between matrix and intermembrane space at fixed membrane potential, according to the concept of Wilson and Erecinska and others, reviewed by Hassinen (24). The ANT-provided steady state concentration of ADP in matrix space has been assumed to be about 25-fold higher due to electrogeniety of ADP - ATP exchange reaction (25) than their levels in the mitochondrial intermembrane space at each time step. The sum of ADP and ATP in matrix space was constant, 10 mM. Activity of ATP-synthase in the matrix space was estimated from a simple kinetic scheme Kd
Kp
kf
Ka
E / ADP } E.ADP } E.ADP.Pi | E.ATP } E / ATP kr
where Kd , Kp and Ka are the dissociation constants for ADP, Pi and ATP, respectively ; kf and kr are the rate constants for forward (ATP synthesis) and reverse (ATP hydrolysis) reactions, respectively. The steady state activity of Synthase (vsyn net ) for this scheme can be expressed by the following equation: vnet syn Vfmax 1 [ADP] 1 [Pi]/( Kd 1 Kp 1 Den) - Vrmax 1 [ATP]/(Ka 1 Den) where Vfmax and Vrmax are the maximal rates in the forward (ATP synthesis) and reverse (ATP hydrolysis) reactions, respectively ; Den designates the Denominator of the expression : Den Å 1 / [ATP]/Ka / [ADP]/Kd / [ADP] 1[Pi]/(Kd 1 Kp) [ADP], [Pi] and [ATP] designate the concentrations of these metabolites in the matrix space. The steady state concentration of Pi in matrix space has been assumed to be 10-fold higher (5) than their levels in the mitochondrial intermembrane space. The values of constants used were the following: Ka(ATP) Å 0.462 mM; Kd(ADP) Å 0.1mM; Kp(Pi) Å2.4 mM (26). In this model we directly calculate the metabolite concentrations at each point of diffusion path. Such a calculation of diffusion events in a plane sheet (14) supposes proportionality between the unit of diffusion path length and the space volume, corresponding to this unit. In other words, if the diffusion path lengths in myofibrillar, cytoplasmic and mitochondrial intermembrane spaces (MIS) are in proportion 10 :2 :1, such proportionality should pre-exist in the volumes of these compartments. From the morphometric data of Page (27), taking into account 81.5% of cardiomycyte’s volume in intact rat heart (28), the volumes of myofibrillar, cytoplasmic and MIS compartments can be estimated as 380.6, 79.1 and 39.4 ml * (kg of wm)01, respectively. The proportion between rounded fractional volumes (FV, L*(L of tissue)01) of these compartments is 0.400 :0.080 :0.040 Å 10 :2 : 1. The maximal activities of enzymes in in vivo rat heart at 377C were taken from multiple biochemical data on enzyme distribution, their stoichiometries and catalytic constants (see (29)). The accepted maximal rate of ATP export by mitochondrial ANT at ATP/O2 Å 6 corresponds (71.1 ml O2 *min01 *(100 g of tissue)01) to the upper limit of Elzinga et al. (30) estimation, 54-72 ml O2 *min01 *(100 g of tissue)01. This is in concord with many other determinations (29,31). With commonly used mitochondrial protein content in rat heart, 60 mg*(g 362
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FIG. 2. Calculated net (A) and unidirectional (B) energy fluxes through compartmentalised creatine kinases of heart cell during cyclic contractions of cardiac muscle. CKmit and CKmyo denote the creatine kinase in the mitochondrial and myoplasmic compartments, respectively. An arrow indicates the position of equilibrium, when net ATP production is equal to zero. In Fig. 2A calculations were made for normal fibrillar CK activity (A) or when its activity was increased 5 (B) or 20 (D) times. In Fig. 2B the calculations have been performed for the system with normal content of creatine kinase. It is essential that in Fig. 2B the time-flux integrals for forward (forw) and reverse (rev) reactions of total cell creatine kinase (CKmit/CKmyo) are equal, unlike those for CKmit and Ckmyo .
wm)01 (29,31), the predicted maximal rate of ATP production by in vivo mitochondria is 3.18 mmol ATP*min01 *(mg protein)01. The experimental value for isolated mitochondria is somewhat lower, 2.1-2.4 mmol*min01 *(mg protein)01 (32). The value of maximal ATP production by CKmit was accepted to be 13.3 mmol*s01 *(g wm)01, and that by CKmyo was accepted to be 29.4, thus giving a total activity of 42.7 mmol*s01 *(g wm)01 (19,20,33), which coincides with the experimental value of Ventura-Clapier et al. (34), 9.9 {0.5 mmol*min01 *(mg of fibre protein)01 at 307C, if we correct the value by temperature coefficient (1.75, ref. 35), actual substrate concentrations during measurement and protein content in fibre (110 mg*(g wm) 01). All calculations were carried out using a 486DX2-50 computer, where the calculation of one contraction cycle takes 200 s. The program, written for Turbo Pascal, Version 7.0, is too large to be shown in this paper, but is available from M.K.Aliev on request. The complete version of the model is described elsewhere (36).
RESULTS
The calculated compartmentalised creatine kinase fluxes are shown in Fig. 2A as the rates of net ATP synthesis in the myoplasmic CK reaction (upper curves A,B,D) and in the coupled mitochondrial CK reaction (lower curves A,B,D). In both cases, curves A correspond to the activities of the CK found in the normal heart muscle (see ‘‘Methods’’), curves B correspond to the 5 times increased activity of myoplasmic CK, curves D correspond to the 20 times increased myoplasmic CK activity, at constant activity of mitochondrial CK. In the case D the creatine kinase activity approaches its level in fast twitch skeletal muscle (37). It is the myoplasmic CK reaction that is most significantly activated within contraction cycle and which restores myofibrillar levels of adenine nucleotides at the expense of PCr. Cytoplasmic concentrations of metabolites in resting state and at the peak of contraction calculated by model are shown in Table 1. Zero net synthesis of ATP in CK reaction corresponds to the equilibrium position of this reaction, and Fig. 2A shows that it is practically never completely achieved - only in diastolic phase of the contraction cycle is the CKmyo reaction in a quasiequilibrium state, at minimal constant rate of ATP utilisation. In the mitochondrial CK reaction net ATP synthesis is negative - this reaction continuously uses mitochondrial ATP to produce PCr by a mechanism of functional coupling between CKmit and translocase in heart mitochon363
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TABLE 1 Resting Levels (Rest) and Peak (Peak) Values of Metabolite Concentrations during Cardiac Cycle in Heart Cells’ Cytoplasm Calculated by Mathematical Model (see ‘‘Methods’’) Concentrations in myofibril core (mM) Phase
P1
ADP
ATP
Cr
PCr
Rest Peak
2.9185 3.4375
0.0240 0.2172
8.9760 8.7828
9.8965 10.3475
18.1035 17.6525
dria (10-13). Therefore, this reaction is never in the equilibrium state under conditions of active oxidative phosphorylation. Due to the liberation of ADP in cytoplasm within first part of the contraction cycle (see Fig. 3A), this reaction may be partially shifted, but not completely, in the direction of ATP synthesis. Obviously, these coupled reactions of aerobic PCr production are responsible for restoration of the level of PCr used the contraction cycle (Table 1). If the myoplasmic CK activity is increased 5 or 10 times, it responds more rapidly to the contractile process, and the mitochondrial CK reaction is in a more stable steady state because of decreased cytosolic ADP concentrations (see below, Fig. 3A). This analysis shows that in the systolic phase CK is never in the equilibrium state, independently from the total enzyme activity level. Only in the diastolic phase is the myoplasmic CK in a quasi-equilibrium state, or more precisely, in the metastable steady state (38). The coupled mitochondrial CK is permanently in the metastable steady state far from equilibrium. Fig. 2B shows the calculated unidirectional reaction rates for mitochondrial and total creatine kinase, to simulate the flux determination by phosphorus NMR magnetization transfer method (39). Average values of the fluxes in both direction (areas below CKtot, rev and above CKtot, forw) for the contractile cycle are practically equal, in spite of significant shifting of the reaction from the equilibrium (see ‘‘Discussion’’). Since the mathematical model calculates the concentrations of all metabolites at any moment of the contraction cycle, we used it to calculate the free cytosolic ADP level (Fig. 3A) and the free energy change in the CK reaction (Fig. 3B). Fig. 3A shows what probably happens
FIG. 3. The influence of the activity of creatine kinase in myoplasmic compartment on ADP dynamics (A) and free energy change of creatine kinase reaction (B) in myofibril core during cyclic contraction of heart muscle. Activity of CK in the myoplasmic compartment has been taken normal (A) and 5-fold (B), 10-fold (C), 20-fold (D) elevated. Free energy change of CK reaction, DG, has been calculated by equation DG Å DG7 / 2.3RT log (([ATP] 1 [Cr]) / ([ADP] 1 [Pcr])), where DG7 Å 13.09 kJ/mole is the standard free energy change of CK reaction for apparent equilibrium constant of 160 (40). 364
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to ADP concentration during the contraction cycle in working heart cells. The dotted line in Fig. 3A shows the ADP level calculated from the CK equilibrium equation using the data in Table 1. This value - 30 mM - is close to the generally accepted free cytoplasmic ADP concentration. The mathematical model used in this work gives a very similar value of the ADP concentration for the diastolic phase, which means that application of the simple equilibrium approach is fairly justified at this phase of the contraction cycle. However, that is not true for the systolic phase of the cardiac contraction cycle - in this phase the free cytosolic ADP concentration rises 9 times and then rapidly decreases again in the cardiac cells (Curve A). Only in the cells in which the myoplasmic creatine kinase activity is 10-20 times elevated (this may be the case of the fast twitch skeletal muscle) does ADP concentration even in the systolic phase stay close to that calculated from the CK equilibrium equation (curves C and D in Fig. 3A). Finally, Fig.3B shows the calculated free energy changes of the cytoplasmic CK reaction. In the equilibrium state, this change should be zero. It is zero, or close to it, in the diastolic phase, or in the resting state, especially in the case of highly elevated activity of the enzyme. Fig. 3B directly demonstrates that there is no equilibrium of the CK reaction in the systolic phase in working heart cells. DISCUSSION
The results of this work show that, most probably, the assumption of the creatine kinase equilibrium may be valid in resting muscle and in the diastolic phase of cardiac contraction but perhaps not in contracting heart muscle cells. There are three groups of arguments which have been used as evidence for the CK equilibrium in muscle cells. First, the activity of the enzyme has been thought to sufficiently exceed the value of metabolic flux to allow the equilibrium of the reaction to be achieved (3). Second, the fluxes determined by the magnetisation transfer method by phosphorus NMR have been found to be equal for the forward and reverse reactions (2,39). And third, almost all references are given to the classical experimental work by Veech et al. (1). However, all these arguments are open to critisism. The energy flux in our calculations was 138 mmoles of ATP produced (and used) per min, or 2.3 mmol*s01 *(kg wm)01, while the maximal total activity of CK in direction of ATP synthesis is 42.7 mmol*s01 *(kg wm)01. In forward direction, PCr production, this value is lower by factor of 4 (19) and thus around 10; further, 40% of it this is compartmentized in mitochondria, that leaving in myoplasm the activity of enzyme around 6 mmol*s01 *(kg wm)01. These numbers, 2.3 and 6, are not sufficiently different to establish equilibrium of the CK reaction. For this, a difference by a factor of at least about 20 is required, see curve D in Figs. 2 and 3. The mitochondrial CK, representing significant part of the total activity of the enzyme, is coupled to oxidative phosphorylation and thus permanently out of equilibrium (10, 13). The forward and reverse creatine kinase fluxes measured by NMR should be equal not only in equilibrium, but also in any steady state. This is directly shown by calculation in Fig. 2B. Thus, this second argument is not very convincing. The experimental data by Veech et al. (1) are absolutely convincing but they are valid only for the resting muscle with which the work has been made. This is valid also for the recent work by Wiseman and Kushmerick (2), who again worked with the resting skeletal muscles. However, in the literature there is also the work by Jurgen Daut (38) which has not yet enjoyed too many citations but which is, at least to our knowledge, practically the only serious theoretical analysis of cardiac cell energetics at changing levels of energy fluxes. By using simple mathematical models of ion channels, mitochondrial oxidative phosphorylation, and phosphocreatine shuttle and taking into account ATP utilisation by cytoplasmic ATPases, he showed that ‘‘as long as there is an external energy supply, the system is not at thermodynamic 365
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equilibrium but represents a stable configuration in a steady state’’ (38). Very often, this stable steady state is erroneously taken to represent an equilibrium. The results of our analysis reported here completely support this conclusion. Our model differs from that of Daut by taking into account compartmentation of creatine kinases, high activity of actomyosin ATPase as main user of energy (we did not consider ion pumps) and intracellular diffusion of substrates, but the general principle is similar - in both cases models include energy production, utilisation, and a feedback mechanism. And in both cases the conclusion is the same: the a priori assumption of the creatine kinase equilibrium is not valid for the working heart, and therefore, not simple equilibrium equations but kinetic (mathematical) models should be probably used for adequate description of energy transduction in working muscle cells. Only for the cells with very high cytoplasmic CK activity, such as fast twitch skeletal muscle, and also for the diastolic phase of the heart cells, may the use of the creatine kinase equilibrium equation be justified. ACKNOWLEDGMENTS This work was supported by INTAS Grant 94-4738 and Estonian Science Foundation Grant 2092.
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32. Saks, V. A. (1980) in Heart Creatine Kinase. The Integration of Isozymes for Energy Distribution (Jacobus, W. E., and Ingwall, J. S., Eds.), pp. 109–126. Williams and Wilkins, Baltimore/London. 33. Saks, V. A., Chernousova, G. V., Vetter, R., Smirnov, V. N., and Chazov, E. I. (1976) FEBS Lett. 62, 293–296. 34. Ventura-Clapier, R., Saks, V. A., Vassort, G., Lauer, C., and Elizarova, G. V. (1987) Am. J. Physiol. 253, C444– C455. 35. Bittl, J. A., DeLayre, J., and Ingwall, J. S. (1987) Biochemistry 26, 6083–6090. 36. Aliev, M. K., and Saks, V. A. (1997) Eur. J. Biochem., in press. 37. Iyengar, M. R. J. (1984) Muscle Res. Cell Motil. 5, 527–534. 38. Daut, J. (1987) Biochim. Biophys. Acta 895, 41–62. 39. Ugurbil, K.(1985) J. Magn. Reson. 64, 207–219. 40. Lawson, J. W. R., and Veech, R. L. (1979) J. Biol. Chem. 254, 6528–6537.
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Is There the Creatine Kinase Equilibrium in Working Heart Cells? Valdur A. Saks1 and Maiys K. Aliev* Laboratories of Bioenergetics, Joseph Fourier University, Grenoble, France, and Institute of Chemical and Biological Physics, Tallinn, Estonia; and *Laboratory of Experimental Cardiac Pathology, Cardiology Research Center, Moscow, Russia
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 mg-atom O2 * min01 * (g wet mass)01. 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 equlibrium concept, way of calculating steady state cytoplasmic ADP concentrations at increased workloads is to use kinetic equations q 1996 Academic Press, Inc. and mathematical models of energy metabolism.
It is hardly an exaggeration to say that the basis of muscle bioenergetics is an assumption of the equilibrium state of the creatine kinase reaction in cells. This assumption allows us to use the simple equilibrium equation of the CK reaction to calculate the free cytosolic ADP concentration and to calculate further all derived parameters such as the free energy change (affinity) of ATP hydrolysis, phosphorylation potential, etc. (1-9). Practically all experimental and theoretical studies of heart metabolism have been performed by using this very simple and clear approach (ref. 1-9 are just references to these works). However, there is not much direct experimental evidence for its validity under all possible conditions. The classical reference is the work by Veech et al. (1) which, however, was performed on resting muscle. Recently this problem has been reconsidered by Wiseman and Kushmerick (2) but also for resting muscle. To our knowledge, this problem has not been studied experimentally for working heart with elevated energy fluxes; therefore, this basic proposal is still an assumption a priori. This is why we used a mathematical model of compartmentalised energy transfer and experimentally determined values of the activity of creatine kinase and its compartmentalisation in the heart cells to reinvestigate the question of the state of the creatine kinase reaction in different cellular compartments. The results of this study shows that the assumption of the 1 Address for correspondence: Professor V.A. Saks, Laboratory of Bioenergetics, Institute of Chemical and Biological Physics, Akadeemia tee 23, EE 0026, Tallinn, Estonia. Fax: 372 6 398 382. E-mail: [email protected]. Abbreviations: Cr, creatine; PCr, phosphocreatine; Pi , inorganic phosphate; CK, creatine kinase (EC 2.7.3.2); CKmyo , myoplasmic isoenzyme of creatine kinase; CKmit , mitochondrial isoenzyme of creatine kinase; ANT, adenine nucleotide translocase; wm, mass of wet tissue.
360 0006-291X/96 $18.00 Copyright q 1996 by Academic Press, Inc. All rights of reproduction in any form reserved.
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FIG. 1. The general scheme of compartmentalised energy transfer in cardiac cell as a basis for mathematical modelling. For explanations see the text.
creatine kinase equilibrium is at best only a very rough approximation of the real situation in the cardiac cells at elevated energy fluxes and probably valid only for the diastolic phase of the contraction cycle. More precisely, cytoplasmic ADP concentrations in the ‘‘metastable steady state’’ at increased workloads can be calculated by using mathematical models of energy metabolism. METHODS Fig. 1 shows the general scheme of the compartmentalised energy exchange between mitochondrial and myofibrillar compartments. This scheme is based on the experimental evidence extensively reviewed in refs. 10-13. In mitochondria ATP is synthesised in matrix by ATP-synthase and after translocation across the inner mitochondrial membrane is used for PCr synthesis in the coupled mitochondrial CK reaction; in myofibrils CK is considered to be distributed homogeneously in the cytoplasmic and myofibrillar compartments. In the mathematical model used in this work differential equations for plane diffusion of ATP, ADP, Cr, PCr and Pi along the chosen diffusion path were solved numerically (14) with diffusion constants for myoplasm taken from Meyer et al. (3). The computations on the basis of Runge-Kutta-Nistrom algorithm (15) gave the metabolite concentrations for each of 13th segment of diffusion path at each 0.01 ms time step. The calculated concentrations of substrates along the diffusion pathway have been used for calculations of enzymatic rates at each segment of space and time to take into account the concentration changes due to enzymatic activities. Functional coupling of CKmit and ANT (10-13,16-20) was modelled by means of high local ATP concentration in the space between coupled CKmit and ANT using the experimental data of Fossel et al. (21) which showed that the phenomenon of functional coupling between enzymes appears if the distance between them is smaller than 10 nm. This was taken to be the maximal size of a gap (microcompartment) between CKmit and ANT in which the local ATP concentration is increased due to metabolic channelling. For calculations of local ATP concentration we used the experimental data obtained with isolated heart mitochondria when the creatine kinase reaction was studied under conditions of oxidative phosphorylation. The values of the coefficients of the diffusion restriction from this local compartment were estimated from the deviation of the mass action ratio of CKmit from CK equilibrium constant value observed experimentally by Saks et al. (16) and Soboll et al. (22,23) in coupled rat heart mitochondria under conditions of oxidative phosphorylation. We assumed that these definite changes are due to elevated local ATP concentrations in the gap between ANT and CKmit , which increases due to the activity of ANT and retarded diffusion of ATP out of this gap, due to its specific structure, and intermediate binding of ATP to the active or binding centres. Giving the values of the coefficients of the ATP diffusion restriction from the gap, we calculated the rates of mitochondrial 361
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creatine kinase reaction, comparing the calculated data with experimental results. The value of coefficient giving the best fit was used in the calculations. The kinetics of ATP hydrolysis by myofibrils during contraction was predicted from dynamics of dP/dt change in isovolumic rat hearts: linear increase in ATP hydrolysis rate up to 30th ms (t1), followed by its linear decrease to zero at 60th ms (t2) at heart rate of 333 beats*min01. This kinetic scheme has a simple analytic solution: ATPh Å Acl 1 t21 1 0.5 / Dcl 1 (t2-t1)2 1 0.5 where ATPh is total amount of hydrolysed ATP per cardiac cycle; Acl is the coefficient of acceleration in ATP hydrolysis rate at 0 - t1 time period; Dcl is the coefficient of deceleration in ATP hydrolysis rate at t1 - t2 time period. The taken amount of ATPh Å 0.414 mmol*(kg wm)01 *(cycle)01 corresponds to oxygen consumption of 23 mmol*min01 *(kg wm)01 at a heart rate of 333 beats*min01. CKmit CKmyo and vnet , respectively, were calculated from steady state equation The rates of CKmyo and CKmit reactions, vnet 13 of Saks et al. (19) using the diffusion provided substrate concentrations in each space segment. For CKmit the kinetic constants were taken from (20), the ATP concentrations were local ones, while ADP, Cr and PCr concentrations were those in the mitochondrial intermembrane space (jÅ13, Fig. 1). ATP export by ANT was taken equal to ATP production by ATP-synthase ; for this case the maximal ATP production by ATP-synthase was assumed to be equal to the maximum of ANT activity. Thus, as a first approximation, it was assumed that ANT functions in a rapid equilibrium state, providing a constant ATP/ADP ratio between matrix and intermembrane space at fixed membrane potential, according to the concept of Wilson and Erecinska and others, reviewed by Hassinen (24). The ANT-provided steady state concentration of ADP in matrix space has been assumed to be about 25-fold higher due to electrogeniety of ADP - ATP exchange reaction (25) than their levels in the mitochondrial intermembrane space at each time step. The sum of ADP and ATP in matrix space was constant, 10 mM. Activity of ATP-synthase in the matrix space was estimated from a simple kinetic scheme Kd
Kp
kf
Ka
E / ADP } E.ADP } E.ADP.Pi | E.ATP } E / ATP kr
where Kd , Kp and Ka are the dissociation constants for ADP, Pi and ATP, respectively ; kf and kr are the rate constants for forward (ATP synthesis) and reverse (ATP hydrolysis) reactions, respectively. The steady state activity of Synthase (vsyn net ) for this scheme can be expressed by the following equation: vnet syn Vfmax 1 [ADP] 1 [Pi]/( Kd 1 Kp 1 Den) - Vrmax 1 [ATP]/(Ka 1 Den) where Vfmax and Vrmax are the maximal rates in the forward (ATP synthesis) and reverse (ATP hydrolysis) reactions, respectively ; Den designates the Denominator of the expression : Den Å 1 / [ATP]/Ka / [ADP]/Kd / [ADP] 1[Pi]/(Kd 1 Kp) [ADP], [Pi] and [ATP] designate the concentrations of these metabolites in the matrix space. The steady state concentration of Pi in matrix space has been assumed to be 10-fold higher (5) than their levels in the mitochondrial intermembrane space. The values of constants used were the following: Ka(ATP) Å 0.462 mM; Kd(ADP) Å 0.1mM; Kp(Pi) Å2.4 mM (26). In this model we directly calculate the metabolite concentrations at each point of diffusion path. Such a calculation of diffusion events in a plane sheet (14) supposes proportionality between the unit of diffusion path length and the space volume, corresponding to this unit. In other words, if the diffusion path lengths in myofibrillar, cytoplasmic and mitochondrial intermembrane spaces (MIS) are in proportion 10 :2 :1, such proportionality should pre-exist in the volumes of these compartments. From the morphometric data of Page (27), taking into account 81.5% of cardiomycyte’s volume in intact rat heart (28), the volumes of myofibrillar, cytoplasmic and MIS compartments can be estimated as 380.6, 79.1 and 39.4 ml * (kg of wm)01, respectively. The proportion between rounded fractional volumes (FV, L*(L of tissue)01) of these compartments is 0.400 :0.080 :0.040 Å 10 :2 : 1. The maximal activities of enzymes in in vivo rat heart at 377C were taken from multiple biochemical data on enzyme distribution, their stoichiometries and catalytic constants (see (29)). The accepted maximal rate of ATP export by mitochondrial ANT at ATP/O2 Å 6 corresponds (71.1 ml O2 *min01 *(100 g of tissue)01) to the upper limit of Elzinga et al. (30) estimation, 54-72 ml O2 *min01 *(100 g of tissue)01. This is in concord with many other determinations (29,31). With commonly used mitochondrial protein content in rat heart, 60 mg*(g 362
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FIG. 2. Calculated net (A) and unidirectional (B) energy fluxes through compartmentalised creatine kinases of heart cell during cyclic contractions of cardiac muscle. CKmit and CKmyo denote the creatine kinase in the mitochondrial and myoplasmic compartments, respectively. An arrow indicates the position of equilibrium, when net ATP production is equal to zero. In Fig. 2A calculations were made for normal fibrillar CK activity (A) or when its activity was increased 5 (B) or 20 (D) times. In Fig. 2B the calculations have been performed for the system with normal content of creatine kinase. It is essential that in Fig. 2B the time-flux integrals for forward (forw) and reverse (rev) reactions of total cell creatine kinase (CKmit/CKmyo) are equal, unlike those for CKmit and Ckmyo .
wm)01 (29,31), the predicted maximal rate of ATP production by in vivo mitochondria is 3.18 mmol ATP*min01 *(mg protein)01. The experimental value for isolated mitochondria is somewhat lower, 2.1-2.4 mmol*min01 *(mg protein)01 (32). The value of maximal ATP production by CKmit was accepted to be 13.3 mmol*s01 *(g wm)01, and that by CKmyo was accepted to be 29.4, thus giving a total activity of 42.7 mmol*s01 *(g wm)01 (19,20,33), which coincides with the experimental value of Ventura-Clapier et al. (34), 9.9 {0.5 mmol*min01 *(mg of fibre protein)01 at 307C, if we correct the value by temperature coefficient (1.75, ref. 35), actual substrate concentrations during measurement and protein content in fibre (110 mg*(g wm) 01). All calculations were carried out using a 486DX2-50 computer, where the calculation of one contraction cycle takes 200 s. The program, written for Turbo Pascal, Version 7.0, is too large to be shown in this paper, but is available from M.K.Aliev on request. The complete version of the model is described elsewhere (36).
RESULTS
The calculated compartmentalised creatine kinase fluxes are shown in Fig. 2A as the rates of net ATP synthesis in the myoplasmic CK reaction (upper curves A,B,D) and in the coupled mitochondrial CK reaction (lower curves A,B,D). In both cases, curves A correspond to the activities of the CK found in the normal heart muscle (see ‘‘Methods’’), curves B correspond to the 5 times increased activity of myoplasmic CK, curves D correspond to the 20 times increased myoplasmic CK activity, at constant activity of mitochondrial CK. In the case D the creatine kinase activity approaches its level in fast twitch skeletal muscle (37). It is the myoplasmic CK reaction that is most significantly activated within contraction cycle and which restores myofibrillar levels of adenine nucleotides at the expense of PCr. Cytoplasmic concentrations of metabolites in resting state and at the peak of contraction calculated by model are shown in Table 1. Zero net synthesis of ATP in CK reaction corresponds to the equilibrium position of this reaction, and Fig. 2A shows that it is practically never completely achieved - only in diastolic phase of the contraction cycle is the CKmyo reaction in a quasiequilibrium state, at minimal constant rate of ATP utilisation. In the mitochondrial CK reaction net ATP synthesis is negative - this reaction continuously uses mitochondrial ATP to produce PCr by a mechanism of functional coupling between CKmit and translocase in heart mitochon363
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TABLE 1 Resting Levels (Rest) and Peak (Peak) Values of Metabolite Concentrations during Cardiac Cycle in Heart Cells’ Cytoplasm Calculated by Mathematical Model (see ‘‘Methods’’) Concentrations in myofibril core (mM) Phase
P1
ADP
ATP
Cr
PCr
Rest Peak
2.9185 3.4375
0.0240 0.2172
8.9760 8.7828
9.8965 10.3475
18.1035 17.6525
dria (10-13). Therefore, this reaction is never in the equilibrium state under conditions of active oxidative phosphorylation. Due to the liberation of ADP in cytoplasm within first part of the contraction cycle (see Fig. 3A), this reaction may be partially shifted, but not completely, in the direction of ATP synthesis. Obviously, these coupled reactions of aerobic PCr production are responsible for restoration of the level of PCr used the contraction cycle (Table 1). If the myoplasmic CK activity is increased 5 or 10 times, it responds more rapidly to the contractile process, and the mitochondrial CK reaction is in a more stable steady state because of decreased cytosolic ADP concentrations (see below, Fig. 3A). This analysis shows that in the systolic phase CK is never in the equilibrium state, independently from the total enzyme activity level. Only in the diastolic phase is the myoplasmic CK in a quasi-equilibrium state, or more precisely, in the metastable steady state (38). The coupled mitochondrial CK is permanently in the metastable steady state far from equilibrium. Fig. 2B shows the calculated unidirectional reaction rates for mitochondrial and total creatine kinase, to simulate the flux determination by phosphorus NMR magnetization transfer method (39). Average values of the fluxes in both direction (areas below CKtot, rev and above CKtot, forw) for the contractile cycle are practically equal, in spite of significant shifting of the reaction from the equilibrium (see ‘‘Discussion’’). Since the mathematical model calculates the concentrations of all metabolites at any moment of the contraction cycle, we used it to calculate the free cytosolic ADP level (Fig. 3A) and the free energy change in the CK reaction (Fig. 3B). Fig. 3A shows what probably happens
FIG. 3. The influence of the activity of creatine kinase in myoplasmic compartment on ADP dynamics (A) and free energy change of creatine kinase reaction (B) in myofibril core during cyclic contraction of heart muscle. Activity of CK in the myoplasmic compartment has been taken normal (A) and 5-fold (B), 10-fold (C), 20-fold (D) elevated. Free energy change of CK reaction, DG, has been calculated by equation DG Å DG7 / 2.3RT log (([ATP] 1 [Cr]) / ([ADP] 1 [Pcr])), where DG7 Å 13.09 kJ/mole is the standard free energy change of CK reaction for apparent equilibrium constant of 160 (40). 364
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to ADP concentration during the contraction cycle in working heart cells. The dotted line in Fig. 3A shows the ADP level calculated from the CK equilibrium equation using the data in Table 1. This value - 30 mM - is close to the generally accepted free cytoplasmic ADP concentration. The mathematical model used in this work gives a very similar value of the ADP concentration for the diastolic phase, which means that application of the simple equilibrium approach is fairly justified at this phase of the contraction cycle. However, that is not true for the systolic phase of the cardiac contraction cycle - in this phase the free cytosolic ADP concentration rises 9 times and then rapidly decreases again in the cardiac cells (Curve A). Only in the cells in which the myoplasmic creatine kinase activity is 10-20 times elevated (this may be the case of the fast twitch skeletal muscle) does ADP concentration even in the systolic phase stay close to that calculated from the CK equilibrium equation (curves C and D in Fig. 3A). Finally, Fig.3B shows the calculated free energy changes of the cytoplasmic CK reaction. In the equilibrium state, this change should be zero. It is zero, or close to it, in the diastolic phase, or in the resting state, especially in the case of highly elevated activity of the enzyme. Fig. 3B directly demonstrates that there is no equilibrium of the CK reaction in the systolic phase in working heart cells. DISCUSSION
The results of this work show that, most probably, the assumption of the creatine kinase equilibrium may be valid in resting muscle and in the diastolic phase of cardiac contraction but perhaps not in contracting heart muscle cells. There are three groups of arguments which have been used as evidence for the CK equilibrium in muscle cells. First, the activity of the enzyme has been thought to sufficiently exceed the value of metabolic flux to allow the equilibrium of the reaction to be achieved (3). Second, the fluxes determined by the magnetisation transfer method by phosphorus NMR have been found to be equal for the forward and reverse reactions (2,39). And third, almost all references are given to the classical experimental work by Veech et al. (1). However, all these arguments are open to critisism. The energy flux in our calculations was 138 mmoles of ATP produced (and used) per min, or 2.3 mmol*s01 *(kg wm)01, while the maximal total activity of CK in direction of ATP synthesis is 42.7 mmol*s01 *(kg wm)01. In forward direction, PCr production, this value is lower by factor of 4 (19) and thus around 10; further, 40% of it this is compartmentized in mitochondria, that leaving in myoplasm the activity of enzyme around 6 mmol*s01 *(kg wm)01. These numbers, 2.3 and 6, are not sufficiently different to establish equilibrium of the CK reaction. For this, a difference by a factor of at least about 20 is required, see curve D in Figs. 2 and 3. The mitochondrial CK, representing significant part of the total activity of the enzyme, is coupled to oxidative phosphorylation and thus permanently out of equilibrium (10, 13). The forward and reverse creatine kinase fluxes measured by NMR should be equal not only in equilibrium, but also in any steady state. This is directly shown by calculation in Fig. 2B. Thus, this second argument is not very convincing. The experimental data by Veech et al. (1) are absolutely convincing but they are valid only for the resting muscle with which the work has been made. This is valid also for the recent work by Wiseman and Kushmerick (2), who again worked with the resting skeletal muscles. However, in the literature there is also the work by Jurgen Daut (38) which has not yet enjoyed too many citations but which is, at least to our knowledge, practically the only serious theoretical analysis of cardiac cell energetics at changing levels of energy fluxes. By using simple mathematical models of ion channels, mitochondrial oxidative phosphorylation, and phosphocreatine shuttle and taking into account ATP utilisation by cytoplasmic ATPases, he showed that ‘‘as long as there is an external energy supply, the system is not at thermodynamic 365
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equilibrium but represents a stable configuration in a steady state’’ (38). Very often, this stable steady state is erroneously taken to represent an equilibrium. The results of our analysis reported here completely support this conclusion. Our model differs from that of Daut by taking into account compartmentation of creatine kinases, high activity of actomyosin ATPase as main user of energy (we did not consider ion pumps) and intracellular diffusion of substrates, but the general principle is similar - in both cases models include energy production, utilisation, and a feedback mechanism. And in both cases the conclusion is the same: the a priori assumption of the creatine kinase equilibrium is not valid for the working heart, and therefore, not simple equilibrium equations but kinetic (mathematical) models should be probably used for adequate description of energy transduction in working muscle cells. Only for the cells with very high cytoplasmic CK activity, such as fast twitch skeletal muscle, and also for the diastolic phase of the heart cells, may the use of the creatine kinase equilibrium equation be justified. ACKNOWLEDGMENTS This work was supported by INTAS Grant 94-4738 and Estonian Science Foundation Grant 2092.
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32. Saks, V. A. (1980) in Heart Creatine Kinase. The Integration of Isozymes for Energy Distribution (Jacobus, W. E., and Ingwall, J. S., Eds.), pp. 109–126. Williams and Wilkins, Baltimore/London. 33. Saks, V. A., Chernousova, G. V., Vetter, R., Smirnov, V. N., and Chazov, E. I. (1976) FEBS Lett. 62, 293–296. 34. Ventura-Clapier, R., Saks, V. A., Vassort, G., Lauer, C., and Elizarova, G. V. (1987) Am. J. Physiol. 253, C444– C455. 35. Bittl, J. A., DeLayre, J., and Ingwall, J. S. (1987) Biochemistry 26, 6083–6090. 36. Aliev, M. K., and Saks, V. A. (1997) Eur. J. Biochem., in press. 37. Iyengar, M. R. J. (1984) Muscle Res. Cell Motil. 5, 527–534. 38. Daut, J. (1987) Biochim. Biophys. Acta 895, 41–62. 39. Ugurbil, K.(1985) J. Magn. Reson. 64, 207–219. 40. Lawson, J. W. R., and Veech, R. L. (1979) J. Biol. Chem. 254, 6528–6537.
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