INTRODUCTION

TOP ABSTRACT INTRODUCTION THEORY MATERIALS AND METHODS RESULTS DISCUSSION APPENDIX REFERENCES

The creatine kinase (CK) catalyzes the reversible exchange of high-energy phosphate:
Despite considerable efforts devoted to the study of the flux of this enzyme by ³¹P NMR spectroscopy, there is still some controversy about the equivalence of the various magnetization transfer techniques and about the physiological interpretation of the NMR measured CK fluxes. The development of transgenic mice with specific CK isoform knockout has renewed the interest in the analysis of CK flux (Van Dorsten et al., 1998).

The role of different CK isoforms in the myocardium is still under debate: a cytosolic CK working close to equilibrium might account for the replenishment of ATP stores upon ATP utilization and the energy diffusion across the cell. On the other hand, bound CK specifically localized close to sites of energy production and utilization might play a major role in myocardial energy transduction. Nevertheless, even if the bound isoforms have kinetics different from those of the cytosolic CK, the cell is in steady state, and PCr is only metabolized by CK. Therefore, both total CK fluxes (corresponding to the unidirectional flux of production and consumption of ATP by CK) measured by NMR should be equal.

The main problem in the interpretation of a magnetization transfer experiment in vivo arises from the oversimplification of a highly organized cellular system: in other words, the interpretation of data is always model dependent. Most of the work devoted to cardiac CK flux has been performed by saturation transfer technique (ST). Consistent data have been obtained for the determination of the forward CK flux PCr  ATP (F_f), whereas a large range of values has been reported in the literature for the reverse CK flux ATP  PCr (F_r) (see Table 1). When a discrepancy between F_f and F_r was observed, two main alternative hypotheses were proposed. First, the two-site model of CK reaction has been recognized as an oversimplification of the system: ATP is involved in other exchanges, mainly with P_i (Ugurbil et al., 1986; Spencer et al., 1988), but also with glycolytic metabolites (Matthews et al., 1982; Brindle, 1988). The second hypothesis is the presence of an ATP compartmentation initially suggested by Nunnally and Hollis (1979). The discrepancy between fluxes, which increases with cardiac performance (Koretsky et al., 1985), was further proposed to result from the presence of an additional exchange between either PCr and a small NMR-visible ATP pool (Korestky et al., 1985, 1986) or between PCr and a nonvisible nonsaturated ATP compartment (Zahler et al., 1987; Zahler and Ingwall, 1992).

Inversion transfer (IT) has mainly been performed in muscle by analyzing the initial rate of recovery, which allowed a simplification of the mathematical analysis and a reduction in experimental time (Hsieh and Balaban, 1988; McFarland et al., 1994). However, the complete analysis of the evolution of the magnetization of the inverted and noninverted species permits the determination in the same experiment of both F_f and F_r (Led and Gesmar, 1982). Furthermore, data can then be analyzed without imposing the equilibrium of CK on the system, while this simplification of the Bloch equations is usually applied in the analysis of ST. Such analysis of IT offers a definitive advantage over the other magnetization transfer techniques.

Using IT, we found unequal CK fluxes in myocardium. To interpret these data, we analyzed the consequences for the measured CK fluxes of the presence of an ATP pool not involved in the CK reaction (or in slow exchange), as earlier suggested by Meyer et al. (1982). We considered total cellular ATP and PCr to be fully NMR visible and disturbed by the inversion procedure. The Bloch equations were modified to take into account this additional compartment of ATP, in both cases of an inversion of PCr (inv-PCr) and of ATP (inv-ATP) (see section Theory).

Our aim was to explore the capacity of a full time-course analysis of inversion transfer to reveal experimentally both the specific contributions of ATP compartmentation and ATP-P_i exchange in the CK fluxes of a perfused heart. Based on in vitro simulation we show that the presence of an ATP compartment (not exchanging with PCr) is consistent with the flux discrepancies observed in situ. Moreover, under conditions designed to mask the influence of ATP-P_i exchange, this ATP compartment could be independently quantified in both inv-PCr and inv-ATP protocols.

	THEORY

TOP ABSTRACT INTRODUCTION THEORY MATERIALS AND METHODS RESULTS DISCUSSION APPENDIX REFERENCES

Classical Bloch equations for chemical exchange (McConnell, 1958) had to be modified to account first for the fraction of ATP not involved in the CK reaction, f_ATP, and second for the involvement of ATP in other reactions. In the following sections we refer to a phosphorus species as a "site" and a kinetic compartment as a "compartment."

Model I: two-site two-compartment analysis: basic model

The CK reaction is considered as a two-site exchange of the ³¹P nucleus:
Model I

where k_f and k_r are, respectively, the forward and reverse pseudo-first-order rate constants of the reaction. Considering the magnetization at equilibrium, M_PCr and M_ATP, the forward flux PCr  ATP and the reverse flux ATP  PCr are given respectively by

(1)

(2)

The evolution of magnetization is described by the modified Bloch equations (Ugurbil, 1985), where T_1ATP, T_1PCr are the intrinsic relaxation parameters:

(3)

(4)

The solutions of this system depend on the protocol of magnetic perturbation.

Time-dependent saturation transfer

ATP

ATP

(5)

Inversion transfer

(6)

(7)

1ATP

Model II: two-site three-compartment analysis: modification accounting for a compartment of ATP not involved in CK

Model II

In the case of two pools of ATP, one pool, ATP₁ = (1  f_ATP) · ATP, in fast exchange with PCr, and a second, ATP₂ = f_ATP · ATP, not exchanging (or in slow exchange) with PCr, the evolution of each pools must be considered separately; the time evolution of ATP₁ is described by Eq. 4, and that of ATP₂ by

(8)

The solutions of this new system (Eqs. 3, 4, and 8) depend on the type of magnetization transfer protocol. In time-dependent saturation transfer (TDST), neglecting ATP compartmentation will not affect F_f (measured by saturation of ATP). F_r, measured by saturation of PCr, will also be correct, as pointed out earlier (Meyer et al., 1982; Spencer et al., 1988): the underestimation of k_r (by 1  f_ATP) is indeed exactly compensated for by an overestimation of the ATP content. However, in IT, the presence of an ATP compartment will affect the analysis of both PCr and ATP inversion in a different way.

Inversion of PCr

ATP₂

ATP

ATP1

ATP

ATP1

ATP2

ATP

ATP₁

ATP

ATP₁

Inversion of ATP

ATP1

ATP

ATP₂

(9)

ATP

(10)

1ATP2

ATP

Model III: three-site three-compartment analysis: modification accounting for the implication of ATP in other exchanges

In contrast to PCr which is only metabolized by CK in the cell, ATP is involved in many other cellular reactions. Because of the high activity of ATP synthesis and hydrolysis in muscle, the ATP-P_i exchange has been recognized as a possible main source of artifact in the determination of CK flux: a three-site three-compartment exchange model has been proposed (Ugurbil et al., 1986; Spencer et al., 1988):
Model III

In this frame, elimination of the effect of P_i  ATP exchange by a continuous saturation of P_i (sat-P_i) will reduce the model to a two-site two-compartment exchange (model I) described by a new set of equations analogous in form to Eqs. 3 and 4 (for a complete description, see Ugurbil, 1985):

(11)

(12)

where M^*_PCr and M^*_ATP are the steady-state magnetization under sat-P_i, and 1/T^*_1ATP = k_d + 1/T_1ATP

Model IV: three-site four-compartment analysis: modification accounting for both ATP compartmentalization and the implication of ATP in other exchanges

In the case of ATP compartmentation,
Model IV

A complete description of the system in the absence of P_i saturation is given in the Appendix. With the saturation of P_i this model reduces to model II with modified intrinsic relaxation parameters, if the only consequence of sat-P_i is to mask the influence of the P_i  ATP exchange. Equation 12 applies to the evolution of M_ATP1. The time evolution of M_ATP2 is described as previously by model II and Eq. 8. Notice that the determination of F_f by the saturation of ATP is the only experimental protocol that is not influenced by the presence of a P_i  ATP exchange and can thus be used as a reference for in vivo flux determination.

In summary, this formalism describes how to take into account the presence of an ATP compartment in the analysis of both inversion of PCr and ATP and shows that both protocols can independently quantify an ATP compartment.

	MATERIALS AND METHODS

TOP ABSTRACT INTRODUCTION THEORY MATERIALS AND METHODS RESULTS DISCUSSION APPENDIX REFERENCES

Enzyme solutions

Measurement of CK flux in vitro was performed using two concentric tubes (OD tube 1 = 8 mm, tube 2 = 20 mm). Both tubes contained solutions, the initial composition of which was (in mM) 10 Cr, 5.7 Mg, 1 dithiothreitol, 0.5 EGTA, 100 HEPES, and 15% D₂O. ATP (5 mM), PCr (10 mM), and rabbit muscle creatine kinase (Boehringer) at a concentration of 800 IU/ml were added to tube 1. Variable concentrations of ATP ranging from 0 to 1.2 mM (corresponding to a fraction of ATP₂ not involved in CK reaction ranging from 0 to 50% of the total ATP) were added to tube 2, which did not contain CK. T_1ATP2 stays constant and similar to T_1ATP1 in this protocol. The pH of the final solutions was adjusted with acetic acid at 7.1 at 30°C. The flux measurement was performed at 30°C. To evaluate the possibility of measuring T_1ATP2 in our in vitro system, a second series of experiments was performed in which tube 2 contained a fixed ATP concentration of 1 mM (corresponding to 45% of the total ATP), but its relaxation properties were modified by replacing H₂O in the solution with various amounts of glycerol (from 15 to 70%) to change the viscosity of the solution.

Isolated perfused rat hearts

Animal experimentation was performed in accordance with the Helsinki Accords for Humane Treatment of Animals during Experimentation. Wistar male rats (350-450 g) were anesthetized with ethyl carbamate (2 g/kg), and hearts were perfused by the Langendorff technique at a constant flow of 13.5 ml·min¹ as previously described (Hoerter et al., 1988). Briefly, a latex balloon was inserted into the left ventricle (LV) and inflated with D₂O to isovolumic conditions of work. Mean coronary pressure, LV systolic pressure (LVP), end diastolic pressure (EDP), and heart spontaneous frequency were continuously monitored on a computer (Compaq) via Statham gauges. The rate pressure product (RPP in 10⁴·mmHg·beats· min¹) was used as an index of contractility reflecting the energetic demand. The perfusion solution contained (in mM) 124 NaCl, 6 KCl, 1.8 CaCl₂, 1 MgSO₄, 1.1 mannitol, 10 Na-acetate, and 20 HEPES and was oxygenated with 100% O₂. The pH_o was adjusted to 7.35 at 36.5°C. Hearts were freeze clamped at the end of the experiment to measure their ATP, PCr, and Cr contents (in nmol·mg·/prot.¹) (Hoerter et al., 1988). These values were used to calculate the metabolite concentrations during magnetization transfer. CK flux was expressed in mM·s¹ (assuming cytosolic H₂O volume = 2.72 µl·mg/prot.¹).

NMR

³¹P NMR spectra were acquired on a Innova Varian with a 9.4-T wide-bore magnet in 8-mm- and 20-mm-diameter tubes for the in vitro analysis and in a 20-mm tube for the heart. We used a pulse angle of 80°, 4 K data point acquisition, a spectral width of 10,000 Hz, an acquisition time of 0.205 s, a repetition time of 10 s, zero filling to 8 K, and line broadening of 20 Hz. For all flux measurements, 32-scan spectra were acquired by blocs of eight scans cycling four times through the whole protocol. For the heart experiment, homogeneity was performed on the heart water, the frequency was locked on D₂O contained in the LV balloon, and the 360° pulse duration was measured on the ATP peak. After 20 min of equilibration, four partially saturated spectra (repetition time 2 s, number of scans 32) were acquired. The stability of the preparation was checked by comparing fully relaxed control spectra (repetition time 10 s) acquired before and after the magnetization transfer experiment; any heart showing more than 10% variation in its metabolite content was discarded. These controls were also used to check the complete recovery of magnetization after 10 s of mixing time during inversion protocols. In four hearts TDST of ATP (Bittl and Ingwall, 1985) was performed as a reference for the determination of forward CK flux. Eight spectra were acquired with a duration of ATP saturation ranging from 0 to 9 s (a 9-s irradiation at mirror frequency was used to test radiation spillover). The delays between pulses were adjusted to achieve a constant rate of recurrence of 10 s in each spectrum. Inversion recovery (IR) was used to measure T_1ATP in vitro (eight spectra, 16 scans, delays ranging from 0 to 10 s). The inversion transfer (IT) experiments were performed with a pulse sequence consisting of a frequency-selective sinc pulse (15 ms, bandwidth 300 Hz), a variable mixing time delay (0.2-10 s), a 80° read pulse, and a fixed 10-s delay to allow full relaxation before the next inversion. Each inversion transfer experiment required 26 spectra in vitro (total time 75 min) and 13 spectra for the heart (total time 75 min). Five hearts were used for each protocol of inversion of PCr (inv-PCr) or ATP (inv-ATP). The effect of a shorter repetition time of 4 s was additionally checked in four hearts (inv-PCr, n = 2; inv-ATP, n = 2). In 10 other hearts inv-ATP or inv-PCr was performed under continuous saturation of P_i. Although off-resonance effects of a sat-P_i protocol on PCr could not be checked directly by mirror irradiation, we considered as negligible the spillover of P_i saturation because similar irradiation applied at 2.4 ppm from PCr (chemical shift of P_i = 4.86 ppm from PCr) resulted in a ~3% decrease in PCr.

Analysis

In TDST protocols, the exponential decay of ATP magnetization, estimated by peak areas, was analyzed to determine in the same experiment T_1PCr and k_f (Bittl and Ingwall, 1985). In IT experiments, the adjustment of experimental data with theoretical expression was performed using either the peak areas or the product of peak amplitudes by , as described by Led and Gesmar (1982), which should address the total NMR visible cellular metabolites. , the average ratio of peak area to amplitude, was measured for each heart (mean value 0.61 ± 0.02 and 1.50 ± 0.03, n = 10, for inv-PCr and inv-ATP, respectively). The two analyses gave similar results; only the latter is shown here because it results in smaller data scattering. The evolution of the inverted and noninverted species was fitted to the solutions of Bloch equations, using the Levenberg-Marquardt method. Equations 6 and 7 were used for the two-site two-compartment analysis of inv-PCr and inv-ATP protocol. The adjustable parameters in this analysis were k_f, k_1f, k_r, k_1r, and the magnetizations of PCr and ATP at t = 0 and t = . Two-site three-compartment analysis of the inv-ATP experiment under saturation of P_i had to be performed by a three-exponential fit of M_ATP using Eq. 10. However, because of the number of unknown parameters, the confidence interval for the parameters derived from this analysis was high both in vitro and in the myocardium. To improve this analysis, F_f and T_1PCr measured in the inv-PCr experiment were imposed as fixed parameters (for justification see the Results).

All data were expressed as mean ± SE. Differences between groups were analyzed by t-test, paired t-test, or variance analysis and Student-Newman-Keuls test.

	RESULTS

TOP ABSTRACT INTRODUCTION THEORY MATERIALS AND METHODS RESULTS DISCUSSION APPENDIX REFERENCES

In vitro validation of the model

Variation of fraction of the ATP (f_ATP) that does not participate in the CK reaction

1ATP2

1ATP1

1ATP1

1ATP1

1

1

1ATP1

1

1

View larger version (16K): [in this window] [in a new window]   FIGURE 1   Influence of the presence of an ATP compartment on the in vitro determination of CK flux parameters by inversion transfer protocols. (a) Protocol of inversion of PCr. (b) Protocol of inversion of ATP. Forward and reverse flux (top) as well as Ff/Fr ratio (bottom) were expressed as a function of ATP2 (as a percentage of total ATP) when the fraction of ATP not involved in CK (in tube2) was increased. Fluxes (shown in symbols) were computed by fitting experimental data to Eqs. 6 and 7. The continuous lines were obtained by fitting Eqs. 6 and 7 to kinetics reconstructed from the known fraction f in Eqs. 6 and 11. Input parameters: kf = 0.25 s1, kr = 0.5 s1, T1PCr = 3.5 s, T1ATP1 = T1ATP2 = 2.5 s. Neglecting the ATP compartmentalization in the analysis resulted in errors in flux determination and in Ff/Fr.

Inversion ATP protocol.

1

1ATP1

1ATP2

1

1

1

1

1

1

1

1ATP1

Variation of T_1ATP2 for a constant fraction f_ATP

1ATP2

1ATP2

1ATP2

1ATP2

Application to the perfused rat heart

Characteristics of the hearts

1

1

1

1

View this table: [in this window] [in a new window]   TABLE 2   Parameters of the forward and reverse CK flux in perfused hearts: comparison of the protocols of time-dependent saturation transfer of ATP, inversion transfer of PCr, and inversion transfer of ATP analyzed in the two-site two compartment model I

Inversion transfer

ATP

1

1

View larger version (30K): [in this window] [in a new window]   FIGURE 2   Inversion of PCr in a representative heart. (a) Stacked plot of the spectra obtained for various times of mixing after the sinc pulse selectively inverting PCr (time of mixing in seconds on the right). The dotted line shows the equilibrium magnetization of the noninverted species expected in the absence of inversion. (b) Variation of PCr and ATP magnetizations (in magnetization units) as a function of the time of mixing.

View larger version (34K): [in this window] [in a new window]   FIGURE 3   Inversion of ATP in a representative heart. Same legend as for Fig. 2. Transfer of magnetization between - and ATP could not be demonstrated.

View this table: [in this window] [in a new window]   TABLE 3   ATP inversion transfer experiments in individual rat hearts: analysis in model I (two-site, two-compartment)

Inversion transfer with saturation of P_i

View this table: [in this window] [in a new window]   TABLE 4   Comparison of the parameters of forward and reverse CK fluxes measured in the perfused heart by inversion PCr and inversion of ATP under continuous saturation of Pi magnetization

1ATP1

1

	DISCUSSION

TOP ABSTRACT INTRODUCTION THEORY MATERIALS AND METHODS RESULTS DISCUSSION APPENDIX REFERENCES

Ability of the different techniques to reveal ATP compartmentalization

As shown in vitro, a complete time analysis of the magnetization recoveries in an IT protocol is able to reveal the existence of an ATP compartment isolated from CK. As expected from the theory, neglecting ATP compartmentalization (i.e., performing the analysis in model I) resulted in an apparent flux discrepancy in both inv-PCr and inv-ATP protocols (an underestimation of F_f/F_r in the former and its overestimation in the latter; Fig. 1). The same behavior was observed in myocardium (Table 2), clearly confirming the insufficiency of the two-site, two-compartment exchange model to account for myocardial energy transfer.

The possibility of detecting an ATP compartment by NMR depends on the type of NMR transfer protocol (Table 1). For instance, when ATP P_i exchange was masked, flux discrepancy could not be evidenced by steady state or time-dependent saturation transfer (Ugurbil et al., 1986; Spencer et al., 1988). As discussed in the Theory section and previously reported (Bittl and Ingwall, 1985), such an ATP compartmentalization cannot be revealed by TDST. Furthermore, its effects will be minimized by an analysis of the initial rates of recovery in an IT or a 2D protocol, as easily demonstrated from the Bloch equations (Meyer et al., 1982; Korestky et al., 1985; DeFuria, 1985). Indeed, no discrepancy between the F_f and F_r has ever been revealed by initial rate analysis in muscle (Hsieh and Balaban, 1988; McFarland et al., 1994).

The results of magnetization transfer experiments are also highly dependent on the experimental conditions (Table 1). For example, in glucose substrate and basal working conditions, equal fluxes were observed by a complete analysis of inversion and by steady-state saturation transfer (Degani et al., 1985). The flux discrepancy, when observed, was suggested to be directly related to the level of cardiac performance (Koretsky et al., 1985); indeed both the ATP-P_i exchange and the amount of ATP present in the mitochondrial matrix (Soboll and Bunger, 1981) are directly related to work. Moreover, most authors, except the group of Ingwall (Bittl and Ingwall, 1985; Bittl et al., 1987; Spencer et al., 1988), observing that the flux discrepancy seen in vivo (Koretsky et al., 1986; Hsieh and Balaban, 1988; Mora et al., 1992) or in hearts using acetate or pyruvate (Nunally and Hollis, 1979; Matthews et al., 1982; Ugurbil et al., 1986; Zweier and Jacobus, 1987) disappeared with glucose utilization (Matthews et al., 1982; Ugurbil et al., 1986; Zweier and Jacobus, 1987), suggested that the contribution of contaminating reactions or ATP compartmentalization was masked by the higher CK flux observed in glucose. Last, various pulse protocols were used in the different studies. Mora et al. (1992), using a long repetition time of 10 s, allowing relaxation of each species, as in our work, could also reveal the apparent flux discrepancy. In contrast, when using a short repetition time of 4 s (similar to T_1PCr), like that of Degani et al. (1985), we could no longer find evidence of the flux discrepancy (F_f/F_r was 1.04 in inv-PCr and 1.08 in inv-ATP, n = 2). This might suggest that some reaction contributing to the detected flux was eliminated by fast pulsing. Although the exact contributions of the various factors (work, substrate, pulse conditions) are difficult to appreciate, we believe that they may explain the impossibility of experimentally detecting the presence of an ATP compartment in some previous work.

We further demonstrated that when P_i magnetization was continuously saturated during inversion experiments, the parameters of forward CK flux were similar in protocols of inversion (Table 4) and saturation of ATP (Table 2) and thus can be consistently determined. Absolute flux values (Table 5) were also similar to F_f previously measured by ATP saturation (Koretsky et al., 1986; Ugurbil et al., 1986; Stepanov et al., 1997), in which neither ATP compartmentation nor ATP-P_i exchange induces errors in CK parameters. Although Koretsky et al. (1985) and Brindle (1988) previously suggested that the inversion and the saturation protocols differ in their capacity for CK flux detection, here we show that, when inversion was performed with saturation of P_i, the two techniques were equivalent for the detection of the forward flux. The advantage of the complete analysis of an IT experiment over the other experimental protocols is, however, its ability to quantify ATP compartmentalization by two independent methods (inv-PCr and inv-ATP).

Flux discrepancy observed with saturation of P_i can be understood in the hypothesis of an ATP compartmentalization

The origin of the observed discrepancy of forward and reverse flux has been alternately attributed to the existence of an ATP compartmentation (model II; Nunnally and Hollis, 1979), the exchange of ATP with species other than PCr (model III; Ugurbil et al., 1986; Spencer et al., 1988), or the influence of a small invisible ATP pool in saturation protocols (Koretsky et al., 1985; Zahler et al., 1987). We do not favor the last as the source of flux discrepancy observed in our inversion protocol. Indeed, in a saturation protocol, the influence of a small invisible ATP pool on the evolution of M_PCr could be detected. However, in a pulse labeling technique like ATP inversion, the change in PCr magnetization being proportional to the size of the inverted compartment, such a small invisible ATP pool would have a minimal effect on the exchange, as discussed earlier (Koretsky et al., 1985; Brindle, 1988). Furthermore, this invisible ATP must be small because the ATP content of a normoxic heart is identical when measured by NMR or biochemistry (Humphrey and Garlick, 1991). Thus the exclusive hypothesis of an invisible ATP pool would not be able to account for our inversion data.

The continuous saturation of P_i resonance makes it possible to mask the influence of the ATP-P_i exchange on the measured CK kinetics (Ugurbil et al., 1986). We indeed observed a clear convergence between the data obtained in vitro and those obtained in perfused rat heart with sat-P_i. All data of both inv-ATP and inv-PCr protocols (Table 4) could thus be understood in the hypothesis of an ATP compartment that does not exchange with PCr in model II. This two-site, three-compartment model is a minimal model for cardiac CK explored with saturation of P_i, i.e., a model fitting the data with the smallest number of unknown parameters (two fluxes, one fraction of ATP and T₁s).

How to understand the data obtained without saturation of P_i

Sat-P_i decreased the steady-state magnetization of both PCr and ATP by ~15%, as already observed (Ugurbil et al., 1986). Furthermore, sat-P_i affected kinetic parameters of the forward and reverse CK, as shown by comparison of Tables 4 and 2. Considering the only consequence of sat-P_i to be the masking of P_i  ATP exchange, it should be possible to theoretically reconstruct the data of Table 2 simply by adding the influence of this exchange to the experimental results of Table 4. The simulation (shown in the Appendix and Table 6) suggests that experimental data of Table 2 and the decrease in steady-state magnetization induced by P_i saturation were not fully described by the models considered. As already suggested in the analysis of saturation transfer protocol (Brindle, 1988), the mask of P_i  ATP exchange per se is not expected to have such an influence on CK flux determination. Moreover, the equivalent decrease in steady-state magnetizations M_PCr and M_ATP induced by sat-P_i was not anticipated (Table 6). This suggests that sat-P_i might not just eliminate the contribution of the ATP-P_i exchange, but might also affect other cellular reactions or metabolites implying PCr: an exchange between PCr and ATP₂ appears to be a good candidate for contributing to the decreased M_PCr. In conclusion, model IV should be refined to account for the results observed in the absence of P_i saturation.

Physiological considerations and their expected NMR consequences

The model developed here allowed us to explain both inversion experiments with sat-P_i, suggesting that the system studied by NMR could be mimicked with the minimal simple assumption of an ATP not being involved in the CK reaction. Moreover, this fraction, 20-33% of total cellular ATP, was in the range of mitochondrial ATP content described in the literature for isolated cardiac mitochondria, isolated cardiac myocytes, or hearts performing medium work (Asimakis and Sordall, 1981; Soboll and Bunger, 1981; Geisbuhler et al., 1984). In the hypothesis of ATP₂ localized in the mitochondrial matrix (ATP₂ = ATP_m), a more physiological scheme can be proposed. Indeed, we have not considered until now the NMR complexity arising from the specific localization of CK isoforms in myocardium (Nunnally and Hollis, 1979; Koretsky et al., 1985; Zahler et al., 1987), particularly the high proportion of mitochondrial CK (mito-CK  20% of total CK) localized in the intermembrane space of mitochondria in the vicinity of translocase. Fig. 4, which schematizes the myocardial phosphorus exchanges, includes cytosolic and mitochondrial CK and the restriction of diffusion for CK metabolites, which separates their function.

View larger version (49K): [in this window] [in a new window]   FIGURE 4   Schematic representation of myocardial CK. The model takes into account compartmentalization of mitochondrial CK isoenzyme (CKm) located in the intermembrane in the vicinity of translocase. CKc refers to both cytosolic and myofibrillar CK. Gray areas, metabolite compartment: Pi, ATP1, ATP2 and PCr. Subscript m relates to mitochondrial matrix, c to cytosol, and im to intermembrane space (between the inner and outer mitochondrial membranes). k, rate constants: kf and kr, CK flux of ATP and PCr synthesis, respectively. kt, rate constant of ATP efflux from mitochondrial matrix by adenine nucleotide translocase. The influx of ATP to the matrix was neglected because under high activation of mitochondrial respiration (i.e., when the heart works) the translocase predominantly extrudes ATP from the matrix to the mitochondrial intermembrane space. ks and kh, rate constants of mitochondrial ATP synthesis and hydrolysis, respectively. The presence of oxidative substrate (acetate or pyruvate) is well known to inhibit myocardial glycolytic ATP production in normoxia. Thus the Pi