³¹P Saturation Transfer Spectroscopy Predicts Differential Intracellular Macromolecular Association of ATP and ADP in Skeletal Muscle

Abstract

The kinetics of phosphoryl exchange involving ATP and ADP have been investigated successfully by in vivo ³¹P magnetic resonance spectroscopy using magnetization transfer. However, magnetization transfer effects seen on the signals of ATP also could arise from intramolecular cross-relaxation. This relaxation process carries information on the association state of ATP in the cell. To disentangle contributions of chemical exchange and cross-relaxation to magnetization transfer effects seen in ³¹P magnetic resonance spectroscopy of skeletal muscle, we performed saturation transfer experiments on wild type and double-mutant mice lacking the cytosolic muscle creatine kinase and adenylate kinase isoforms. We find that cross-relaxation, observed as nuclear Overhauser effects (NOEs), is responsible for magnetization transfer between ATP phosphates both in wild type and in mutant mice. Analysis of ³¹P relaxation properties identifies these effects as transferred NOEs, i.e. underlying this process is an exchange between free cellular ATP and ATP bound to slowly rotating macromolecules. This explains the β-ATP signal decrease upon saturation of the γ-ATP resonance. Although this usually is attributed to β-ADP ↔ β-ATP phosphoryl exchange, we did not detect an effect of this exchange on the β-ATP signal as expected for free [ADP], derived from the creatine kinase equilibrium reaction. This indicates that in resting muscle, conditions prevail that prevent saturation of β-ADP spins and puts into question the derivation of free [ADP] from the creatine kinase equilibrium. We present a model, matching the experimental result, for ADP ↔ ATP exchange, in which ADP is only transiently present in the cytosol.

Introduction

Phosphoryl exchange reactions are the backbone of energy transduction in living systems (1). The possibility to assess the rates of some key phosphoryl exchange reactions in vivo is a unique property of magnetization transfer (MT)² methods in ³¹P MR spectroscopy (2, 3). These methods involve specific magnetic labeling of a phosphate spin system and subsequent observation of exchange of its members with other phosphate spin systems. In MT studies performed on muscles and brain, γ-ATP phosphate has played a central role. This phosphate participates in multiple exchange reactions, most prominently those catalyzed by creatine kinases (CK) in these tissues, but also by adenylate kinases (AK), nucleotide diphosphate kinases, and ATPases. In skeletal muscle, magnetic labeling by selective saturation of the γ-ATP phosphorus signal is known to reduce the intensity of the signals of phosphocreatine (PCr) and inorganic phosphate (P_i). The decreases result from ATP-producing chemical exchange reactions

Upon saturation of the γ-ATP signal, CK activity reduces the PCr signal intensity, whereas the P_i signal intensity decays proportional to the activity of mitochondrial F₁F₀-ATPase and the combination of glycolytic enzymes glyceraldehyde-3-phosphate dehydrogenase (GAPDH) and phosphoglycerate kinase (4).

Apart from the reduction of the PCr and P_i signal intensity, the β-ATP signal intensity also decreases upon irradiation of the γ-ATP spins (3, 5–14). This effect, which has received relatively little attention, is usually attributed to contributions from several phosphoryl exchange pathways. As γ-ATP and β-ADP spins resonate at nearly the same frequency, the β-ADP spins are easily co-saturated with the γ-ATP spins. This may affect the β-ATP signal according to the reverse CK reaction (ATP + Cr → ADP + PCr + H⁺) and even more so if AK, F₁F₀-ATPase and/or glycolytic enzymes also contribute to the ATP to ADP conversions involving the chemical exchange

in which k_ADP,for and k_ADP,rev represent pseudo first order rate constants, meaning that they not only represent the intrinsic rate constant but are also determined by enzyme and substrate concentrations. Unless stated otherwise, this holds for all equations used in this study.

A detailed investigation of the reduction of the β-ATP signal has been carried out by Le Rumeur et al. (5). They studied the kinetics of ATP to ADP β-phosphoryl exchange in resting and contracting rat skeletal muscle. An interesting conclusion following from their work was that deriving the β-phosphoryl conversion from the reduction of the β-ATP signal in resting muscle highly underestimates the expected value that is obtained from the γ-ATP-PCr exchange in the CK reaction. In fact, a more complex picture applies as in addition to chemical exchange, the effect on the β-ATP signal could be caused by cross-relaxation leading to nuclear Overhauser enhancement (NOE).

In this study, we aimed to assess contributions from cross-relaxation and from chemical exchange to the reduction of the β-ATP signal. This is of importance first for a proper understanding of this effect but also because the extent of these contributions critically depends on the physical state of ATP and ADP in vivo. Finally, the results also constitute a test for the validity of the common practice to calculate free ADP concentrations in skeletal muscle from the CK reaction, which assumes that this reaction is at (near-)equilibrium (15–17). To assist in the distinction between cross-relaxation and chemical exchange, we compared MT effects in ³¹P MR spectroscopy of skeletal muscle of wild type mice and mutant mice, which lack cytosolic CK and AK activities (only mitochondrial CK and AK remain) and therefore have strongly reduced phosphoryl transfer capacity (18).

By carefully analyzing the ³¹P relaxation properties of all three phosphates in ATP, we show that the reduction of the β-ATP signal is not caused by phosphoryl exchange reactions but by so-called transferred NOEs brought about by the interaction of ATP with slowly tumbling cellular components. Our experiments also indicate that in resting skeletal muscle, conditions prevail in which the β-phosphate resonance of ADP participating in the β-phosphoryl exchange cannot be saturated. To account for these experimental results, we propose that ADP in muscle cells at rest is associated with immobile (slowly tumbling) structures with a solid state-like character and participates in the ADP ↔ ATP exchange reaction, wherein it is only transiently freely present in the cytosol.

EXPERIMENTAL PROCEDURES

Animal Subjects and in Vitro Samples

In vivo MR experiments were performed on compound mutant mice lacking the genes for both the cytosolic isoforms of muscular CK (M-CK) and AK (AK1) (MAK^−/−: n = 13, 8.5 ± 5.0 months, 29.5 ± 4.0 g) and the wild type littermates (WT: n = 10, 10.1 ± 3.0 months, 27.7 ± 3.5 g). Residual phosphoryl transfer capacity still exists, resulting from the presence of mitochondrial isoforms ScCKmit and AK3 in muscles of these animals (accounting for ∼8% and ∼1–2% of wild type activities, respectively (18)). The generation of MAK^−/− mice has been described elsewhere (18). All experimental procedures were approved by the local animal ethics committee. In vitro measurements were performed on a solution containing: 7 mm ATP, 10 mm MgCl, 35 mm PCr, and 1 mm EDTA in 100 mm Tris-HCl buffer, pH = 7.5.

NMR Experiments

³¹P MR experiments on murine skeletal muscle were carried out at 7.0 tesla, in a 120-mm horizontal bore, magnet (Magnex Scientific, Abingdon, UK) interfaced to an MR spectrometer (MR Solutions, Surrey, UK) operating at 121.53 MHz for ³¹P. MR spectra were acquired from the hind leg of the mice with a 9-mm diameter solenoid coil (19). A low power continuous wave pulse (γB₂ = 320 radians/s) was applied prior to the acquisition pulse to saturate signals selectively for variable durations (t): 0.2, 0.5, 1.0, 1.5, 2.0, 3.0, and 5.0 s. The spectra were acquired using 64 averages at a repetition time of 7 s. Signal decreases in PCr, P_i, β-ATP, and α-ATP were determined upon saturation of the γ-ATP/β-ADP signals. Similarly, signal decreases in γ-ATP, β-ATP, and α-ATP were observed when positioning the irradiation pulse at the PCr, α-ATP, and β-ATP resonances, respectively. For each experiment, control spectra with the irradiation pulse at mirror frequencies were acquired to correct for radio frequency bleeding.

Data Analysis MR Spectra

Signal integrals were fitted in the time domain with the program MRUI (AMARES fitting algorithm) using Gaussian line shapes for P_i, PCr, γ-ATP, α-ATP, NADPH, and β-ATP at 4.8, 0, −2.5, −7.5, −8.2, and −16.2 ppm, respectively. The line widths of P_i and NADPH signals were constrained to 1.5 and 1.0 times that of PCr. The PCr and P_i signal intensities were scaled to the β-ATP signal and corrected for T₁ saturation. Tissue concentrations were calculated assuming that ATP levels of both WT and MAK^−/− mice in this study were 7.8 ± 0.08 mm (19). Tissue pH was obtained from the chemical shift difference between PCr and P_i (20). Monoexponential functions were fitted to the time dependent decays obtained in the relaxation measurements using a non-linear least square method: the Levenberg-Marquardt algorithm (GraphPad Prism, San Diego CA).

RESULTS

High Energy Phosphate Levels and CK Activity

In vivo ³¹P MR spectra of WT and MAK^−/− skeletal muscle acquired without the application of saturation pulses look very similar (Fig. 1). Analysis of the resonance positions and intensities shows that the pH and the levels of phosphate-containing metabolites in MAK^−/− mice are virtually equal to those in WT littermates except for slightly decreased PCr levels (Table 1). Thus, stationary conditions with near normal levels of phosphorylation of Cr are achieved in MAK^−/− mice despite the lack of cytosolic M-CK. However, the rate at which this steady state is reached is profoundly different. This point is best illustrated by the smaller reduction of the PCr signal upon selective saturation of the γ-ATP spins in the MAK^−/− mice. The PCr signal declines as a function of the length of the saturation pulse (Fig. 2) according to

in which M_zA⁰ is the PCr equilibrium magnetization, M_zA(t) is the PCr magnetization after the saturation pulse of duration t, ρ_A is the is the relaxation constant of the PCr spins, A, and k_for is the pseudo first order rate constant in forward direction, PCr → ATP, see reviews (2, 3).

FIGURE 1.

³¹P MR spectra of skeletal muscle of WT and MAK^−/− mice recorded in the presence and absence of saturation of the γ-ATP(/β-ADP) signals. For both groups, the spectra on the left are unperturbed; in the spectra on the right-hand side, the γ-ATP resonance at −2.5 ppm is saturated by a pulse of 5-s duration (gray arrow). The second spectrum from the right (WT mice, saturated γ-ATP/(β-ADP)) shows a large decrease of the PCr signal intensity as a result of the saturation of the γ-ATP resonance, whereas the second spectrum on the far right (MAK^−/− mice, saturated γ-ATP/(β-ADP)) shows only a very small perturbation as a result of the saturation of the γ-ATP signal. Both groups show decreases in β-ATP signal and a small decrease in P_i.

TABLE 1.

Tissue concentrations and pH in hind limb muscle of WT and MAK^−/− mice

All values are presented as mean ± S.D. Muscle tissue concentrations of P_i and PCr are calculated assuming a tissue [ATP] of 7.8 mm and corrected for T₁ relaxation effects.

	[PCr]	[Pi]	pH
	mm	mm
WT	23.7 ± 2.3	2.8 ± 0.4	7.27 ± 0.08
MAK−/−	21.0 ± 2.6a	2.6 ± 0.8	7.25 ± 0.04

^a Statistical difference determined with a two-tailed student t-test (p < 0.05).

FIGURE 2.

Reduction of the PCr signal intensity upon selective saturation of the γ-ATP resonance in WT (■) and MAK^−/− (●) mice as a function of the duration of the saturation pulse. MAK^−/− mice show a clearly reduced MT effect on the PCr resonance when compared with WT littermates, which implies a lower forward rate through the CK reaction. Control spectra with the irradiation pulse at mirror frequency (at 2.5 ppm) were acquired to correct for radio frequency bleeding; i.e. the magnetization of PCr upon saturation of the γ-ATP was corrected for off-resonance effects by subtraction of the magnetization of PCr (M₀). Error bars indicate mean ± S.E.

It is clear that the absence of cytosolic M-CK activity in the mutant muscle results in strongly reduced MT effects on the PCr signal intensity when compared with MT effects in WT. The time dependence of the WT PCr signal could be fitted with a monoexponential function, indicating that the effect of the possible cross-relaxation between the phosphorous and proton spins in PCr is negligible (21), as is tacitly assumed in the derivation of Equation 1. The pseudo first order rate constants (k_CK,for) of the CK-mediated exchange in forward direction (PCr → ATP) obtained in this way reflect the strongly decreased exchange in the mutant mice when compared with that of the WT littermates (Table 2).

TABLE 2.

Unidirectional pseudo first order rates and fluxes in muscle of WT and MAK^−/− mice

Rates and fluxes were determined from decreases in PCr and P_i upon saturation of the γ-ATP/β-ADP resonances. All values are presented as mean ± S.D.

	WT	MAK−/−
PCr → ATP
kCK,for (s−1)a	0.43 ± 0.05	0.04 ± 0.01b
ρPCr (s−1)	0.41 ± 0.06
FCK,for (mm · s−1)	10.2 ± 1.5	0.84 ± 0.24b
Pi → ATP
kPi,for (s−1)	0.23 ± 0.03c	0.18 ± 0.04
FPi,for (mm · s−1)	0.64 ± 0.13	0.47 ± 0.18

^a To improve the accuracy of the determination of the small k_CK,for in the MAK^−/− mice the value for T₁^int was assumed to be equal to the value determined in the WT mice and for both MAK and WT.

^b Curve is significantly different from WT (F-test using a 0.95 confidence interval).

^c The mono exponential function for P_i → ATP was fitted according to Equation 1 assuming an intrinsic auto relaxation time of 1.95 s (19, 39).

MT Effects in ATP in the Presence and Absence of M-CK and AK Activity

To determine the flux via the CK-mediated reaction from decreases in PCr signal intensity, the γ-ATP resonance is selectively saturated in in vivo ³¹P saturation transfer applications. When we applied this procedure, we observed that the PCr signal also decreased upon saturation of the β-ATP signal. This unanticipated behavior was only found for the WT mice; in the mutants, the PCr remained unaltered (Fig. 3). This suggests participation of the CK-mediated reaction in this MT effect in the WT mice. However, between β-ATP and PCr, no direct phosphate exchange does occur. Because the absence of this effect in MAK^−/− mice eliminates off-resonance saturation as a cause of this effect, the reduced PCr signals in WT mice can only be ascribed to a chemically relayed NOE, i.e. cross-relaxation between β- and γ-ATP spins followed by CK-mediated exchange.

FIGURE 3.

The ³¹P MR signal of PCr under the influence of the saturation of the β-ATP resonance as a function of the duration of the saturating pulse. The length of the saturation pulse, from left to right, is: 0.2, 0.5, 1, 1.5, 2, 3, and 5 s. PCr signals are shown for MAK^−/− (left) and WT mice (right). Line broadening is 5 Hz.

Indeed, steady state saturation of the β-ATP signal leads to a signal reduction of 22 ± 5% not only at the γ-ATP resonance but also at the α-ATP signal intensity (25% ± 8% for WT). To complete this picture, we also irradiated the α-ATP and γ-ATP resonances and observed similar MT effects on the β-ATP spin system. Within the experimental accuracy of our approach, all these effects were of similar magnitude, ranging from 21 to 26% (Fig. 4). This symmetry is expected if the MT effects are caused by dipolar cross-relaxation between the phosphorous spins, leading to NOE effects. NOE involvement is corroborated by the MT to the β-ATP signal upon irradiation of the α-ATP signal, which rules out the contribution of chemical exchange reactions to these magnetic transfer effects. In this respect, it is worth mentioning that the decrease in signal intensity upon saturation of directly neighboring phosphates was equal for WT and MAK^−/− skeletal muscle. Hence M-CK and AK1 activity cannot be held responsible for the MT effects between the phosphates of ATP. In contrast to the NOE effects that occur between directly neighboring phosphorous spins, the magnetization transfer between α- and γ-ATP spins (only investigated for WT mice) turned out to be very small (γ-ATP decreased with 5 ± 4% upon α-ATP saturation). This can easily be explained by the larger distance (4.5 Å) between the two outer phosphates.

FIGURE 4.

Saturation transfer effects between ³¹P spins within ATP as a function of the duration of the saturation pulse. MT effects between α-β and β-γ are similar for both WT and MAK^−/− mice. MT effects between α- and γ-ATP were small and within the detection limits (see results obtained for WT mice) Signal intensities are presented as mean values ± S.E. Dotted lines represent fits of monoexponential curves to the experimental data assuming ρ to be equal in all mice and for all ATP signals.

Absence of NOE in ATP in Vitro

To further investigate the results, we set out to measure NOE effects between the phosphates of ATP for a 7 mm ATP solution, but without success. No NOEs could be detected. The different behavior of ATP in vivo and in vitro becomes clear when we consider the relaxation properties of the phosphorous spins in ATP in more detail. It has been well established that two relaxation mechanisms dominate the relaxation behavior of the ³¹P spins in ATP: the dipole-dipole relaxation and the relaxation induced by the chemical shift anisotropy (CSA). For a ³¹P two-spin system, e.g. the α- and β-phosphates in ATP, the longitudinal relaxation is determined by the auto-relaxation constants ρ_dip and ρ_CSA arising from the dipole-dipole and the CSA relaxation, respectively, and by the cross-relaxation constant, σ, arising from the dipole-dipole interaction. The contributions of these different relaxation constants to the relaxation behavior of a two-spin ³¹P-³¹P spin system with an interspin distance of 3 Å have been plotted in Fig. 5A as a function of the rotational correlation time, τ_c. This figure shows that the CSA contribution is dominating the relaxation entirely for 3 · 10⁻¹¹ < τ_c < 2 · 10⁻⁸ s. For larger tumbling times, i.e. τ_c > 2 · 10⁻⁸ s, the dipolar relaxation starts to contribute significantly, and for τ_c > 10⁻⁷ s, it becomes the predominant relaxation mechanism. For ATP free in solution, τ_c = 0.3 ns (22) (indicated in Fig. 5 by the dashed vertical lines). As expected, in this situation, the CSA relaxation rate constant (ρ_CSA = 0.718 s⁻¹) largely exceeds the auto-relaxation and cross-relaxation constants due to dipolar interactions, which amount to ρ_dip = 0.006 s⁻¹ and σ = 0.003 s⁻¹. Given the expression for the steady state NOE (for derivation, see supplemental material),

we expect a negligible steady state NOE effect (η_ss = +0.004). Only when the dipole-dipole mechanism becomes predominant may NOEs be induced. This is shown in Fig. 5B (solid line), where the steady state NOE has been plotted as a function of τ_c. It is clear that NOE effects are negligible for molecules with τ_c < 10 ns, which is in agreement with the aforementioned experiments on ATP free in solution.

FIGURE 5.

Spin-lattice relaxation rate constants, steady state NOEs, and trNOEs as a function of τ_c derived for a ³¹P two-spin system. A, the different relaxation rate constants contributing to the relaxation in a ³¹P-³¹P system. ρ_dip and ρ_CSA are the auto-relaxation rate constants due to dipole-dipole interactions (gray) and chemical shift anisotropy (CSA, black), and σ is the cross-relaxation rate constant (gray, dashed). B, steady state Overhauser enhancement factor (η_ss) for a ³¹P-³¹P two-spin system (gray) as a function of τ_c calculated on the basis of Equation 2 and steady state transferred NOE as a function of the τ_c of the bound fraction (τ_c,bound) calculated using Equation 3 for P_b = 10% and P_b = 5% (dashed line). C, simulated steady state MT effects on β-ATP due to trNOE and ATP → ADP conversion based on Equation 7. trNOE without (dark dashed line) and with ATP → ADP conversion assuming k_ADP,rev = 0.01 s⁻¹, k_ADP,rev = 0.1 s⁻¹, k_ADP,rev = 1 s⁻¹, and k_ADP,rev = 1.4 s⁻¹ (solid lines). Note that for k_ADP,rev = 1.4 s⁻¹ (corresponding with the reverse rate of the CK reaction), a reduction of about 65% is expected at the β-ATP signal. D, simulated steady state MT effect due to transferred NOE for varying exchange rates between the free and bound ATP pools: k_fb/k_bf = 1000 s⁻¹/9000 s⁻¹ (solid line), k_fb/k_bf = 10 s⁻¹/90 s⁻¹ (dashed line), and k_fb/k_bf = 1 s⁻¹/9 s⁻¹ (dotted line), where k_ADP,rev = 1.4 s⁻¹. Note that k_fb and k_bf have a minor influence on η_ss only for τ_c,bound ≫ 10⁻⁶. All plots were calculated based on a ³¹P resonance frequency of 121.4 MHz and a distance between the phosphorous nuclei r = 3.0 · 10⁻¹⁰ m.

Transferred NOE in ATP

Further examination of the solid curve in Fig. 5B shows that NOE effects can only be expected for higher values of the rotational correlation time, e.g. the NOE effects observed in vivo for the phosphates in ATP (η_ss ∼−0.25) occur when τ_c ≅ 30 × 10⁻⁹ s. This would mean that τ_c has increased by a factor of 100, when considering in vivo rather than in vitro conditions. This seems very unlikely; several experiments indicate that the τ_c of cytosolic ATP in skeletal muscle does not deviate much from its in vitro value (see “Discussion”). However, the effective correlation time of ATP increases when its rotational motion is restricted by binding to larger molecules. In case exchange between the bound and free ATP occurs, NOE effects generated in the bound state may be transferred to ATP in the free state, designated the transferred NOE (trNOE). For this situation, the expression for the steady state trNOE is given by the equation below (see supplemental material and Ref. 23).

Here, k_fb is pseudo first order association rate constant of complex formation, k_bf is the dissociation rate constant, P_b and P_f are the fractions of ATP in the bound and free state, respectively, ρ_f and ρ_b are the auto relaxation rate constants in the free and bound state, and similarly, σ_f and σ_b are the cross-relaxation constants in the free and bound state. Using Equation 3, the steady state trNOE effect was calculated as a function of τ_c of the bound fraction (τ_c,bound), for P_b equal to 5 and 10% (Fig. 5B, dashed lines). In the calculation it was assumed that k_fb = k_assoc[E] in which k_assoc = 1 · 10⁸ m⁻¹s⁻¹ (23), the association rate constant, and k_bf = 9000 s⁻¹, leading to a concentration of free binding sites [E] = 1.10⁻⁵ m. Examination of Fig. 5B shows that ATP has to bind to structures with a τ_c,bound ≅ 10⁻⁶ s to be able to account for the observed trNOEs. The result is not very sensitive to the choice of k_bf (see below and Fig. 5D).

Combining Transferred NOE and ATP-ADP Exchange

Above, we have shown that the MT effects between ATP phosphate signals arise from cross-relaxation, which is responsible for the observed NOEs (see supplemental Fig. S1). However, it seems odd that the decrease of the β-ATP signal during selective saturation of the γ-ATP/β-ADP resonance is not influenced by ATP-producing chemical exchange reactions. To investigate this aspect, we considered the following reaction.

The left-hand part of this expression represents the exchange between bound and free ATP, and the right-hand part represents the transition between β-ATP and β-ADP mediated by CK, AK, ATPases, and/or GAPDH/phosphoglycerate kinase activities. We focus on the behavior of the β-ATP resonance when the γ-ATP and β-ADP resonances are saturated. The steady state MT effect for this reaction scheme is presented in Equation 4 (for the derivation, see supplemental material). The first two terms on the right-hand side give rise to the trNOE, discussed in the previous section; the last term on the right-hand side represents the effect of the additional exchange on the β-ATP resonance.

The pseudo first order rate constant of the reverse CK reaction was determined in WT mice by saturating the PCr spins: k_CK,rev = 1.4 s⁻¹. It dominates over the contribution of the ATPase/glycolysis in the ATP → ADP reaction in resting skeletal muscle (∼0.08 s⁻¹) and the AK reaction, which is known to be only 15% of the total ATP turnover in WT skeletal muscle at rest (18). Using Equation 4, we calculated the MT effect expected on the β-ATP resonance for k_ADP,rev ranging from 0.01 to 1.4 s⁻¹ (Fig. 5C). For the maximum value (1.4 s⁻¹), corresponding with the CK-mediated exchange, the β-ATP signal shows a reduction of 65%. Thus far, such a large MT effect on the β-ATP signal has not been detected in vivo.

To assess the effect of different conversion rates between free and bound ATP on the MT effect on the β-ATP signal, we calculated this effect, including ADP-ATP exchange, with k_ADP,rev = 1.4 s⁻¹, for different values of k_fb and k_bf (Fig. 5D). This reveals that the influence of these rates is negligible.

DISCUSSION

The participation of ATP in phosphoryl exchange reactions can be analyzed by MT experiments in ³¹P MR spectroscopy. However, MT may also occur by cross-relaxation between spins leading to signal attenuation called NOE. The nature and extent of NOEs can provide interesting information on the biophysical state of molecules in cells. The MT effect on the β-ATP resonance after saturating the co-resonating γ-ATP and β-ADP signals is of particular interest as it may arise both from cross-relaxation and from chemical exchange, which in muscles is dominated by cytosolic muscle CK and AK reactions. To resolve this ambiguity, we performed MT experiments on skeletal muscles of wild type mice and of mice lacking CK and AK activity. The results indicate that in resting muscles, a small fraction of ATP is bound to large macromolecules, and that the magnetization effect on the β-ATP resonance mentioned above is caused by cross-relaxation.

Cross-relaxation between the Phosphorous Spins in ATP

MT experiments carried out on solutions of ATP do not demonstrate the presence of ³¹P-³¹P NOEs (see “Results” and Refs. 5 and 24). Here, however, we present several experiments that show that Overhauser effects between the phosphorous spins of ATP do occur in vivo. A case in point is the experiment in which saturation of the β-ATP signal leads to decreases in the PCr signal in WT mice. Because the β-ATP phosphate is not converted into the phosphate group of PCr by any reaction, this decrease can only be attributed to a relayed Overhauser effect (25), i.e. magnetization is transferred by cross-relaxation from β-ATP to γ-ATP and subsequently to the PCr signal through the CK reaction. In MAK^−/− mice, the flux through the CK reaction is lowered so much that the last step becomes ineffective, explaining why the effect is no longer observed (Fig. 3).

By the same token, saturation of the α-ATP resonance leads to a reduction of the β-ATP resonance intensity. Again, because no direct or relayed reactions are known in which an α-phosphate is promoted to a β-phosphate in ATP, the reduction in signal intensity has to be attributed to an NOE effect.

Saturation of the β-ATP resonance not only leads to an effect on the PCr signal but also reduces the intensity of the α- and the γ-ATP resonances, and it does so in a symmetric way, i.e. the signal reductions are about the same as that of the β-ATP resonance if either the α-ATP or the γ-ATP resonances are saturated. This is expected when dipole-dipole relaxation is governing the MT. These physical considerations are corroborated by the results obtained for the double-mutant MAK^−/− mice. The mutants, which are M-CK-deficient, exhibited only a minor flux through the (residual mitochondrial) CK reaction in both directions. As the AK activity in MAK^−/− mice is only about 1% when compared with WT mice (18), we assumed negligible fluxes through the AK reaction as well. In this light, the equal reductions of the β-ATP signal in WT and MAK^−/− mice lead us to conclude that M-CK and AK1 activity contribute insignificantly to the observed MT effect. Furthermore, it is remarkable that not only are all steady state MT effects between nearest neighbor phosphates about the same in WT and MAK^−/− mice but also that the time constants of the signal decays are equal.

Transferred NOEs

Although the preceding section implies that NOE effects explain the MT between ATP phosphates seen in vivo, we have to discuss the observation that no NOEs are seen for solutions of ATP. Overhauser effects are only observed when the dipole-dipole relaxation mechanism dominates the spin-lattice relaxation. It is, however, well established that ³¹P spins are also subjected to relaxation induced by the chemical shift anisotropy (26, 27). We calculated the auto-relaxation constants, ρ_dip and ρ_CSA, and the cross-relaxation constant, σ, for a ³¹P two-spin system as a function of τ_c and demonstrated, given that τ_c ∼3 · 10⁻¹⁰ s for ATP in solution, the CSA contribution dominates the relaxation process (Fig. 5A). Consequently, the NOE effect in ATP in solution is negligible (Fig. 5B). It is generally assumed that the rotational correlation time of cytosolic ATP is not too different from that of ATP in solution. This is reasonable because the translational diffusion of cytosolic ATP is only reduced by a factor of 2–3 (28–30), and the τ_c of small proteins in intact oocytes diminishes by the same amount when compared with that in aqueous solutions (31). This means that the observed NOEs can only be interpreted as being transferred NOEs. When the rotational motion of ATP becomes restricted by binding to larger molecules, this is feasible. Given that there exists a dynamic equilibrium between the free and a “bound” form of ATP, NOEs created in the bound form may be transferred to the free form, where they become NMR visible as trNOE effects.

To estimate the magnitude of these effects, we calculated trNOEs assuming that 5 or 10% of the intracellular ATP occurs in the bound form. Although an enormous variety of proteins are known to form complexes with ATP (32), the calculations show that we can already rule out a large class of proteins; the τ_c of the ATP complexes must be around 10⁻⁶ s to obtain a trNOE of about 20% for the β-ATP signal when the γ-ATP resonance is saturated (Fig. 5B). This sets a limitation to the size of molecular structures involved. Smaller enzymes such as CK (81-kDa dimeric isoform with a τ_c of 7.4 ns (22)) and/or AK (25-kDa monomeric isoform 1) can thus be disregarded as candidates. In fact, this is confirmed by the similar NOEs observed for the MAK^−/− and WT littermates.

Not only does the size of a receptor molecule determine the magnitude of the trNOE. The rotational motion of a small ATP-binding protein can also be greatly restricted when it is embedded in a membrane or cytoskeleton-bound. This was, for instance, demonstrated for adenosine nucleotide translocases (∼30 kDa), which, when embedded in the inner mitochondrial membrane, obtain a τ_c ≅ 10⁻⁶ s (33). The binding of ATP to macromolecules does not necessarily need to be functional in energy metabolism. The adenosine moiety and phosphate group make ATP a suitable candidate for stacking and electrostatic interactions with other compounds (32).

Absence of Exchange-mediated MT Effects on the β-ATP Signal

The conclusion that the reduction of the β-ATP signal upon saturation of the γ-ATP signal is a trNOE effect raises the question why chemical β-ATP → β-ADP conversions do not or only negligibly contribute to this effect? To investigate this, we derived an expression for the steady state reduction of the β-ATP signal (Equation 4) for the situation that both trNOE and ADP-ATP exchange are present. For simplicity, we only incorporated the MT effect arising from the reverse CK reaction (i.e. k_ADP,rev = 1.4 s⁻¹, Table 2). This leads to an expected reduction of 65% of the β-ATP signal, which is at odds with our experimental results and those reported in the literature, where reductions of 20–30% have been reported. It is noted in passing that a similar observation has been made previously by Le Rumeur et al. (5) in their study of rat skeletal muscle. Accounting for additional phosphorylation reactions (i.e. AK, glycolytic activity, ATPases, and nucleotide di- or monophosphate kinases) would have lowered the expected β-ATP resonance intensity even more.

The calculation of the exchange-mediated reduction of the β-ATP signal is based on accepted practice to use the creatine kinase equilibrium to derive the free cytosolic ADP concentration. The fact that in vivo no MT effects ≥0.65 have been seen on the β-ATP resonance casts serious doubts on this approach.

However, relatively large MT effects can be observed in in vitro experiments, as reported by Koretsky et al. (24) and Brindle and Radda (34). They showed that for solutions containing CK, PCr, Cr, ADP, ATP, and free Mg²⁺ mimicking the in vivo concentrations presumed for the near equilibrium CK reaction, saturation of the γ-ATP/β-ADP indeed resulted in a significant reduction of the β-ATP resonance intensity. The effect could not be attributed to an NOE effect, which accords with our analysis; NOEs cannot be expected under in vitro conditions. Thus, in this situation, the reduction of the β-ATP signal is caused by the ATP to ADP conversion.

So how can the apparently conflicting in vivo and in vitro results, of which the latter are in accordance with the predictions in Fig. 5C, be reconciled? The following possibilities come to mind. 1) The β-ADP signal is not properly saturated. 2) The β-ADP is properly saturated, but the effect of the β-phosphoryl exchange is outcompeted by spin-lattice relaxation due to ATP binding to various proteins or receptors. 3) The ADP taking part in the CK reaction is in a state in which its β-resonance cannot be saturated.

With respect to the first point, we notice that the co-saturation of the β-ADP resonance (≈0.4 ppm upfield from γ-ATP) may not be optimal. However, control experiments in which we observed an unchanged signal reduction of the β-ATP in human muscle at 3 tesla, when the carrier frequency of the saturation pulse was varied from +0.1 to −0.8 ppm (steps 0.05–0.1 ppm) and the observations of Koretsky et al. (24) render this option very unlikely.

In situation 2, β-ADP is saturated, but due to its low concentration with respect to ATP, the effect of β-phosphoryl exchange is less effective than that of exchange between γ-ATP and PCr. Basically, this need not form an impediment for the observation of the β-phosphoryl exchange as was shown by in vitro experiments (24, 34). However, in vivo, ATP is involved in many reactions in which it binds to proteins, and one could imagine that the effect of the β-phosphoryl exchange on the β-ATP resonance is undone by a much more effective T₁ relaxation than in the in vitro situation. Careful examination of Fig. 5A shows that this is not to be expected. At in vitro-like conditions (τ_c ∼0.3 ns), the T₁ relaxation through the chemical shift anisotropy is very effective, and still, the MT effect of β-phosphoryl exchange is observed (24, 34). For higher values of the rotational correlation times, corresponding with ATP binding to medium-sized proteins, T₁ becomes even longer. For complex formation, leading to much longer rotational correlation times (e.g. 10⁻⁶ s), T₁ becomes shorter, but not dramatically (T₁ ≈ 0.5 s). In Equation 7, which describes the decrease of the β-ATP resonance as a result of β-phosphoryl exchange and the binding of ATP to slowly tumbling receptors at the presumed CK equilibrium, these effects are incorporated, and it leads to the reduction of the β-ATP signal indicated in Fig. 5C. In summary, at the conditions prevailing in our experiments, this relaxation effect does not nullify the MT effect of the β-phosphoryl exchange.

In situations 1 and 2, the assumption that the cytosolic ADP concentration can be derived from the CK equilibrium still holds. This is no longer true for situation 3, which we consider below. Here, we deal with ADP that is involved in the CK reaction, whereas its β-resonance cannot be saturated.

A Model for ADP ↔ ATP Conversion

For situation 3, we propose a model in which the CK reaction proceeds via transiently free ADP, which is drawn from a pool of bound ADP of which the spin population cannot be saturated (Fig. 6). This situation can be represented by the following two equations

and

Here, ADP_bound is the bound, non-saturable ADP, and ADP_trans is the ADP transiently present in the cytosol. For this situation, the overall rate constants for the conversion of ADP_bound to ATP (k_ex) and its reverse (k_ex,rev) are

and

In this model, the steady state situation is maintained, and an equilibrated free concentration of ADP, commonly derived from the CK equilibrium, need not be invoked.

FIGURE 6.

Scheme of the phosphoryl exchange reactions in which cytosolic ATP is involved, including the role of bound ATP and ADP. The NOEs generated in the bound ATP are transferred to the free ATP through the exchange reaction characterized by k_st and k_ts. The ATP ↔ ADP conversion proceeds via transiently free ADP. The rate constant k_ex,rev does not represent a separate path but is a combination of the rate constants in the individual reaction steps (see Equations 5 and 6). The scheme presented explains the experimental observations.

We consider the limit that k_ts ≫ k_{ADP_CK,for}[CK]. In this case, the overall rate constants reduce to

and

Characteristic of this limit is that ADP exchanges many times between the free and the bound state before it gets caught in the CK reaction. In other words, the overall forward reaction (k_ex) proceeds via a pre-equilibrium, which lies far to the left. In the reverse direction, the reaction from ATP to ADP_trans, k_{ADP_CK,rev}, and the CK concentration determines the overall rate constant. Thus, in both directions, the overall rate constants are linearly dependent on [CK]. This concurs with the observation that the pseudo first order rate constants (k_CK,for and k_CK,rev) that can be derived from Fig. 2 for the mutant and WT mice indicate that they are proportional to CK activity, reflecting its concentration. A linear relation between k_CK,for and CK activity (V_max) has been noticed previously with different expression levels of the M-CK isoform (35).

It is inherent in the present approach that saturation of the spin population of bound ADP is not possible. This condition applies if the ADP resonance is inhomogeneously broadened, which occurs, for example, when ADP is bound to relatively rigid cellular structures with a solid state-like character. Due to the anisotropy of the chemical shift, the resonances are then spread over a region of about 180 ppm, and only a negligible part of the bound spin population will be saturated. Relatively rigid cellular structures with ADP binding capacity, e.g. components of the cell cytoskeleton, for instance, myofibrils and actin filaments, are possible candidates for this type of binding (36), but mitochondria have also been suggested for this role (2).

Conclusions

Central to the discussion in this study has been the small reduction (∼20%) of the β-ATP signal upon saturation of the γ-ATP signal. Understanding this effect requires that a distinction is being made between chemical exchange and cross-relaxation and that the relaxation properties of the phosphorous spins are properly accounted for. The results obtained show that the reduction of the β-ATP signal is caused by transferred NOE effects made possible by binding-unbinding of ATP, i.e. exchange between a state of free diffusion and bound state in which the rotational freedom is restricted. The reduction of the β-ATP signal is not or only negligibly caused by β-phosphoryl exchange. Consequently, ADP participating in the CK reaction comes from a source where its spin system cannot be saturated. To account for these results, we propose a model in which free cytosolic ADP is only transiently present in skeletal muscle at rest. The concentration of this ADP is much less than that of the predicted free [ADP], derived by calculation from the CK equilibrium, which is already too low for in vivo detection by ³¹P MR spectroscopy.

It remains to be investigated whether in circumstances of high intensity exercise in muscle, the free ADP concentration may increase to such an extent that its binding sites on the solid state-like structures become saturated and the free ADP pool might become accessible to NMR saturation. To our knowledge, NMR visible in vivo signals of free ADP have only been observed in AK1-deficient muscle during isometric tetanic contractions (37).

The reduction of the β-ATP signal upon saturation of the γ-ATP resonance has been reported in numerous studies. For instance, in an early study on perfused heart (14) and later, similar effects have been reported repeatedly for hearts (7, 12, 13), as well as for skeletal muscle (5, 10, 11), for kidney (7), for T47D human breast cells (9), for Chlamydomonas reinhardtii (38), and for rat and human brain (6, 8). Taken collectively, these findings imply that the observed magnetization transfer between γ-ATP and β-ATP is not tissue-specific. Interestingly, the similarity of the effect suggests a common mechanism, i.e. mode of ATP binding in different cell types and tissues. Until now, the MT effect was frequently attributed to ATP ↔ ADP exchange mediated by CK, AK, and/or ATPases. In view of the present results, it is more likely due to transferred NOE effects.