Kinetics of creatine kinase in heart: a 31P NMR saturation- and inversion-transfer study

The kinetics of the phosphate exchange by creatine kinase (CK) was studied in solution and in the Langendorff-perfused rat heart at 37 degrees C. 31P inversion-transfer (IT) and saturation-transfer (ST) methods were applied. The kinetic parameters obtained by the two magnetization transfer methods were the same, whether in solution or in the perfused heart. Inversion transfer is the more efficient method, yielding the kinetic constants for the exchange and the relaxation rates of the transferred phosphate in both substrates, in one experiment. In solution the forward (kF) and reverse (kR) pseudo-first-order rate constants for the CK reaction (kF = k1[MgADP][H+]; kR = k-1[creatine]) as well as the concentrations of phosphocreatine (PCr), MgATP, and creatine (Cr) remained constant between pH 6.9 and pH 7.8. Equilibrium at this pH region is therefore maintained by compensating changes in the concentration of MgADP. The forward and reverse fluxes in the perfused heart were equal with an average flux ratio (fluxF/fluxR) of 0.975 +/- 0.065 obtained by both methods. Average values of kF and kR were 0.725 +/- 0.077 and 1.12 +/- 0.14 s-1, respectively. These results clearly indicate that the CK reaction in the Langendorff-perfused heart is in equilibrium and its rate is not limited by the diffusion of substrates between different locations of the enzyme. There is therefore no indication of compartmentation of substrates of the CK reaction.     

Measurement of an individual rate constant in the presence of multiple exchanges: application to myocardial creatine kinase reaction

Forward [creatine phosphate (CP)----adenosine 5'-triphosphate (ATP)] and reverse (ATP----CP) fluxes of myocardial creatine kinase (CK) measured by using 31P nuclear magnetic resonance (NMR) and conventional saturation transfer (CST) methods are unequal; this is a paradoxical result because during steady state fluxes into and out of the CP pool must be the same. These measurements, however, treat the CK reaction as a two-site exchange problem and ignore the presence of the ATP gamma in equilibrium Pi exchange involving the ATPases. We have applied a method [U?urbil, K. (1985) J. Magn. Reson. 64, 207] based on the saturation of multiple resonances, by which a single unidirectional rate constant can be measured unequivocally in the presence of multiple exchanges, to the measurement of CK fluxes in isovolumic rat hearts perfused under three different conditions; two of the three perfusion conditions showed a large discrepancy in the CK fluxes determined by CST, and one did not. In contrast, when the effect of the ATP gamma in equilibrium Pi exchange on the CK rate measurements was eliminated, multiple saturation transfer (MST) measurements on the same hearts yielded equal forward and reverse fluxes in all cases. The rate constant for the ATP gamma----CP conversion measured by MST was larger than the value obtained by the conventional methodology whereas both methods gave the same rate constant in the CP----ATP direction. These results demonstrate that the cause of the paradoxical data obtained by CST measurements of CK kinetics is the ATP gamma in equilibrium Pi exchange and that CK rates when determined rigorously are consistent with the CK reaction being in equilibrium.(ABSTRACT TRUNCATED AT 250 WORDS)     

High efficiency of energy flux controls within mitochondrial interactosome in cardiac intracellular energetic units

The aim of our study was to analyze a distribution of metabolic flux controls of all mitochondrial complexes of ATP-Synthasome and mitochondrial creatine kinase (MtCK) in situ in permeabilized cardiac cells. For this we used their specific inhibitors to measure flux control coefficients (C(vi)(JATP)) in two different systems: A) direct stimulation of respiration by ADP and B) activation of respiration by coupled MtCK reaction in the presence of MgATP and creatine. In isolated mitochondria the C(vi)(JATP) were for system A: Complex I - 0.19, Complex III - 0.06, Complex IV 0.18, adenine nucleotide translocase (ANT) - 0.11, ATP synthase - 0.01, Pi carrier - 0.20, and the sum of C(vi)(JATP) was 0.75. In the presence of 10mM creatine (system B) the C(vi)(JATP) were 0.38 for ANT and 0.80 for MtCK. In the permeabilized cardiomyocytes inhibitors had to be added in much higher final concentration, and the following values of C(vi)(JATP) were determined for condition A and B, respectively: Complex I - 0.20 and 0.64, Complex III - 0.41 and 0.40, Complex IV - 0.40 and 0.49, ANT - 0.20 and 0.92, ATP synthase - 0.065 and 0.38, Pi carrier - 0.06 and 0.06, MtCK 0.95. The sum of C(vi)(JATP) was 1.33 and 3.84, respectively. Thus, C(vi)(JATP) were specifically increased under conditions B only for steps involved in ADP turnover and for Complex I in permeabilized cardiomyocytes within Mitochondrial Interactosome, a supercomplex consisting of MtCK, ATP-Synthasome, voltage dependent anion channel associated with tubulin βII which restricts permeability of the mitochondrial outer membrane.     

Myofibrillar creatine kinase: reversible binding to contractile proteins, stoichiometric ratio to myosin and its functional role

Rat heart myofibrils were isolated and purified in three different media: sucrose medium; EGTA medium; EGTA+ATP medium. All preparations were characterized by similar Ca2+-sensitive ATPase activities and were practically free of mitochondrial and sarcolemmal contaminations. However, they contained different amounts of creatine kinase. In preparations which showed the most intact ultrastructure, the activity of creatine kinase was 0.99 +/- 0.12 IU/mg. It was found that creatine kinase can be bound to myofibrils in a reversible manner with Kd = 0.16 mg/ml = 1.8 X 10(-6) M; the creatine kinase/myosin ratio was estimated to be approximately 1:10. The localization of creatine kinase was found to be a basis for the high turnover rate of ATP in the coupled creatine kinase and ATPase reactions occurring in cardiac myofibrils.     

31P-saturation-transfer nuclear-magnetic-resonance measurements of phosphocreatine turnover in guinea-pig brain slices.

The technique of 31P saturation-transfer n.m.r. was used to determine the forward and the reverse rate constants of creatine phosphotransferase in superfused guinea-pig cerebral tissues in vitro. The calculated forward rate constant of 0.22 +/- 0.03s-1 compared well with a previously reported value for rat brain in vivo [Shoubridge, Briggs & Radda (1982) FEBS Lett. 140, 288-292]. The reverse rate constant was found to be 0.55 +/- 0.10s-1. 3. By using concentrations of ATP and phosphocreatine estimated previously for this superfused preparation [Cox, Morris, Feeney & Bachelard (1983) Biochem. J. 212, 365-370], forward and reverse flux rates were calculated to be 0.68 and 0.72 mumol X s-1 X g-1 respectively. The concordance of forward and reverse fluxes contrasts with the situation observed in vitro in other tissues, and suggests that the creatine phosphotransferase reaction is at equilibrium under the conditions used here. 4. Lowering the concentration of glucose in the superfusing medium from 10mM to 0.5mM had no significant effect on phosphocreatine concentration or on the forward (ATP-generating) flux through creatine phosphotransferase. The results indicate that a normal phosphocreatine content in the presence of lowered glucose availability is reflected by an unchanged turnover rate.     

Cardiac creatine kinase metabolite compartments revealed by NMR magnetization transfer spectroscopy and subcellular fractionation

In the perfused rat heart NMR inversion transfer revealed the existence of a compartment of ATP not exchanging through creatine kinase (CK), as demonstrated by an apparent discrepancy between the forward (F(f)) and reverse (F(r)) CK flux if this compartment was neglected in the analysis [Joubert et al. (2000) Biophys. J. 79, 1-13]. To localize this compartment, CK fluxes were measured by inversion of PCr (inv-PCr) or gamma ATP (inv-ATP), and the distribution of metabolites between mitochondria and cytosol was studied by subcellular fractionation. Physiological conditions were designed to modify the concentration and distribution of CK metabolites (control, adenylate depletion, inhibition of respiration, KCl arrest). Depending on cardiac activity, mitochondrial ATP (mito-ATP) assessed by fractionation varied from 11% to 30% of total ATP. In addition, the apparent flux discrepancy increased together with mito-ATP (F(f)/F(r) ranged from 0.85 to 0.50 in inv-PCr and from 1.13 to 1.88 in inv-ATP). Under conditions masking the influence of the ATP-P(i) exchange on CK flux, the ATP compartment could be directly quantified by the apparent flux discrepancy; its size was similar to that of mito-ATP measured by fractionation. Thus NMR inversion technique is a potential tool to assess metabolite compartmentation in the whole organ.     

Use of inversion spin transfer to monitor creatine kinase kinetics in rat skeletal muscle in vivo

A simple multipulse sequence has been used to monitor creatine kinase kinetics in rat skeletal muscle in vivo. Using these procedures, the forward (ATP synthesis) and reverse fluxes (phosphocreatine synthesis) have been calculated to be 8.98 +/- 0.6 and 10.7 +/- 0.8 mumoles/g wet wt/s (n = 5) respectively. These results suggest that in resting skeletal muscle most of the gamma ATP observed in 31P NMR spectra is cytosolic and rapidly exchanging with phosphocreatine. The high flux rates reflect the high catalytic capacity of creatine kinase in skeletal muscle.     

Rate of phosphate release after photoliberation of adenosine 5'-triphosphate in slow and fast skeletal muscle fibers.

Inorganic phosphate (Pi) release was determined by means of a fluorescent Pi-probe in single permeabilized rabbit soleus and psoas muscle fibers. Measurements of Pi release followed photoliberation of approximately 1.5 mM ATP by flash photolysis of NPE-caged ATP in the absence and presence of Ca2+ at 15 degrees C. In the absence of Ca2+, Pi release occurred with a slow rate of 11 +/- 3 microM . s-1 (n = 3) in soleus fibers and 23 +/- 1 microM . s-1 (n = 10) in psoas fibers. At saturating Ca2+ concentrations (pCa 4.5), photoliberation of ATP was followed by rapid force development. The initial rate of Pi release was 0.57 +/- 0.05 mM . s-1 in soleus (n = 13) and 4.7 +/- 0.2 mM . s-1 in psoas (n = 23), corresponding to a rate of Pi release per myosin head of 3.8 s-1 in soleus and 31.5 s-1 in psoas. Pi release declined at a rate of 0.48 s-1 in soleus and of 5.2 s-1 in psoas. Pi release in soleus was slightly faster in the presence of an ATP regenerating system but slower when 0.5 mM ADP was added. The reduction in the rate of Pi release results from an initial redistribution of cross-bridges over different states and a subsequent ADP-sensitive slowing of cross-bridge detachment.     

Reaction rates of creatine kinase and ATP synthesis in the isolated rat heart. A 31P NMR magnetization transfer study

The NMR technique of magnetization transfer can be used to define intracellular reaction kinetics. In order to determine the relationship between ATP synthesis and flux through the creatine kinase reaction in the intact heart, we used this technique to measure flux through the creatine kinase reaction in the isolated, isovolumic rat heart at five levels of cardiac performance and oxygen consumption. The unidirectional reaction rate constants (s-1) calculated from a two-site exchange model for both the forward and reverse creatine kinase reactions increased with cardiac performance and oxygen consumption. As the rate-pressure product varied from 0 to 44.7 X 10(3) mm Hg/min and oxygen consumption rose from 5.9 to 45.8 mumol of O2/g dry weight/min, kforward increased from 0.27 to 1.30 and kreverse increased from 0.31 to 1.14. The relationship between creatine kinase flux and oxygen consumption, and thus ATP synthesis, took the form of the Michaelis-Menten equation. Rates of ATP synthesis estimated from magnetization transfer were similar to values calculated from oxygen consumption. The longitudinal relaxation time of creatine phosphate (2.06 s), the gamma-phosphorus atom of ATP (0.75 s), and inorganic phosphate (0.81 s) did not change with cardiac performance. These results show that myocardial energy transfer via the creatine kinase reaction is closely coupled to energy production.     

Evidence for myocardial ATP compartmentation from NMR inversion transfer analysis of creatine kinase fluxes

The interpretation of creatine kinase (CK) flux measured by (31)P NMR magnetization transfer in vivo is complex because of the presence of competing reactions, metabolite compartmentation, and CK isozyme localization. In the isovolumic perfused rat heart, we considered the influence of both ATP compartmentation and ATP-P(i) exchange on the forward (F(f): PCr --> ATP) and reverse (F(r)) CK fluxes derived from complete analysis of inversion transfer. Although F(f) should equal F(r) because of the steady state, in both protocols when PCr (inv-PCr) or ATP (inv-ATP) was inverted and the contribution of ATP-P(i) was masked by saturation of P(i) (sat-P(i)), F(f)/F(r) significantly differed from 1 (0.80 +/- 0.06 or 1.32 +/- 0.06, respectively, n = 5). These discrepancies could be explained by a compartment of ATP (f(ATP)) not involved in CK. Consistently, neglecting ATP compartmentation in the analysis of CK in vitro results in an underestimation of F(f)/F(r) for inv-PCr and its overestimation for inv-ATP. Both protocols gave access to f(ATP) if the system was adequately analyzed. The fraction of ATP not involved in CK reaction in a heart performing medium work amounts to 20-33% of cellular ATP. Finally, the data suggest that the effect of sat-P(i) might not result only from the masking of ATP-P(i) exchange.     

Regulation of energy flux through the creatine kinase reaction in vitro and in perfused rat heart. 31P-NMR studies

Fluxes catalyzed by soluble creatine kinase (MM) in equilibrium in vitro and by the creatine kinase system in perfused rat hearts were studied by 31P-NMR saturation transfer method. It was found that in vitro both forward and reverse fluxes through creatine kinase at equilibrium were almost equal and very stable to changes in phosphocreatine/creatine ratio (from 0.2 to 3.0) as well as to changes in pH (from 7.4 to 6.5 or 8.1), free Mg2+ concentration and 2-fold decrease of total adenine nucleotides and creatine pools (from 8.0 to 4.0 mM and from 30 to 14 mM, respectively). In the rat hearts perfused by the Langendorff method the creatine kinase-catalyzed flux from phosphocreatine to ATP was increased by 50% when oxygen consumption grew from 8 to 55 mumol/min per g of dry wt. due to transition from rest to high workload. These changes could not be exclusively explained on the basis of the equilibrium model by activation of heart creatine kinase due to some decrease in [phosphocreatine]/[creatine] ratio (from 1.8 to 0.8) observed during transition from rest to high workload. Analysis of our data showed that an increase in the flux via creatine kinase is correlated with an increase in the rate of ATP synthesis with a linearity coefficient higher than 1.0. These data are more consistent with the concept of energy channeling by phosphocreatine shuttle than with that of the creatine kinase equilibrium in the heart.     

The activity of creatine kinase in frog skeletal muscle studied by saturation-transfer nuclear magnetic resonance.

1. The activity of creatine kinase in intact anaerobic frog muscle at 4 degrees C at rest and during contraction was investigated by using saturation-transfer 31P n.m.r. 2. At rest, the measured forward (phosphocreatine to ATP) reaction flux was 1.7 X 10(-3) M . s-1 and the backward flux was 1.2 X 10(-3) M . s-1. The large magnitude of both fluxes shows that creatine kinase is active in resting muscle, so the observed constancy of [phosphocreatine] demonstrates that the enzyme and its substrates are at equilibrium. 3. The apparent discrepancy between the fluxes must arise largely from an underestimation of the backward flux resulting from interaction of ATP with other systems, e.g. via adenylate kinase. For purposes of further calculation we have therefore adopted 1.6 X 10(-3) M . s-1 as an estimate of both fluxes. 4. During contraction, when the creatine kinase reaction is no longer at equilibrium, the net rate of phosphocreatine breakdown, estimated directly from the change in area of the inorganic phosphate peak, was 0.75 X 10(-3) M . s-1. Saturation transfer indicates that the forward reaction flux remains at approx. 1.6 X 10(-3) M . s-1 and the backward flux decreases to about 0.85 X 10(-3) M . s-1. 5. The activity of creatine kinase during contraction is large enough to account for the well-established observation that, during contraction, the concentration of ATP falls by less than 2-3%. The reaction catalysed by creatine kinase is driven forward during contraction by the large relative increase in the concentration of free ADP, which is more than doubled. 6. The observation that the forward flux does not increase during contraction and that the backward flux decreases can most simply be explained on the basis of competition of reactants for a limited amount of enzyme.     

Respiratory control in the glucose perfused heart. A 31P NMR and NADH fluorescence study

The phosphate metabolites, adenosine diphosphate (ADP), inorganic phosphate (Pi), and adenosine triphosphate (ATP), are potentially important regulators of mitochondrial respiration in vivo. However, previous studies on the heart in vivo and in vitro have not consistently demonstrated an appropriate correlation between the concentration of these phosphate metabolites and moderate changes in work and respiration. Recently, mitochondrial NAD(P)H levels have been proposed as a potential regulator of cardiac respiration during alterations in work output. In order to understand better the mechanism of respiratory control under these conditions, we investigated the relationship between the phosphate metabolites, the NAD(P)H levels, and oxygen consumption (Q02) in the isovolumic perfused rat heart during alterations in work output with pacing. ATP, creatine phosphate (CrP), Pi and intracellular pH were measured using 31P NMR. Mitochondrial NAD(P)H levels were monitored using spectrofluorometric techniques. Utilizing glucose as the sole substrate, an increase in paced heart rate led to an increase in Q02 from 1.73 +/- 0.09 to 2.29 +/- 0.12 mmol Q2/h per g dry wt. No significant changes in the levels of Pi, PCr, ATP, or the calculated ADP levels were detected. Under identical conditions, an increase in heart rate was associated with a 23 + 3% increase in NAD(P)H fluorescence. Thus, under the conditions of these studies, an increase in Q02 was not associated with an increase in ADP or Pi. In contrast, increases in Q02 were associated with an increase in NAD(P)H. These data are consistent with the notion that increases in the mitochondrial NADH redox state regulate steady-state levels of respiration when myocardial work is increased.     

Imaging of human brain creatine kinase activity in vivo

Creatine kinase activity and high-energy phosphate concentration have been investigated using localized 31P spectroscopy in the human brain in vivo. The phase-modulated rotating frame imaging technique, incorporating magnetization transfer and inversion recovery, has been used to produce a 1-dimensional rate profile map of steady-state enzyme activity. Large differences in the flux from phosphocreatine (PCr) to ATP have been discovered between volumes of human brain consisting of predominantly gray (2.0 cm) and white (4.5 cm) matter. The concentration of PCr changes slightly (2.0 cm = 5.20 +/- 0.45 mmol.l-1, 4.5 cm = 4.63 +/- 0.31 mmol.l-1), while the ATP concentration remains within limits (3.30 +/- 0.4 mmol.l-1). No change in pHi was detected between the two regions in normal volunteers (n = 6). The forward rate constant of the PCr----ATP reaction in regions of predominantly gray matter (0.30 +/- 0.04 s-1) was twice that of white matter (0.16 +/- 0.02 s-1) in vivo.     

Phosphate free perfusion prevents washout of tissue creatine in Langendorff perfused rabbit heart.

Rabbit hearts were perfused with Krebs-Henseleit bicarbonate buffer supplemented with 15 mM glucose and 10 mU/ml of insulin +/- Pi. At the end of 60 min the hearts were freeze-clamped and the content of ATP, creatine phosphate, creatine, lactate, pyruvate, DHAP and 3-P glycerate were determined enzymatically in neutralized perchloric acid tissue extracts. The free cytosolic ADP and Pi and the cytosolic NAD+ redox and phosphorylation potentials were calculated from the measured metabolite concentrations. Pi free perfusion resulted in increased creatine, free cytosolic ADP and cytosolic phosphorylation potential, decreased calculated free Pi and no change in cardiac ATP and creatine phosphate content. The increase in the cytosolic phosphorylation potential was due to the lowering of cytosolic free Pi. The increase in ADP was due to the increase in creatine. The increase in creatine appeared to be due to an inhibition of creatine efflux from the heart during Pi free perfusion which was mediated by an enhanced Na+ electrochemical gradient.     

Regulation of energy flux through the creatine kinase reaction in vitro and in perfused rat heart: P-NMR studies

Fluxes catalyzed by soluble creatine kinase (MM) in equilibrium in vitro and by the creatine kinase system in perfused rat hearts were studied by ³¹P-NMR saturation transfer method. It was found that in vitro both forward and reverse fluxes through creatine kinase at equilibrium were almost equal and very stable to changes in ratio (from 0.2 to 3.0) as well as to changes in pH (from 7.4 to 6.5 or 8.1), free Mg²⁺ concentration and 2-fold decrease of total adenine nucleotides and creatine pools (from 8.0 to 4.0 mM and from 30 to 14 mM, respectively). In the rat hearts perfused by the Langendorff method the creatine kinase-catalyzed flux from phosphocreatine to ATP was increased by 50% when oxygen consumption grew from 8 to 55 μmol/min per g of dry wt. due to transition from rest to high workload. These changes could not be exclusively explained on the basis of the equilibrium model by activation of heart creatine kinase due to some decrease in ratio (from 1.8 to 0.8) observed during transition from rest to high workload. Analysis of our data showed that an increase in the flux via creatine kinase is correlated with an increase in the rate of ATP synthesis with a linearity coefficient higher than 1.0. These data are more consistent with the concept of energy channeling by phosphocreatine shuttle than with that of the creatine kinase equilibrium in the heart.     

Kinetics of ATP and inorganic phosphate release during hydrolysis of ATP by rabbit skeletal actomyosin subfragment 1. Oxygen exchange between water and ATP or phosphate

We have used the technique of phosphate: water oxygen exchange to measure the rate of ATP and Pi release and Pi binding to myosin subfragment 1 and actomyosin subfragment 1 from rabbit skeletal muscle. The oxygen exchange distributions for ATP and Pi release fit a simple kinetic model with a single set of rate constants for each step. For actomyosin subfragment 1 (20 degrees C, pH 7.0, I = 50 mM), the rate constant governing ATP release is approximately 8 s-1, Pi release is at approximately 60 s-1 and Pi rebinds to an ADP state at greater than 120 M-1 s-1. These rate constants are similar to those that may occur for undistorted cross-bridges within glycerinated rabbit psoas fibers (Bowater, R., Webb, M. R., and Ferenczi, M. A. (1989) J. Biol. Chem. 264, 7193-7201.     

Activity of creatine kinase in a contracting mammalian muscle of uniform fiber type.

We investigated whether the creatine kinase-catalyzed phosphate exchange between PCr and gamma ATP in vivo equilibrated with cellular substrates and products as predicted by in vitro kinetic properties of the enzyme, or was a function of ATPase activity as predicted by obligatory "creatine phosphate shuttle" concepts. A transient NMR spin-transfer method was developed, tested, and applied to resting and stimulated ex vivo muscle, the soleus, which is a cellularly homogeneous slow-twitch mammalian muscle, to measure creatine kinase kinetics. The forward and reverse unidirectional CK fluxes were equal, being 1.6 mM.s-1 in unstimulated muscle at 22 degrees C, and 2.7 mM.s-1 at 30 degrees C. The CK fluxes did not differ during steady-state stimulation conditions giving a 10-fold range of ATPase rates in which the ATP/PCr ratio increased from approximately 0.3 to 1.6. The observed kinetic behavior of CK activity in the muscle was that expected from the enzyme in vitro in a homogeneous solution only if account was taken of inhibition by an anion-stabilized quaternary dead-end enzyme complex: E.Cr.MgADP.anion. The CK fluxes in soleus were not a function of ATPase activity as predicted by obligatory phosphocreatine shuttle models for cellular energetics.     

87Rb, 23Na and 31P nuclear magnetic resonance spectroscopy of the perfused rat kidney

87Rb, 23Na and 31P nuclear magnetic resonance (NMR) were used to monitor changes in renal cations and energetics during the induction of hypoxia in the isolated perfused rat kidney. The NMR-determined unidirectional Rb+ flux in normoxic kidneys was shown to be a good measure of net intracellular K+ influx in the perfused rat kidney model. The changes in 87Rb, 23Na and 31P spectra following the induction of hypoxia are consistent with hypoxic depletion of intracellular adenosine triphosphate (ATP) and a subsequent decrease in Na-K-ATPase transport activity. The exponential rate constant for 87Rb+ efflux measured during Rb+ uptake in normoxic kidneys (0.12 +/- 0.01 min-1) was not significantly different to the rate constant for 87Rb+ efflux during the induction of hypoxia (0.16 +/- 0.07 min-1). We conclude that there is no direct effect of hypoxia on renal cellular membrane integrity and that renal cell sensitivity to hypoxia is due to an inability to sustain cellular ion gradients following depletion of intracellular ATP.     

Analysis of 31P NMR spectra of enzyme-bound reactants and products of adenylate kinase using density matrix theory of chemical exchange

31P NMR spectra of equilibrium mixtures of enzyme-bound reactants and products of the adenylate kinase reaction (formula; see text) were analyzed by using computer simulations based on density matrix theory of chemical exchange. Since adenylate kinase has the unique feature that the reactants in the reverse direction are both ADP molecules, which are indistinguishable off the enzyme, the density matrix equations are formulated for the ABC + D in equilibrium A'B' + A"B" exchange appropriate for the reaction, in which the interchange of A'B' and A"B" is explicitly introduced. It is shown that the consideration of this interchange is essential to explain the experimentally observed line shapes. By comparison of the computer-simulated spectra with various values for the rates of the exchange with the experimental spectra for porcine adenylate kinase at pH 7.0 and T = 4 degrees C, the following characteristic rates were determined: interconversion rates, 375 +/- 30 s-1 (ATP formation) and 600 +/- 50 s-1 (ADP formation); interchange rates of donor and acceptor ADP's, 100 +/- 30 s-1 (in the presence of optimal Mg2+ concentration), 1500 +/- 100 s-1 (in the absence of Mg2+). It is shown that under the conditions of the experiments the interchange rate is the lower limit of the dissociation rate of ADP (or MgADP from the acceptor site if Mg2+ was present) from the enzyme complexes. The significance of these interchange rates and their values relative to the interconversion rates is discussed with special reference to the role of the Mg2+ ion in the differentiation of the two nucleotide binding sites on adenylate kinase.