Magnetization Transfer Methods Research Articles

Macromolecular Proton Fraction as a Myelin Biomarker: Principles, Validation, and Applications.

Macromolecular proton fraction (MPF) is a quantitative MRI parameter describing the magnetization transfer (MT) effect and defined as a relative amount of protons bound to biological macromolecules with restricted molecular motion, which participate in magnetic cross-relaxation with water protons. MPF attracted significant interest during past decade as a biomarker of myelin. The purpose of this mini review is to provide a brief but comprehensive summary of MPF mapping methods, histological validation studies, and MPF applications in neuroscience. Technically, MPF maps can be obtained using a variety of quantitative MT methods. Some of them enable clinically reasonable scan time and resolution. Recent studies demonstrated the feasibility of MPF mapping using standard clinical MRI pulse sequences, thus substantially enhancing the method availability. A number of studies in animal models demonstrated strong correlations between MPF and histological markers of myelin with a minor influence of potential confounders. Histological studies validated the capability of MPF to monitor both demyelination and re-myelination. Clinical applications of MPF have been mainly focused on multiple sclerosis where this method provided new insights into both white and gray matter pathology. Besides, several studies used MPF to investigate myelin role in other neurological and psychiatric conditions. Another promising area of MPF applications is the brain development studies. MPF demonstrated the capabilities to quantitatively characterize the earliest stage of myelination during prenatal brain maturation and protracted myelin development in adolescence. In summary, MPF mapping provides a technically mature and comprehensively validated myelin imaging technology for various preclinical and clinical neuroscience applications.

Longitudinal assessment of recovery after spinal cord injury with behavioral measures and diffusion, quantitative magnetization transfer and functional magnetic resonance imaging.

Spinal cord injuries (SCIs) are a leading cause of disability and can severely impact the quality of life. However, to date, the processes of spontaneous repair of damaged spinal cord remain incompletely understood, partly due to a lack of appropriate longitudinal tracking methods. Noninvasive, multiparametric magnetic resonance imaging (MRI) provides potential biomarkers for the comprehensive evaluation of spontaneous repair after SCI. In this study in rats, a clinically relevant contusion injury was introduced at the lumbar level that impairs both hindlimb motor and sensory functions. Quantitative MRI measurements were acquired at baseline and serially post-SCI for up to 2 wk. The progressions of injury and spontaneous recovery in both white and gray matter were tracked longitudinally using pool-size ratio (PSR) measurements derived from quantitative magnetization transfer (qMT) methods, measurements of water diffusion parameters using diffusion tensor imaging (DTI) and intrasegment functional connectivity derived from resting state functional MRI. Changes in these quantitative imaging measurements were correlated with behavioral readouts. We found (a) a progressive decrease in PSR values within 2 wk post-SCI, indicating a progressive demyelination at the center of the injury that was validated with histological staining, (b) PSR correlated closely with fractional anisotropy and transverse relaxation of free water, but did not show significant correlations with behavioral recovery, and (c) preliminary evidence that SCI induced a decrease in functional connectivity between dorsal horns below the injury site at 24 h. Findings from this study not only confirm the value of qMT and DTI methods for assessing the myelination state of injured spinal cord but indicate that they may also have further implications on whether therapies targeted towards remyelination may be appropriate. Additionally, a better understanding of changes after SCI provides valuable information to guide and assess interventions.

R1correction in amide proton transfer imaging: indication of the influence of transcytolemmal water exchange on CEST measurements

Amide proton transfer (APT) imaging may potentially detect mobile proteins/peptides non-invasively in vivo, but its specificity may be reduced by contamination from other confounding effects such as asymmetry of non-specific magnetization transfer (MT) effects and spin-lattice relaxation with rate R1 (=1/T1). Previously reported spillover, MT and R1 correction methods were based on a two-pool model, in which the existence of multiple water compartments with heterogeneous relaxation properties in real tissues was ignored. Such simple models may not adequately represent real tissues, and thus such corrections may be unreliable. The current study investigated the effectiveness and accuracy of correcting for R1 in APT imaging via simulations and in vivo experiments using tumor-bearing rats subjected to serial injections of Gd-DTPA that produced different tissue R1 values in regions of blood-brain-barrier breakdown. The results suggest that conventional measurements of APT contrast (such as APT* and MTRasym ) may be significantly contaminated by R1 variations, while the R1 -corrected metric AREX* was found to be relatively unaffected by R1 changes over a broad range (0.4-1 Hz). Our results confirm the importance of correcting for spin-lattice relaxation effects in quantitative APT imaging, and demonstrate the reliability of using the observed tissue R1 for corrections to obtain more specific and accurate measurements of APT contrast in vivo. The results also indicate that, due to relatively fast transcytolemmal water exchange, the influence of intra- and extracellular water compartments on CEST measurements with seconds long saturation time may be ignored in tumors.

Enhancement of magnetization transfer effects by inter-molecular multiple quantum filtered NMR

There are a number of methods that give MRI contrasts based on changes of the water M z magnetization as a result of magnetization transfer to macromolecules. In the present work we report that a combination of these methods with inter-molecular multiple quantum coherences (iMQC) gives enhanced effects. For the magnetization transfer contrast (MTC) method an effect of ( M z / M 0) becomes ( M z / M 0) l where l is the rank of the tensors constituting the iMQC. A similar trend was found upon combining iMQC with the Goldman–Shen experiment. It is pointed out that the method is general for all magnetization transfer methods, including the nuclear Overhauser effect.

Experimental and Theoretical Study of the Hydride Migration to Ethylene in an Electron-Rich Cobalt Complex

The kinetics and energetics of β-migratory insertion in the electron-rich cobalt ethylene hydride complex [(PMe3)3Co(H)(C2H4)] (1) were studied with experimental and theoretical techniques. The activation parameters were established in toluene solution using 1H magnetization transfer methods. Data obtained over the temperature range 265−290 K gave ΔH⧧ = 16.4 ± 0.6 kcal mol-1 and ΔS⧧ = 8 ± 2 cal mol-1 K-1. The structural and energetic parameters have also been determined by DFT electronic structure calculations. The global minimum thus obtained is in agreement with the experimental findings. The same holds true for the activation energies for migratory insertion as well as for β-elimination. Comparison of the activation parameters with those for other complexes suggests an increase of the barrier of migratory insertion with increasing electron richness of the metal center, which destabilizes species with agostic metal−H−C interactions. It is proposed that there may even be cases where an agostic structure ...

PH imaging

Acid-base balance is altered in a variety of common pathologies, including COPD, ischemia, renal failure, and cancer. Because of robust cellular pH homeostatic mechanisms, most of the pathological alterations in pH are expressed as changes in the extracellular, systemic pH. There are data to indicate that altered pH is not simply an epiphenomenon of metabolic or physiologic imbalance but that chronic pH alterations can have important sequelae. MRSI and MRI measurements indicate that pH gradients of up to 1.0 pH unit can exit within 1-cm distance. Although measurement of blood pH can indicate systemic problems, it cannot pinpoint the lesion or quantitatively assess the magnitude of excursion from normal pHe. Hence, there is a need to develop pHe measurement methods with high spatiotemporal resolution. The two major approaches being investigated include magnetization transfer methods and relaxation methods. pH-dependent MT effects can observed with endogenous signals or exogenously applied CEST agents. While endogenous signals have the advantage of being fully noninvasive and relatively straightforward to apply, they lack a full biophysical characterization and dynamic range that might be afforded by future CEST agents. pH-dependent relaxivity also requires the injection or infusion of exogenous contrast reagents. In both MT and relaxographic approaches, the magnitude of the effect, and, thus, the ability to quantify pHe, depends on a spatially and temporally varying concentration of the CR. A number of approaches have been proposed to solve this problem and, once it is solved, pH imaging methods will be applicable to human clinical pathologies.

Accurate quantitation of water-amide proton exchange rates using the phase-modulated CLEAN chemical EXchange (CLEANEX-PM) approach with a Fast-HSQC (FHSQC) detection scheme.

Measurement of exchange rates between water and NH protons by magnetization transfer methods is often complicated by artifacts, such as intramolecular NOEs, and/or TOCSY transfer from C alpha protons coincident with the water frequency, or exchange-relayed NOEs from fast exchanging hydroxyl or amine protons. By applying the Phase-Modulated CLEAN chemical EXchange (CLEANEX-PM) spin-locking sequence, 135 degrees (x) 120 degrees (-x) 110 degrees (x) 110 degrees (-x) 120 degrees (x) 135 degrees (-x) during the mixing period, these artifacts can be eliminated, revealing an unambiguous water-NH exchange spectrum. In this paper, the CLEANEX-PM mixing scheme is combined with Fast-HSQC (FHSQC) detection and used to obtain accurate chemical exchange rates from the initial slope analysis for a sample of 15N labeled staphylococcal nuclease. The results are compared to rates obtained using Water EXchange filter (WEX) II-FHSQC, and spin-echo-filtered WEX II-FHSQC measurements, and clearly identify the spurious NOE contributions in the exchange system.

A dynamic 15N NMR study of kinetic hydrogen/deuterium isotope and tunnel effects on the triple proton transfer in crystalline 3,5‐dimethylpyrazole

AbstractUsing dynamic solid state 15N CPMAS NMR spectroscopy (CP≡cross polarization, MAS≡magic angle spinning) the kinetics of the degenerate intermolecular triple proton and deuteron transfer in the cyclic trimers of 15N‐labeled polycrystalline 3,5‐dimethylpyrazole (DMP) have been studied in a wide temperature range. At high temperatures, rate constants of the various isotopic HHH, HHD, HDD, and DDD transfer reactions are obtained in the millisecond timescale by lineshape analysis of partially deuterated doubly 15N‐labeled DMP. At low temperatures, the kinetics were followed by magnetization transfer methods in the laboratory frame. In order to suppress artifacts arising from 15N‐spin diffusion these experiments were performed on singly 15N labeled DMP, partially diluted in the non‐labeled material. As multiple kinetic hydrogen/deuterium isotope effects on triple proton transfer reactions have not yet been studied these effects are modeled theoretically for the single barrier case involving a concerted proton motion and for the triple barrier case where the three protons are transferred stepwise. The experimental kinetic isotope effects obey the rule of the geometric mean, i.e. kHHH/kHHD ≈︁ kHHD/kHDD ≈︁ kHDD/kDDD ≈︁ 3.6 i.e. ≈︁ kHHH/kDDD ≈︁ 47 at 300 K, which is indicative of a single barrier where all hydrons loose zero‐point energy in the transition state. At low temperatures, strong deviations from an Arrhenius behavior are observed for all isotopic reactions, indicating incoherent triple hydron tunneling processes, which are described in terms of a modified Bell tunneling model.

Kinetic Study of the Dynamic Behavior of [M(C6F5)X(OPPynPh3-n)] (M = Pd, Pt; X = C6F5, Halide; n = 1−3): Activation Parameters for the Restricted Rotation about the M−Aryl Bond and for the Py Associative Exchange

The behavior in CDCl3 of complexes of the type [M(C6F5)X(OPPynPh3-n)] (M = Pd, Pt; X = C6F5; halide; n = 1−3) has been studied by 19F and 1H NMR spectroscopy. For the nonplanar N,N-chelating ligands with n = 2, 3, two processes have been observed and their activation parameters, ΔG⧧, ΔH⧧, and ΔS⧧, have been determined, using magnetization transfer (MT) or line-shape analysis methods. The rotation of the C6F5 groups about the M−Cipso bond occurs in the square-planar species without dissociation, and its rate depends on the size of the coordinated atom X, in the order C6F5 > Cl > Br > I. The rotation for the last three is very slow and is detected only by MT. With OPPy3 the occurrence of associative exchange of free and coordinated Py groups is observed (studied only for X = C6F5, Cl), the rate depending on M and X in the order Pd > Pt and Cl > C6F5. Only for [Pd(C6F5)Cl(OPPy3)] is this rate faster than the C6F5 rotation, producing the effect of an apparent rotation with anomalously low activation parameter...

Structural studies of imidazole-cytochrome c: Resonance assignments and structural comparison with cytochrome c

Two-dimensional nuclear magnetic resonance spectroscopy (2D NMR) was used to obtain extensive proton resonance assignments of Im-cyt c complex which is a possible analog of a late folding intermediate of cytochrome c. Assignments were made nearly completely for the main-chain and the side-chain protons (all except Gly29). As starting points for the assignment of the Im-cyt c, a limited set of protons was initially assigned by use of 2D NMR magnetization transfer methods to correlated resonances in the Im-cyt c with assigned resonances in the native cyt c. The subsequent search focused on recognition of main-chain NOE connectivity patterns, with use of previously assigned residues to place NOE-connected segments within the amino acid sequence. The observed patterns of main-chain NOEs provided some structural information and suggested potentially significant differences between Im-cyt c and the native cyt c. Differences in NOES involving side-chain protons were reported and analyzed. There was evidence for conformational changes induced by the breakage of FeS bond. It was concluded that the Im-cyt c had undergone a rearrangement of several regions forming the heme pocket of the protein. The structural understanding of these effects of the mutation may be essential to elucidate the changes in function and kinetic mechanism of cyt c folding.

Comparison of ROESY and EXSY Methods Using Bloch Equations

A comparison of longitudinal and transverse frame magnetization transfer methods is provided using modified Bloch equations for a two-spin system representative of a methylene group exchanging between two chemically distinct sites. This simple formalism incorporates chemical shift, auto- and cross-relaxation terms, chemical exchange first-order rate constants and r.f. field terms for ROESY experiments. Overhauser and exchange magnetization transfer is emulated at three limits of molecular reorientation time (τc). The calculated build up curves suggest a parasitic effect of ROE on chemical exchange magnetization transfer. In addition, for molecules harboring spin systems exchanging between sites such that the exchange rate approximates the transverse cross-relaxation rate, and reorienting in solution at rates slower than that defined by the CAMELSPIN limit (ω0τc≈1.118), the calculations suggest observation of exchange or Overhauser cross peaks may be compromised. Finally, the effect of off-resonance spin locking r.f. power level is explored upon exchange or Overhauser build-up curve profiles. The results suggest off-resonance approaches that at low r.f. spin locking power may adversely affect ROE or exchange build-up rates and may compromise either exchange rate determination or internuclear distance estimation.

ChemInform Abstract: Structural Analysis of Oligosaccharide Chains of Glycolipids by Magnetization Transfer Methods

AbstractChemInform is a weekly Abstracting Service, delivering concise information at a glance that was extracted from about 100 leading journals. To access a ChemInform Abstract of an article which was published elsewhere, please select a “Full Text” option. The original article is trackable via the “References” option.

ＮＭＲ磁化移動法を利用した糖脂質糖鎖構造の解析

Identification of sugar components and sugar linkages is required for structural determination of oligosaccharide chains. Several magnetization transfer methods, such as multiple relayed COSY and homonuclear Hartmann-Hahn methods are useful to extract subspectra of constituent monosaccharides. Individual monosaccharides give characteristic cross peak patterns due to their chemical shifts and spin-spin couplings so that we can identify the sugar types. The linkages of each sugar residue can be subsequently determined by the analysis of NOESY spectra. Thus, the chemical structure of oligosaccharide chains can be elucidated by non-empirical manner. We have applied this method to determine the chemical structure of oligosaccharide chains of a novel glycolipid from a sea urchin.

Combination of 31P-NMR magnetization transfer and radioisotope exchange methods for assessment of an enzyme reaction mechanism: rate-determining steps of the creatine kinase reaction

The theoretical analysis of a reversible enzyme reaction performed in this work shows that the 31P-NMR magnetization (saturation) transfer technique combined with a radioisotope exchange method may potentially provide information on the position of rate-determining step(s). It depends on chemical shifts of NMR signals of nuclei of interest in free and enzyme-bound forms of substrate(s) and product(s) of the reaction. The creatine kinase reaction ( MgATP + creatine ▪ MgADP + P-creatine ) has been used as a model. Chemical shifts of 31P in binary, ternary and transitional state substrate-enzyme complexes have been estimated by the variable frequency saturation transfer (VFST) method. This method is based on selective irradiation of numerous points in the spectrum and observation of changes in the intensity of visible line(s) which occur due to chemical exchange between it and lines which are not visible in the routine spectrum. Also, dissociation rate constants of MgADP-containing complexes were determined. Magnetization exchange rates, P-creatine ▪[γ-P]MgATP and [β-P]MgADP ▪[β-P]MgATP, were compared with radioisotope exchange rates, [γ- 32P-MgATP ▪P-creatine and [ 3H]MgADP ▪MgATP at different [ P-creatine] [ creatine] ratios and at different temperatures. All these exchange rates were close to each other at 30–37°C and [ PCr] [ Cr] ratios lower than 2. It is concluded that phosphoryl group transfer is the rate-determining step of the overall creatine kinase reaction under these conditions. However, at lower temperatures (below 25°C) or at high [ PCr] [ Cr] ratios ([ADP] < 20 μM) the rate-determining step seems to be shifted toward dissociation of nucleotide substrates from enzyme-substrate complexes, since exchange rates became significantly different. This approach is useful for analysis of mechanism of enzymatic reactions and also can be applied to non-enzymatic reactions and evaluation of small rapidly exchangeable metabolite pools.

Assignment of paramagnetically shifted resonances in the 1H NMR spectrum of horse ferricytochrome c

The proton resonances of the heme, the axial ligands, and other hyperfine-shifted resonances in the 1H nuclear magnetic resonance spectrum of horse ferricytochrome c have been investigated by means of one- and two-dimensional nuclear Overhauser and magnetization transfer methods. Conditions for saturation transfer experiments in mixtures of ferro- and ferricytochrome c were optimized for the cross assignment of corresponding resonances in the two oxidation states. New resonance assignments were obtained for the methine protons of both thioether bridges, the beta and gamma meso protons, the propionate six heme substituent, the N pi H of His-18, and the Tyr-67 OH. In addition, several recently reported assignments were confirmed. All of the resolved hyperfine-shifted resonances in the spectrum of ferricytochrome c are now identified. The Fermi contact shifts experienced by the heme and ligand protons are discussed.

31P NMR studies of the thermodynamics and kinetics of the creatine kinase reaction.

The thermodynamic and kinetic parameters of the reaction catalyzed by creatine kinase (CK) were measured in vitro in the temperature range 13 to 35 degrees C, using 31P NMR spectroscopy, including magnetization transfer methods. The apparent equilibrium constant of the reaction and the associated enthalpy for the formation of ATP at 35 degrees C, pH 8.2, and excess [Mg2+] were 3.5 x 10(9) M-1 and -2.4 +/- 0.5 kcal/mol, respectively. The rates at equilibrium at 35 degrees C catalyzed by 1 unit/ml CK were 12.4 and 10.7 microM/s at pH 7 and 8, respectively. The rate constants per 1 unit CK/1 ml at 35 degrees C, pH 7, were 1.3 x 10(8) s-1 M-2 and 9.9 x 10(-3) s-1 M-1 in the direction of ATP and PCr formation, respectively. The activation energies in both directions were similar and corresponded to 15 +/- 2 kcal/mol at pH 7 and 17.5 +/- 1.5 kcal/mol at pH 8. Comparison of in vivo results with the above in vitro data may provide information regarding the activity and kinetics of the CK reaction.

Proton resonance assignments of horse ferricytochrome c

Two-dimensional nuclear magnetic resonance spectroscopy (2D NMR) was used to obtain extensive resonance assignments in the 1H NMR spectrum of horse ferricytochrome c. Assignments were made for the main-chain and C beta protons of 102 residues (all except Pro-44 and Gly-84) and the majority of side-chain protons. As starting points for the assignment of the oxidized protein, a limited set of protons was initially assigned by use of 2D NMR magnetization transfer methods to correlate resonances in the oxidized form with assigned resonances in the reduced form [Wand, A. J., Di Stefano, D. L., Feng, Y., Roder, H., & Englander, S. W. (1989) Biochemistry (preceding paper in this issue)]. Given the complexity of the spectrum due to the size of this protein (104 residues) and its paramagnetic center, the initial search for side-chain spin systems in J-correlated spectra was successful only for the simplest side chains, but the majority of NH-C alpha H-C beta H subspin systems (NAB sets) could be identified at this stage. The subsequent search for sequential NOE connectivities focused on NAB sets, with use of previously assigned residues to place NOE-connected segments within the amino acid sequence. Selective proton labeling of either the slowly or the rapidly exchanging amide sites was used to simplify the spectra, and systematic work at two temperatures was used to resolve ambiguities in the 2D NMR spectra. These approaches, together with the use of magnetization transfer methods to correlate reduced and oxidized cytochrome c spectra, provide multiple cross-checks to verify assignments.

31P magnetization transfer studies of creatine kinase kinetics in living rabbit brain.

The kinetics of the CK reaction in the living rabbit brain was studied by three 31P magnetization transfer methods: inversion recovery (IR), inversion transfer (IT), and steady-state saturation transfer (SSST). Longitudinal relaxation rates (tau -1) were determined from IR and IT experiments. The values were 0.88 +/- 0.08 s-1 for PCr and 2.45 +/- 0.39 s-1 for gamma-ATP. Analysis of the results of SSST experiments in which gamma-ATP was saturated yielded a forward rate constant kF of 0.53 +/- 0.07 s-1. Upon saturation of PCr no change in the gamma-ATP signal could be detected in SSST. An average reverse rate constant (kR +/- S.D.) of 0.52 +/- 0.04 s-1 was estimated by analyzing IT data from three experiments with selective inversion of gamma-ATP. The standard error of kR was 50%. The average [PCr]/[ATP] of 1.21 +/- 0.16 together with the values of kF and kR yielded a forward-to-reverse flux ratio of 1.23. Within our limits of accuracy this ratio was not significantly different from 1.0, thus suggesting that in the brain the forward and reverse CK fluxes are equal.

High-resolution calcium-43 NMR in solids

The resolution afforded by alkaline earth ion NMR in solution is often insufficient to obtain individual lines for chemically distinct sites, particularly in macromolecular environments (Z-4). The problem inherent in a small chemical shift range of about 70 ppm is aggravated further by broadening associated with the often complex spin relaxation driven by the nuclear electric quadrupole interactions with fluctuating electric field gradients (5). The dynamical part of the broadening may be defeated if the nucleus to be observed is immobilized. The solid-state experiment has been successful on a number of nonintegral spin quadrupole nuclei where the central (+f c-) -1) transition is exploited and the residual second-order quadrupole broadenings are minimized by rapid sample rotation at the magic angle (6-9). However, the possible gain in resolution is made at the cost of decreased sensitivity because only the central transition in a ; or $ manifold is observed (IO). In principle, the loss may be regained using magnetization-transfer methods such as those exploited by Pines, Gibby, and Waugh (II). Double-resonance approaches have been discussed for calcium fluoride (12,13), and a direct detection of calcium-43 reported using adiabatic demagnetization methods at low temperature (14). We report here observation of the high-resolution calcium-43 NMR spectrum using CP-MASS methods which demonstrates the feasibility of the more routine experiment in a noncubic environment and defines several of the critical experimental parameters. Figure 1 shows the CP-MASS calcium-43 NMR spectrum of calcium acetate obtained at 4.7 T using a spectrometer constructed in this laboratory. The relevant experimental parameters are summarized in the caption. The proton-calcium doubleresonance probe employed a Doty Scientific stator and rotor coupled to the proton tuning elements using a half wavelength coaxial line tapped at the proton null point for injection and detection of the calcium-43 resonance frequency. The spectrometer used Amplifier Research (AR-200L) and Henry Radio power amplifiers, Nicolet-GE 1280 data system, and a quadrature receiver built in the laboratory. The phase-shifting circuitry was designed after a very similar version by Robert MacKay, Monsanto Chemical Company. The match for the magnetization transfer was found by changing the power level on the calcium side while keeping the proton field fixed at 46 kHz; the optimum cross-polarization rate was found when the strength of the calcium rf field was approximately the same as that which gave w1 for calcium of 45 kHz in a saturated aqueous solution of calcium chloride. For calcium acetate, optimum contact times were long, in the tens of milliseconds range as shown in Fig. 2.

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.