Dynamics and Environment of Mitochondrial Water as Detected by 1 H NMR*

The dynamics and environment of water in suspen- sions of isolated rat liver mitochondria have been investigated by 1 H NMR. NMR longitudinal and transversal relaxation times ( T 1 and T 2 ) were measured in the resus- pension medium (2.65 s and 44.57 ms) and in mitochondrial suspensions (1.74 s and 23.14 ms), respectively. Re- sults showed monoexponential relaxation in both cases, suggesting a fast water exchange across the inner mito- chondrial membrane. Ferromagnetically induced shift of the extramitochondrial water with nonpermeant fer- romagnetic particles revealed no detectable water signal from the intramitochondrial compartment, confirm- ing the fast exchange case. Simulations on a two-compartment model indicated that the intra- mitochondrial water residence time has an upper limit of approximately 100 (cid:109) s. Calculated intramitochondrial relaxation times revealed that the intramitochondrial environment has an apparent viscosity 30 times larger than the resuspension medium and 15 times larger than the cytosol of erythrocytes. The higher apparent viscosity of the mitochondrial matrix could account for reduc- tions of more than one order of magnitude in the diffusion coefficient of water and other substrates, limitations in the rate of enzymatic reactions which are diffusion controlled and a more favorable formation of multienzyme complexes. (cid:50) K 0 exp ( (cid:50) (cid:116) / T 1 )) and M ( t ) (cid:53) K 1 (cid:49) M (0)exp ( (cid:50) (cid:116) / T 2 ), respec- tively. Curve fitting was performed using a nonlinear least squares regression program (IGOR TM , WaveMetrics, Lake Oswego, OR). Double exponential magnetization recoveries for T 1 and T 2 measurements were also fitted to evaluate the data for the existence of double exponential as opposed to single exponential behavior. The following equations were used: M ( t ) (cid:53) M a ( (cid:96) )(1 (cid:50) K 0exp( (cid:50) (cid:116) / T 1 a )) (cid:49) M b ( (cid:96) )(1 (cid:50) K 1exp( (cid:50) (cid:116) / T 1 b )), and M ( t ) (cid:53) K 0 (cid:49) K 1 (cid:49) M a (0)exp( (cid:50) (cid:116) / T 2 a ) (cid:49) M b (0)exp( (cid:50) (cid:116) / T 2 b ), where the a and b subscripts represent two magnetically different water environ- ments. Chi square values ( (cid:120) 2 ) obtained from the monoexponential and biexponential fits, were analyzed using the Student’s t test. A kinetic model was developed to estimate the water residence time in the intramitochondrial environment from measurements of the re- laxation times of the mitochondrial and the resuspension medium. For this purpose, we used a for modeling system dynamics in biology, based on the Euler algorithm for the numerical integration of simultaneous differential equations (STELLA TM , High Performance Systems, Lyme, NH). T 2 relaxation curves were simulated for different values of the water residence time in the intra- and extra- mitochondrial space and compared to the experimentally observed T 2 values of mitochondrial suspensions, using (cid:120) 2 criterion for the goodness of fit. These comparisons were further

The dynamics and environment of water in suspensions of isolated rat liver mitochondria have been investigated by 1 H NMR. NMR longitudinal and transversal relaxation times (T 1 and T 2 ) were measured in the resuspension medium (2.65 s and 44.57 ms) and in mitochondrial suspensions (1.74 s and 23.14 ms), respectively. Results showed monoexponential relaxation in both cases, suggesting a fast water exchange across the inner mitochondrial membrane. Ferromagnetically induced shift of the extramitochondrial water with nonpermeant ferromagnetic particles revealed no detectable water signal from the intramitochondrial compartment, confirming the fast exchange case. Simulations on a twocompartment model indicated that the intramitochondrial water residence time has an upper limit of approximately 100 s. Calculated intramitochondrial relaxation times revealed that the intramitochondrial environment has an apparent viscosity 30 times larger than the resuspension medium and 15 times larger than the cytosol of erythrocytes. The higher apparent viscosity of the mitochondrial matrix could account for reductions of more than one order of magnitude in the diffusion coefficient of water and other substrates, limitations in the rate of enzymatic reactions which are diffusion controlled and a more favorable formation of multienzyme complexes.
Adequate understanding of the dynamics of water at the cellular level involves the determination of the water exchange rate across the different intracellular membranes and the study of the water environment within the different organelles (1)(2)(3)(4). Considerable evidence has been accumulated with erythrocytes on the kinetics of water exchange across the plasma membrane (2, 4 -10), as well as on the physical properties of the cytosolic compartment (11). However, the transport of water across the inner mitochondrial membrane and the environmental properties of the intramitochondrial space remain poorly understood. These two aspects are of particular metabolic relevance since a general belief indicates that viscosity and slow diffusion of metabolites in the matrix could affect the activity of a variety of intramitochondrial enzymes (12)(13)(14)(15)(16). However, to our knowledge no direct measurements on the physical prop-erties of the intramitochondrial environment exist to support these hypotheses.
In this report we study the dynamics of water in mitochondrial suspensions, providing values for the mean residence time 1 (17) of water in the intramitochondrial space and estimates for matrix viscosity. Our methodology is based on comparisons of the 1 H NMR longitudinal (T 1 ) 2 and transversal (T 2 ) relaxation times of the water protons in the mitochondrial suspensions with those observed in the resuspension medium without mitochondria. This approach is specially suited for the noninvasive study of the water environment in biological systems since the magnetic relaxation properties of the water protons are a direct consequence of their translational and rotational motions.

MATERIALS AND METHODS
Preparation and Characterization of Rat Liver Mitochondria-Mitochondria were prepared by differential centrifugation (18) from the liver of adult male Wistar rats (250 -300 g) fed ad libitum using 300 mM mannitol, 0.5 mM EDTA (pH 7.2) as isolation medium and 300 mM mannitol, 20 mM HEPES/KOH (pH 7.2) as resuspension medium. Protein concentration was measured immediately after preparation by the biuret method using bovine serum albumin as a standard. Respiratory control ratios (RCR) were routinely determined polarographically in all mitochondrial preparations prior to NMR experiments using glutamate and malate as substrates (19). Preparations with RCRs smaller than 4 were discarded. Intramitochondrial volume was measured essentially as described by Dawson et al. (20). Mitochondrial suspensions (at 75 mg of protein/ml) were incubated for 3 min at 25°C, in a medium containing 3 H 2 O (100,000 cpm/ml) and [ 14 C]sucrose (100,000 cpm/ml) to determine the total water volume and the extramitochondrial volume, respectively. The difference between both volumes was taken as the matrix space. Electron microscopy was performed on three mitochondrial preparations following the protocol of Lang (21). Mitochondria showed the expected spherical morphology with internal cristae (17,22). 1 H NMR Spectroscopy-Longitudinal (T 1 ) and transversal (T 2 ) relaxation times of the water protons were measured on the resuspension medium without mitochondria and on mitochondrial suspensions prepared as described above. An AM-360 Bruker spectrometer (360. 13 MHz, 1 H frequency) equipped with a 5-mm 1 H selective probe was used. T 1 was determined by the inversion-recovery sequence (--/2acquire). T 2 was measured by the Carr-Purcell-Meiboom-Gill spin-echo sequence (/2----acquire). Acquisition conditions were: 7 s (/2) pulse, 10-ppm spectral width, 8K words data table, and 4 scans per spectrum. The temperature dependence of T 1 and T 2 was measured using a Bruker variable temperature unit (B-VT 1000, temperature stability Ϯ 0.1°C). In these experiments, a temperature-calibrated coaxial capillary containing ethylene glycol (100%) was inserted in * This work was supported in part by Grants PM 92/0011-PB 94/0011 from the Spanish DGICYT and AE-00219/94 from the Community of Madrid. The costs of publication of this article were defrayed in part by the payment of page charges. This article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact. ‡ Present address: Departamento de Cristalografía, Centro de Investigación y Desarrollo, C.S.I.C., Avda. Jordi Girona, 18 -26, 08031 Barcelona, Spain.
Nonpermeant dextran-coated ferromagnetic iron particles were prepared by alkalinizing (pH 11.0) a solution of Cl 2 Fe (10 mg/ml) and Cl 3 Fe (15 mg/ml) in the presence of dextran (M r 40,000, Pharmacia, Uppsala) (23). The ferromagnetic particles coated with dextran were separated from free dextran prior to use using a Sephacryl S-300 column (23). Electron microscopy of these preparations revealed spherical particles with diameters in the range of 30 -50 nm. Iron concentration of preparations was determined by the thiocyanate method, measuring the absorbance of the iron-thiocyanate complex at 460 nm (24).
Viscosity Measurements-Model solutions of resuspension medium with increasing concentration of glycerol (0, 10, 30, 60, and 75%) were prepared. The dynamic viscosity of the resuspension medium was measured (22°C) for three of these samples (i.e., partial substitution by glycerol at 0, 30, and 60%, v/v), using a Brookfield viscometer (model RVT, Brookfield Engineering Laboratories, Stoughton, MA). T 1 and T 2 measurements were performed on all the model solutions and compared with T 1 and T 2 measurements performed in mitochondrial suspensions.
Data Analysis and Model Simulations-T 1 and T 2 values were obtained from non linear three parameter fits of the longitudinal and transversal equilibrium magnetization recoveries to the equations , respectively. Curve fitting was performed using a nonlinear least squares regression program (IGOR TM , WaveMetrics, Lake Oswego, OR). Double exponential magnetization recoveries for T 1 and T 2 measurements were also fitted to evaluate the data for the existence of double exponential as opposed to single exponential behavior. The following equations were used: where the a and b subscripts represent two magnetically different water environments. Chi square values ( 2 ) obtained from the monoexponential and biexponential fits, were analyzed using the Student's t test.
A kinetic model was developed to estimate the water residence time in the intramitochondrial environment from measurements of the relaxation times of the mitochondrial suspension and the resuspension medium. For this purpose, we used a package for modeling system dynamics in biology, based on the Euler algorithm for the numerical integration of simultaneous differential equations (STELLA TM , High Performance Systems, Lyme, NH). T 2 relaxation curves were simulated for different values of the water residence time in the intra-and extramitochondrial space and compared to the experimentally observed T 2 values of mitochondrial suspensions, using 2 criterion for the goodness of fit. These comparisons were further completed with a test for randomness or trends of residuals in every fit (25). Fig. 1 summarizes the results of T 1 (A) and T 2 (B) measurements, performed on mitochondrial suspensions (closed circles) and on the resuspension medium without mitochondria (open circles). The water relaxation times observed in these suspensions, are determined by the decay of magnetically labeled water in the intramitochondrial space, in the external resuspension medium and by the exchange of magnetically labeled water between these two environments. T 1 (T 2 ) measurements of the resuspension medium (n ϭ 6) and of the mitochondrial suspensions (n ϭ 5) were always monoexponential with values of 2.65 Ϯ 0.2 s (44.57 Ϯ 2.2 ms) and 1.74 Ϯ 0.1 s (23.14 Ϯ 1.6 ms), respectively. These results indicate that the relaxation times of intramitochondrial water are significantly shorter than those of water in the resuspension medium. Furthermore, the results shown in Fig. 1 provide information on the rate of exchange of water between the two environments. A fast exchange rate between the intramitochondrial space and the resuspension medium would yield a single exponential relax-ation behavior, while a slow or intermediate exchange would result in a more complex behavior. We fitted the data of Fig. 1 to both a single exponential and a double exponential. There was no significant difference in 2 from both single and double exponential fits, and when double exponential was used, the values of both fitted rate constants were virtually identical. However, there was a consistent tendency for the 2 of the single exponential fit to be slightly lower.

RESULTS
The fast exchange situation is confirmed in the experiment of Fig. 2, which shows the water resonance of the resuspension medium (A and C) and of mitochondrial suspensions (B and D), before (A and B) and after (C and D) the addition of 7.5 mg of iron/ml of nonpermeant, dextran-coated ferromagnetic particles. Ferromagnetic shift of extramitochondrial water revealed no detectable water signal from the intramitochondrial space (D). This result confirms that the exchange of water across the mitochondrial membrane must occur faster than the difference in frequency between the shifted and unshifted resonances (26). Since the frequency difference between these two resonances is 936 Hz, the exchange of water across the mitochondrial membrane must be faster than 1.07 ms. Water exchange across the mitochondrial membrane was further characterized with a study of the variation of T 1 and T 2 in mitochondrial suspensions with protein concentration and temperature. The dependence of the relaxation times on the mitochondrial protein content is shown in Fig. 3. In these experiments, the final incubation volume was maintained constant at 0.5 ml and the amount of liver mitochondria increased up to 110 mg/ml. An approximately linear decrease in T 1 (Fig.  3A) and T 2 (Fig. 3B) was observed for increasing protein concentrations. The decrease is due to the shorter relaxation times of intramitochondrial water and to the progressive increase in the relative contribution of intramitochondrial space to the overall relaxation observed. Measurements of the intramitochondrial water in the mitochondrial suspensions gave values of 1.3 Ϯ 0.1 l/mg of protein (n ϭ 7). Thus, the titration shown in Fig. 3 covers an intramitochondrial volume range of up to 143 l/ml. Total water content was determined in the same samples used for T 1 and T 2 measurements, measuring the dry/wet weight ratio. A total H 2 O content of 8.4 Ϯ 1 l of H 2 O/mg of protein or 840 l of H 2 O/ml of sample was determined for mitochondrial suspensions of 100 mg of protein/ml. For this protein content, the intramitochondrial volume represents approximately 12-16% of the total water volume, the proportion of mitochondrial matrix space normally found in liver cells (27). Fig. 4 depicts measurements of the temperature dependence for T 1 (A) and T 2 (B) of the resuspension medium alone and of a typical mitochondrial suspension. In the resuspension medium, T 1 increased linearly, whereas T 2 increased in a nonlinear fashion. This result suggest that T 2 relaxation in the resuspension medium is dependent on more than one process. The activation energies (Ea) calculated from the temperature dependence of T 1 and T 2 in the resuspension medium, for the 22-50°C interval, were Ϫ4.8 kcal/mol and Ϫ6.3 kcal/mol, respectively. These activation energies are within the range previously reported for the self-diffusion of water (28,29). In the mitochondrial suspension, T 1 showed a biphasic behavior. It increased up to 32°C and decreased at higher temperatures. Additional experiments with different mitochondrial suspensions (n ϭ 3) confirmed this behavior, but the transition temperature varied slightly between the samples (32-35°C). The Ea values calculated below the transition temperature (from Ϫ3.8 to Ϫ4.8 kcal/mol) for these mitochondrial suspensions are also consistent with the values for the self diffusion of water, being similar to the Ea of the resuspension medium. In con-FIG. 2. Chemical shifts of the water resonance before and after the addition of ferromagnetic particles to the resuspension medium and to mitochondrial suspensions. A, resuspension medium; B, mitochondrial suspension (90 mg of protein/ml); C, same as in A with ferromagnetic particles (7.6 mg of iron/ml); D, same as in B with ferromagnetic particles (7.6 mg of iron/ml). Note the absence of intramitochondrial residual water signal after the shift of the extramitochondrial water; E, stock solution of ferromagnetic particles (15.3 mg of iron/ml).

FIG. 3. Effects of the increase in mitochondrial protein concentration on the relaxation times T 1 (A) and T 2 (B) of water. T 1 and
T 2 values were determined in mitochondrial suspensions containing increasing protein concentrations in a final incubation volume of 0.5 ml. For each mitochondrial sample, several measurements of T 1 and T 2 were taken (n ϭ 3 to 6). The S.E. is very small and cannot be appreciated from the plot.
trast, Arrhenius analysis of the linear portion above the transition temperature gave much higher Ea values in the range of 3.8 -6.4 kcal/mol (35-57°C). The biphasic trend suggests the presence of two different relaxation mechanisms having dominant effects below or above the transition temperature.
The values of intramitochondrial relaxation times are thought to be dependent mainly on the mitochondrial content of paramagnetic ions and on the viscosity of the matrix microenvironment. We investigated the potential contribution of free paramagnetic ions to the relaxation times observed by measuring the T 1 and T 2 relaxation times in mitochondrial suspensions prepared in the absence or presence of 0.5 mM EDTA in the isolation and resuspension medium. Values of 1.46 s (29.91 ms) or 1.63 s (33.34 ms) were obtained for T 1 (T 2 ) in the absence or presence of 0.5 mM EDTA, respectively. Increasing the concentration of EDTA to 1 mM did not further increase the values of T 1 or T 2 . These results indicate that free paramagnetic ions contribute at most 10% of the observed relaxation in suspensions of rat liver mitochondria. In addition, EPR measurements on typical mitochondrial suspensions (n ϭ 2) showed no free Mn 2ϩ signal detectable at maximum EPR sensitivity (results not shown). Our results confirm previous findings indicating very small contributions of paramagnetic ions to mitochondrial relaxation times (30,31). Thus, intramitochondrial viscosity may be considered as the main determinant of intramitochondrial relaxation under our experimental conditions. To inves-tigate the influence of viscosity on intramitochondrial relaxation times, measurements of T 1 and T 2 were performed on model solutions of the resuspension medium containing increasing concentrations of added glycerol (Fig. 5). These measurements were compared with intramitochondrial T 1 and T 2 values calculated for a fast water exchange situation (see "Discussion"). Calculated intramitochondrial T 1 (T 2 ) values were 0.6 Ϯ 0.06 s (5.8 Ϯ 0.6 ms) (n ϭ 6). Interpolation of these values (arrows) on the calibration curve obtained with model solutions, indicated that the matrix space behaves similarly to a solution of the resuspension medium containing approximately 52-59% glycerol. We performed measurements of the dynamic viscosity of the resuspension medium without glycerol, and with two concentrations of added glycerol, namely 30 and 60% (v/v). The viscosities were (mean Ϯ S.E., n ϭ 4) 1.3 Ϯ 0.1, 20.0 Ϯ 1.4, and 44.5 Ϯ 2.5 cP, respectively. Thus, intramitochondrial viscosity would be similar to that of a 55% glycerol solution, approximately 40 cP. DISCUSSION Our results indicate that the water exchange time between the intramitochondrial matrix and the external resuspension medium is faster than the NMR relaxation time scales. To provide a more quantitative estimate of the water residence time in the intramitochondrial matrix, we implemented a model consisting of two compartments, A and B, representing the extra-and intramitochondrial environments respectively, separated by a semipermeable membrane (Fig. 6). The model where dM a /dt and dM b /dt are given by Ref. 32.
T 2a and T 2b refer to the transversal relaxation times of water in the external medium and in the mitochondrial matrix, respectively. The relaxation times of the water in the external medium (T 2a ) and in mitochondrial suspensions (T 2 ) can be determined experimentally (Fig. 1). The relaxation time of water (T 2b ) in the mitochondrial matrix can be calculated, because of the fast water exchange, using the expression: where P a and P b represent the fractional contributions to the total volume of compartments A and B, determined by the 3 H 2 O and [ 14 C]sucrose distributions, respectively. Using Equation 4 we obtained values of 0.6 Ϯ 0.06 s (5.8 Ϯ 0.6 ms) for intramitochondrial T 1 (T 2 ). With these values it became possible to simulate the T 2 relaxation behavior of the water resonance in mitochondrial suspensions (dM T /dt) as a function of a and b (Fig. 7). Values of b were varied iteratively to mimic the experimental magnetization recoveries. The corresponding values of a were calculated for every simulation to satisfy the equilibrium condition P a / a ϭ P b / b . Fig. 7A shows model simulations of the observed relaxation behavior for the limiting cases of very slow or absent water exchange ( b , a 3 ϱ) and of fast water exchange ( b Ͻ Ͻ T 2b , a Ͻ Ͻ T 2a ). In addition, the figure depicts, superimposed to the simulations, the experimental points for T 1 and T 2 relaxation of mitochondrial suspensions and their corresponding single exponential fits. The figure shows that the fast exchange simulation resembles closely the experimental data, while the no water exchange situation is clearly different from the observed results. We performed additional simulations in the fast exchange regime, for the interval 0.5 ms Ͼ b Ͼ 0.02 ms. In these cases, the plot of residuals of every fit (Fig. 7B) revealed more clearly the goodness of the fit than the direct superposition of simulated data over experimental values. Fig. 7B shows that values of b smaller than 0.1 ms give very similar residual trends to those of the experimental values, indicating that b must be smaller than 0.1 ms. To our knowledge, this estimate represents the first approximation to the water residence time in the mitochondrial matrix.
Insight about the mobility of the water molecule in the intramitochondrial space may be obtained from the relationship of the relaxation times with the rotational correlation time ( c ) (26). T 2 values of the extra (intra) mitochondrial medium were 44.57 Ϯ 2.15 ms (5.79 Ϯ 0.59 ms), which led to calculated values of c of 4.5 ϫ 10 Ϫ10 s (6.2 ϫ 10 Ϫ9 s), respectively. Thus, water rotational mobility in the matrix is significantly restricted as compared to the extramitochondrial medium. Moreover, water protons in distilled water at 20°C have a c of about 3 ϫ 10 Ϫ12 s (33,35), approximately three orders of magnitude shorter than the matrix correlation times.
The dynamic interpretation of intramitochondrial relaxation times deserves further attention. Several reports have shown that water in tissues, cells (34 -37), or even in intact mitochondria (38), is heterogeneously distributed in different phases. Phase heterogeneity is thought to be the result of the different physical properties of water molecules in the "bulk solvent" and those "bound or adsorbed" to macromolecules or cellular surfaces (39). While bulk solvent water is able to rotate freely, water bound or adsorbed on macromolecular surfaces is though to adopt the correlation time of the host macromolecule (33). The exchange of water molecules between these different phases is thought to be fast in the NMR time scales (33,40). Thus, during the T 2b relaxation period, water molecules have a defined probability (0 Ͻ p i Ͻ1) to relax in a variety of intramitochondrial microenvironments, including bulk rotational freedom and an array of restricted macromolecular rotations (T 2i ). Thus, T 2b can be expressed as: Accordingly, the effective intramitochondrial correlation time for water ( c ) calculated above from T 2b , contains the weighted average of the contributions from the different correlation times experienced by the water molecule during its intramitochondrial relaxation. As indicated in the results section, viscosity is thought to be the main determinant of reduced water mobility in the matrix. Intramitochondrial relaxation times were found to be similar to those of glycerol suspensions of 40 cP. This apparent matrix viscosity is approximately 15 times larger than the apparent viscosity of the cytoplasm in human erythrocytes (2.10 cP) (11).
Finally, an important aspect of the present study relates to the influence that elevated matrix viscosity can have on the kinetics of intramitochondrial reactions. The diffusion coefficients (D) of water and substrates are inversely related to the viscosity () by the Einstein-Stokes relationship D ϭ kT/6r 0 where k is the Boltzman constant, T the absolute temperature, and r 0 the Stokes radius of the molecule under study (11). Thus, a 15 times increase in the average viscosity of the intramitochondrial environment as compared to the cytoplasm can account for an identical reduction in the diffusion coefficient of water and even for a larger reduction in the diffusion coefficient for larger substrates. These reductions can introduce kinetic limitations in those mitochondrial reactions which are diffusion controlled, mainly hydration-dehydration and proton transfer reactions (41). Notably, recent evidence indicates that cytosolic and mitochondrial aminotransferases of alanine and aspartate experience different solvent exchange environments in the perfused liver (42). Further effects of intramitochondrial viscosity would be to favor the formation of enzyme aggregates or multienzyme complexes. These complexes have been also proposed to occur in the mitochondrial matrix (13)(14)(15). However, to our knowledge no direct evidence on the physical properties of the intramitochondrial environment was previously available.