(Received for publication, December 1, 1995; and in revised form, February 8, 1996)
From the
The dynamics and environment of water in suspensions of isolated
rat liver mitochondria have been investigated by H NMR. NMR
longitudinal and transversal relaxation times (T
and T
) 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
two-compartment model indicated that the intramitochondrial water
residence time has an upper limit of approximately 100 µs.
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, 5, 6, 7, 8, 9, 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 properties 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 ()(17) of water in the intramitochondrial space and
estimates for matrix viscosity. Our methodology is based on comparisons
of the
H NMR longitudinal (T
) (
)and transversal (T
) 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.
Nonpermeant dextran-coated ferromagnetic
iron particles were prepared by alkalinizing (pH 11.0) a solution of
ClFe (10 mg/ml) and Cl
Fe (15 mg/ml) in the
presence of dextran (M
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) .
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, High Performance Systems, Lyme, NH). T
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
values of mitochondrial suspensions, using
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. 1summarizes the results of T (A) and T
(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
(T
)
measurements of the resuspension medium (n = 6) and of
the mitochondrial suspensions (n = 5) were always
monoexponential with values of 2.65 ± 0.2 s (44.57 ± 2.2
ms) and 1.74 ± 0.1 s (23.14 ± 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. 1provide
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 relaxation
behavior, while a slow or intermediate exchange would result in a more
complex behavior. We fitted the data of Fig. 1to both a single
exponential and a double exponential. There was no significant
difference in
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
of the single
exponential fit to be slightly lower.
Figure 1:
Longitudinal (T) and transversal (T
)
equilibrium magnetization recoveries in the resuspension medium (open symbols) and in mitochondrial suspensions (closed
symbols). Mitochondrial suspensions had a protein content of 100
mg of protein/ml. The results are mean ± S.E. of six
measurements in the resuspension medium and five measurements on
different mitochondrial preparations.
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.
Figure 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).
Water exchange across the mitochondrial membrane was
further characterized with a study of the variation of T and T
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
(Fig. 3A) and T
(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 ± 0.1 µl/mg
of protein (n = 7). Thus, the titration shown in Fig. 3covers an intramitochondrial volume range of up to 143
µl/ml. Total water content was determined in the same samples used
for T
and T
measurements,
measuring the dry/wet weight ratio. A total H
O content of
8.4 ± 1 µl of H
O/mg of protein or 840 µl of
H
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) .
Figure 3:
Effects of the increase in mitochondrial
protein concentration on the relaxation times T (A) and T
(B) of water. T
and T
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
and T
were taken (n = 3 to
6). The S.E. is very small and cannot be appreciated from the
plot.
Fig. 4depicts
measurements of the temperature dependence for T (A) and T
(B) of the
resuspension medium alone and of a typical mitochondrial suspension. In
the resuspension medium, T
increased linearly,
whereas T
increased in a nonlinear fashion. This
result suggest that T
relaxation in the
resuspension medium is dependent on more than one process. The
activation energies (Ea) calculated from the temperature
dependence of T
and T
in the
resuspension medium, for the 22-50 °C interval, were
-4.8 kcal/mol and -6.3 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
showed a biphasic behavior. It
increased up to 32 °C and decreased at higher temperatures.
Additional experiments with different mitochondrial suspensions (n = 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 -3.8 to -4.8 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 contrast, 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.
Figure 4:
Temperature dependence of T (A) and T
(B) values of
the resuspension medium (open symbols) and of a representative
mitochondrial suspension (closed symbols). The mitochondrial
suspension had a protein content of 100 mg/ml. The data points of the
resuspension medium are expressed as mean ± S.E. with at least
six measurements for every temperature. One representative
mitochondrial sample is shown.
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 and T
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
(T
) 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
or T
. 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 = 2) showed no
free Mn
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
investigate the influence of viscosity on intramitochondrial relaxation
times, measurements of T
and T
were performed on model solutions of the resuspension medium
containing increasing concentrations of added glycerol (Fig. 5).
These measurements were compared with intramitochondrial T
and T
values calculated for
a fast water exchange situation (see ``Discussion'').
Calculated intramitochondrial T
(T
) values were 0.6 ± 0.06 s (5.8
± 0.6 ms) (n = 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 ± S.E., n = 4) 1.3 ± 0.1, 20.0 ± 1.4, and 44.5
± 2.5 cP, respectively. Thus, intramitochondrial viscosity would
be similar to that of a 55% glycerol solution, approximately 40 cP.
Figure 5:
T (A) and T
(B) dependence of viscosity.
Measurements were performed on model solutions consisting of the
resuspension medium with partial substitutions of glycerol (0, 10, 30,
60, 75%, v/v). Interpolation of calculated intramitochondrial T
and T
values (arrows) indicate that the mitochondrial matrix has an
apparent viscosity similar to that of a 55% glycerol
solution.
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 considered the T relaxation of magnetically labeled protons of
free water in the extramitochondrial (M
) and
intramitochondrial (M
) compartments, the
experimentally observed relaxation of all water molecules in the sample (M
) and the exchange of water across the inner
mitochondrial membrane. This exchange is expressed in terms of the
water residence times in the external medium and in the mitochondrial
matrix,
and
, respectively. The
decay of the NMR signal observed experimentally (M
), contains the addition of the decays of the
macroscopic magnetization from both compartments, M
and M
,
Figure 6:
Two compartment model for the analysis of
transversal relaxation data from intra- and extramitochondrial
compartments in the presence of water exchange. Compartment A refers to the extramitochondrial medium and compartment B to the intramitochondrial space. The magnetically labeled water
protons in these compartments are M and M
, with relative populations P
and P
.
The mean residence time of water in both compartments,
and
, and the relaxation times in
each compartment, T
and T
, determine the observed
relaxation behavior (M
) of the sample.
Simulations of the experimental behavior of M
can be obtained by adjusting the values of
and
(cf. Fig. 7).
Figure 7:
Representative model simulations of the
kinetics of water exchange across the inner mitochondrial membrane.
Simulations of experimental T (A)
relaxation curves for different mitochondrial preparations (100 mg/ml, n = 4) were obtained using the model of Fig. 6.
The continuous line with open symbols (
) is a
simulation for the case of no water exchange
(
,
). The dashed line is a simulation for the case of fast
water exchange with
< 100 µs. Closed symbols (
) indicate experimental measurements. B, residuals plot obtained for the experimental results fitted
to a single exponential (
-
) and to simulations
performed in the interval 0.5 ms >
>
0.02 ms. Note that the residuals obtained from the simulations mimic
better those of the experimental data for the interval 100 >
> 20 µs.
where dM/dt and
dM
/dt are given by (32) .
T and T
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
) and in mitochondrial suspensions (T
) can be determined experimentally (Fig. 1). The relaxation time of water (T
) in the mitochondrial matrix can be
calculated, because of the fast water exchange, using the expression:
where P and P
represent the fractional contributions to the total volume of
compartments A and B, determined by the
H
O and [
C]sucrose
distributions, respectively. Using we obtained values of
0.6 ± 0.06 s (5.8 ± 0.6 ms) for intramitochondrial T
(T
). With these values it
became possible to simulate the T
relaxation
behavior of the water resonance in mitochondrial suspensions
(dM
/dt) as a function of
and
(Fig. 7). Values of
were varied iteratively to mimic the experimental magnetization
recoveries. The corresponding values of
were
calculated for every simulation to satisfy the equilibrium condition P
/
= P
/
.
Fig. 7A shows model simulations of the observed relaxation behavior for
the limiting cases of very slow or absent water exchange
(,
) and of fast water
exchange (
T
,
T
). In
addition, the figure depicts, superimposed to the simulations, the
experimental points for T
and T
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 >
> 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
smaller than 0.1 ms give very similar
residual trends to those of the experimental values, indicating that
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 () (26) . T
values
of the extra (intra) mitochondrial medium were 44.57 ± 2.15 ms
(5.79 ± 0.59 ms), which led to calculated values of
of 4.5
10
s (6.2
10
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
of about 3
10
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, 35, 36, 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 relaxation period, water molecules
have a defined probability (0 < p
<1) to
relax in a variety of intramitochondrial microenvironments, including
bulk rotational freedom and an array of restricted macromolecular
rotations (T
). Thus, T
can be expressed as:
Accordingly, the effective intramitochondrial correlation time
for water () calculated above from
T
, 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 = kT/6
r
where k is the Boltzman constant, T the absolute
temperature, and r
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.