Departments of Medicine and Physiology, Cardiovascular Research Institute, University of California, San Francisco, California, 94143-0521
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Abstract |
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Abstract. It is thought that the high protein density in
the mitochondrial matrix results in severely restricted
solute diffusion and metabolite channeling from one
enzyme to another without free aqueous-phase diffusion. To test this hypothesis, we measured the diffusion
of green fluorescent protein (GFP) expressed in the mitochondrial matrix of fibroblast, liver, skeletal muscle, and epithelial cell lines. Spot photobleaching of GFP
with a 100× objective (0.8-µm spot diam) gave half-times for fluorescence recovery of 15-19 ms with >90%
of the GFP mobile. As predicted for aqueous-phase diffusion in a confined compartment, fluorescence recovery was slowed or abolished by increased laser spot size or bleach time, and by paraformaldehyde fixation.
Quantitative analysis of bleach data using a mathematical model of matrix diffusion gave GFP diffusion coefficients of 2-3 × 107 cm2/s, only three to fourfold less
than that for GFP diffusion in water. In contrast, little
recovery was found for bleaching of GFP in fusion with
subunits of the fatty acid
-oxidation multienzyme complex that are normally present in the matrix. Measurement of the rotation of unconjugated GFP by time-resolved anisotropy gave a rotational correlation time
of 23.3 ± 1 ns, similar to that of 20 ns for GFP rotation
in water. A rapid rotational correlation time of 325 ps
was also found for a small fluorescent probe (BCECF, ~0.5 kD) in the matrix of isolated liver mitochondria.
The rapid and unrestricted diffusion of solutes in the
mitochondrial matrix suggests that metabolite channeling may not be required to overcome diffusive barriers.
We propose that the clustering of matrix enzymes in
membrane-associated complexes might serve to establish a relatively uncrowded aqueous space in which solutes can freely diffuse.
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Introduction |
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THE mitochondrial matrix is the aqueous compartment enclosed by the inner mitochondrial membrane. The very high density of enzymes and other
proteins in the matrix, which may be as high as 270-560 mg
protein/ml (Srere, 1980; Goodsell, 1991
), makes it the
most crowded aqueous cellular compartment. Theoretical considerations have suggested that the diffusion of metabolite- and enzyme-sized solutes might be severely restricted in the mitochondrial matrix (Hackenbrock et al.,
1986
; Watford, 1990
; Welch and Easterby, 1994
). It has
been proposed that biochemical events occur by a metabolite channeling mechanism, where metabolites are passed from one enzyme to another in an organized complex
without aqueous-phase diffusion (Srere, 1987
; Somogyi et
al., 1987
; Ovadi et al., 1991; Watford, 1990
; Westerhoff and
Welch, 1992
). Although extensive evidence for enzyme
clustering in the mitochondrial matrix has been reported
(Welch, 1977
; Von Hippel and Berg, 1989
; Srere and Ovadi, 1990
; Robinson and Srere, 1995), which is consistent with metabolite channeling, there has been no direct
measurement of solute diffusion in the matrix.
The challenges to measure solute diffusion in the mitochondrial matrix of living cells are to selectively label the
matrix with probes that do not bind to resident proteins,
and to visualize probe diffusion in a compartment whose
caliber is near the resolution limit of the light microscope.
The only report on solute mobility in the mitochondrial matrix uses isolated liver mitochondria and labeling by carboxyfluorescein (CF)1, a small fluorescent probe that crosses
the mitochondrial limiting membranes and becomes deesterified and trapped in the matrix (Scalettar et al., 1991). A
high steady state fluorescence anisotropy for CF was
found, which was taken as evidence for severely restricted solute mobility in the matrix. A concern of the CF study,
in addition to the use of isolated mitochondria and the
measurement of rotational rather than translational diffusion, was that CF binding to matrix protein was not considered. As will be shown here, BCECF (a CF analogue)
binding in isolated mitochondria gives high steady state anisotropy values that cannot be interpreted in terms of
solute mobility in the aqueous-phase of the mitochondrial
matrix.
The purpose of this study was to measure solute translational and rotational mobility in the mitochondrial matrix
of intact cells. Our strategy was to label the matrix with
GFP alone and in fusion with resident matrix proteins.
GFP translation was measured by photobleaching recovery and GFP rotation by time-resolved anisotropy. GFP
has been shown to be an excellent reporter solute for the analysis of cytoplasmic viscosity (Swaminathan et al.,
1997) and for the labeling of various intracellular compartments including mitochondria (Rizzuto et al., 1995
; Cole
et al., 1996
; De Giorgi et al., 1996; Gerdes and Kaether,
1996
). Many of the optical and analytic methods used in
this study had been developed in our laboratory for the
analysis of solute rotational mobility (Fushimi and Verkman, 1991
; Bicknese et al., 1993
) and translational mobility (Kao et al., 1993
; Seksek et al., 1997
) in the cytoplasm and
nucleus. The photobleaching recovery experiments indicated that nearly all GFP in the mitochondrial matrix was
mobile and diffused only a few times slower than if the
matrix contained only saline; the time-resolved anisotropy
measurements indicated very little hindrance of the matrix
to GFP rotation. In addition, time-resolved anisotropy measurements of BCECF rotation in isolated rat liver mitochondria prepared and labeled as described by Scalettar
et al. (1991)
indicated that although a substantial fraction
of BCECF was in a bound state, unbound BCECF rotated
rapidly within the matrix. Together these studies indicate
relatively free and rapid diffusion of solutes within the mitochondrial matrix and do not support the view that protein crowding severely restricts solute movement.
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Materials and Methods |
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Cell Culture and Transfection
CHO-K1 cells (ATCC CRL9618), L6 cells (CRL1458), HepG2 cells (HB8065), and LLC-PK1 cells (CL101.1) were cultured on 18-mm-diam round glass coverslips at 37°C in 95% air, 5% CO2. CHO cells were cultured in Ham's F12 medium, L6 and LLC-PK1 cells in DME-H21, and HepG2 cells in Eagle's MEM supplemented with nonessential amino acids and Na pyruvate; all media contained 10% fetal bovine serum, penicillin (100 U/ml), and streptomycin (100 µg/ml). Cells were transfected 1 d after plating at which time they were ~80% confluent. Cells in each well of a six-well plastic dish containing a coverglass were transfected with a mixture consisting of 1 µg of plasmid DNA encoding various GFP-fusion constructs and 12 µg Lipofect-AMINE reagent (GIBCO BRL, Gaithersburg, MD) in a 0.2-ml vol of OPTI-MEM (GIBCO BRL). After 5 h the transfection mixture was replaced with 1 ml of culture medium. Cells were used 2 d after transient transfection.
GFP Targeting Constructs
For expression of COX8-GFP, the targeting presequence of subunit
VIII of human cytochrome c oxidase (COX8; Rizzuto et al., 1992) was
PCR amplified using human kidney cDNA as template and primers:
sense 5
-GCCCAAGCTTATCATGTCCGTCCTGACGCC-3
; antisense, 5
-CGAATTCCTTCCCCTCCGGCGGCAACG-3
(engineered HindIII
and EcoRI restriction sites underlined). COX8 was subcloned into eukaryotic expression vector pcDNA3.1 (Invitrogen Corp., Carlsbad, CA) at HindIII/EcoRI sites. The coding sequence of humanized GFP was PCR
amplified from plasmid pEGFP-C1 (CLONTECH Laboratories, Inc., Palo Alto, CA) using primers: sense 5
-GGAATTCGTGTGCAAGGGCGAGGAGCTGTTCAC-3
; antisense 5
-GCTCTAGATTA CTTGTACAGCTCGTCCATGCCG-3
(engineered EcoRI and XbaI sites underlined). GFP was ligated downstream and in frame with COX8 at EcoRI/
XbaI sites.
Fusion constructs containing MFAB or
MFAB (
and
subunits of
rat mitochondrial fatty acid
-oxidation multienzyme complex) downstream from COX8-GFP were prepared as follows. The mature peptide of
MFAB (78.6 kD; these data are available from GenBank/EMBL/DDBJ under accession number D16478; Kamijo et al., 1993
) was amplified using
primers: sense 5
-GGACTAGTTCTAGAACCATATTAATTATGGAGT-3
, antisense 5
-GGACTAGTTCACTGGTAGAACTTCTTGCGAGTT-3
(engineered SpeI restriction sites underlined), and
MFAB (47.5 kD, accession number D16478) using primers: sense 5
-GGACTAGTTCTGCCCCAGCTGTCCAGACCAAG-3
, antisense 5
-GGACTAGTTTTTGGGTAGGCTTCCACAATCAT-3
(engineered SpeI restriction
sites underlined) using rat liver cDNA as template.
MFAB or
MFAB
were ligated downstream and in frame with COX8-GFP at an XbaI site
and orientation was screened by restriction digestion. All constructs were
confirmed by sequence analysis and cell-free translation.
Isolation and Labeling of Mitochondria
Liver mitochondria were isolated by a modification of the original procedure of Schneider et al. (1948). The liver from a male Sprague-Dawley rat (~250 g) was excised, cooled in isotonic KCl, cut into 5-mm slices, and then transferred to homogenization buffer (250 mM sucrose, 10 mM Na phosphate, pH 7.4). The liver was homogenized with a Potter-Eljvehem homogenizer, nuclei and debris were sedimented at 600 g for 10 min, and the supernatant was centrifuged at 8,500 g for 10 min to pellet mitochondria. The pellet was washed twice, resuspended in 3 ml of the sucrose buffer, and loaded with the fluorescent probe BCECF within 4 h of isolation. A 0.5-ml aliquot of the mitochondrial suspension (2 mg protein/ml) was incubated with 10 µM BCECF for 15 min at 23°C, and external BCECF was removed by 4-6 washes. By fluorescence microscopy at 100×, mitochondria appeared as bright green dots on a black background.
Fluorescence Recovery After Photobleaching
Fluorescence recovery after photobleaching (FRAP) measurements were carried out on an apparatus described previously (Kao et al., 1996). An Argon ion laser beam (488 nm, Innova 70-4; Coherent Inc., Palo Alto, CA) was modulated by two serial acoustooptic modulators (1.5 µs response time) and directed onto the stage of an inverted epifluorescence microscope (Diaphot; Nikon Inc., Melville, NY). The microscope was also equipped for full-field epiillumination to visualize all cells to target the focused laser beam. The full-field and laser beams were reflected by a dichroic mirror (510 nm) onto the sample by an objective lens (100× oil Fluor NA 1.3 [Nikon Inc.]; Leitz 40× quartz glycerol NA 0.65 [The Leitz Co., Overland Park, KS]; or 20× dry NA 0.75 [Nikon Inc.]). For most experiments, the laser beam power was set to 200-500 mW (488 nm) and the attenuation ratio (the ratio of bleach to probe beam intensity) was set to 5,000-15,000. Sample fluorescence was filtered by serial barrier (Schott glass OG 515) and interference (530 ± 15 nm) filters and detected with a photomultiplier, transimpedance amplifier and 14-bit analog-to-digital converter. A gating circuit that controls the voltage of the second dynode was used to decrease photomultiplier gain during photobleaching. Signals were sampled before the bleach and over three different time intervals after the bleach: high resolution data (1 MHz sampling rate) over 10-100 ms, low resolution data (generally 104 points) over 0.1-10 s, and final signal data (103 points) at a specified late time. High and low resolution data were binned into 200 points each for storage and analysis. For FRAP measurements in mitochondria, 10-15 individual fluorescence recovery curves (each from a different cell) were averaged. For experiments in which cell volume was changed, cells were exposed to hypoosmolar (150 mOsm, 1:1 PBS/water) or hyperosmolar (600 or 900 mOsm, PBS containing 300 or 600 mM sucrose) buffer for 5-15 min. Unless otherwise specified, measurements were done at 23°C in a temperature-controlled darkroom.
Analysis of FRAP Data
As described in the Appendix, fluorophore diffusion coefficients (D, in cm2/s) were determined from recovery half-times (t1/2) using a mathematical model of diffusion in the mitochondrial matrix. The t1/2 value was determined as the time after the bleach pulse at which the fluorescence was equal to the mean of the fluorescence just after the bleach and that when essentially all recovery had occurred (post-bleach). The fluorescence just after the bleach was determined operationally as the average fluorescence at 50-75 µs after the end of the bleach. The post-bleach fluorescence was generally determined as the average fluorescence at a time equal to >100 t1/2 intervals. The percentage recovery was computed from pre- and post-bleach fluorescence and the percentage bleaching. t1/2 was computed using a quadratic polynomial fitted to a small interval of the recovery curve surrounding an estimated t1/2 computed from an initial exponential regression of the full recovery curve.
Time-resolved Anisotropy Measurements
Fluorescence lifetime and anisotropy decay measurements were carried
out in the frequency domain by cuvette fluorimetry using a Fourier Transform Fluorimeter (48000 MHF; SLM Instruments Inc., Urbana, IL), or by
fluorescence microscopy using epifluorescence microscope optics in place
of the cuvette compartment (Fushimi and Verkman, 1991). For microscopy measurements, the impulse-modulated, vertically polarized light
(488 nm) was reflected onto the sample by a 510-nm dichroic mirror and
objective lens; emitted fluorescence was filtered by a 515-nm cut-on filter
and passed through a rotatable analyzing calcite polarizer. Analysis of
lifetime and time-resolved anisotropy were performed by a comparative
approach as described previously (Verkman et al., 1991
). Fluorescein in
0.1 N NaOH was used as a 4.0-ns lifetime standard. Anisotropy decay
measurements done by microscopy required the inclusion of a geometric
factor (generally ~1.2) to correct for the differential detection of parallel
versus perpendicular emission polarization arising mainly from differential reflectivity of the dichroic mirror.
Confocal Microscopy
Cells were visualized using a Nipkow wheel confocal microscope (The Leitz
Co. with Technical Instruments coaxial-confocal attachment) and cooled
CCD camera detector (Photometrics Ltd., Tuscon, AZ) as described previously (Seksek et al., 1995). Cells were viewed using a 100× oil immersion objective (NA 1.4) with a z-resolution of ~1 µm.
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Results |
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To label the mitochondrial matrix of living cells with a fluorescent probe, cells were transfected with cDNA encoding humanized GFP fused in frame with the targeting presequence of subunit VIII of human cytochrome c oxidase. After entering the matrix the presequence is cleaved to give unconjugated, soluble GFP. GFP translational diffusion was measured by FRAP and rotational diffusion by time-resolved anisotropy. Fig. 1 A shows a confocal fluorescence micrograph of CHO cells transfected with the GFP construct. GFP was localized selectively to the mitochondrial matrix, seen as elongated structures present throughout the cytoplasm. Similar mitochondrial appearance was found for transfected HepG2 liver cells, L6 skeletal muscle cells and LLC-PK1 epithelial cells (not shown). These cell lines were chosen for study because of the importance of mitochondrial metabolism in liver, muscle, and epithelial cell physiology.
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Spot photobleaching was carried out to measure GFP translational diffusion. Fig. 1 B shows the kinetics of fluorescence recovery after photobleaching of cells expressing GFP in the matrix. Bleaching was done using a 0.8-µm-diam spot and a brief bleach time of 40 µs. Laser intensity was set to give 15-20% bleaching. Similar recovery kinetics were observed for each of the cell types with recovery to 82-91% of initial fluorescence, with t1/2 for recovery of 15-19 ms. Because of the finite mitochondrial size, the 82- 91% recovery indicates that >90% of the GFP is mobile. The prompt and nearly complete fluorescence recovery was an unexpected observation, and suggested relatively free and rapid diffusion of GFP in the mitochondrial matrix.
Photobleaching experiments were done to confirm that
the recovery curves in Fig. 1 B represent GFP translational
diffusion in the matrix. Fluorescence recovery was sensitive to laser spot diameter (Fig. 2 A), with t1/2 of 17 ± 2, 61 ± 6, and 305 ± 28 ms for diameters of 0.8, 1.3, and 4 µm,
respectively. t1/2 would not depend on spot size if recovery
were due to reversible GFP photobleaching such as that
involving triplet state relaxation (Periasamy et al., 1996;
Swaminathan et al., 1996
). Further evidence that the fluorescence recovery results exclusively from GFP translational diffusion is that paraformaldehyde fixation, which
immobilizes GFP without affecting its fluorescence, abolished the recovery (Fig. 2 B). Therefore, the recovery signal arises from irreversible GFP bleaching and diffusion of
unbleached GFP into the bleached area. Finally, it was
predicted that increased bleach time would result in a decreased rate and extent of recovery due to the finite length
and volume of individual mitochondria. As bleach time increases, unbleached GFP from outside of the bleach spot
diffuses into the bleach beam, effectively widening the
bleach zone and depleting unbleached GFP from the matrix. Fig. 2 C shows that increased bleach time gives slowed
and less complete fluorescence recovery, with no recovery
for very long (500 ms) bleach time. By visual inspection,
individual mitochondria of 4-7 µm length could be made
nonfluorescent by a 500-ms bleach time (0.8-µm-diam
spot), indicating a continuously open mitochondrial lumen.
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Mitochondria can assume two configurations that are interconvertable in response to metabolic status (Hackenbrock, 1968; Halestrap, 1989
; Scalettar et al., 1991
): an
orthodox state where the matrix takes up ~90% of mitochondrial volume and a condensed state where the matrix
contracts to ~55%. Experimental induction of the condensed state by hyperosmolality slowed fluorescence recovery giving a t1/2 of 41 ± 4 ms (Fig. 2 D). Similar results
were obtained with 2-deoxyglucose to induce the condensed state. Recovery was the same in isosmolar and hypoosmolar solutions (15-17 ms), consistent with the expectation that under normal metabolic conditions mitochondria are in the orthodox state.
To relate t1/2 to diffusion coefficients (D) for GFP translational mobility in the mitochondrial matrix, a mathematical model was developed that predicted fluorescence recovery from laser spot diameter, mitochondrial geometry,
and D (see Appendix). Fig. 3 A (top) shows a mitochondrion as a cylinder of length 2L with laser beam of diameter 2h. The beam is directed to a spot at position along
the mitochondrial axis. For this simple situation, Fig. 3 B
shows the computed time evolution of unbleached fluorophores along the mitochondrion (see legend for parameters). There is progressive broadening of the bleached area
as diffusion along the axis of the mitochondrial matrix occurs. The fluorescence distribution is uniform throughout
the matrix at infinite time, but lower than initial fluorescence because of the finite matrix volume. To compute the
fluorescence recovery kinetics, F(t), for FRAP studies as
done in Fig. 1 B, the diffusion equation was solved taking
into account different orientations of mitochondria with respect to the bleach beam (angle
, Fig. 3 A, bottom) and
different bleaching locations along the mitochondrial axis
(parameter
). As given in the Appendix, appropriate integration and normalization was done over the probe beam
zone, as well as over parameters
and
.
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Fig. 3 C shows the predicted time dependence of fluorescence recovery on diffusion coefficient D for relevant
model parameters. Recovery rate increased with increasing D, with a best fit to the experimental data for D = 2.6 × 107 cm2/s. As explained in the model development (see
Appendix), D values were fairly insensitive to mitochondrial geometry and the precise angular distribution. Fig.
3 D gives the relationship between t1/2 and D, showing D
for GFP in the mitochondrial matrix versus water and fluorescein in water.
A simplified form of the model (open cylinder, where L
is infinite) was tested by measuring the fluorescence recovery of an aqueous solution of fluorescein in a thin
(~0.5-µm-diam) glass capillary. Thin capillaries were
pulled as done for single cell microinjection (Seksek et al.,
1997) and filled with the aqueous solution. Fig. 3 E shows
fluorescence recoveries measured with 100× and 20× objectives. Effective beam diameters for these objectives were predicted from optical parameters to be 0.8 and 4 µm,
respectively, and confirmed experimentally (Kao et al.,
1993
). Recovery t1/2 values of 0.82 and 18 ms were measured using the 100× and 20× objectives, predicting the
correct D of 2.5-2.8 × 10
6 cm2/s.
The GFP translational diffusion coefficients determined
above represent a lower limit. In relating t1/2 to D it was assumed that the mitochondrial lumen does not contain obstructions such as cristae (see Discussion), and that GFP
does not bind to matrix components. To estimate the mobile fraction of GFP and to determine the GFP rotational
diffusion coefficient, time-resolved anisotropy decay was
measured by frequency-domain microfluorimetry. In water, GFP has a fluorescence lifetime of ~2.8 ns and rotates
freely with an apparent correlation time of 20 ns (Swaminathan et al., 1997). The fluorescence lifetime of GFP in
mitochondria was 2.4-2.7 ns and the GFP rotational correlation time was 23.3 ± 1 ns (n = 10; Fig. 4 A), similar to
that of 20 ns in water. Therefore, GFP is not bound and
the matrix does not hinder GFP rotation. This result is
consistent with the paradigm that rotation of unbound solutes is affected only to a small extent even in crowded media (Fushimi and Verkman, 1991
).
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As explained in the Introduction, the steady state
anisotropy of CF in the matrix of isolated mitochondria
was reported to be high, suggesting hindered diffusion
(Scalettar et al., 1991). Our results with GFP in the mitochondrial matrix of living cells suggest that much smaller
molecules like CF or BCECF should diffuse rapidly unless
highly bound. To resolve this apparent discrepancy, we reexamined the rotational mobility of BCECF in suspensions of freshly isolated mitochondria from rat liver. The
BCECF steady state anisotropy was measured to be 0.23 ± 0.01, similar to that of ~0.25 reported for CF by Scalettar et al. (1991)
. A fluorescence lifetime of 3.5-3.7 ns was
found for BCECF in the matrix, the same as that in saline.
Analysis of time-resolved anisotropy (Fig. 4 B) indicated
anisotropic rotation with two correlation times: a short
time of 325 ± 11 ps (fraction 0.51) corresponding to rapid rotation of unbound BCECF, and a longer time of 59 ± 4 ns for bound BCECF (n = 20). Short rotational correlation times (260-375 ps) were also measured in mitochondria that were suspended in buffers with osmolalities of
200-600 mOsm. Control measurements on mitochondria
with different amounts of BCECF labeling (by changing concentration and labeling time) and different amounts of
solution scattering (by adding unlabeled mitochondria) indicated no depolarization or scattering artifact (not shown).
These results indicate rapid rotational diffusion of a metabolite-size solute in the mitochondrial matrix, and that
the high BCECF steady state anisotropy is related to
BCECF binding rather than to slowed aqueous-phase rotational diffusion.
As discussed below, one proposed explanation for the
rapid diffusion of GFP in the matrix is that many matrix
proteins reside in membrane-associated complexes so as
to create an uncrowded central aqueous space. To investigate this possibility, we tried to measure the mobility of a
soluble protein normally present in the matrix. Fusion
constructs were made in which GFP was fused downstream and in-frame from several different matrix enzymes (very long chain acyl CoA dehydrogenase, and
subunits of rat mitochondrial fatty acid
-oxidation multienzyme complex,
-aminolevulinate synthase). Transient
expression of each of these constructs gave GFP targeting
to a vesicular compartment with poor mitochondrial localization. After testing various other GFP-fusion constructs, selective mitochondrial targeting was achieved by inserting the
or
subunits of the rat mitochondrial fatty acid
-oxidation multienzyme complex (Kamijo et al., 1993
)
downstream from the COX8-GFP construct (Fig. 5 A).
Transfected cells had the same appearance as those expressing the COX8-GFP cDNA, and immunoblot analysis
with GFP antibody showed the predicted sizes of the fusion proteins. Fig. 5 B shows photobleaching results for
CHO cells transfected in parallel with the COX8-GFP and
the two fusion constructs. Whereas the majority of the unconjugated GFP (from COX8-GFP cDNA) was mobile
and diffused rapidly as found above, the GFP-fusion proteins had little mobility. These results suggest that the fusion proteins bind strongly to slowly moving components
of the matrix or are located in a highly viscous subcompartment of the matrix.
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Discussion |
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The mitochondrion is the cellular organelle involved in oxidative metabolism and energy production. It is spatially
organized into a porous outer membrane, an intermembrane space, an inner membrane, and an inner aqueous
compartment known as the matrix. The inner membrane is
the site of the electron transport pathway, whereas the matrix is the site of numerous biochemical events such as the
tricarboxylic acid cycle and the fatty acid oxidation pathway. Although both the sites and sequences of these and
other mitochondrial reactions are well established, little is
known about the spatial organization of metabolism or the
diffusional mobilities of enzymes and substrates. It is
widely believed that mitochondrial enzymes and substrates are spatially organized and fairly static (for review
see Ovadi, 1995). It has even been proposed that mitochondrial water is in an organized or vicinal state, and that
protein crowding in the matrix changes the basic physical chemistry of enzyme reactions. This study was done to
measure for the first time the translational mobility of molecular solutes in the matrix.
Several a priori considerations predict that solute translational diffusion in the mitochondrial matrix might be
slow and severely hindered. Polymer theory (Phillies,
1987, 1989
; Han and Herzfeld, 1993
) and measurements of
solute diffusion in solutions containing dextrans and proteins (Furakawa et al., 1991
; Kao et al., 1993
) suggest that
solute diffusion time (proportional to inverse diffusion
coefficient) is an increasing exponential function of the
concentration of macromolecular solutes. Thus, it is predicted that the diffusion of a small solute in the crowded
mitochondrial matrix (27-56 vol% solids) might be slowed
by 50-1,000-fold compared with its diffusion in water. The
translational diffusion of larger, enzyme-sized solutes might
be slowed even more. In addition, recent measurements of
the motion of FITC-dextrans and Ficolls (4-2,000 kD) in
cytoplasm suggest a percolation phenomenon (Seksek et al., 1997
), where the translational diffusion of solutes greater
than a certain size is severely hindered. The percolation
threshold is predicted theoretically to be strongly dependent on obstacle density (Saxton, 1993
), and it was found
that the motion of even small FITC-dextrans was hindered
in shrunken cells (Seksek et al., 1997
). Together these considerations suggest that the mitochondrial matrix, if it is indeed a crowded protein solution, would severely hinder
solute diffusion.
Our strategy to measure the mobility of enzyme-size
macromolecules in the mitochondrial matrix of living cells
was to target GFP fusion constructs to the matrix and to
use biophysical methods to measure GFP diffusion. GFP
has suitable photophysical properties for use as a probe of
solute mobility. The three-amino acid chromophore in
GFP is fixed rigidly within a barrel structure (Yang et al., 1996; Örmo et al., 1996). The consequent absence of depolarizing GFP rotations due to segmental chromophore
motion permits interpretation of the GFP rotational correlation time in terms of the microviscosity of surrounding
fluid (Swaminathan et al., 1997
). The brightness, relative
photostability (compared with fluorescein), and irreversible photobleaching properties of GFP facilitate the measurement of its translational diffusion. Recent measurements of GFP translational diffusion in cytoplasm
(Swaminathan et al., 1997
) are in agreement with measurements of the diffusion of comparably-sized FITC-dextrans and Ficolls (Seksek et al., 1997
). Although individual
mitochondria were easily visualized by fluorescence microscopy at high magnification, rapid photobleaching
could not easily be done on single mitochondria because
of the poor signal-to-noise ratios associated with wide amplifier bandwidth and practical difficulties in locating and targeting single mitochondria by the probe beam with
minimal bleaching. Our approach was to use signal averaging by measuring the fluorescence recovery of multiple mitochondria. The fluorescence recovery signals obtained
from multiple mitochondria were quite good; however, the
quantitative determination of absolute diffusion coefficients required the development of a mathematical model
of solute diffusion in the mitochondrial matrix.
The mathematical model was used to deduce diffusion
coefficients from fluorescence recovery kinetics. The
model assumed the mitochondrial matrix to be a thin cylinder of specified length without internal barriers. The
curved shape of some mitochondria (see Fig. 1 A) would
have little effect on the validity of the one-dimensional
computation since mitochondria are thin and have small
radii of curvature compared with beam diameter. Average mitochondrial length and the angular spread of orientations were estimated from serial confocal micrographs. It
was assumed that bleach time is very short compared with
diffusional recovery time. This assumption is valid even
for the 100× objective where the bleach time of <0.25 ms
was much less than the recovery times of 15-20 ms. The
computations shown were done for uniform beam profile.
As discussed by Axelrod et al. (1976) for conventional two-dimensional spot photobleaching, this approximation
is reasonably valid for practical laser/lens systems; the
same considerations would apply for bleaching of long
thin mitochondria where bleach profile is nearly constant
across the thin cylindrical matrix compartment. The determination of absolute diffusion coefficient by the model
was validated experimentally by measurements of fluorescein diffusion in water that was confined to thin capillary
tubes. In addition, the model was found to be fairly insensitive to exact values of the mitochondrial length and angular distribution parameters.
From these considerations, the assumption of most
questionable validity in the computation of GFP diffusion
coefficient is that the matrix does not contain internal barriers. Electron micrographs of mitochondria show cristae
of various sizes and shapes that may be cell type specific.
Notwithstanding the potential of fixation artifacts in the
micrographs, the dimensions of the cristae generally appear to be small compared with mitochondrial diameter.
Therefore, the D values reported here must formally be
considered as lower limits to actual D. We recently used a
Monte-Carlo random walk approach to quantify the effect
of fixed barriers on diffusion in complex organellar geometries (Ölveczky and Verkman, 1998). A general conclusion of the computations on mitochondria-like cylinders
was that significant slowing of diffusion required quite large and/or numerous internal cristae-like barriers. In
simulated spot photobleaching experiments, an ~25% decrease in apparent diffusive transport rate required a single thin transverse obstacle occluding 93% of mitochondrial lumen area, a single obstacle occluding 50% of the
lumen but of width >0.5 µm, or 10 equally spaced thin 50% obstacles alternately occluding opposite halves of the
cylinder. From these considerations, we conclude that the
mitochondrial cristae probably have minimal influence on
apparent GFP diffusion in mitochondria. In any case, the
presence of cristae could only yield a higher GFP diffusion
coefficient, which does not affect the principal conclusion
of our study concerning free and rapid solute diffusion in
the mitochondrial matrix.
The relatively mild hindrance to solute translational diffusion by the matrix was an unexpected observation in
view of the theoretical expectations mentioned above.
Several explanations for the mild hindrance are proposed.
The degree of solute crowding in the mitochondrial matrix
has not been accurately determined and may be less than
the generally quoted values of 27-56 vol%. An intriguing
possibility is that many of the matrix proteins may be organized peripherally in membrane-associated macromolecular complexes. A central region with relatively low protein
density and low viscosity might thus be created in which
solute diffusion is rapid and unrestricted. Last, it is becoming evident that the description of solute translational diffusion in cellular aqueous compartments will require considerations of anomalous diffusion mechanisms such as
percolation, sieving, and possibly superdiffusion and diffusive channeling (Nagle, 1992; Saxton, 1994
; Feder et al.,
1996
). Although preliminary theoretical treatment of these issues has been done for two-dimensional diffusion in
membranes (Saxton, 1993
, 1994
), adequate models do not
exist for analysis of anomalous diffusion in three-dimensional
cellular aqueous compartments.
Time-resolved anisotropy measurements of BCECF in
the matrix of isolated liver mitochondria indicated that the
rotational mobility of unbound BCECF was very rapid. A
slowly rotating component was also identified and attributed to BCECF binding. The alternative possibility for the
slow component, slow rotation of unbound BCECF in a
viscous microenvironment, is unlikely based on our previous analyses of BCECF anisotropy decay in various cellular compartments. Rapid rotation of unbound BCECF and
slow rotation of bound BCECF were also reported in bulk
(Fushimi and Verkman, 1991) and membrane-adjacent (Bicknese et al., 1993
) cytoplasm. It was concluded that
the rotation of a small unbound fluorophore provides information about the fluid-phase or short-range microviscosity of an aqueous environment. Conceptually, the in
situ rotation of a small fluorophore that does not undergo
collisional interactions with macromolecular solutes should
probe the local aqueous environment; for example, the rotation of fluorescein is not altered in agarose gels or gelatin because the fluid pockets containing fluorescein are
water-filled. The results in mitochondria suggest that the
fluid environment is waterlike and do not support the existence of vicinal-type water that is much more viscous
than normal water. Further, the resolution of the rotation
of bound and unbound BCECF in the matrix of liver mitochondria provides an explanation for the high CF steady
state anisotropy measured by Scalettar et al. (1991)
. Thus, as concluded for analysis of fluorophore rotation in cytoplasm (Dix and Verkman, 1990
; Fushimi and Verkman,
1991
), steady state anisotropy cannot be related directly to
aqueous-phase microviscosity.
The significance of enzyme clustering and metabolite
channeling in the mitochondrial matrix has been controversial. Metabolite channeling has been described as the
sequential transfer, by covalent or noncovalent binding, of
metabolites from one active site to another on a clustered
assembly of enzymes (Watford, 1990; Ovadi, 1991
; Welch
and Easterby, 1994
). Metabolite channeling would provide an efficient mechanism to accelerate metabolic events if
the rate-limiting step is substrate diffusion to an active site
on an enzyme rather than the subsequent biochemical reaction. There is a substantial body of kinetic evidence supporting an apparent channeling mechanism for certain
metabolic reactions (Ovadi, 1995
; Lindbladh et al., 1994
;
Elcock and McCammon, 1996). The results reported here
do not directly address whether metabolic channeling occurs, because it is possible that GFP does not report on the
environment in which soluble intermediates move from
enzyme to enzyme. But if GFP does report on the environment of soluble intermediates, then the rapid GFP diffusion suggests that channeling mediated by enzyme clusters
may not be necessary to overcome solute diffusive barriers. The biophysical measurements indicated rapid and
unhindered GFP rotational diffusion in the mitochondrial
matrix and only mildly slowed translational diffusion compared with that in water. Solute rotation can occur in
nanoseconds and translation across the width of a 0.5-µm
mitochondrion in tens of milliseconds. These rates are substantially higher than those of most biochemical reactions. We would propose that enzyme clustering occurs not for
metabolite channeling, but for establishing an uncrowded,
relatively enzyme-free aqueous space in which solutes can
freely diffuse. Thus, enzyme clustering could provide a
simple and elegant solution to the problem of maintaining
rapid diffusion in a crowded cellular environment.
![]() |
Appendix |
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![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
Mathematical Model of Diffusion in Mitochondria
A mathematical model was developed to compute the
time course of fluorescence recovery, F(t), in mitochondria as a function of fluorophore diffusion coefficient, D,
and mitochondrial geometry. Each mitochondrion was
modeled as a cylinder of length 2L, at an orientation defined by angle with respect to the laser beam (Fig. 3 A).
The laser beam was assumed to have a uniform circular disk profile with radius h. The bleach time was taken to be
infinitely short. One-dimensional diffusion (along the
length axis of the mitochondrion) of unbleached fluorophore, C(x,t), is described by the diffusion equation:
![]() |
(A1) |
subject to the initial conditions: C(x,0) = (1 K1)C0 for
h < x <
+ h, and C(x,0) = C0 for all other x, and the
boundary conditions: dC(
L, t)/dx = dC(L, t)/dx = 0. K1
is the bleach depth that depends on the intensity of the
bleach pulse, and the distance between the center of the
mitochondrion and the center of the laser beam.
The solution to Eq. A1 with the specified initial and boundary conditions is:
![]() |
(A2) |
![]() |
Eq. A2 describes fluorescence recovery when the laser
beam is perpendicular to the axis of the mitochondrion.
For a mitochondrion orientated at an angle, , the effective laser beam diameter (2h
) is a function of
: h
(
) = h/cos
(see Fig. 3 A). This consideration makes C(x, t,
) in
Eq. A2 a function of
, C(x, t,
,
), where h is replaced by
h/cos
. The fluorescence recovery is computed by averaging the time-dependent fluorescence emission over
, assuming equal probability for bleaching along the length of
the mitochondria:
![]() |
(A3) |
where the mitochondrial orientation is assumed to be random for between 0 and
max. Analysis showed the computed diffusion coefficient to be relatively insensitive to
max. (Less than 14% change in predicted D for 0 <
max
<45° when t1/2 = 15 ms.) The cos
term in the integrand
accounts for the random orientational distribution.
The normalized fluorescence, F(t)/F(0), was computed
by solving the Eqs. A2 and A3 numerically using an algorithm written in C. The integration step sizes were L/20, /30,
and h/100 for
,
, and x, respectively.
![]() |
Footnotes |
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Received for publication Received for publication 11 November 1997 and in revised form 23 December 1997..
1. Abbreviations used in this paper: ![]() |
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