High Km of oxidative phosphorylation for
ADP in skinned muscle fibers: where does it stem from?
Olav
Kongas1,2,
Tai
L.
Yuen3,
Marijke J.
Wagner3,
Johannes H. G. M.
van Beek3, and
Klaas
Krab3
1 Laboratory for Physiology, Institute
for Cardiovascular Research, Vrije Universiteit Medical Center
1081 BT Amsterdam; 3 Faculty of Earth
and Life Sciences, Department of Molecular Cell Physiology,
Vrije Universiteit, 1081 HV Amsterdam, The
Netherlands; and 2 Department of Mechanics
and Applied Mathematics, Institute of Cybernetics, Tallinn
Technical University, 12618 Tallinn, Estonia
 |
ABSTRACT |
Mitochondria in
saponin-skinned cardiac fiber bundles were reported to have an order of
magnitude lower apparent affinity to ADP than isolated
mitochondria. Although ADP was measured outside the bundles, it was
thought that the low affinity was not caused by diffusion gradients
because of relatively short diffusion distances. Here we test the
hypothesis that considerable ADP diffusion gradients exist and can be
diminished by increasing the intrafiber ADP production rate. We
increased the ADP-producing activity in rat heart skinned fiber bundles
by incubating with 100 IU/ml yeast hexokinase and glucose.
Consequently, we observed a significant decrease of the apparent
Michaelis constant (Km) to ADP of the
respiration rate of bundles from 216 ± 59 to 50 ± 9 µM.
Fitting the results with a mathematical model, we estimated the
Km of mitochondria in the bundles to be 25 µM.
We conclude that the affinity to ADP of in situ mitochondria in heart
is of the same order of magnitude as that of isolated mitochondria.
mitochondria; heart; soleus; adenosine triphosphatase; diffusion; Michaelis constant; adenosine 5'-triphosphate
 |
INTRODUCTION |
THE REGULATION OF respiration by ADP
has been extensively studied in isolated mitochondria. The apparent
affinity of isolated mitochondria to ADP is well characterized by
Michaelis-Menten-type kinetics with Michaelis constants
(Km) ranging from 10 to 20 µM. With
permeabilized cell techniques (chemical skinning) it became possible to
study the regulation of respiration on mitochondria in situ
(9). Interestingly, it was found that mitochondria in
saponin-skinned heart or soleus fibers possess an apparent Km (Kapp) to ADP of
200-400 µM (for review, see Ref. 17). This affinity
to ADP is an order of magnitude lower than that observed after
isolation of mitochondria from these tissues.
The large difference between mitochondrial affinities in situ and in
vitro was explained as follows: the diffusion gradients of ADP between
oxygraph medium and mitochondria are negligible, but the mitochondrial
outer membrane acts as a major diffusion barrier in situ, whereas most
of its barrier function is lost during isolation of mitochondria
(17). This hypothesis has been supported by several
experimental observations. For instance, the
Kapp for the isolated permeabilized
myocytes was reported to range from 150 (9) to 250 (14) µM, although the radius of a myocyte is merely
6-8 µm. Furthermore, incubating skinned fiber bundles briefly in
hypoosmotic medium, which causes mitochondrial swelling and breakage of
mitochondrial outer membranes, results in increased affinity of the
bundles to ADP at low ADP levels (16). Finally, mild
proteolytic treatment of skinned fiber bundles results in a significant
decrease of Kapp, ascribed to a loss of control
of outer mitochondrial membrane permeability (12).
On the other hand, in skinned fiber bundle studies, the ADP
concentration is determined in the incubation medium. There exist diffusion gradients between the medium and the cores of such bundles; however, the magnitude of these gradients is not known. Using a
mathematical reaction-diffusion model, we designed an experiment: in
bundles where large diffusion gradients exist, these gradients can be minimized by adding an ATP-consuming enzyme that produces ADP
inside the bundles.
In this study, we examined the effect of yeast hexokinase (HK) as
an ATP-consuming enzyme on Kapp of skinned fiber
bundles from rat heart and soleus. We found that HK is able to cause a remarkable decrease of Kapp, suggesting the
existence of large ADP gradients in these bundles that are reduced by
increased intrafiber ADP production. We thereby show that the affinity
of in situ mitochondria to ADP is of the same order of magnitude as
that of isolated mitochondria.
 |
GLOSSARY |
General
AK |
adenylate kinase
|
HK |
hexokinase
|
NS-ATPase |
all nonspecific background ATPases of the sample together
|
IMS |
mitochondrial intermembrane space
|
Concentrations
ATP, ADP, AMP, Pi |
concentration of ATP, ADP, AMP, or Pi, respectively
|
Meti, Metc, Meto |
concentration of a metabolite (ATP, ADP, AMP, or Pi)
in the mitochondrial intermembrane space (i), cytosolic compartment
(c), or oxygraph medium (o), respectively
|
Mg |
Free magnesium level
|
Kinetic constants
Vmax |
maximal rate
|
Km |
Michaelis-Menten constant
|
Kapp |
apparent Km of the respiration of the sample for
ADP
|
Kmito |
Km of mitochondria for ADP in the sample
|
V |
maximal mitochondrial ATP synthesis rate
|
KADP, KPi |
Km values of ATP synthesis for the IMS
concentrations of ADP and Pi, respectively
|
QP/O |
ADP-to-O ratio of oxidative phosphorylation
|
V ,
V |
maximal forward and backward reaction rates of adenylate
kinase, respectively
|
K1 to K4,
K 1 to K 4,
KI |
binding constants of adenylate kinase
|
V |
Vmax of NS-ATPases
|
Khyd |
Km of NS-ATPases
|
V |
Vmax of hexokinase
|
KHK |
Km of hexokinase
|
KDT, KDD |
magnesium binding constants of ATP and ADP, respectively
|
Diffusion
Reff |
effective diffusion distance for metabolites in a sample, effective
radius of the bundles in a sample
|
DMet |
in vitro diffusion coefficient of the metabolite Met
|
Pic |
characteristic diffusion restriction of the outer mitochondrial
membrane
|
Volumes
Vcyt, VIMS |
fractional volumes of cytosolic (cyt) and IMS compartments with respect
to the cell volume
|
Qs/o |
ratio of the sample volume to the oxygraph medium volume
|
 |
METHODS |
Preparation.
Skinned fiber bundles were prepared according to the method described
by Seppet et al. (19). Briefly, unanesthetized male or
female Wistar rats weighing 300-350 g were decapitated, chests were opened, and hearts were excised while still beating and put into
cooled solution A (see Solutions). Cooled hearts
were cut into halves, and muscle strips (3-5 mm long and
1-1.5 mm in diameter) were cut from the endocardium of the left
ventricles along the fiber orientation to avoid mechanical damage of
the cells. Muscle strips (3-4 mm long, ~1 mm in diameter) were
also taken from the soleus (oxidative, slow-twitch muscle). By using
sharp-ended needles, fiber bundles were partly separated from each
other, leaving only small areas of contact of bundles with radii of
10-50 µm (see DISCUSSION). Thereafter, bundles were
transferred into Eppendorf test tubes (volume 2 ml) with cooled
solution A (see Solutions) containing 50 µg/ml
of saponin and were incubated on ice while being mildly shaken for 30 min for complete solubilization of the sarcolemma. Permeabilized
(skinned) fiber bundles were then washed in solution B for
10 min at 4°C; this procedure of washing was repeated two times to
remove metabolites and soluble enzymes.
Preincubation with HK.
In most of the respiration measurements, we used the yeast type IV HK
as an exogenous soluble ADP-regenerating enzyme. In this case, the
three washings in solution B (see above) were done in the
presence of the same activity of HK (in IU/ml) as used in the
subsequent respiration measurement.
Respiration rate measurements.
The skinned fiber bundles were incubated in an oxygraph in 1 ml
solution B with 1 mg/ml BSA added. HK, if present, was
activated by adding 25 mM glucose. Steady rates of oxygen uptake were
recorded at various ADP levels during the linear phase. Determinations were carried out at 25°C using a Clark-type oxygen electrode. The
medium was stirred vigorously. The medium equilibrated with air
contained 215 µM oxygen.
Measurements of the rate of background ATPases.
Nonspecific background ATPase (NS-ATPase) activity of the fiber bundles
was measured using an assay in which formation of ADP was coupled to
NADH oxidation. Skinned fiber bundles of rat heart or soleus were
prepared as described above, except that washing solution B
contained 5 mg/ml BSA. The bundles were incubated in a cuvette
containing 1.5 ml solution C. The medium was continuously stirred. Changes in optical density at 340 nm were recorded before and
after addition of different amounts of ATP at 25°C. The reaction rates were estimated from the stable linear portions of the recordings.
Solutions.
All solutions contained 2.77 mM CaK2EGTA, 7.23 mM
K2H2EGTA, 6.56 mM MgCl2, 0.5 mM
dithiothreitol, and 20 mM imidazole. The calculated buffered free
calcium level was 0.1 µM, a condition that prevents contraction of
the bundles. Solution A additionally contained 50 mM
potassium 2-(N-morpholino)ethanesulfonate (K-MES), 5.3 mM
Na2ATP, 15 mM phosphocreatine, and 50 µg/ml saponin.
Solution B contained 100 mM K-MES, 3 mM
K2HPO4, 5 mM glutamate, and 2 mM malate.
Solution C was the same as solution B but was
complemented with 25 IU/ml pyruvate kinase, 25 IU/ml lactate
dehydrogenase, 0.24 mM NADH, 1 mM phosphoenolpyruvate, and
3.2 µM antimycin to inhibit oxidative phosphorylation. The pH of all
solutions was adjusted to 7.1 at 25°C. The chemicals were obtained
from Sigma or Boehringer.
Statistics.
Data are presented as means ± SE except for Fig. 3, where they
are given as means ± SD to demonstrate the significant difference of variances (F-test) between the groups. If the variances
were not significantly different, then the hypotheses about means were tested with Student's t-test. Otherwise, a more general
Welch's t-test was used. We chose a P value of
0.05 as the determinate of significance.
 |
MATHEMATICAL MODEL |
The samples used in our experiments contain bundles of various
sizes per sample cross section, surrounded by oxygraph medium. Measured
Kapp of a sample therefore represents a weighted
average of apparent Km values of the bundles in
a sample. The model represents the "average" bundle of a sample,
surrounded by oxygraph medium, that has the same
Kapp as the whole sample.
The model has two unknown parameters. The first of these,
Kmito, is the Km of the
mitochondrial respiration to stimulation by ADP. The second,
Reff, characterizes the effective diffusion distance from the well-mixed oxygraph medium to the core of the bundle.
Reff encompasses the diffusion paths through the
permeabilized cells in the bundle and through the unstirred water
layers surrounding the bundle. By fitting our model output to the
experimental results, we found Kmito = 25 µM and Reff = 35 µm (see MODELING
RESULTS).
Figure 1 depicts a schematic
representation of the model. The model consists of a cylindrical fiber
bundle with radius Reff where the
reaction-diffusion processes of metabolites are considered, surrounded
by an oxygraph medium compartment with a homogeneous distribution of
metabolites. Within the bundle exist two compartments, the cytosolic
and IMS compartments, with uniform distributions of the enzyme
concentrations and of the fractional volumes of compartments over the
bundle (bidomain principle). Diffusion is allowed only in the cytosolic
compartment.

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Fig. 1.
Schematic representation of the mathematical model.
A: fiber bundle, modeled as a cylinder with radius
Reff. The bundle has a uniform distribution of
mitochondrial and background ATPase activities, and it exchanges
metabolites with the surrounding medium via diffusion. Inside the
bundle, the background ATPase, adenylate kinase (AK), and ATP synthesis
(OxPhos) reactions are modeled. B: enlarged representation
of the mitochondrion and its immediate environment. The metabolites are
exchanged between the cytosolic and mitochondrial intermembrane space
(IMS) compartments via diffusional fluxes through the mitochondrial
outer membrane. The permeability of the latter is manipulated to
control Kmito, the Michaelis-Menten constant of
respiration to ADP, in the model.
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In the model, the following metabolites are considered: ATP, ADP, AMP,
and Pi. The cytosolic and the IMS compartments are separated by a partly permeable mitochondrial outer membrane. In the
IMS compartment, we consider the AK and ATP synthesis reactions. The
latter takes place in the matrix but is driven by ADP and Pi concentrations in the IMS. In the cytosol, ATP
hydrolysis by both NS-ATPases and HK occurs. A detailed description
with equations is given in the APPENDIX.
 |
EXPERIMENTAL RESULTS |
Figure 2 demonstrates that the
presence of 100 IU/ml yeast HK with 25 mM glucose as a substrate causes
a remarkable decrease of Kapp without
significant effect on the maximal oxygen uptake (VO2
max). To estimate the influence of incubation with HK
to VO2 max, we measured
VO2 at 2 mM ADP, which yielded 5.30 ± 0.15 µmol·g wet wt
1·min
1 for control
and 5.26 ± 0.20 µmol·g wet
wt
1·min
1 for HK-incubated fibers
(means ± SE; n = 8 and 7, respectively; P > 0.05).

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Fig. 2.
Influence of yeast HK on respiration. The example data
sets demonstrate that incubation of skinned cardiac fiber bundles with
100 IU/ml HK and 25 mM glucose causes a decrease in
Kapp without significant effect on
VO2 max. For control,
Kapp = 360 µM and
VO2 max = 5.06 µmol·g wet
wt 1·min 1; for HK,
Kapp = 76 µM and
VO2 max = 4.97 µmol·g wet
wt 1·min 1. See text for definitions.
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Figure 3 shows the dependence of
Kapp on the activity of the exogenously added
HK. Kapp decreased gradually (means ± SD)
from 216 ± 59 µM (n = 12) for control to 50 ± 9 µM
(n = 5) for 100 IU/ml HK. The reduction of
Kapp was accompanied by a significant decrease
of its variance.

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Fig. 3.
Dependence of Kapp on the activity
of exogenously added HK. Data points are approximated with a line
obtained from model simulations. The best least-squares fit, calculated
using individual data points, was obtained with
Reff = 35 µm and
Kmito = 25 µM. Data represent means ± SD
for (from left) 12, 3, 7, 3, and 5 experiments. The variance
of group VHK = 0 was compared with
variances of other groups (F-test); a significant difference
was found with group VHK = 100 IU/ml
(P = 0.015). The mean of the group
VHK = 0 was significantly different from
those of all other groups (P = 0.0036, Welch's
t-test). See text for definitions.
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Figure 4 demonstrates the influence of
the location of the HK activity on Kapp. For
some bundles (denoted as groups L and N in Fig.
4), we applied the 30-min preincubation procedure. However, for
groups K and M, HK was added only to the oxygraph
medium immediately before the measurement, so that no time was
available for HK to equilibrate between the medium and the fiber
interior. If glucose was absent (no HK activity; groups K
and L), then Kapp remained unaffected. With glucose present, Kapp
decreased. Kapp was significantly lower for
bundles preincubated with HK compared with the nonpreincubated bundles
(groups M and N), demonstrating that the lowering
of Kapp is due to enzymatic kinase activity
inside the bundles.

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Fig. 4.
Influence of glucose and location of HK on
Kapp. Groups K and L, no
glucose is added. Groups K and M, HK is added to
the medium just before determination of Kapp
[no preincubation (preinc)]. Group N, control (glucose
present and preincubation with HK). Error bars show SE for 4 (K and L) or 9 (M and N)
experiments. *P = 0.016, t-test. The
difference between M and N is 27 µM.
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We also tested the effect of HK for skinned soleus fiber bundles. HK
(100 IU/ml) reduced the Kapp from 218 ± 46 (SD) µM (n = 5, control) to 49 ± 12 µM
(n = 3; Welch's test, P = 0.0015).
To be able to simulate the influence of NS-ATPases on
Kapp (see MODELING RESULTS), we
measured their apparent activity in rat heart and soleus bundles (Fig.
5). Different amounts of heart bundles
were used in these measurements (5.5-15.2 mg wet wt tissue); however, the results did not depend on the amount of tissue. The ATP
dependence of both heart and soleus NS-ATPases is consistent with
Michaelis-Menten kinetics.

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Fig. 5.
Nonspecific background ATPase activity for heart and
soleus. The measured data were approximated by Michaelis-Menten
kinetics (means ± SE) where Km = 770 ± 70 µM and Vmax = 6.14 ± 0.20 µmol·g wet wt 1·min 1
(n = 8) for heart, and Km = 1,100 ± 300 µM and Vmax = 5.11 ± 0.60 µmol·g wet wt 1·min 1
(n = 8) for soleus fibers. See text for definitions.
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 |
MODELING RESULTS |
In this section, we present an analysis of the experimental
results using the mathematical reaction-diffusion model of the fiber bundle.
Figure 6 shows the simulated ADP
concentration profiles along the bundle radius at a half-maximal
respiration rate of the bundle (VO2 = 10 µmol·g dry wt
1·min
1) for
Kmito = 25 µM. Figure 6A shows
the ADP profile calculated at the parameter values (including
Reff = 35 µm) that best fit the experimental
results in Fig. 3 (see below). In this case, a relatively high
Kapp results from the high ADP gradients inside the bundle. In the outer layer, the mitochondria respire above their
half-maximal rate. In contrast, the core of the fiber negligibly exchanges adenine nucleotides with the outer layer or the medium and
respires at a very low rate, which is determined by the activity of the
NS-ATPases. The kinetics of the NS-ATPase used in the model were
determined from Fig. 5. Reducing Reff to a
radius of a typical cardiomyocyte (Fig. 6B) results in a
decrease of Kapp. Figure 6C shows the
influence of the ATP-consuming activity on Kapp. In addition to the NS-ATPase activity, we assumed the presence of 100 IU/ml HK in the cytosolic compartment. The increase of the
ATP-consuming activity means that smaller ADP fluxes from the oxygraph
medium are needed to keep the bundle respiration rate at the
half-maximal level. Reduced ADP flux from the medium results in a
reduced Kapp.

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Fig. 6.
Simulated ADP concentrations along the bundle radius r
at half-maximal respiration rate of the bundle. ADP level in the
oxygraph medium was assumed to be constant (ideal mixing) and equal to
Kapp. For A-D,
Kmito = 25 µM was used. A:
assuming Reff = 35 µm,
Kapp can be as high as 216 µM. Mitochondria in
the outer layer respire above their half-maximal rates while those in
the fiber core are close to state 4. Kapp and Kmito differ
considerably. B: assuming Reff = 8 µm, a typical myocyte radius, Kapp and
Kmito differ only moderately from each other.
C: with Reff = 35 µm, the
effect of adding 100 IU/ml HK was simulated using Eq. 23.
D: combination of effects from B and
C.
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In the medium, the ADP concentration is set to be equal to
Kapp, and the ATP and AMP concentrations are set
to zero. Because the AMP concentration remains everywhere in the bundle
below 5 µM in these simulations (data not shown), the local ATP
concentration can be approximated by Kapp
ADP.
Figure 7 shows
Kapp as a function of VHK
for varying Kmito and
Reff. The solid line is the optimal solution,
obtained at Kmito = 25 µM and
Reff = 35 µm. This is an identical line
to that in Fig. 3, obtained by fitting the model to the experimental
data. The thick dashed line shows the simulation assuming that the
mitochondrial outer membrane is the major diffusion barrier
(Kmito = 200 µM and
Reff = 8 µm). The increase of
Kmito was obtained by reducing the mitochondrial
outer membrane permeability in the model while keeping the
KADP of oxidative phosphorylation seen from the
intermembrane space at 25 µM. Figure 7 also shows the sensitivity of
the optimal solution (solid line) to the parameters
Kmito and Reff (see
legend to Fig. 7 for details). Briefly, changing
Kmito results in a nearly parallel shift of the
Kapp while Reff affects
the Kapp mostly at low
VHK values.

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Fig. 7.
Effects of Reff and
Kmito on simulated Kapp.
Solid line (control) is the solution fitted to the data in Fig. 3,
yielding parameter estimates Reff = 35 µm
and Kmito = 25 µM. Dashed and dotted line,
Reff reduced to a typical radius of a cardiac
myocyte (Reff = 8 µm,
Kmito = 25 µM). Thick dashed line shows
the dependency expected if the mitochondrial outer membrane were a
major diffusion barrier to ADP fluxes (Reff = 8 µm and Kmito = 200 µM). Thin dashed
lines show the effect of Reff on model behavior:
Reff = 40 (top) and 30 (bottom) µm. Dotted lines show the effect of varying
Kmito: Kmito = 35 (top) and 15 (bottom) µM. See text for definitions.
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Simulations of the NS-ATPase measurements indicate that the
Km values of the NS-ATPases given in Fig. 5 are
overestimated by ~10-15 µM because of small ATP gradients.
 |
DISCUSSION |
The present study was designed to investigate the finding that in
situ rat cardiac mitochondria in saponin-skinned fiber bundles possess
low affinity to ADP compared with isolated mitochondria. We manipulated
the intrafiber ATP-consuming activity by incubating the skinned fiber
bundles with 100 IU/ml yeast HK and observed a significant decrease of
Kapp (see Fig. 3). The lowest
Kapp measured (50 µM) shows an upper limit for
Kmito. We observed a similar decrease of
Kapp for skinned soleus fiber bundles. These
results were obtained without affecting the maximal respiration rate or modifying the mitochondrial outer membrane permeability.
Therefore, the mitochondrial outer membrane cannot be a major
diffusion barrier in these bundles.
An important assumption in interpreting our experiments has been that
the yeast HK does not affect the mitochondrial outer membrane
permeability. This assumption is supported by the following observations. First, many groups have failed to show the significant binding of yeast HK by mammalian or yeast mitochondria while, in
contrast, those mitochondria bind the mammalian type I HK avidly (for
review, see Ref. 24). Although the yeast HK and mammalian type I HK have similar amino acid sequences, the former lacks the
hydrophobic NH2-terminal segment that has been shown to be critical for binding of the type I isoenzyme (13).
Furthermore, adding dextran to the medium of suspended mitochondria
tends to decrease the affinity of mitochondria to ADP (5).
Therefore, the change of osmolarity caused by adding a high
concentration of HK would increase, rather than decrease,
Kapp.
Saks et al. (15) claimed that the diffusion of metabolites
between the oxygraph medium and the bundle interior is so rapid that
considerable concentration differences between the interior of fibers
and medium (tens or hundreds of micromolars) are not possible. The
underlying assumption has been that the effective diffusion distance
(the effective fiber bundle radius Reff) is similar to the radius of the average cardiac myocyte (6-8 µm). The Kapp for isolated permeabilized myocytes has
been reported to range from 150 (9) to 250 (14) µM. However, to our knowledge, nobody has ruled out
the possible formation of small aggregates of permeabilized myocytes in
the oxygraph in these measurements, nor has the
Reff for skinned fiber bundles been reliably
measured. Visual inspection of the samples under a microscope revealed
an inhomogeneous geometry of the bundles with their apparent radius ranging from 10 to 50 µm. Model fitting of the data yielded
Reff = 35 µm and suggested the existence
of considerable diffusion gradients (see Fig. 6).
The Kapp of the bundles varied strongly between
our experiments, ranging from 150 to 400 µM. The reason might be the
variance of Reff, which depends on the
mechanical separation procedure of bundles (see METHODS).
We found the average Kapp to be ~200 µM.
HK (4 IU/ml) has been observed earlier to have no effect on kinetic
parameters (16, 19), which is in agreement with our findings (Fig. 3). Only if there were a rapid and unrestricted diffusion of metabolites between the bundle core and medium would 4 IU/ml HK provide an excess amount of total ATP-consuming activity compared with the total ATP production capacity of a sample. However, much higher HK activity is actually needed to observe significant effects on Kapp because high activity is needed
specifically inside the bundles.
Modification of mitochondrial or NS-ATPase activity of the samples by
chemical and potentially nonspecific means was avoided by changing the
overall ATP-consuming activity with known amounts of HK. This approach
allows more straightforward interpretation of the results than some
previously used approaches in which calcium or magnesium levels were
manipulated (15). In those experiments, modifying either
free calcium or free magnesium caused no significant effect on
Kapp. However, one cannot exclude that changes
in intrafiber ADP production rate are balanced by parallel effects on mitochondria.
The model we used for our simulations is only an approximation. The
effective bundle radius Reff, found by data
fitting (see Fig. 3), can differ from the real average bundle radius in
our samples because unstirred water layers may exist around the
bundles. The geometry of the sample (e.g., average number of fibers in bundles) does depend on the mechanical fiber separation procedure. However, our simulations show that the choice of
Reff affects the simulated
Kapp only for low ATP-consuming activities,
whereas it has a minor effect at high activities (see Fig. 7). The
value of 25 µM for Kmito, found by fitting the
experimental Kapp data at high ATP-consuming
activities, is only slightly higher than the typical
Km of isolated mitochondria (10-20 µM).
However, it is an order of magnitude lower than
Kapp = 200-400 µM.
Independent support of a low Kmito in skinned
rat heart fiber bundles comes from the observations that, when
respiration was activated by ADP that was produced endogenously by
NS-ATPase reactions, the half-maximal respiration rate was achieved at
~25 µM ADP (19). In these experiments, the authors
added different amounts of ATP to the oxygraph, allowed steady
concentrations to be established, recorded the respiration rate, and
measured the ADP level in the oxygraph medium by HPLC. Because there
was no enzyme in the medium that could actively take up ADP, the
measured ADP level was equal to the ADP level inside the bundles. Our
model analysis indicates that the endogenously produced ADP level that
yielded 50% of the respiration rate (25 µM ADP) reflected the real
Kmito (Fig. 8).

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Fig. 8.
Model fit of the dependence of the relative respiration
rate on the level of endogenously produced ADP. Experimental data from
Seppet et al. (19) were simulated (ADP concentrations in
the medium and rates calculated after 2 min of simulated reaction time)
using a maximal mitochondrial ATP synthesis rate of 203 µM/s and a
maximal ATP hydrolysis rate of 270 µM/s.
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Mild proteolytic treatment of skinned heart and soleus fiber bundles
causes a decrease of Kapp from 300-400 to
50-80 µM (12). The possibility that the decrease
was caused by the increase in NS-ATPase activity was recently examined
by Saks et al. (15). They measured NS-ATPase activities
for five groups of skinned heart fiber bundles treated with 0 (control)
to 5 µM of trypsin during 5 min at 4°C (see Fig. 7B of
Ref. 15) and concluded that the NS-ATPase activity was not
affected by a trypsin treatment. However, the NS-ATPase activities
differed from each other by ~50% between the 0 (control) and 50 nM
groups (Kapp = 300 and 123 µM,
respectively). A two-sided t-test (n = 2/group) performed by us yielded P = 0.0224.
Therefore, we conclude that trypsin treatment may increase the
NS-ATPase activity. This is in accordance with observations that the
mild tryptin treatment of canine cardiac microsomes, consisting largely
of sarcoplasmic reticulum vesicles, activates the rate of the
oxalate-facilitated calcium uptake up to 2.8-fold compared with control
(8).
The increase of the intrafiber diffusion coefficient by depleting the
fibers of myosin by treatment with 800 mM KCl has been observed to
increase rather than decrease Kapp
(16). This observation has been used to support the
hypothesis of a low mitochondrial outer membrane permeability. However,
the expected decrease of Kapp may be compensated
by reduced NS-ATPase activity, because part of this activity is likely
linked to the extracted myosin.
In conclusion, we found that increasing intrafiber ATP-consuming
activity without affecting the permeability of the mitochondrial outer
membrane causes a decrease of Kapp of skinned
heart and soleus fiber bundles. These results cannot be explained by
the theory that the outer mitochondrial membrane acts as a major
diffusion barrier in these bundles. Our simulations suggest the
existence of large ADP diffusion gradients between mitochondria and the surrounding medium and the reduction of the gradients if intrafiber ADP
production is increased. We propose that the affinity of the in situ
and probably also in vivo mitochondria to ADP in heart and soleus is of
the same order of magnitude as that of isolated mitochondria.
 |
APPENDIX |
The reaction-diffusion equations of the model form a set of
partial differential equations. The equations are given in polar coordinates. The reaction rates (in µM/s) are normalized to total cell volume. The parameters used in the modeling are given in Table
1.
The balance equations for the metabolite concentrations in the IMS are
as follows
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(1)
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(2)
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(3)
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(4)
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where Vsyn and VAK
are the ATP synthesis and the AK reaction rates, respectively, and
JMet are the diffusion fluxes from the IMS to
the cytosolic compartment (Met denoting the metabolite involved).
VIMS is the fractional volume of the IMS compartment with
respect to the cell volume.
et denotes the partial
derivative of Met with respect to time (
Met/
t).
The equations for the cytosolic compartment are as follows
|
(5)
|
|
(6)
|
|
(7)
|
|
(8)
|
where Vhyd and VHK
denote the reaction rates of NS-ATPase and HK. Vcyt is the
fractional volume of the cytosolic compartment, DMet are the diffusion constants of metabolites
Met in solution, and the products DMet × Vcyt represent the diffusion constants adjusted for the
reduction of free diffusion space. The symbol
2 denotes
the Laplace operator in polar coordinates if radial symmetry is held,
i.e.
|
(9)
|
where r is the radial coordinate in the bundle.
The equations for the oxygraph medium compartment are as follows
|
(10)
|
|
(11)
|
|
(12)
|
|
(13)
|
where Qs/o is the ratio of the sample volume and the
oxygraph volume. Here
|
(14)
|
is the diffusional flux of the metabolite Metc from
the bundle to the oxygraph medium per unit of bundle volume. The
concentrations Meto are also the boundary conditions for
the cytosolic concentrations, i.e.
|
(15)
|
for all metabolites in the model. At the other boundary,
r = 0, the no-flux condition applies.
For the AK reaction, we derived the full kinetic equations, because in
some simulations the AK works far from equilibrium. We calculated the
magnesium-bound and magnesium-free forms, denoted by prefixes m or f,
respectively, of ATPi and ADPi as follows
|
(16)
|
|
(17)
|
|
(18)
|
|
(19)
|
where Mg is the free magnesium concentration. AMPi
was assumed to be mostly in the magnesium-free form (2).
The AK reaction rate VAK took into account the
inhibitory effects of ADP and AMP via formation of the nonproductive
complexes ADP·AK·ADP, AMP·AK·ADP, and AMP·AK·MgADP
(10)
|
(20)
|
where
|
(21)
|
The mitochondrial ATP synthesis rate was simulated by
Michaelis-Menten-type kinetics
|
(22)
|
The respiration rate was estimated as
VO2 = Vsyn/(2 × QP/O).
The rate of ATP consumption by HK was simulated as
|
(23)
|
because, in the experiments, the glucose concentration of 25 mM
was well above its Km = 80 µM, and the
glucose-6-phosphate concentration was estimated to remain far below its
Km = 30 mM, whereas both ATP and ADP
concentrations remained close to or below their
Km (150 and 230 µM, respectively). The
dissociation constants for yeast HK were taken from Ref.
22.
The rate of ATP consumption by the NS-ATPases was simulated
analogously to Eq. 23
|
(24)
|
We assumed here that the ATP synthesis rate by these ATPases in
response to stimulation by ADP is negligible.
Diffusional fluxes between the compartments are as follows.
|
(25)
|
|
(26)
|
|
(27)
|
|
(28)
|
where Pic reflects the permeability
of the outer mitochondrial membrane and affects the
Kmito = ADPc
ADPi + KADP calculated at the
half-maximal ATP synthesis rate. Positive direction of the flux is from
the IMS to the cytosol.
The rate equations of the model form a system [Eqs.
1-8 and Eqs. 10-13] that was solved
simultaneously. The partial differential equations were transformed
using a finite differences approximation scheme with a uniform grid
along the bundle radius. The resulting system of ordinary differential
equations was solved by a backward differentiation formula that is able
to treat stiff equations, using the DVODE package. The precision of a
solution was tested by comparing it with the solution for a 2-fold
denser grid and for a 10-fold smaller relative tolerance of the
integrator. Convergence was obtained at a grid step
r
1
µm and relative tolerance 10
7. To fit to the
experimental data, the model parameters were optimized by a modified
Levenberg-Marquardt algorithm, using the LMDIF least-squares solver.
To improve the moiety conservation in the model, the spatial
derivatives of the cytosolic metabolite concentrations at the bundle
surface were estimated from the quadratic approximations to the
concentrations' profiles at the boundary
where Metc,n,
Metc,n
1, and
Metc,n
2 are the approximations to
Metc at nth, (n
1)th, and
(n
2)th grid point, respectively, with the
nth grid point residing at the boundary.
The implicit parameter Kapp was
calculated by optimizing ADPo to yield the half-maximal
respiration rate. At each optimization step, the levels of the
metabolites in the oxygraph were kept constant (Qs/o = 0) as follows: ATPo = 0, AMPo = 0, Pio = 3 mM. ADPo was modified
(Levenberg-Marquardt), and the resulting respiration rate was obtained
after the transients vanished (t = 60 s). The parameter
Kmito was manipulated by changing
Pic in Eqs. 25-28, and it was
estimated as Kapp for the bundle with a very
small radius (Reff = 0.1 µm) where the
diffusional gradients were negligible.
 |
ACKNOWLEDGEMENTS |
We are grateful to Drs. A. V. Kuznetsov and G. J. M. Stienen for valuable advice and help with experimental procedures and to Dr. G. Wardeh for providing the animals. We thank Dr. S. P. Elmore and Ing. F. ter Veld for many helpful discussions and critical remarks about the manuscript.
 |
FOOTNOTES |
This research was supported by a Marie Curie Fellowship of the European
Community program Improving Human Research Potential and the
Socioeconomic Knowledge Base under contract number HPMF-CT-1999-00309 and by Estonian Science Foundation Grant ETF4704.
Address for reprint requests and other correspondence: O. Kongas, Dept. of Mechanics and Applied Mathematics, Institute of Cybernetics, Tallinn Technical University, Akadeemia 21, 12618 Tallinn,
Estonia (E-mail: kongas{at}ioc.ee).
May 1, 2002;10.1152/ajpcell.00101.2002
 |
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