Download Diffusion of myoglobin in skeletal muscle cells

Pfl/igers A r c h - E u r J Physiol (1995) 430:519-525
9 Springer-Verlag 1995
Simon Papadopoulos 9 Klaus D. Jiirgens
Gerolf Gros
Diffusion of myoglobin in skeletal muscle cells
- dependence on fibre type, contraction and temperature
Received: 26 October 1994/Received after revision and accepted: 17 February 1995
Abstract We measured the diffusion coefficient of myo-
globin (DMb) inside mammalian skeletal muscle cells
with a microinjection technique. A small bolus of horse
Mb was injected into a single muscle fibre and the subsequent time-dependent changes of the Mb profiles
along the fibre axis were measured with a microscopephotometer. For fibres of the rat soleus muscle at 22 ~ C,
a DMb of 1.3"10 -7 cmZ/s was found, confirming a result
obtained previously by us for rat diaphragm muscle
with a photo-oxidation technique. In the extensor digitorum longus muscle of the rat, a higher value of
1.9 9 10 - 7 cm2/s was measured. Auxotonic muscle contractions did not change the apparent DMb. For the temperature range between 22 ~ C and 37 ~ C, a temperature
coefficient, Q~0, of 1.5 was calculated. The implication
of this result for the role of Mb in the facilitation of
oxygen transport was examined. Model calculations
show that with this relatively low DMb value, the intracellular oxygen supply can be improved only slightly.
Key words Diffusion coefficient 9 Muscle cells 9
Myoglobin 9 Microinjection 9 Oxygen 9 Facilitated
diffusion 9 Intracellular oxygen transport 9 Rat
Introduction
In mammalian muscle tissue myoglobin (Mb) serves as
an intracellular oxygen (02) reservoir. Besides its function as an 02 storage protein, Mb can also contribute
to 02 transport in the sarcoplasm. 02 is bound to M b
near the capillaries, where the partial pressure of 02
(PO2) is relatively high, and the oxygenated protein
diffuses along its concentration gradient and releases
02 at locations where the PO2 is low, i.e. near the mitochondria. The degree to which intracellular 02 transS. Papadopoulos - K. D. Jfirgens ([]) 9 G. Gros
Zentrum Physiologie, Medizinische Hochschule,
D-30623 Hannover, Germany
port is enhanced by this facilitated 02 diffusion depends
on the Mb concentration and on the intracellular
mobility of this haemoprotein. In red muscles of terrestrial mammals the Mb concentration is generally
below 0.5 mM. The intracellular diffusion coefficient of
Mb (Dvb) in intact mammalian skeletal muscle cells,
however, has not been determined until recently. So far
the value of DMb employed in most mathematical models estimating the degree of facilitated 02 transport
within muscle cells has been taken from measurements
of the self-diffusion coefficient in 18 g/dl aqueous Mb
solutions, as reported by Riveros-Moreno and
Wittenberg in 1972 [20]. The considerably lower DMb
value obtained in 1968 by Moll [18] in homogenates of
rat skeletal muscles has hardly ever been used in model
calculations.
In 1988, Baylor and Pape [1] determined DMb in (normally Mb-free) frog muscle fibres into which M b was
injected. The value of DMb obtained from these experiments amounts to only one quarter of the figure found
in 18 g/dl Mb solution. Recently in our laboratory,
measurements of DMb of intrinsic Mb within intact
mammalian muscle cells [11] were achieved with a
method based on the photo-oxidation of oxymyoglobin (MbO2) using ultraviolet light (UV-photo-oxidation method). At 22 ~ C, the DMb value found with this
technique in diaphragm muscles of the rat amounts to
one-fifth of the self-diffusion coefficient in 18 g/dl Mb
solutions.
One aim of the present work was to check whether
the results obtained with the UV-method can be
reproduced by a microinjection technique applied to
mammalian skeletal fibres. We performed these measurements on two different muscles, the red soleus and
the white extensor digitorum longus (EDL) of the rat,
in order to see whether there is a dependence of DMb
on muscle fibre type.
Furthermore, we investigated the influence of auxotonic muscle contractions on the intracellular mobility of Mb. We also studied the temperature dependence
520
o f D v b in t h e r a n g e b e t w e e n 2 2 ~
a n d 37 ~ C. T h e
implication of our results for the contribution of facili t a t e d 0 2 d i f f u s i o n t o t o t a l i n t r a c e l l u l a r 0 2 t r a n s p o r t is
discussed.
Materials and methods
The soleus and the EDL muscles were obtained from female Wistar
rats (230-280 g). During preparation of a fibre bundle the muscles
were kept in carbogen-equilibrated Ringer solution. The PO2 in the
preparation dish ranged between 40 kPa and 50 kPa (300 and 375
Torr, respectively). The bundles prepared this way consisted of
between 2 and 20 fibres. Only intact fibres of the bundles, i.e. fibres
without visible alterations along their entire length, were used for
the experiments. The fibre bundle was mounted into a chamber perfused with carbogen-equilibrated Ringer solution (pH 7.4). It was
held under tension and placed into a small groove of a glass block
in order to prevent sagging and to minimize movement artefacts
during the measurements. The length of the sarcomeres varied from
bundle to bundle between 2.5 pm and 3.2 gm. The temperature of
the chamber was maintained at either 22 ~ C or 37 ~ C.
For the microinjection experiments, an experimental setup as
described previously [1] was used with some modifications. The sample chamber was mounted on a computer-controlled scanning stage
which is part of a microscope-photometer (Zeiss PM 03). The fibre
bundle was transluminated with light from a halogen bulb and the
transmitted light collected by means of a water immersion objective with 2 m m working distance (Nikon x40, the overall
magnification was • 640). A rectangular diaphragm, variable in
height and width, was used to define the fibre area in which the
intensity of the transmitted light was to be measured. The height
of the area was chosen to be about 20% less than the fibre diameter (40-80 gm); the width usually was 20 gm. The measuring wavelength was set by a monochromator (bandwidth 5 nm) and the light
intensity measured with a photomultiplier, which was connected to
an AD-converter of a personal computer. The scanning stage,
monochromator and photomultiplier were controlled by a personal
computer via a programmable interface.
For the microinjection, a fibre segment was chosen that had constant fibre diameter, intact structure and no noticeable remnants of
the perimysinm. Fibres on the edge of the bundle exhibited more
favourable signal-to-noise ratios compared to the fibre multilayers
in the central region of the bundle and, therefore, were preferred
for these experiments. The microinjection site was selected under
visual control with a joy-stick connected to the control unit of the
scanning stage. The minimum step size (0.1 gm) of the stage permitted precise positioning in three co-ordinates. During a scan the
scanning stage moved stepwise (100 or 200 steps) along the longitudinal axis of the fibre and, at each step, the intensity of the transmined light was measured. A scan performed in this manner took
less than 1 rain for a fibre segment of 1000-2000 gm. In this way,
an adequate temporal and spatial resolution compared to the relatively slow diffusion process could be achieved. Prior to the
microinjection of Mb, a reference scan was made in order to measure the light intensity distribution of the native cell. After microinjection, up to 15 scans were performed at different times to record
the changes of the transmittance profiles caused by axial diffusion
of Mb.
In some of the experiments on soleus fibres, series of auxotonic
contractions were carried out between the scans. In these cases one
end of the fibre bundle was fastened to a U-shaped spring. The
compliance of the spring was chosen so as to permit maximum contraction of the bundle during stimulation, but also a return of the
sarcomere spacing to its original value after the contraction. In this
way, the fibre bundles usually contracted to at least 60% of their
initial length. The fibres were stimulated at 50 Hz (pulses of 1 ms
duration) once every second for 400 ms. Since a cycle of contrac-
tions lasted for 20 min, the bundle shortened 1200 times between
two successive photometric scans.
Ferric Mb from horse skeletal muscle (Serva) was used for the
injections. The lyophilized powder was dissolved in phosphate buffer
(pH 7.2). Insoluble material was removed by centrifugation (20 min,
2000 g). Ultrafiltration membranes were used to remove large protein aggregates (Amicon, YM100) and to concentrate the solution
(Amicon, YM5) to a final concentration of around 17 mM. The
material was frozen and stored at - 8 0 ~ C.
Micropipettes for injection of Mb were drawn from acid-cleaned
capillaries (10 cm length, 1.2 mm outer and 0.8 mm inner diameter) of borosilicate glass by a programmable horizontal puller
(Mecanex, BB-CH). The tip diameter ranged between 0.7 gin and
1.8 gm. The pipette tips were back-filled with thawed and recentrifuged Mb solution and mounted onto a Piezo-micromanipulator
(M/irzhfiuser, PM 10-1). Injection of the protein into the muscle
fibre was performed by applying pressure to the back of the
micropipette (WPI, pneumatic pico pump); injection took no longer
than 3 s. The fibre structure at the penetrated site was usually unaltered by the procedure. Each injection was of about 30-50 pl of the
17 mM Mb solution. The longitudinal spread of Mb along the fibre
due to the pressure injection and the time delay between removal
of the pipette and start of the scan led to an initial Mb distribution extending over a maximal distance of + 150 bun from the injection site. From the absorbance profile obtained immediately after
injection, a local maximal cellular Mb concentration of 2 m M was
estimated. This means that the total intracellular protein concentration of 24 g/dl wasincreased at this site by not more than 3g/dl.
This slight initial inhomogeneity of intracellular protein concentration was neglected in the calculation of DMb.
The absorbance profiles of the scanned fibre were calculated
from the measured light intensities before (reference scan) and after
injection of Mb. Assuming validity of Beer's law, the Mb concentration is proportional to the absorbance (A). Since the maximal
value of A of the metmyoglobin (MetMb) was at 409 nm in the
Soret band, this wavelength was used for the measurements. The
method applied to determine DMb from the absorbance profiles
measured at different times after injection is based on a numerical
solution (Crank-Nicolson algorithm) of the differential equation
describing the one-dimensional diffusion process, where c denotes
concentration, t time and x diffusion path:
de
d2c
~ - = DMu dx 2
(1)
Although enzymatic reduction of MetMb can take place within the
muscle cell, the effect can be neglected here because of the large
excess of injected MetMb in relation to the reduction capacity of
the enzymes [11].
The concentration profile measured directly after injection was
taken as the initial condition required to solve the differential equation. The curves recorded afterwards were fitted as an ensemble to
the solution of the differential equation by varying DM,owith a leastsquares method. Although up to 1 min is required to record one
absorbance profile, for practical reasons (definition of the initial
condition) each profile has been considered as being recorded at a
fixed time. We have estimated that this simplification leads to an
error in DMbof less than 1% as long as the time differences between
corresponding points in two successive profiles are identical.
Results
F i g u r e 1 s h o w s a n e x a m p l e o f a set o f e x p e r i m e n t a l
absorbance profiles obtained from a soleus fibre and
t h e c o r r e s p o n d i n g b e s t fit c u r v e s .
A s s h o w n in T a b l e 1, e v a l u a t i o n o f t h e r e s u l t s
obtained from injections into soleus fibres yielded a
521
0.5
i
i
i
--,300
-- I ;50
0
i
i
150
,:300
0.4
A 4Q9
0.3
0.2
0.1
O.13
I
longitudinal fibre axis [/u.m ]
Fig. 1 Distribution of the myoglobin (Mb) concentration along a
muscle fibre 2.5, 5, and 10.5 min after injection. Shown are the
absorbance profiles measured at 409 n m (A409) and the best fits from
the numerical solution of the diffusion equation. The absorbance
profile measured immediately after the injection (0 rain) is taken as
the initial condition for the solution of the differential equation
value for DMb of 1.25' 10 - 7 cm2/s. In EDL fibres a
significantly higher (P < 0.001) value of 1.87" 10 7
cm2/s was found. At 37 ~ C for soleus, a DMb value of
2 . 2 0 10 - 7 cm2/s was measured. From the values
obtained at 22 ~ C and 37 ~ C a temperature coefficient,
Q10, of 1.46 was derived. In soleus, the influence of contractions on Mb mobility was investigated. The value
Of DMb calculated from the contraction experiments was
1.3310 -7 cm2/s, which is not significantly different
from the value found in resting fibres. The value Of DMb
obtained from soleus muscles using the injection
technique was not significantly different from the figure
we found previously in rat diaphragm muscle using a
photo-oxidation technique, which leaves the fibres
unaltered mechanically and is based on the diffusion
of intrinsic Mb.
Discussion
The DMb values found in this study are remarkably
small compared to those measured in aqueous Mb
solutions. In highly diluted solution, a 10 times greater
value of DMb is found. In a Mb solution concentrated
to 18 g/dl, which has been proposed to represent cytoplasmic conditions for macromolecular diffusion [20],
Table 1 Diffusion coefficients
of Mb ( D M b ) in rat skeletal
muscles. Values are means
+ SEM. (EDL Extensor
digitorum longus)
Rat muscle
Soleus
Soleus
Soleus
EDL
Diaphragm
the diffusivity of Mb at 22 ~ C is about 5 times larger
than the intracellutar diffusivity measured here.
There are other factors besides the intracellular viscosity that could slow down the mobility of Mb within
a muscle cell. One is binding of the protein to immobile structures. Histological investigations of the intracellular distribution of Mb led to contradictory results.
A homogeneous distribution [9] as well as binding to
different cell structures [12, 13] have been reported. Mb
injected into frog muscles was reported to bind relatively weakly and fully reversibly, leading to a reduction of the apparent DMb by not more than 10-20%
compared to conditions under which no binding occurs
[1]. Electrostatic interactions between Mb and
myofilaments are not likely to be very strong since the
net charge of the Mb is very low at normal intracellular pH.
Hindrance of the diffusion process can also be
expected by the highly structured cytoskeletal system
and contractile apparatus of the muscle cell. The spatial arrangement of the components of the contractile
apparatus probably causes remarkable geometrical hindrance of the mobility of macromolecules, especially
when molecules move through spaces the dimensions
of which are of the same order of magnitude as the
size of the moving molecule. Moreover; it has been
shown in theoretical studies that periodically arranged
obstacles can dramatically reduce the diffusion
coefficient when the size of the moving particle
approaches the interobstacle distance [3]. These kinds
of effects are likely to occur in muscle cells since the
molecular diameter of Mb (3.5 nm) is not very different
from several lattice spacings in the sarcomeres. The distances between the filaments as well as the Z-disc and
M-line spacings are all in the range of 5-10 nm.
The results we obtained for red and white rat muscles are in accordance with the role of this hindrance.
The value of 1.3 9 10 -7 cm2/s that we found in fibres
of the soleus at 22 ~ C with the microinjection method
is in excellent agreement with the value of 1.2.10 -7
cm2/s measured in our laboratory in the rat diaphragm
muscle, using a completely different method (Table 1).
Like the soleus muscle, the diaphragm consists predominantly of Mb-rich type I fibres. In contrast, the
EDL muscle of the rat is composed mainly of type II
fibres. Here we found a 50% larger DMb value than for
the soleus muscle. It is known from morphological
Parameter
Technique
Number of
experiments
Temperature
(~
DMb
(x 10 -7 cm21s)
injection
injection
injection and contraction
injection
UV-Photo-oxidation [11]
12
24
7
12
76
22
37
22
22
22
1.25
2.20
1.33
1.87
1.17
+ 0.13
_+ 0.12
+ 0.07
+ 0.08
+ 0.08
522
studies of these two rat muscles that there are considerable differences in their cell structure. A striking
difference occurs in the thickness of their Z-discs, which
has been reported to be 112 nm in soleus and 64 nm
in EDL [21]. It may well be that one of the main obstacles for longitudinal diffusion of Mb is the lattice-like
arrangement of the molecules forming the Z-discs. The
same may hold for the M-lines, since it has been shown
that fibres with wider Z-discs tend to have wider
M-lines as well [22]. Furthermore, the number of the
mitochondria, which may also act as obstacles of
macromolecular diffusion, is about 65% larger in the
slow oxidative soleus fibres than in the fast EDL fibres
[211.
Both of o u r DMb values are in the same range as the
result of Baylor and Pape [1]. From microinjection
studies using frog skeletal muscle fibres, in which intrinsic Mb is absent, Baylor and Pape [1] obtained a value
of 1.6 - 10 - 7 cm2/s at 22 ~ C. There is also good agreement with the result of Moll [18], who reported a DMb
value of 1.5 9 10 - 7 cm2]s (20 ~ C ) in homogenates of red
muscles of the rat.
Our results hold for the axial DMb in muscle cells.
For the physiological role of Mb-facilitated 02 transport, however, the radial diffusivity might be of more
relevance. No direct measurements of radial DMb have
been reported so far, but it is known from measurements of the radial diffusion of other proteins of similar size that, within skinned muscle fibres and at
physiological concentrations, the radial diffusion
coefficient is about one-tenth of that which holds for
dilute aqueous solutions [17]. Thus, there is evidence
that intracellular axial and radial protein diffusion
coefficients are reduced to a similar extent.
In order to test whether muscle contractions
influence the mobility of Mb, repetitive auxotonic contractions of the fibre bundles of the soleus muscle were
performed. In spite of considerable contractile activity
between the measurements, no effect o n / ) M b could be
noted. This means that convectional Mb transport,
which could increase the apparent )DMb , does not occur
during muscle contractions. This result supports ideas
that the consistency of the cytoplasm is more that of
a viscoelastic gel [16] than that of an aqueous solution.
Baylor and Pape [1] investigated the effect of isometric
contractions on the mobility of Mb injected into frog
skeletal muscle; they also noticed no significant change
in the apparent DMb.
The microinjection technique turned out to be well
suited for measurements at body temperature. Under
the physiological condition of 37 ~ C in the soleus muscle, DMB amounts to 2.2 9 10 -7 cmZ/s. Since many investigations are performed at room temperature, it is useful
to have a measure of the temperature dependence of
intracellular DMB. From our results obtained at 22 ~ C
and 37 ~ C we calculate a Q10 of 1.5. This is somewhat
smaller than the value of 1.6 that Baylor and Pape [1]
determined in frog muscles in the temperature range
between 16~ and 22 ~ C. For muscle homogenates,
Moll [18] reported a Ql0 of 1.4 in the temperature range
of between 20 ~ C and 37 ~ C. All these values are larger
than those in simple aqueous protein solutions, in
which, due to the temperature dependence of the viscosity of water, a Q10 of about 1.3 holds. This may be
due to the fact that the temperature dependence of the
structural hindrances of Mb mobility is more pronounced than that of cytosolic viscosity.
Reliable knowledge about the intracellular mobility
of Mb is greatly significant for estimations of the 02
transport from capillaries to the mitochondria. It has
been attempted to evaluate, experimentally and in vitro,
the role of Mb-facilitated 02 diffusion in intact cells
and in muscle tissue. This was carried out mainly by
abolishing functional Mb in the cell and then observing the consequences for 02 consumption.
The results obtained by different groups are contradictory. Whereas in one study [10] no contribution of
Mb-facilitated diffusion to the intracellular 02 transport was found, experimental evidence for facilitated
diffusion was reported in several other studies. Cole [5]
found a nearly 50% reduction in 02 consumption of
dog gastrocnemius muscle after treating Mb with
hydrogen peroxide (H202). He observed this reduction
in moderately working muscles, perfused with almost
completely O2-saturated blood at an arterial PO2 of
10.3 kPa (77 Torr). The venous POz values are not given
in his paper, but can be estimated at not less than 4 kPa
(30 Torr) from the given 02 consumption and the 02
binding curve of dog blood. It is questionable whether
facilitated 02 diffusion can play a significant role in
Cole's [5] preparation at a capillary PO2 greater than
4 kPa (30 Torr). From the Krogh-cylinder model (cylinder radius Rcy I m_ 25 btm, capillary radius reap = 2 gm,
other data see legend of Fig. 2) we calculate that, at
the 02 consumption measured by Cole [5], a PO2 of
1.7 kPa (13 Torr) at the capillary muscle cell boundary should be sufficient to provide the 02 required by
the cell without any facilitated diffusion. Although Cole
[5] reported that application of H202 for a brief time
did not affect a variety of parameters important for
normal muscle activity, it may not be totally excluded
that this highly potent oxidant also had undesirable
effects on muscular function and that these are responsible for the measured drop in active tension generation and in 02 consumption.
Another group of studies, in our opinion, has been
performed under conditions of severe tissue hypoxia.
Taylor et al. [23] found, compared to non-treated
hearts, a faster decrease of adenosine 5'-triphosphate
(ATP) and phosphocreatine concentrations in rat
hearts after blocking Mb with nitrite, when the animals started to breath an O2-free gas mixture, i.e. when
severe hypoxia was provoked, de Koning et al. [15]
found a reduction in 02 consumption in slabs of
chicken gizzard (300- to 700-btm thick) after blocking
Mb with carbon monoxide (CO). This study was
523
carried out with a PO2 of 0 Pa at one side and up to
10 kPa (75 Torr) on the other side of the sample. With
the data given by the authors it can be calculated from
the Warburg equation that the thickness of their samples far exceeded the critical thickness, i.e. large hypoxic
areas must have been present in the muscle tissue. To
a lesser degree this holds also for the experiment of
Wittenberg et al. [24], who measured a drop in 02 consumption of fibre bundles from pigeon breast muscle
(300- to 600-btm thick) treated with nitrite. We conclude
that all these measurements only show that Mb-facilitated 02 diffusion plays a role under conditions of
extremely low tissue PO2. For this situation, the present diffusion coefficient also predicts a significant facilitation of Oz diffusion (see Fig. 2, below). However, we
suggest that neither our results nor those cited provide
evidence of a significant contribution of Mb to intracellular 02 transport under physiological conditions.
To provide a quantitative assessment of the degree
of Mb-mediated facilitated 02 diffusion, mathematical
modelling studies have been employed (see e.g. [19]).
As mentioned before, a critical parameter in these studies is the value Of DMb chosen for the muscle fibre. Since
no measurements of intracellular DMb have been available until recently, in general, values in the range of
5 9 10 - 7 cm2/s to 23 9 10 - 7 cm2/s were chosen [6]. Most
authors referred to the value derived from the study of
Riveros-Moreno and Wittenberg [20] using Mb solutions, i.e. 8 9 10 - 7 cm2/s for a 18 g/dl Mb solution, (e.g.
[7, 8]). Since it appears now that this value is much
larger than that which holds for intact muscle fibres,
the modelling studies have generally overestimated the
contribution of Mb to total 02 transport.
Therefore, we recalculated the contribution of Mbfacilitated 02 diffusion to total 02 transport in the muscle cell. From a Krogh-cylinder model with PO2ob being
the PO2 at the cell boundary on the inner surface of
the cylinder and a PO2 of zero on the outer surface of
the cylinder, the ratio of facilitated oxygen diffusion
(VO2Mb) to free 02 diffusion (gO2free) is calculated [11]
as:
gO2Mb
~'O2free
DMb " CMb
-- N o ' ( r O 2 c b -1- P50)
(2)
CMb is the total Mb concentration in the cell water, K0
is Krogh's diffusion constant for 02 and Ps0 is the 02
half-saturation pressure of Mb. Equation 2 is derived
from the Krogh model, but since it is independent of
geometrical factors, it also holds for other geometrical
models of 02 supply to muscle cells, provided that the
boundary conditions are equivalent.
Figure 2 shows a plot of the flux ratio gO2Mb/g O2fre e
as function of the PO2cb. The shapes of these curves
can be understood as follows. It can be derived from
Eq. 2 that ~)~O2Mb/~'~O2freeis proportional to the ratio
[MbO2]ob/PO2cb, where [MbO2]ob is the concentration of
MbO2 at the cell boundary, as it prevails in the cell
considered. Since [MbO2]ob under the chosen conditions
5.0
I
]
I
t
I
I
I
15
I
20
i
25
30
~
55
I
40
4.5
4.0
L 3.5
~o
,=
O
3.0
2,5
2.[}
1.5
1.0
0.5
0,0
OI
5
I
10
I
45
50
P02.b [Torr]
Fig. 2 T h e ratio o f Mb-facilitated 02 diffusion a n d free 02 diffusion
(1702Mfl 170~f~e) as f u n c t i o n o f t h e p a r t i a l p r e s s u r e o f 02 (PO2)
a v a i l a b l e at t h e b o u n d a r y , PO2cb. F o r trace a:DMb = 8 " 10 - 7
cm2/s (18 g / d l M b s o l u t i o n ) ; K0 = 1.31" 10 -12 m o l 9 c m -~ .
rain - 1 - T o r r -1 or 1 . 7 5 - 1 0 - ~ ~
1 . m i n - 1 . p a - i [14].
For
trace b: DMb = 2.2 " 10 - 7 cm2/s (intracellnlar); K0 =
1.31 9 10 -12 m o l - c m -1 9 m i n -1 9 T o r r -1 or 1.75 9 10 - I ~ tool 9
c m -1 - m i n - I - Pa - I . F o r b o t h c u r v e s CMb = 300 g m o l / 1 , Ps0 =
307 P a (2.3 T o r r ) a n d T = 37 ~ C were a s s u m e d . (DMu D i f f u s i o n
coefficient o f M b , K0 K r o g h ' s diffusion c o n s t a n t for 02, Pso 02
half saturation pressure of Mb)
reaches a maximum at
a P O 2 c b of about 2.67 kPa (20
decreases linearly above this
PO2 with increasing PO2cb. Below a PO2 of 2.7 kPa,
[MbO2]cb/PO2cb increases rapidly and, at very low PO2cb
values, reflects the slope of the 02 dissociation curve
of Mb. This is seen in the steep increase of 12OzMb/[/>O2free
at very low PO2cb values.
It can be seen from Fig. 2 that the Mb-facilitated
02 flux at a PO2cb of 1.3 kPa (10 Torr) amounts to only
25 % of the flux of free 02, if the DMb value measured
by us is used (curve b), whereas ~*O2Mb would be 90%
of the flux of free 02, if the value obtained in 18 g/dl
Mb solution is inserted (curve a). This means that
even in the PO2 range where hypoxia starts to occur
in a heavily exercising muscle (PO2cb 1.3-2.7 kPa,
10-20 Torr) the contribution of Mb-facilitated
diffusion to intracellular 02 transport is relatively small.
It may be noted that average tissue PO2 values lower
than 1.3 kPa (10 Torr) have indeed been shown to provoke a sharp increase in lactate/pyruvate ratio in exercising human gastrocnemius muscle [4]. The maximal
possible ratio of Mb-facilitated to free 02 diffusion
(occurring at the anoxic condition of PO2c b -'-)0 kPa)
amounts to merely 1.3 at the intracellular Mb diffusivity found in this study. This is only about one quarter
of what would be obtained with the DMb holding for
18 g/dl Mb solution. Recently, a considerably larger
value for K0 than that applied here was reported [2]. If
this value of 3.35 9 10 -l~ mol 9 cm -1 9 min -1 - Pa -1
(2.51 9 10 -12 mol 9 cm -1 9 rain -1 - Torr -1) is applied,
the significance of Mb-facilitated 02 diffusion is further reduced by nearly a factor of 2.
The effect of Mb-facilitated diffusion on the overall
02 transport in red muscle cells can also be expressed
Torr),
[MbO2]cb/PO2cb
524
in a different manner. From Eq. 2 it is calculated by
how much the PO2ob required to fulfill a given 02
demand has to be increased (~PO2cb) if facilitated
diffusion does not take place.
W i t h the definition:
PO2cbnf = PO2cb + ~-PO2cb
(3)
the following relation is derived:
DMb " CMb
PO2~b~f = POzcb ' I ~ ~ "(P--O22
+--Ps0) + 11
(4)
E q u a t i o n 4 represents the situation where the PO2 at
the capillary surface o f the K r o g h cylinder meets the
O2 d e m a n d o f the tissue in such a way that the PO2 at
the outer surface o f the cylinder is zero. Thus, increasing POzob a n d PO2ob~f values here is associated with
increasing 02 c o n s u m p t i o n o f the tissue.
F o r P 0 2 >>Pso Eq. 5 holds:
~PO2cb = ~PO2bfac = DMb " CMb/Ko
(5)
this is a m e a s u r e o f the m a x i m a l possible PO2 d r o p
due to facilitated diffusion.
Figure 3 shows by h o w much, at a given 02 cons u m p t i o n , POzcb has to be increased if facilitated
diffusion does n o t occur. With increasing PO2 values,
c o r r e s p o n d i n g to an increasing O2 c o n s u m p t i o n o f
the tissue, the difference between PO2ob~f and PO2:b
(trace a-trace c and trace b-trace c, respectively) increases
until it reaches 8PO2:bfa:. With the value o f DMb r e p o r t e d
here, facilitated diffusion m a x i m a l l y allows a reduction
o f the O2 pressure h e a d by only 400 P a (3 Torr), c o m p a r e d to 1.5 k P a (11 Torr) calculated with the DMb
Fig. 3 A comparison is shown between the PO2 required to meet
a certain 02 demand, when facilitated diffusion takes place
(PO2cu) and the corresponding value required when facilitated
diffusion is absent (PO2cb~f). The different curves correspond to
the following sets of parameters. Trace a : DMb = 8 ' 10 - 7 c m 2 / s
(18 g/dl Mb solution); K0 = 1.31 9 10 -12 mol 9 cm -1 9 min -1 9
Torr -1or 1.75' 10 10mol.cm i . m i n - a . p a - 1 1 1 4 ] . F o r t r a c e
b: DMb = 2.2 9 10 .7 cm2/s (intracellular); K0 = 1.31 -10 -12 mol 9
cm 1 . m i n - l . T o r r - l o r 1 . 7 5 . 1 0 - 1 0 m o l . c m Z'min - l ' P a -1.
For both curves CMb = 300 gmo1/1, Ps0 = 307 Pa (2.3 Torr) and
T = 37~ were assumed. Curve c is the line of identity
"&" 5O
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40
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0
5
10
15 20 25
P02, b [Torr]
30 35 40 45 50
(with facilit~Led diffusion)
holding for 18 g / d l M b solution. If, for example, without Mb-facilitated diffusion a PO2cbnf o f 1.3 k P a (t0
Torr) is required to fulfill a certain 02 d e m a n d , the corresponding PO2cb with facilitated diffusion could be
reduced to 1.03 k P a (7.7 Torr) at a DMb o f 2.2 " 10 -7
cm2/s, whereas 453 P a (3.4 Torr) would be needed at a
DMb o f 8 " 10 -7 cm2/s. The conclusion f r o m these calculations is that Mb-facilitated diffusion with the present DMb value reduces the necessary O2 pressure h e a d
by n o t m o r e t h a n 400 Pa (3 Torr), which is far less t h a n
has been expected so far.
S u m m a r i z i n g o u r results, we c o m e to the conclusion
that the diffusivity o f M b inside skeletal muscle cells is
considerably smaller t h a n a s s u m e d in m a n y theoretical studies. We c o n f i r m the result o b t a i n e d previously
in o u r l a b o r a t o r y with a completely different m e t h o d .
DMb is i n d e p e n d e n t o f m u s c u l a r contractions but, to a
certain extent, is influenced by the fibre type. M o d e l
calculations show that with the M b diffusivity m e a sured in this study, Mb-facilitated 02 t r a n s p o r t is o f
m i n o r i m p o r t a n c e for intracellular 02 transport.
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