Articles in PresS. Am J Physiol Heart Circ Physiol (April 20, 2012). doi:10.1152/ajpheart.00131.2012
1
Oxygen dependence of respiration in rat spinotrapezius muscle in situ
2
Aleksander S. Golub and Roland N. Pittman
3
Department of Physiology and Biophysics, Medical College of Virginia Campus,
4
Virginia Commonwealth University, Richmond, VA 23298-0551
5
6
Running head:
7
Oxygen dependence of respiration
8
9
Correspondence to:
10
11
Aleksander S. Golub, Ph.D.
12
Department of Physiology and Biophysics
13
Medical College of Virginia Campus
14
Virginia Commonwealth University
15
1101 E. Marshall Street
16
P. O. Box 980551
17
Richmond, VA 23298-0551
18
19
Tel: (804) 828-9760
20
Fax: (804) 828-7382
21
22
E-mail: [email protected]
1
Copyright © 2012 by the American Physiological Society.
23
ABSTRACT
24
The oxygen dependence of respiration in striated muscle in situ was studied by measuring the
25
rate of decrease of interstitial PO2 (oxygen disappearance curve, ODC) following rapid arrest of
26
blood flow by pneumatic tissue compression which ejected red blood cells from the muscle
27
vessels and made the ODC independent from oxygen bound to hemoglobin. After the
28
contribution of photo-consumption of oxygen by the method was evaluated and accounted for,
29
the corrected ODCs were converted into the PO2 dependence of oxygen consumption, VO2,
30
proportional to the rate of PO2 decrease. Fitting equations obtained from a model of
31
heterogeneous intracellular PO2 were applied to recover the parameters describing respiration in
32
muscle fibers, with a predicted sigmoidal shape for the dependence of VO2 on PO2. This curve
33
consists of two regions connected by the point for critical PO2 of the cell (i.e., PO2 at the
34
sarcolemma when the center of the cell becomes anoxic). The critical PO2 was below the PO2
35
for half maximal respiratory rate (P50) for the cells. In six muscles at rest the rate of oxygen
36
consumption was 139±6 nl O2/cm3·s and mitochondrial P50 was k = 10.5±0.8 mmHg. The range
37
of PO2 values inside the muscle fibers was found to be 4 to 5 mmHg at the critical PO2. The
38
oxygen dependence of respiration can be studied in thin muscles under different experimental
39
conditions. In resting muscle the critical PO2 was substantially lower than the interstitial PO2 of
40
53±2 mmHg, a finding which indicates that VO2 under this circumstance is independent of
41
oxygen supply and is discordant with the conventional hypothesis of metabolic regulation of the
42
oxygen supply to tissue.
43
44
45
Key Words: skeletal muscle, respiratory rate, interstitial PO2, oxygen disappearance
curve, phosphorescence quenching method, cell PO2 gradient
2
46
47
INTRODUCTION
The coordination of oxygen demand and supply in skeletal muscle and in the heart is
48
carried out by a mechanism not yet completely understood. Current cardiovascular texts propose
49
the century-old hypothesis of metabolic control of capillary blood flow as the accepted theory of
50
local autoregulation (review: (38) ). According to this hypothesis, a decline of oxygen delivery
51
leads to a decrease of intracellular PO2, an evoked release of a metabolic vasodilator into the
52
extracellular space, the dilation of arterioles and, eventually, an increase in the flow velocity of
53
blood and number of perfused capillaries. A key aspect of this model is the oxygen dependence
54
of cellular metabolism, making the mitochondria or entire cell sensitive to an inadequate oxygen
55
supply (11).
56
The oxygen dependence of respiration for isolated mitochondria and cells is represented
57
by a hyperbolic curve empirically described by Hill’s equation (Eq. 10) (29, 39, 46, 59, 60) with
58
the parameters Vm (maximal respiratory rate), Hill coefficient = 1 to 1.4 and P50 (PO2
59
corresponding to a VO2 of one- half Vm). The curve shows the relative independence of the rate
60
of respiration at high PO2 and a strong dependence at low PO2, while the point of transition of
61
the two portions of the curve defines the critical PO2, Pcrit.
62
It was shown in early studies that the oxygen consumption of isolated mitochondria and
63
cells remains relatively independent of the PO2 in their environment over a wide range of PO2
64
(10, 22, 25, 29, 56). A suspension of isolated mitochondria is insensitive to PO2 elevation above
65
1 mmHg (10, 13, 14, 40, 60). Suspensions of isolated resting muscle cells show values of
66
apparent P50 higher than those in mitochondria, yet much lower than the PO2 in venous blood,
67
which is approximately equilibrated with the tissue around capillaries (2, 14, 24, 26, 35, 39).
68
Thus, based on measurements made on isolated mitochondria and myocytes, mitochondria may
3
69
not serve as oxygen sensors monitoring the physiological PO2 level in tissue because of their low
70
critical PO2 (54).
71
Oxygen consumption by mitochondria depends on the rate of biochemical processes and
72
the availability of substrates and oxygen (7, 10, 13, 14, 60). At the cellular level, the oxygen
73
dependence of respiration is modulated by the cellular functional state and its capacity for
74
oxygen transport. Diffusivity and solubility of oxygen, in concert with cell size and the spatial
75
distribution of mitochondria, appear to be additional determinants of the oxygen dependence of
76
respiration (2, 4, 21, 24, 37, 48, 53).
77
On the tissue/organ level, the external control of cell respiration (via contraction) and
78
microcirculatory control of oxygen delivery appear in addition to the existing mechanisms of
79
regulation at the levels of individual mitochondria and cells. It is also suggested that inhibiting
80
cytochrome c oxidase with nitric oxide produces the contribution of intercellular regulation of
81
muscle respiration by all tissue cells including the vascular endothelium (8, 12, 42). Thus, the
82
factors affecting the oxygen dependence of respiration in the tissue lead to a set of parameters
83
Vm, P50, and Pcrit different from those obtained in isolated cells and mitochondria. The
84
importance of the study of oxygen dependence of respiration in situ was well formulated by
85
Wilson (54): "The oxygen dependence of cellular oxidative phosphorylation remains highly
86
controversial. Quantitative knowledge of that dependence is critical for understanding of not
87
only cellular biochemistry but also a wide range of physiological functions that help to regulate
88
both metabolism and the oxygen delivery system. Is mitochondrial oxidative phosphorylation
89
dependent on the oxygen pressures in normal tissues?” In order to answer this question, new
90
approaches for the study of the oxygen dependence of respiration in living muscle in situ have
91
been sought.
4
92
With the introduction of the polarographic method for measuring oxygen in tissues it
93
became possible to record the disappearance of oxygen caused by a momentary stoppage of
94
blood flow. The interpretation of these curves was aimed at obtaining information on the rate of
95
tissue respiration and its dependence on oxygen tension in the tissue (9, 34). The method was not
96
widely used because of the complexity of accounting for the contribution of oxygenated blood
97
and the limitations associated with the microelectrode technique of measuring oxygen.
98
The invention of the phosphorescence quenching method (PQM) paved the way for the
99
measurement of PO2 in microscopic volumes of various organs (52, 61). Now one can record
100
separate measurements of oxygen in the microvessels (3, 49, 62), interstitial fluid (44, 50, 58)
101
and within individual muscle cells (45). Interstitial oxygen tension takes on an intermediate
102
value between the intra-capillary and intra-cellular PO2, reflecting the current balance between
103
rates of delivery and consumption of oxygen by muscle fibers. Furthermore, the interstitial
104
oxygen tension is the PO2 on the surface of muscle cells, representing the boundary condition for
105
the diffusion of oxygen into the cell. The critical PO2 of skeletal muscle in situ was determined
106
for the first time in 1999 by recording the fall in interstitial PO2 caused by the rapid arrest of
107
blood flow (36). As a criterion for the critical oxygen tension, workers used an increase of
108
NADH fluorescence and a sharp change in the rate of decline in interstitial PO2. In normally
109
perfused resting muscle the authors reported venular PO2 = 17.7 mmHg and a 3 mmHg PO2
110
decrease to the interstitial PO2 of 14.6 mmHg. Interstitial critical PO2 as defined by the two
111
different criteria mentioned above was found to be in the range 2.4 – 2.9 mmHg, which was
112
slightly higher than that in isolated muscle fibers.
113
114
In our present work we develop this approach by improving the quality of the PO2
measurements through reducing the artifact of oxygen consumption caused by the
5
115
phosphorescence quenching method in a stationary fluid. Correction for the artifacts is done
116
when calculating the oxygen disappearance curve (ODC) recorded in the interstitium. We also
117
present a model for the interpretation of the dynamics of the interstitial PO2 decline due to
118
oxygen consumption by muscle fibers in order to develop a new fitting model for the analysis of
119
experimental data on the oxygen dependence of respiration in muscle.
120
121
METHODS
122
In this paper we propose a method for the analysis of the oxygen disappearance curves
123
(ODCs) in the intersitium of a thin skeletal muscle produced by the rapid pneumatic compression
124
of the tissue. The measuring procedure for PO2 and VO2 in a muscle using the phosphorescent
125
oxygen probe loaded into the interstitial space has been published before (18). However,
126
previously we used only the initial part of an ODC to evaluate the respiration rate in the
127
spinotrapezius muscle. In our present work we have developed an approach for analysis of the
128
entire ODC in order to determine the oxygen dependency of respiration of the muscle fibers in
129
situ.
130
A thin planar muscle prepared for intravital microscopy (1) was placed between a
131
thermo-stabilized sapphire plate and a gas barrier film. The interstitial space of the muscle was
132
loaded with an albumin bound phosphorescent oxygen probe. Blood flow in the muscle was
133
interrupted by rapidly inflating a bag of transparent film attached to the objective lens. Also, the
134
removal of RBCs from the muscle in the measuring volume was achieved and confirmed by
135
microscopic observation. For the PO2 measurements, a brief light pulse (laser 532 nm, 15 ns
136
duration, 1 pulse per second) was used to excite the probe inside a tissue disk of radius 300 µm.
6
137
In the following analysis we use the flash number, n, as the independent variable instead
138
of time. The index n = 0 denotes the variable before the onset of compression. The first flash
139
after compression is denoted by n = 1. Under the conditions described above, the interstitial PO2
140
= P0 for normal blood flow in capillaries. Then, the rapid compression of the muscle removes
141
RBCs from the vessels, leaving only physically dissolved oxygen in the tissue. From that
142
moment the interstitial PO2 inside the illuminated tissue disk is measured, thus forming the ODC
143
data set (Pn) (see Fig. 1).
144
The rate of PO2 change inside the sampled volume (P´n) depends on three components:
145
first, the metabolic or cellular oxygen consumption component (Vn) which is the subject of
146
interest; second, the photo-consumption by the method itself (KPn); and third, the diffusion
147
oxygen inflow from the surrounding tissue, proportional to the PO2 difference Z(pn – Pn) at the
148
boundary of the illuminated region. Here (pn) is the PO2 outside the illuminated tissue disk at the
149
moment of the n-th flash, and the parameters K and Z are empirical coefficients of oxygen photo-
150
consumption and inflow, respectively, which can be evaluated by fitting the experimental test
151
data to the equations that follow. In order to account for all the factors influencing the measured
152
rate of PO2 decrease, consider the equation:
153
Pn′ = −Vn − KPn + Z ( p n −
Pn )
154
[1]
The data set (Pn) is obtained from the experimental ODC, and the rate of PO2 drop (P´n)
155
can be calculated by differentiating the ODC. The goal is to evaluate the rate of tissue
156
respiration VO2 from the metabolic component Vn , which is calculated for a flash rate F = 1 Hz
157
and the oxygen solubility in the muscle (α = 39 nl O2/(cm3 mmHg), (30) ) as:
158
VO2 = V0 Fα
[2]
7
159
We can simplify Eq. 1 for the case when the metabolic component is absent (Vn = 0), for
160
example, in a sample of dead tissue excised after the experiment (18). The ODC recorded in the
161
sample under the same conditions of measurements as in vivo can be used for the evaluation of
162
the coefficients K and Z and verification of the validity of assumptions underlying the model. In
163
that case the tissue outside the illuminated disk remains saturated with oxygen at an initial steady
164
state PO2 of pn = P0.
165
166
167
The solution of Eq. 1 under these conditions predicts an exponential decline of PO2:
Pn =
P0
[ Z + K exp(−( K + Z )n)]
K +Z
[3]
In the presence of oxygen inflow across the boundary of the illuminated region of tissue,
168
the ODC approaches an asymptotic PO2 (Pa) formed by equilibrium between the processes of
169
oxygen photo-consumption and inflow:
170
171
172
Pa
Z
=
P0 K + Z
When oxygen inflow is negligible, as in the case of an excitation area much larger than
the area of detection, the PO2 asymptotically approaches zero and Eq. 3 is transformed into:
Pn = P0 exp( −173
Kn )
174
[4]
[5]
In our previous work we have shown that Eq. 3 is a good fitting model of the ODC in
175
non-respiring tissue. In this special test we have determined values for the coefficients K (=
176
4.1·10-3) and Z (= 1.5·10-3) for correction of measurements made in situ (18). These coefficients
177
are dimensionless; however, since we have omitted the flash rate 1 Hz in the equations for
178
simplicity, the dimension appears as [s-1].
179
180
Oxygen dependence of respiratory rate (VO2 vs. PO2) for muscle fibers in situ. In
our present work we employed the phosphorescent probe distributed in muscle interstitial
8
181
(extracellular and extravascular) space. Rapid (~0.1 s pressure elevation) application of external
182
pressure to the tissue expels the RBCs from the vessels and makes the ODC independent of
183
hemoglobin. That experimental situation opens the opportunity to recover the dependence of
184
muscle VO2 on PO2 in the interstitial space, i.e. on the surfaces of the muscle fibers. In that case,
185
the entire ODC from P0 to near zero PO2 level has to be analyzed. With rising flash number, n,
186
the difference between external and internal PO2 (pn – Pn) increases, so the contribution of
187
oxygen inflow must be taken into account.
188
189
190
191
192
193
Following tissue compression PO2 in the tissue outside the illuminated spot decreases
only due to tissue respiration (no photo-consumption), so that the rate of PO2 change is:
p n′ = −Vn
[6]
If coefficient Z is not small enough to ignore the oxygen inflow, then the Vn can be
obtained through the iterative calculation:
n −1
pn = P0 −  Vi
[7]
i =0
194
195
Thus, combining Eqs. 1 and 7:
n −1
V n = ZP0 − Pn′ − ( K + Z ) Pn − Z  Vi
[8]
i =0
196
197
Analysis of an ODC can be greatly simplified if the inflow contribution is negligible and
the time course of the oxygen consumption rate after occlusion can then be expressed as:
Vn = − Pn′ −198
KPn
[9]
199
This is possible when the illuminated spot is much larger than the region of detection, but
200
is not always acceptable because of the intention to avoid light exposure of adjacent sites in case
201
of subsequent multiple measurements in the same muscle. Our data were collected in the
202
presence of oxygen inflow, so that is why Eq. 8 was used in the analysis.
9
203
The obtained Vn are separated from the artifacts and can be converted into VO2 according
204
to Eq. 2. A plot of (VO2)n vs. (Pn) values at sequential flashes represents the oxygen dependence
205
of respiration for muscle fibers in situ (Fig. 5) which can be fit with a sigmoid curve, described
206
by Hill’s equation, to evaluate the parameters Vm - maximal respiration rate for a collection of
207
muscle fibers (hereafter the symbol V is used to designate the rate of oxygen consumption), P50 -
208
oxygen tension for half-maximal respiration rate, and a - Hill coefficient:
209
V =
Vm Pna
P50a + Pna
[10]
210
However, this empirical approach gives only a limited understanding of the dependence
211
of the rate of cell respiration on oxygen level. For that purpose we developed a model to relate
212
interstitial PO2 and the rate of mitochondrial respiration per unit volume of the cell.
213
Interpretation of the oxygen dependence curves. Since the oxygen probe is distributed
214
in the interstitial space, it reports the PO2 on the surface of muscle fibers, at the sarcolemma,
215
both during steady state and during the transient conditions of the ODC. Thus, the curve relating
216
respiration to the PO2 on the surface of muscle cells can be analyzed using an appropriate model.
217
That model should take into account the respiratory dependence of microscopic intracellular
218
volumes (related to the functional activity of mitochondria) and the PO2 gradient in cells
219
produced by the transport resistance due to diffusion.
220
Our model is based on the assumption that all oxygen sinks (mitochondria) in the muscle
221
fibers are identical to each other in their respiratory properties, which means they obey a
222
hyperbolic equation (39, 40, 53, 60), written below in a normalized form:
223
v
p
=
VM
k+p
[11]
10
224
where v is the local specific oxygen consumption (by an elementary volume); VM is the maximal
225
volume-specific O2 consumption, which is the same for the entire tissue (Vm) and for the
226
elementary volumes inside the cells (VM), so that we can set Vm = VM; p is the local intracellular
227
PO2, and k is the local PO2 corresponding to the half-maximal respiration rate (i.e., P50 for
228
mitochondria). We have attempted to explain the origin of the sigmoidal oxygen dependence of
229
muscle cell respiration (Eq. 10) on the basis of the hyperbolic oxygen dependence of
230
mitochondrial respiration (Eq. 11) and the intracellular gradient of PO2. In a generalized muscle
231
fiber (Fig. 2) the elementary volumes of the cell are depicted by concentric isobars. However, all
232
these sinks in the muscle cells are localized in tissue volumes under different local oxygen
233
tension p that creates heterogeneity in oxygen consumption rates inside the cell.
234
In our experiments the parallel changes in interstitial PO2 and VO2 (P and V) were
235
determined as values obtained at the sarcolemma (Fig. 2). There is no requirement of any special
236
shape (circular, hexagonal, etc.) of the fiber cross-section; it can be quite natural. The only
237
assumption is the existence of a PO2 gradient inside the muscle fibers, expressed as the
238
difference, Δ = P - Pc between the surface (i.e., interstitial) PO2 = P and PO2 = Pc in the center of
239
the fiber, i.e., the point in the fiber with the lowest PO2.
240
A fraction of tissue volume f, having a given PO2 = p (isobaric volumes), also has the
241
same respiration rate v (Fig. 2). As a first approximation we can consider the distribution f(p) to
242
be a Uniform (or Rectangular, Fig. 3) distribution having a width Δ = P – Pc and a density f =
243
1/Δ, meaning that the total volume is equal to unity and the probability density function can be
244
applied to represent the tissue volume distribution as a function of PO2. This approach also will
245
allow us to define the first and second moments of this distribution, yielding its mean value and
246
width. Our aim is the recovery of information on the properties of intracellular respiration by
11
247
determining best fit parameters for experimental data points using the equations generated by the
248
model.
249
The Uniform distribution of the intracellular volume based on PO2, with density f = 1/Δ,
250
is presented in the diagrams of Fig 3. Interstitial PO2 = P is the right border of the cellular
251
volume distribution on the oxygen tension p having width Δ.
252
physiological situations in the muscle fiber: 1) Normoxia, P > Δ; 2) Critical PO2, P = Δ; and 3)
253
Hypoxia, P < Δ. When P > Δ all isobaric volumes f in a cell have PO2 > 0 and participate in
254
oxygen consumption. When P = Δ, Pc = 0 and v = 0 at the center of the fiber; this value of P is
255
known as “critical.” For P < Δ some deep volumes presented by the shaded region left of zero
256
PO2 are excluded from respiration. Since negative PO2 values are impossible, that part of the
257
cell volume also has PO2 = 0 and total V is the sum (or integral, see Eq. 12) of the oxygen
258
consumption rates only in volumes having PO2 > 0.
259
There are three possible
The total oxygen consumption rate V is the sum of respiratory rates, v, of the isobaric
260
volumes multiplied by their volume fractions (f = 1/Δ). Generally, using Eq. 11, the total oxygen
261
consumption rate normalized to the maximal rate VM can be written as:
P
262
263
264
265
V
p
1
=
⋅ dp
VM Pc k + p Δ
[12]
This expression can be presented in a form convenient for integration:
V
V= M
Δ
P
p
 k + p dp
[13]
Pc
The limits of integration of Eq. 13 are different for each of the situations shown in Fig. 3,
266
and the solutions for V are also different. The consumption curve (i.e., V as a function of P) for
267
a generalized muscle fiber or tissue consists of two different regions which correspond to two
268
different interstitial PO2 conditions:
12
269
270
Normoxic, P > Δ
V1 =
VM
Δ
[Δ + k log(1 −
)]
Δ
k+P
[14]
271
272
Hypoxic, P < Δ
V2 =
VM
k
[ P + k log(
)]
Δ
k+P
[15]
273
274
275
The line formed by the points separating the two regions of V(P), that is V for P = Δ
(middle plot), is described by the equation for the critical PO2:
V3 = V M +
VM k
k
log(
)
P
k+P
276
Critical, P = Δ
[16]
277
The equations obtained for the normoxic and hypoxic ranges (Eqs. 14 and 15) of
278
interstitial PO2 can be used as fitting models for the analysis of experimental curves on the
279
oxygen dependence of respiration, while Eq. 16 may be applied for accurate evaluation of the
280
critical PO2.
281
Equations 14-16 make it possible to predict the behavior of the oxygen dependence of
282
cellular respiration for different ranges of the intracellular PO2 gradient and oxygen demand.
283
The set of theoretical curves generated for different Δ’s are shown in Fig. 4. The curves are
284
calculated for a set of parameters (VM = 100 nl O2/(cm3·s), k = 10 mmHg and Δ = 0, 5, 10, 20,
285
30, 40 mmHg) to demonstrate the effect of an intracellular oxygen gradient on the oxygen
286
dependency of respiration. The first curve (Fig. 4, curve 1) is the oxygen dependence for
287
mitochondria described by Eq. 11. This is the same relationship for a whole cell in the absence
288
of an oxygen gradient due to intracellular diffusion resistance. When the different contributions
289
of the diffusion resistance occur, the PO2 difference between the sarcolemma and core (Fig. 4,
290
curves 2-6, Δ = 5 - 40 mmHg) leads to a sigmoidal appearance of the cellular respiration
13
291
dependence on PO2. This connection allows us to determine the parameters for the
292
mitochondrial respiratory dependency on oxygen from the observed experimental oxygen
293
dependency of oxygen consumption for whole cells. Each of the five solid curves (2 to 6)
294
consists of two regions, a normoxic region described by V1 and a hypoxic region described by
295
V2, according to Eqs. 14 and 15, respectively. The dashed line (curve 7) corresponds to the
296
situation (critical PO2) described by V3 (Eq. 16), indicating the points separating the normoxic
297
and hypoxic regions of the curves. The same curves plotted as a double- logarithmic plot (right
298
panel of Fig. 4) demonstrate that the hypoxic regions are transformed into straight lines, which
299
turn into hyperbolic lines above the dashed line 7, corresponding to the critical dependence, V3.
300
Curve 1 represents the case when there is no PO2 difference between the cellular surface and the
301
core, for example, in the case of zero diffusion resistance or a very thin cell. An increase in
302
diffusion resistance or thickness of the cells leads to a proportional shift in curve 7 to the right.
303
The same effect is caused by an increase in k, which reflects a greater oxygen dependence of
304
mitochondrial respiration.
305
Animal experiments. The experimental protocol followed for these measurements was
306
previously published in detail (18). All procedures were approved by the Institutional Animal
307
Care and Use Committee of Virginia Commonwealth University. Six female Sprague-Dawley
308
rats were initially anesthetized with a mixture of ketamine/acepromazine (72/3 mg/kg, i.p.).
309
Once femoral vein access was obtained, the animals received supplemental anesthesia as a
310
continuous intravenous infusion of alfaxalone acetate (Alfaxan, Schering-Plough Animal Health,
311
Welwyn Garden City, UK; approximately 0.1 mg/kg/min). At the termination of an experiment,
312
Euthasol (150 mg/kg, pentobarbital component, iv.; Delmarva, Midlothian, VA) was
313
administered while the animal was under a surgical plane of anesthesia. The spinotrapezius
14
314
muscle was used for measurement of interstitial PO2 and the surgical preparation was similar to
315
the original description by Gray (1, 19). The muscle was placed on a thermo-stabilized (37 °C)
316
pedestal of the animal platform (17). The muscle was covered with gas barrier plastic film
317
(Saran, Dow Corning, Midland, MI). An objective-mounted film airbag connected to a pressure
318
controller allowed organ compression at 130 mmHg, which rapidly squeezed blood out of
319
microvessels in the thin spinotrapezius muscle (15). Circular regions of muscle 600 µm in
320
diameter and containing no large microvessels were selected for VO2 measurements. The PO2
321
was sampled once a second during 200 s of PO2 data collection in a reactive hyperemia-type
322
protocol. Before rapid airbag inflation the interstitial PO2 at normal tissue perfusion (i.e.,
323
baseline) was recorded for 30 seconds. This was followed by 90 seconds of muscle compression
324
to arrest blood flow, after which the airbag was deflated for the remainder of the recording
325
period (i.e., 80 s). This protocol was repeated at 3-11 different sites around the muscle, with 5-
326
10 min intervals between measurements. Preparation quality and viability were confirmed by a
327
return of interstitial PO2 to baseline between consecutive measurements. The measurement of
328
PO2 with PQM has been described in detail previously (18). Respiration rates, Vn, were
329
calculated according to Eq. 8. Each ODC was differentiated using a 5-point differentiation
330
smoothing function, after checking that this procedure had no effect on the fitting analysis. The
331
Levenberg-Marquardt algorithm was used for PO2 calculations to fit the multiple
332
phosphorescence decays (one PO2 value per second for 200 s) with a program put together using
333
the LabView software platform (National Instruments, Austin, TX). Statistical calculations and
334
parameter fitting were made with the Origin 7.0 software package. All data are presented as
335
mean ± SE (number of measurements).
336
15
337
RESULTS
338
The oxygen disappearance curves were recorded at 34 sites in 6 spinotrapezius muscles
339
with measurements at 3-11 sites per muscle. Curves obtained in the same muscle were aligned
340
(time base “correction”) and averaged (see Fig. 1, as an example). Measures described
341
previously were taken to reduce the artifact of oxygen photo-consumption, and its contribution at
342
the normal interstitial PO2 was 0.6%. The effect of oxygen inflow into the detection area was
343
noticeable at the lowest PO2’s (accounting for 3.5% of the PO2 change). Equation 8 was used,
344
along with these measured values, to correct the oxygen disappearance curves. The resulting
345
corrected curves were used to calculate the dependence of oxygen consumption on PO2, which
346
was then plotted and fit with Hill’s equation (Eq. 10). The parameters recovered for the total
347
data set were: Vm = 120.9 ± 7.7 nl O2/(cm3·s); P50 = 11.1 ± 0.9 mmHg; and the exponent a = 2.0
348
± 0.1.
349
For further analysis of the oxygen dependency of respiration we used fitting Eqs. 14 and
350
15 (see Fig. 5) to estimate the intracellular PO2 range Δ, VM and k . The parameters VM , k and
351
Δ1 were determined first for the normoxic region of the curve (Eq. 14), which comprises most of
352
its length; then the hypoxic region of the curve was fit (Eq. 15) at fixed VM and k taken from the
353
first procedure, to make a second estimation of the PO2 range, Δ2. An example of such an
354
analysis is shown in Fig. 5 (the same data set as in Fig. 1), where most of the points belong to the
355
normoxic region of the curve described by Eq. 14 and the low PO2 segment was fit with Eq. 15.
356
A double-logarithmic plot facilitates finding the point of separation between the two regions of
357
the overall curve; it could also be calculated using Eq. 16.
358
359
The set of curves averaged for each muscle was homogeneous, but the range in maximal
and minimal VM and k among the muscles was twofold (see Table 1). The average difference
16
360
between the intracellular PO2 ranges calculated with Eqs. 14 and 15 (i.e., Δ1 and Δ2) was within 1
361
mmHg and these data sets are well correlated (R = 0.87, p = 0.025). A high correlation was also
362
found between VM and k (R = 0.94, p = 0.0055), while the other parameter sets showed no
363
significant correlation. It follows from the derivation of Eq. 16 that the critical PO2 is equal to Δ
364
and, for the value obtained for Δ of 4 - 5 mmHg, the corresponding critical oxygen consumption
365
is 21.2 - 25.2 nl O2/(cm3·s).
366
367
DISCUSSION
368
Further improvement of the optical technique (PQM) to measure PO2 in living organs,
369
including corrections for instrumental artifacts and incorporation of several significant technical
370
innovations, made it possible to update the study of tissue respiration in situ previously made by
371
Richmond et al. (36). In order to eliminate the intravascular phosphorescence signal, the oxygen
372
probe was loaded directly by diffusion into the intercellular space of the thin muscle. To
373
eliminate the influence of intravascular oxygen, the flow arrest was performed by pneumatic
374
compression of the muscle, which squeezed RBCs out of the microvessels. The pressure in the
375
air bag rapidly rose to a level above the systolic blood pressure and extrusion of blood from the
376
compressed muscle was monitored with video microscopy. The diameter of the measuring area
377
was increased to 600 μm (vs. 20 μm in (36)) to include the interstitial space around 10 muscle
378
fibers and make the diameter of the measuring volume similar to its depth. The larger sampling
379
volume allowed us to reduce the excitation energy density and flash rate to 1.8 pJ/μm2 and F =
380
1Hz (vs. 31 pJ/μm2 and 50 Hz in (36)) and provided a phosphorescence decay signal with signal-
381
to-noise ratio good enough for analysis of individual decays.
17
382
These technical improvements significantly reduced the photo-consumption of oxygen by
383
this method (16, 18). That is why the interstitial PO2 in our experiments was significantly higher
384
at rest: 53 mmHg vs. 15 mmHg in the study by Richmond et al (36). Similar values of interstitial
385
PO2 in skeletal muscles have been reported by other workers. Recent studies of interstitial
386
oxygenation with the PQM using new oxygen probes found that the peak of the histogram of
387
interstitial PO2 in mouse skeletal muscle corresponded to 41 mmHg (57, 58). The interstitial
388
PO2 measured near 1-st, 2-nd and 3-rd order arterioles in rat cremaster muscle varied between
389
51- 29 mmHg (43). In the rat diaphragm muscle average microvascular PO2 was normally about
390
50 mmHg, which may also indicate similar PO2’s in the interstitium (32). Peri-arteriolar PO2 for
391
2A arterioles in cat muscle, measured with a microelectrode, was found to be 52 - 40 mmHg,
392
depending on the PO2 of the superfusate (6). In the rat spinotrapezius muscle the PO2 values
393
obtained with a microelectrode in the vicinity of venules were close to 50 mmHg (27). It should
394
be noted that the reference volume of a polarographic electrode is not limited to the interstitial
395
space, but also includes the intracellular content having a lower PO2 than that in the interstitium.
396
The PQM also opened the possibility to localize PO2 measurements in a selected compartment:
397
intravascular, interstitial or intracellular (23, 58).
398
Recording the ODCs in a stationary interstitial fluid requires a series of tens of light
399
pulses, so the artifact of accumulated photo-consumption should be considered and corrected for.
400
To accomplish this, a mathematical model of oxygen measurements in a microscopic volume of
401
muscle was formulated and the contribution of photo-consumption and diffusional inflow of
402
oxygen was determined and used to correct the data. In future experiments the analysis can be
403
simplified by increasing the size of the excitation area compared to the area of signal detection,
404
which will make the contribution of oxygen inflow negligible.
18
405
Corrected data on the metabolic component of ODCs were converted to respiration rates
406
and plotted against the corresponding values of PO2, thus forming a scatter plot of oxygen
407
dependency of muscle fiber respiration in situ. The data obtained were well approximated by
408
Hill’s equation (Eq. 10) which was used to determine the parameters Vm = 120.9 nl O2/(cm3·s),
409
P50 = 11.1 mmHg and the exponent a = 2.0. The sigmoidal curve describing the oxygen
410
dependency of respiration does not contain a specific point indicating the critical PO2 associated
411
with the appearance of an anoxic core in muscle fibers. This fact limits the usefulness of an
412
empirical fitting model, and points out the need for finding an analytical description of the
413
oxygen dependence of cell respiration, based on knowledge of oxygen uptake by mitochondria
414
and the intracellular oxygen gradient created by the diffusional influx of oxygen into a cell.
415
There are a number of papers on mathematical modeling of oxygen diffusion combined
416
with its consumption within a tissue slice or a given cell geometry. These models are aimed at
417
finding the shape of the PO2 profile in a flat sheet, sphere or circular cylinder. The oxygen
418
dependency of respiration is assumed to be constant (20) or possess a specific Michaelis-Menten
419
(ММ) kinetics (28, 33). The latter possibility (Eq. 11) is a good representation for the kinetics of
420
mitochondrial respiration (53) sometimes being used with the caveat of "pseudo" MM kinetics.
421
Many of the published models are presented in the form of numerical solutions and/or are
422
applicable only to ideal geometric forms, which reduce their practical value for the analysis of
423
experimental results. For this purpose it is necessary to find a quantitative explanation, relating
424
the properties of mitochondrial respiration (pseudo-MM kinetics) with a heterogeneous
425
distribution of intracellular oxygen, which leads to a sigmoidal curve describing the collective
426
oxygen dependency.
19
427
We have presented a curve of the collective oxygen dependency as a product of the
428
oxygen consumption kinetics of individual oxygen sinks (pseudo-MM) and the cell volume
429
distribution on the basis of PO2 isobars, given by a simple probability density function. This
430
approach allowed us to describe the heterogeneity of the oxygen distribution inside a cell with
431
two parameters: the PO2 on the cell surface P and the width of the intracellular PO2 distribution
432
Δ, which arose from the combined diffusion and chemical reaction inside the cell. P and Δ have
433
relatively straightforward physiological meanings and they can be converted into statistical
434
moments of the intracellular PO2 distribution. We aimed to obtain fitting functions (Eqs. 14, 15,
435
16) that could be applied to experimental data to recover the parameters P and Δ and predict the
436
shape of the oxygen dependency for oxygen consumption in a skeletal muscle. This approach
437
has the potential to be extended to form a histogram-like model, in which several Uniform
438
distributions with different weighting coefficients can be recovered by fitting the experimental
439
points of the ODC. The first attempts at direct measurements of PO2 distributions within
440
cardiomyocytes (31) showed that the distribution of mitochondrial PO2 may depend on the
441
fraction of oxygen in the inspired gas mixture and, therefore, knowledge of the characteristics of
442
this distribution are necessary for understanding the functional state of cells.
443
In order to establish the validity of the Uniform distribution to describe the heterogeneity
444
of intracellular PO2, let us compare the radial profiles of PO2 in the case of a muscle fiber in the
445
form of a circular cylinder of radius R. As a simple example, we consider the conventional case
446
of constant, uniform oxygen consumption VO2 and p(r)>0 throughout the fiber. For this
447
situation the radial dependence of PO2 is:
448
[17]
20
449
where DO2 is the diffusion coefficient and α is the solubility of oxygen. From this equation the
450
volume fraction of the fiber contained within radius r is related to PO2 at this radius by
451
[18]
452
where the PO2 at the center of the fiber (r = 0) is Pc = P - VO2R2/4DO2α. The PO2 volume
453
density function, f(p), for this situation is given by its definition, f(p) = 4α DO2/VO2R2. Note
454
that the right hand side of this equation is 1/(P – Pc) or 1/Δ. This is exactly the value of f(p) used
455
for the Uniform distribution in Eq. 12. For the Michaelis-Menten kinetics used to describe the
456
PO2 dependence of mitochondrial oxygen consumption in our model (Eq. 11), the PO2 profile
457
will still be parabolic to a good approximation and thus the Uniform distribution given by f(p) =
458
1/Δ will be appropriate.
459
A parabolic profile is the typical result for oxygen diffusion / consumption in a
460
cylindrical fiber (20) and has been repeatedly confirmed in experiments on isolated muscle cells
461
(47, 48). However, the observation of a parabolic PO2 profile does not necessarily require
462
correspondence with Hill’s model (20) in which the oxygen consumption by elementary cell
463
volumes is independent of the PO2. The diffusion coefficient, DO2, can be calculated according
464
to Hill’s model as (4, 20, 45):
465
DO 2 =
R 2 ⋅ VO 2
4P ⋅ α
[19]
466
Calculations based on the values of parameters at the critical PO2 (Table 1) gives DO2 =
467
0.25·10-6 cm2 / s, which is much smaller than literature values (2, 5, 30). An explanation of this
468
discrepancy lies in the inapplicability of Hill’s model to the situation in real cells in which
469
respiration is dependent on oxygen tension over wide limits (53, 56). This wider PO2
470
dependency range is described by Wilson et al (53, 56) such that changes in the concentrations of
21
471
various intracellular metabolic factors work together to maintain a relatively constant oxygen
472
consumption in the face of decreasing PO2. However, below a critical PO2 changes in the
473
concentrations of these substances are not able to work together to maintain oxygen consumption
474
and it begins to fall. An additional factor to consider is the significant difference between the
475
shape of muscle cells and a circular cylinder. Replacing the square of the radius by the cross-
476
sectional area (45, 51) in the calculation of the diffusion coefficient using Hill’s model is
477
incorrect.
478
It should be noted that the proposed model is shape-independent and based on the
479
assumption of intracellular heterogeneity in PO2, which can be described by a Uniform
480
distribution defined by the two parameters P and Δ. Mathematical solutions of the model
481
formulated by Eq. 12 for the three situations of cellular oxygenation -- normoxic, hypoxic and
482
critical -- are represented by the sigmoidal composite curve consisting of two regions connected
483
at the point of critical PO2. On a double-logarithmic plot the low PO2 region (Eq. 15) appears as
484
a straight line in contrast to the hyperbolic region (Eq. 14, Fig. 4, right panel). Remarkably, this
485
property of the oxygen dependence curves was discovered earlier and used to determine the
486
critical PO2 in experiments with isolated muscle cells (4). The resulting Eqs. 14-16 do not have
487
a formal resemblance to Hill’s equation, although the resulting sigmoidal curves are obviously
488
similar to it, but depend only on the difference of PO2 between the surface and center of the
489
muscle fibers (Fig. 4). By accounting for the oxygen dependence of mitochondrial respiration,
490
we obtained a description of their collective effect at the cellular level, which somewhat changes
491
the understanding of critical PO2 and the oxygen dependency of cellular respiration. The actual
492
critical PO2, corresponding to zero PO2 at the cell core, can be even lower than P50 for small Δ,
493
although the oxygen dependence of respiration extends to much higher PO2 (see Fig. 5).
22
494
The parameters recovered by fitting the experimental oxygen dependency curves (i.e.,
495
VO2 vs PO2) with Eqs. 14-16 are presented in Table 1. Relatively small differences were
496
observed in the asymptotic values of VM from the two models we considered (121 nl O2/cm3s
497
from Eq. 10 and 139 nl O2/cm3s from Eqs. 14-16). Practically no differences were found
498
between the P50 = 11.1 mmHg obtained for muscle fibers using Hill’s equation (Eq. 10) and k =
499
10.5 mmHg for mitochondrial respiration. It is well known that the P50 for coupled isolated
500
mitochondria under a sufficient concentration of ATP is about 0.5 - 1 mmHg, while in presence
501
of an uncoupler, P50 is less than 0.03 mmHg (14, 60). It has also been shown that diffusion
502
limitations approximately double the value of P50 in isolated cells (26, 39, 53). The oxygen
503
dependence of respiration in isolated mitochondria and cells is usually studied with vigorous
504
stirring to reduce the contribution of diffusion resistance (14, 60). For cells in organs and tissues
505
convective effects are limited to blood flow through nearby microvessels, while both interstitial
506
fluid and sarcoplasm are essentially stationary in a resting striated muscle. There is a possibility
507
that the P50 value is dependent on the diffusional resistance to oxygen transport between the
508
capillary to mitochondria, and this may be part of the explanation as to why the oxygen
509
dependence of respiration extends to greater than 30 mmHg (53, 55). The question of the extent
510
to which diffusion of oxygen determines the oxygen dependence of cellular respiration in situ is
511
extremely important, but poorly understood.
512
The PO2 difference, Δ, and critical PO2 estimated with Eqs. 14 and 15 yielded close
513
results and all 6 pairs of values are well correlated. In this regard, one may consider the possible
514
distortion of the curve of oxygen dependency through interference caused by the presence of
515
myoglobin. Due to the very low P50 for myoglobin (2.39 mmHg at 37 oC and pH =7.0; (41)), it
516
is highly saturated at normal PО2, so that the effect on oxygen dependency should occur only at
23
517
low PO2. If the effect of myoglobin is not negligible, then the difference in the observed values
518
of Δ1 and Δ2 would be expected to be significant, but they are not (Table 1). The final resolution
519
of this issue will require experiments in which the influence of muscle myoglobin has been
520
eliminated; however, close agreement between Δ1 and Δ2 indicates the marginal impact of
521
myoglobin in the spinotrapezius muscle.
522
The definitions of critical PO2 are different for mitochondria and cells. The contribution
523
of diffusion resistance to Pcrit in isolated mitochondria is negligible due to their small size, while
524
for the whole cell it can be the determining factor at a high level of metabolism. In a muscle, a
525
sharp increase in NADH fluorescence reports mitochondrial anoxia, while an abrupt change in
526
the rate of decline of extracellular PO2 corresponds to Pcrit for the myocytes (35, 36). Critical
527
oxygen tension in the cells of the spinotrapezius muscle was measured in isolated cells and in
528
situ, and Pcrit in isolated cells was 1.25 mmHg, somewhat lower than the in situ value of 2.9
529
mmHg (35, 36). According to our data, a Pcrit of 4 to 5 mmHg is close to these values, but too
530
low for involvement of the critical PO2 in oxygen sensing by resting myocytes. However, due to
531
diffusion limitations the oxygen dependency of respiration extends to the range of physiological
532
oxygen pressure in the interstitium (53, 56) or 53 mmHg in the present study. It should be noted
533
that the sensitivity of the respiratory rate to oxygen is small at this PO2, but it may increase with
534
increasing intracellular differences of PO2 (right shift in Fig. 4) caused by an augmentation in
535
metabolic activity or cell diameter.
536
Taking advantage of the range of variability of the parameters obtained in six muscles,
537
we assessed the connections among them and found that VM and k are strongly correlated. This
538
correlation indicates a self-similarity of the oxygen dependence curves for various rates of
539
metabolism. In that case curves with different VM are located to the right of the line passing
24
540
through the origin with а slope equal to the diffusion resistance of the cell (VO2/PO2). Given the
541
small number of muscles studied, this relationship can be considered only hypothetically
542
possible. Later, this phenomenon can be studied with greater precision, considering the ability of
543
muscles to increase their maximum oxygen consumption many-fold. In the proposed model VM
544
is assumed to be the same for different values of Δ, which simplifies the analysis, but limits its
545
applicability. Clearly, a significant increase in Δ is the result of increased respiration rate and, in
546
the analysis of future experiments with stimulated oxygen consumption, the physical relationship
547
between VM and Δ will be taken into account.
548
In conclusion, we have developed an approach to study the oxygen dependence of
549
respiration in a skeletal muscle in situ, using PO2 measurements in interstitial fluid made with
550
phosphorescence quenching microscopy and rapid pneumatic compression of the tissue. The
551
metabolic component of the oxygen disappearance curve was used to construct a plot of oxygen
552
dependency of cell respiration, which was analyzed using a model for oxygen consumption
553
developed for the situation of heterogeneous PO2. The model predicted a number of properties
554
for the oxygen dependence of cellular respiration associated with the existence of a respiratory-
555
induced PO2 gradient in cells: 1) the dependence has a sigmoidal shape with an increasing
556
rightward P50 shift with increasing intracellular PO2 gradient; 2) the dependence is described by
557
two different functions, which represent normoxic and hypoxic regions of the model, whose
558
graphs are connected at the point for the critical PO2 of the cell; and 3) at physiological values of
559
the intracellular PO2 gradient, the critical PO2 for the cells is below their P50.
560
Above the critical PO2 or critical oxygen delivery, as usually understood, most published
561
studies demonstrate that oxygen consumption is independent of oxygen delivery.
Our analysis
562
showed that, although the critical cellular PO2 is much lower than the physiological oxygen
25
563
tension in the interstitium for resting muscle, the oxygen dependency of cellular respiration may
564
reach high PO2 values. To what extent the respiratory oxygen dependency of muscle fibers
565
determines their ability to serve as oxygen sensors in the regulation of oxygen delivery can be
566
established in future experiments applying this novel method to the situation of enhanced oxygen
567
consumption caused by muscle stimulation and uncoupling of oxidative phosphorylation.
568
569
GRANTS
570
This research is supported by National Heart, Lung, and Blood Institute Grants HL-18292
571
and HL-79087.
572
573
DISCLOSURES
574
No conflicts of interests, financial or otherwise, are declared by the authors.
575
576
26
577
578
TABLES
579
Table 1.
580
Parameter estimation for oxygen dependency of respiration in six spinotrapezius muscles
581
in situ
Muscle #
1
2
3
4
5
6
NODC
6
6
11
3
3
5
P0 (mmHg)
69.1 ± 1.3
33.1 ± 3.8
55.9 ± 4.4
59.8 ± 1.4
49.2 ± 1.0
48.5 ±1.4
VM (nl O2/cm3s)
138.8
111.5
107.6
167.7
209.8
182.1
k (mmHg)
9.41
7.95
6.46
10.79
19.26
18.06
Mean ± SE
34
52.9 ± 2.0
139.1 ± 6.1
10.5 ± 0.8
Δ1 (mmHg) Δ2 (mmHg)
3.27
3.02
3.89
3.15
6.67
4.78
6.63
7.05
4.23
3.10
4.52
3.42
5.0 ± 0.2
4.0 ± 0.2
582
583
The best-fit parameters of oxygen consumption and PO2 gradients in six spinotrapezius
584
muscles, evaluated with Eqs. 14 and 15. NODC is the number of sites in the same muscle used for
585
averaging the ODCs. Weighted means for 34 ODCs are presented at the bottom line. The
586
interstitial PO2 measured just before the onset of tissue compression is denoted by P0. The
587
mitochondrial PO2 corresponding to half-maximal oxygen consumption is denoted by k. The
588
intracellular PO2 range evaluated from Eq. 14 is Δ1 and from Eq. 15 is Δ2.
589
590
591
592
593
594
595
27
596
597
FIGURE LEGENDS
598
599
Figure 1. A typical oxygen disappearance curve (ODC) as an average of 5 curves
600
recorded at different sites in the same muscle. PO2 values correspond to those measured in the
601
interstitial fluid using phosphorescence quenching microscopy and thus represent PO2 on the
602
surface of muscle fibers at the measurement site.
603
Figure 2. Cross-section of a generalized muscle fiber. For the current interstitial oxygen
604
tension at the surface of the muscle fiber, P, the total respiration rate by the cell is V and the core
605
(i.e. center) PO2 is Pc. For an isobaric fraction of the cellular volume, f, the local PO2 is p and
606
the local consumption rate is v. The intracellular PO2 range, P - Pc, is Δ.
607
Figure 3. Uniform distribution of the tissue volume as a function of p (variable
608
intracellular PO2) presented for three distinct situations. For normoxic conditions the
609
distribution for all elementary volumes of cells have p > 0; at the critical PO2 the distribution is
610
characterized by the condition Pc = 0; while for the hypoxic case, the width of the distribution of
611
the respiring volume of tissue is reduced (anoxic part of volume is shaded).
612
Figure 4. Theoretical curves for the oxygen dependency of respiration generated for a set
613
of parameters (VM = 100 nl O2/(cm3·s), k = 10 mmHg and Δ = 0, 5, 10, 20, 30, 40 mmHg). Left
614
panel: Curve 1, with Δ = 0, represents the mitochondrial PO2 dependence according to Eq. 11
615
without any diffusional resistance and PO2 gradients. The five other solid curves (2 through 6)
616
represent the PO2 dependencies for PO2 differences between the cell surface and its core of 5-40
617
mmHg. Each curve consists of two regions, the normoxic region described by V1 and the
618
hypoxic region described by V2, according to Eqs. 14 and 15, respectively. The dashed line
28
619
(curve 7) corresponds to the critical PO2 curve, V3 (Eq. 16), indicating the points which separate
620
the normoxic and hypoxic regions of the curves. Right panel: The same curves plotted on a
621
double-logarithmic plot to demonstrate that the hypoxic regions are straight lines, which turn into
622
hyperbolic lines above the threshold line 7 for critical dependency of oxygen consumption on
623
PO2, V3.
624
Figure 5. A typical plot of the oxygen dependency for respiration of the rat
625
spinotrapezius muscle. The data set was transformed from the ODC shown in Fig. 1. The
626
parameters estimated by fitting these data are: VM = 138.8 nl O2/(cm3·s), k = 9.4 mmHg and Δ =
627
3.0 and 3.3 mmHg. PO2 values plotted on the horizontal axis correspond to interstitial PO2 on the
628
surfaces of the group of muscle fibers at the site of these measurements.
629
630
631
632
633
634
635
636
637
638
639
640
641
29
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
REFERENCES
1.
Bailey JK, Kindig CA, Behnke BJ, Musch TI, Schmid-Schoenbein GW, and Poole
DC. Spinotrapezius muscle microcirculatory function: effects of surgical exteriorization. Am J
Physiol Heart Circ Physiol 279: H3131-3137, 2000.
2.
Baranov VI, Belichenko VM, and Shoshenko CA. Oxygen diffusion coefficient in
isolated chicken red and white skeletal muscle fibers in ontogenesis. Microvasc Res 60: 168-176,
2000.
3.
Behnke BJ, Barstow TJ, Kindig CA, McDonough P, Musch TI, and Poole DC.
Dynamics of oxygen uptake following exercise onset in rat skeletal muscle. Respir Physiol
Neurobiol 133: 229-239, 2002.
4.
Belichenko VM, Baranov VI, Novosel'tsev SV, and Shoshenko KA. [Coefficient of
oxygen diffusion in fibers of the skeletal muscles]. Aviakosm Ekolog Med 36: 31-38, 2002.
5.
Bentley TB, Meng H, and Pittman RN. Temperature dependence of oxygen diffusion
and consumption in mammalian striated muscle. Am J Physiol 264: H1825-1830, 1993.
6.
Boegehold MA and Johnson PC. Periarteriolar and tissue PO2 during sympathetic
escape in skeletal muscle. Am J Physiol 254: H929-936, 1988.
7.
Brown GC. Control of respiration and ATP synthesis in mammalian mitochondria and
cells. Biochem J 284 ( Pt 1): 1-13, 1992.
8.
Brown GC and Cooper CE. Nanomolar concentrations of nitric oxide reversibly inhibit
synaptosomal respiration by competing with oxygen at cytochrome oxidase. FEBS Lett 356: 295298, 1994.
9.
Buerk DG, Nair PK, Bridges EW, and Hanley TR. Interpretation of oxygen
disappearance curves measured in blood perfused tissues. Adv Exp Med Biol 200: 151-161, 1986.
10.
Chance B and Williams GR. Respiratory enzymes in oxidative phosphorylation. I.
Kinetics of oxygen utilization. J Biol Chem 217: 383-393, 1955.
11.
Chandel NS and Schumacker PT. Cellular oxygen sensing by mitochondria: old
questions, new insight. J Appl Physiol 88: 1880-1889, 2000.
12.
Cooper CE and Giulivi C. Nitric oxide regulation of mitochondrial oxygen consumption
II: Molecular mechanism and tissue physiology. Am J Physiol Cell Physiol 292: C1993-2003,
2007.
13.
Gnaiger E. Bioenergetics at low oxygen: dependence of respiration and phosphorylation
on oxygen and adenosine diphosphate supply. Respir Physiol 128: 277-297, 2001.
14.
Gnaiger E, Steinlechner-Maran R, Mendez G, Eberl T, and Margreiter R. Control of
mitochondrial and cellular respiration by oxygen. J Bioenerg Biomembr 27: 583-596, 1995.
15.
Golub AS, Barker MC, and Pittman RN. PO2 profiles near arterioles and tissue
oxygen consumption in rat mesentery. Am J Physiol Heart Circ Physiol 293: H1097-1106, 2007.
16.
Golub AS and Pittman RN. PO2 measurements in the microcirculation using
phosphorescence quenching microscopy at high magnification. Am J Physiol Heart Circ Physiol
294: H2905-2916, 2008.
17.
Golub AS and Pittman RN. Thermostatic animal platform for intravital microscopy of
thin tissues. Microvasc Res 66: 213-217, 2003.
30
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
18.
Golub AS, Tevald MA, and Pittman RN. Phosphorescence quenching
microrespirometry of skeletal muscle in situ. Am J Physiol Heart Circ Physiol 300: H135-143,
2011.
19.
Gray SD. Rat spinotrapezius muscle preparation for microscopic observation of the
terminal vascular bed. Microvasc Res 5: 395-400, 1973.
20.
Hill AV. The diffusion of oxygen and lactic acid through tissues. Proceedings of the
Royal Society of London Series B 104: 39-96, 1928.
21.
Hill AV. On the time required for diffusion and its relation to processes in muscle.
Proceedings of the Royal Society of London 135: 446-453, 1948.
22.
Hill DK. Oxygen tension and the respiration of resting frog's muscle. J Physiol 107: 479495, 1948.
23.
Hogan MC. Phosphorescence quenching method for measurement of intracellular PO2
in isolated skeletal muscle fibers. J Appl Physiol 86: 720-724, 1999.
24.
Jones DP and Kennedy FG. Analysis of intracellular oxygenation of isolated adult
cardiac myocytes. Am J Physiol 250: C384-390, 1986.
25.
Kempner W. Effect of oxygen tension on cellular metabolism. J cell comp physiol 10:
339-363, 1937.
26.
Kennedy FG and Jones DP. Oxygen dependence of mitochondrial function in isolated
rat cardiac myocytes. Am J Physiol 250: C374-383, 1986.
27.
Lash JM and Bohlen HG. Perivascular and tissue PO2 in contracting rat spinotrapezius
muscle. Am J Physiol 252: H1192-1202, 1987.
28.
Lin SH. Oxygen diffusion in a spherical cell with nonlinear oxygen uptake kinetics. J
Theor Biol 60: 449-457, 1976.
29.
Longmuir IS. Respiration rate of rat-liver cells at low oxygen concentrations. Biochem J
65: 378-382, 1957.
30.
Mahler M, Louy C, Homsher E, and Peskoff A. Reappraisal of diffusion, solubility,
and consumption of oxygen in frog skeletal muscle, with applications to muscle energy balance.
J Gen Physiol 86: 105-134, 1985.
31.
Mik EG, Ince C, Eerbeek O, Heinen A, Stap J, Hooibrink B, Schumacher CA,
Balestra GM, Johannes T, Beek JF, Nieuwenhuis AF, van Horssen P, Spaan JA, and
Zuurbier CJ. Mitochondrial oxygen tension within the heart. J Mol Cell Cardiol 46: 943-951,
2009.
32.
Poole DC, Wagner PD, and Wilson DF. Diaphragm microvascular plasma PO2
measured in vivo. J Appl Physiol 79: 2050-2057, 1995.
33.
Popel AS. Diffusion in tissue slices with metabolism obeying Michaelis-Menten kinetics.
J Theor Biol 80: 325-332, 1979.
34.
Reneau DD and Halsey JH, Jr. Interpretation of oxygen disappearance rates in brain
cortex following total ischaemia. Adv Exp Med Biol 94: 189-198, 1977.
35.
Richmond KN, Burnite S, and Lynch RM. Oxygen sensitivity of mitochondrial
metabolic state in isolated skeletal and cardiac myocytes. Am J Physiol 273: C1613-1622, 1997.
36.
Richmond KN, Shonat RD, Lynch RM, and Johnson PC. Critical PO(2) of skeletal
muscle in vivo. Am J Physiol 277: H1831-1840, 1999.
37.
Robiolio M, Rumsey WL, and Wilson DF. Oxygen diffusion and mitochondrial
respiration in neuroblastoma cells. Am J Physiol 256: C1207-1213, 1989.
38.
Rowell LB. Ideas about control of skeletal and cardiac muscle blood flow (1876-2003):
cycles of revision and new vision. J Appl Physiol 97: 384-392, 2004.
31
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
39.
Rumsey WL, Schlosser C, Nuutinen EM, Robiolio M, and Wilson DF. Cellular
energetics and the oxygen dependence of respiration in cardiac myocytes isolated from adult rat.
J Biol Chem 265: 15392-15402, 1990.
40.
Scandurra FM and Gnaiger E. Cell respiration under hypoxia: facts and artefacts in
mitochondrial oxygen kinetics. Adv Exp Med Biol 662: 7-25, 2010.
41.
Schenkman KA, Marble DR, Burns DH, and Feigl EO. Myoglobin oxygen
dissociation by multiwavelength spectroscopy. J Appl Physiol 82: 86-92, 1997.
42.
Shen W, Hintze TH, and Wolin MS. Nitric oxide. An important signaling mechanism
between vascular endothelium and parenchymal cells in the regulation of oxygen consumption.
Circulation 92: 3505-3512, 1995.
43.
Shibata M, Ichioka S, Ando J, and Kamiya A. Microvascular and interstitial PO(2)
measurements in rat skeletal muscle by phosphorescence quenching. J Appl Physiol 91: 321-327,
2001.
44.
Smith LM, Golub AS, and Pittman RN. Interstitial PO(2) determination by
phosphorescence quenching microscopy. Microcirculation 9: 389-395, 2002.
45.
Stary CM and Hogan MC. Effect of varied extracellular PO2 on muscle performance in
Xenopus single skeletal muscle fibers. J Appl Physiol 86: 1812-1816, 1999.
46.
Steinlechner-Maran R, Eberl T, Kunc M, Margreiter R, and Gnaiger E. Oxygen
dependence of respiration in coupled and uncoupled endothelial cells. Am J Physiol 271: C20532061, 1996.
47.
Takahashi E and Asano K. Mitochondrial respiratory control can compensate for
intracellular O(2) gradients in cardiomyocytes at low PO(2). Am J Physiol Heart Circ Physiol
283: H871-878, 2002.
48.
Takahashi E and Doi K. Impact of diffusional oxygen transport on oxidative
metabolism in the heart. Jpn J Physiol 48: 243-252, 1998.
49.
Torres Filho IP and Intaglietta M. Microvessel PO2 measurements by
phosphorescence decay method. Am J Physiol 265: H1434-1438, 1993.
50.
Torres Filho IP, Leunig M, Yuan F, Intaglietta M, and Jain RK. Noninvasive
measurement of microvascular and interstitial oxygen profiles in a human tumor in SCID mice.
Proc Natl Acad Sci U S A 91: 2081-2085, 1994.
51.
van der Laarse WJ, des Tombe AL, van Beek-Harmsen BJ, Lee-de Groot MB, and
Jaspers RT. Krogh's diffusion coefficient for oxygen in isolated Xenopus skeletal muscle fibers
and rat myocardial trabeculae at maximum rates of oxygen consumption. J Appl Physiol 99:
2173-2180, 2005.
52.
Vanderkooi JM, Maniara G, Green TJ, and Wilson DF. An optical method for
measurement of dioxygen concentration based upon quenching of phosphorescence. J Biol Chem
262: 5476-5482, 1987.
53.
Wilson DF. Contribution of diffusion to the oxygen dependence of energy metabolism in
cells. Experientia 46: 1160-1162, 1990.
54.
Wilson DF. Quantifying the role of oxygen pressure in tissue function. Am J Physiol
Heart Circ Physiol 294: H11-13, 2008.
55.
Wilson DF and Erecinska M. Effect of oxygen concentration on cellular metabolism.
Chest 88: 229S-232S, 1985.
56.
Wilson DF, Erecinska M, Drown C, and Silver IA. The oxygen dependence of cellular
energy metabolism. Arch Biochem Biophys 195: 485-493, 1979.
32
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
57.
Wilson DF, Lee WM, Makonnen S, Apreleva S, and Vinogradov SA. Oxygen
pressures in the interstitial space of skeletal muscle and tumors in vivo. Adv Exp Med Biol 614:
53-62, 2008.
58.
Wilson DF, Lee WM, Makonnen S, Finikova O, Apreleva S, and Vinogradov SA.
Oxygen pressures in the interstitial space and their relationship to those in the blood plasma in
resting skeletal muscle. J Appl Physiol 101: 1648-1656, 2006.
59.
Wilson DF, Owen CS, and Erecinska M. Quantitative dependence of mitochondrial
oxidative phosphorylation on oxygen concentration: a mathematical model. Arch Biochem
Biophys 195: 494-504, 1979.
60.
Wilson DF, Rumsey WL, Green TJ, and Vanderkooi JM. The oxygen dependence of
mitochondrial oxidative phosphorylation measured by a new optical method for measuring
oxygen concentration. J Biol Chem 263: 2712-2718, 1988.
61.
Wilson DF, Vanderkooi JM, Green TJ, Maniara G, DeFeo SP, and Bloomgarden
DC. A versatile and sensitive method for measuring oxygen. Adv Exp Med Biol 215: 71-77,
1987.
62.
Zheng L, Golub AS, and Pittman RN. Determination of PO2 and its heterogeneity in
single capillaries. Am J Physiol 271: H365-372, 1996.
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
33
815
816
817
34
Figure 2