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J Physiol. 2007 January 15; 578(Pt 2): 595–603.
Published online 2006 October 12. doi: 10.1113/jphysiol.2006.116061.
PMCID: PMC2075141
Myoglobin translational diffusion in rat myocardium and its implication on intracellular oxygen transport
Ping-Chang Lin, Ulrike Kreutzer, and Thomas Jue
Department of Biochemistry and Molecular Medicine, University of California Davis, Davis, CA 95616-8635, USA
Corresponding author T. Jue: Department of Biochemistry and Molecular Medicine, University of California Davis, Davis, CA 95616-8635, USA. Email: tjue/at/ucdavis.edu
Received June 26, 2006; Accepted October 5, 2006.
Abstract
Current theory of respiratory control invokes a role of myoglobin (Mb)-facilitated O2 diffusion in regulating the intracellular O2 flux, provided Mb diffusion can compete effectively with free O2 diffusion. Pulsed-field gradient NMR methods have now followed gradient-dependent changes in the distinct 1H NMR γ CH3 Val E11 signal of MbO2 in perfused rat myocardium to obtain the endogenous Mb translational diffusion coefficient (DMb) of 4.24 × 10−7 cm2 s−1 at 22°C. The DMb matches precisely the value predicted by in vivo NMR rotational diffusion measurements of Mb and shows no orientation preference. Given values in the literature for the Krogh's free O2 diffusion coefficient (K0), myocardial Mb concentration and a partial pressure of O2 that half saturates Mb (P50), the analysis yields an equipoise diffusion PO2 of 1.77 mmHg, where Mb and free O2 contribute equally to the O2 flux. In the myocardium, Mb-facilitated O2 diffusion contributes increasingly more than free O2 diffusion when the PO2 falls below 1.77 mmHg. In skeletal muscle, the PO2 must fall below 5.72 mmHg. Altering the Mb P50 induces modest change. Mb-facilitated diffusion has a higher poise in skeletal muscle than in myocardium. Because the basal PO2 hovers around 10 mmHg, Mb does not have a predominant role in facilitating O2 transport in myocardium but contributes significantly only when cellular oxygen falls below the equipoise diffusion PO2.
 
A cornerstone of respiratory regulation stands on the capacity of myoglobin (Mb) to store O2 or to facilitate O2 transport. In marine mammals, the high concentration of Mb could certainly supply O2 during a dive or apnoea (Dolar et al. 1999; Guyton et al. 1995; Kooyman, 1998; Ponganis et al. 2002). In adaptation to high altitude, enhanced Mb expression increases the O2 depot (Gimenez et al. 1977; Terrados et al. 1990). These observations agree with the correlation between Mb concentration (O2 supply) and oxidative capacity in different species (Wittenberg & Wittenberg, 2003). Yet, in spontaneously beating rat heart, Mb can prolong normal heart function for only a few seconds (Chung & Jue, 1996). Without any Mb, neither myocardial nor skeletal muscle function suffers any apparent physiological impairment (Garry et al. 1998; Godecke et al. 1999).

The physiology canon also states that Mb can facilitate O2 diffusion. In contrast to the low solubility of O2, the high O2 carrying capacity of Mb can confer an advantage in transporting O2 from the sarcolemma to the mitochondria (Wittenberg, 1970; Wittenberg & Wittenberg, 1989). In vitro studies have confirmed that O2 diffuses faster in solution containing Mb than in Mb-free solution. Mb exhibits sufficient mobility and O2 carrying capacity to compete effectively with free O2 (Johnson et al. 1996). In vivo, however, the contribution of Mb-facilitated O2 diffusion remains unclear. Without a definitive translational diffusion coefficient for Mb (DMb) in vivo, the theory of Mb-facilitated diffusion languishes for experimental confirmation.

Over the years, researchers have attempted to estimate endogenous Mb diffusion in the cell by measuring Mb diffusion in concentrated solution, in tissue homogenate and in myoglobin-free frog muscle (Moll, 1968; Riveros-Moreno & Wittenberg, 1972; Baylor & Pape, 1988). The results have varied widely. Fluorescence recovery after photobleaching (FRAP) techniques have recently tracked the photoxidation of Mb in superfused rat diaphragm or the diffusion of microinjected modified Mb in isolated muscle fibre. These experiments have determined a low DMb that cannot support any significant role for Mb in facilitating O2 diffusion (Jurgens et al. 1993; Papadopoulos et al. 2001).

However, the FRAP experiments do not actually measure endogenous Mb diffusion and utilize model systems that do not adequately mimic respiring tissue (Groebe, 1995). Moreover, they disagree with the in vivo NMR observation of Mb rotational diffusion, which predicts a much faster DMb (Livingston et al. 1983; Wang et al. 1997).

Because the 1H NMR can detect the distinct γCH3 Val E11 signal of MbO2 in myocardium at −2.8 ppm, an opportunity exists to apply pulsed-field gradient technique to map endogenous Mb translational diffusion in perfused myocardium (Stejskal & Tanner, 1965; Kreutzer et al. 1992). Indeed, MbO2 diffuses with an average coefficient about 4 times faster than the FRAP-determined diffusion coefficient and shows no orientation preference. The DMb also matches precisely the value predicted by the NMR rotational diffusion analysis (Wang et al. 1997).

Given the Mb concentration in tissue, the partial pressure of O2 that half saturates Mb (P50) and the DMb, the analysis establishes an equipoise diffusion PO2 in the cell, where Mb and free O2 contribute equally to O2 transport. In the basal state rodent myocardium or skeletal muscle, Mb cannot play a significant role in facilitating O2 diffusion. In contrast, marine mammal muscle with a high Mb concentration can utilize Mb-facilitated O2 diffusion under all physiological conditions. The conclusion agrees with Mb studies in which rat myocardium inhibited with a significant fraction of CO-bound Mb exhibits no sign of respiration or metabolism impairment (Glabe et al. 1998; Chung et al. 2006). The NMR-determined translational diffusion coefficient of endogenous Mb in respiring myocardium has established a key parameter that does not lend support to the hypothesis that Mb has an overall general role in facilitating O2 transport in respiring tissue. Instead, the DMb defines the physiological conditions in which Mb can contribute significantly to the intracellular O2 flux.

Methods

Protein preparation
Mb solution was prepared from lyophilized horse heart protein (Sigma Chemical Inc.). The preparation of MbCO solution followed the procedure previously described (Kreutzer et al. 1993). The same process was also applied to prepare the haemoglobin (Hb) solution, in which Hb was extracted from human erythrocytes (Wang et al. 1997).

Animal preparation and heart perfusion
Animal care and experimental procedures followed the guidelines of the NIH Office for Laboratory Animal Welfare and were approved by the University of California Davis Institutional Animal Use and Care Committee. The procedure for rat heart perfusion was performed as previously described (Chung & Jue, 1999; Kreutzer & Jue, 2004). Male Sprague-Dawley rats (350–400 g) were anaesthetized by an intraperitoneal injection of sodium pentobarbital (65 mg kg−1) and heparinized (1000 U kg−1). The heart was quickly isolated and perfused in Langendorff perfusion apparatus, with Krebs-Henseleit buffer maintained at room temperature (21–23°C). A peristaltic pump (Rainin Rabbit) maintained a constant, non-recirculating perfusion flow of 12–13 ml min−1.

K+-induced arrest
After a 20 min control period, the perfusate was switched to Krebs-Henseleit buffer containing 92.7 mm NaCl and 30 mm KCl, which stopped the heart beat. The perfusate flow rate was reduced to 50% of control 10 min after the heart stopped beating. High K+ perfusion continued for approximately 7 h. The perfusate was then switched back to 118 mm NaCl, 4.7 mm KCl, and the flow returned to its control level. Perfusion then continued for 20–30 min.

NMR
An Avance 400-MHz Bruker spectrometer measured the 1H/31P signals with a 20 mm micro-imaging gradient probe. The 1H 90 deg pulse was 65 μs. A modified Stejskal-Tanner pulsed-field gradient spin echo or pulsed-field gradient stimulated echo (PG-STE) sequence followed the Val E11 resonance of MbCO and MbO2 at −2.4 ppm and −2.8 ppm, respectively (Stejskal & Tanner, 1965; Price, 1997). The gradient field strength ranged from 0 to 95 G (gauss cm−1). A typical spectrum required 1024 scans and used the following signal acquisition parameters: 8192 Hz spectral width, 4096 data points and 255 ms acquisition time. The H2O line served as the spectral reference, 4.75 ppm at 25°C relative to sodium-3-(trimethylsilyl)propionate-2,2,3,3-d4 at 0 ppm

Diffusion measurements in perfused heart experiments utilized a modified PG-STE sequence that included chemical-shift selective (CHESS) pulses (Haase et al. 1985). For the diffusion measurements, the acquisition parameters included the following: acquisition time of 38.5 ms, spectral width of 10 KHz and 768 data points. A typical spectrum required 16 000 scans or about 24 min of signal accumulation.

For the 31P spectra, the signal acquisition utilized a 55 deg pulse angle, 6494 Hz spectral width, 4096 point data size and a 0.65 s repetition time. The 31P 90 deg pulse was 72 μs calibrated against a 0.1 m phosphate solution. Peak area analysis, calibrated against fully relaxed spectra, determined the phosphocreatine (PCr) and ATP levels. All 31P signals were referenced to PCr peak as 0 ppm A typical spectrum required 256 scans.

Diffusion equation
The NMR determination of the translational diffusion relates signal intensity change with strength of the applied rectangular gradient pulses (Stejskal & Tanner, 1965; Price, 1997):
A mathematical equation, expression, or formula that is to be displayed as a block (callout) within the narrative flow. The name of referred object is tjp0578-0595-m1.jpg
(1)
where S(G) is the signal intensity in an applied field gradient, S(0) is the signal intensity with no applied field gradient, γ is the magnetogyric ratio, δ is the duration of the gradient pulse, Δ is the gradient pulse separation, G and GT are the 1 × 3 and 3 × 1 gradient field tensor and its transpose, D is the 3 × 3 rank-two diffusion tensor and Gi, Gj and Dij are the respective matrix elements. The equation reduces to a linear combination of the product of tensor elements Dij and bij, where
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(2)
To determine molecular diffusion requires measuring the signal intensity as a function of gradient pulses G applied along different directions, reflecting the elements of the b matrix. In the case of isotropic diffusion, the observations corresponding to diagonal elements will not differ, and the equation reduces to a simple expression:
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(3)

O2 transport by Mb and free diffusion
The relative O2 flux by Mb-facilitated diffusion and free O2 derives from following equations:
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(4)
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(5)
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(6)
Where Fo2 is total O2 flux, equation M1 is O2 flux from Mb, equation M2 is O2 flux from free O2, PO2 is partial pressure of O2 at the cell surface, Pr is PO2 at the mitochondria (assumed to be 0), P50 is PO2 that will half saturate Mb (O2 binding affinity of Mb), CMb is Mb concentration, An external file that holds a picture, illustration, etc., usually as some form of binary object. The name of referred object is tjp0578-0595-m8.jpgis PO2 gradient from cell surface to the mitochondria, K0 is Krogh's diffusion constant for free O2, DMb is Mb diffusion coefficient.

The following equation describes the relative contribution to O2 transport:

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(7)

Statistical analysis
Statistical analysis, used Sigma Plot/Sigma Stat program (Systat Software, Inc.) and expressed the data as mean ± s.e.m. Linear least-squares regression determined the slopes, intercepts and correlation coefficients. Statistical significance was determined by two-tailed Student's t test (P < 0.05).

Results

Figure 1 shows the 1H spectra of MbCO in solution measured with a modified PG-STE sequence at different gradient fields applied in the x direction. At 72.8 G, the Val E11 γ-methyl signal of MbCO at −2.4 ppm shows the lowest signal intensity (A in Fig. 1). As the gradient strength decreases from 63.7 to 18.2 G, the signal intensity rises. With applied field gradient 9.1 G, the signal intensity reaches its maximum intensity (H in Fig. 1). The analysis of the natural logarithm of the solution state MbCO and HbCO signal intensity as a function of the square of the gradient strength yields a translational diffusion coefficient of 11.6 × 10−7 cm2 s−1 (1.8 mm Mb) and 7.53 × 10−7 cm2 s−1 (0.75 mm Hb), calibrated against the H2O diffusion coefficient 2.17 × 10−5 cm2 s−1 (Fig. 2). The Mb and Hb diffusion coefficients match literature values (Table 1). Applying the field gradient along either the y or z direction yields identical diffusion coefficient values, as expected for an isotropic, homogeneous solution (data not shown).

Figure 1Figure 1
1H NMR diffusion-weighted spectra of MbCO solution at 22°C
Figure 2Figure 2
Plot of natural logarithm of the signal intensity of H2O, γ CH3 Val E11 signal of MbCO and HbCO versus b (An external file that holds a picture, illustration, etc., usually as some form of binary object. The name of referred object is tjp0578-0595-m9.jpg) with a field gradient applied in the x direction
Table 1Table 1
Diffusion coefficients of Mb/Hb in solutions and in muscles

The perfused rat myocardium at 22°C shows physiological characteristics consistent with previously reported experiments (Table 2; Chung & Jue, 1999; Kreutzer & Jue, 2004). Introducing 30 mm KCl stops heart contraction. Rate pressure product (RPP) decreases from 10.9 ± 0.4 × 103 mmHg min−1 to zero. During the period of K+-induced arrest, oxygen consumption (MVO2) decreases from 14.1 ± 0.6 to 5.0 ± 0.4 μmol min−1 (g dry weight)−1 and ATP level decreases to 95.4 ± 1.6% of control. However, PCr rises to 120.6 ± 4.3% above the basal level. During reperfusion with control buffer, MVO2 returns to 14.0 ± 1.0 μmol min−1 (g dry weight)−1. PCr and ATP levels recover to 93.2 ± 3.2% and 93.9 ± 1.3% of the control level, respectively. RPP returns to 10.5 ± 0.4 × 103 mmHg min−1.

Table 2Table 2
Physiological parameters for perfused heart at 22°C

Figure 3 shows the 1H spectra of the Val E11 γ-methyl signal of MbO2 at −2.8 ppm from perfused myocardium measured with the same modified PG-STE sequence at different gradient fields applied in the y direction: 84.2 G (A) 74.8 G (B) 56.1 G (C) 37.4 G (D) and 4.7 G (E). At 84.2 G, the Val E11 γ-methyl signal of MbO2 shows the lowest signal intensity. As the gradient strength decreases, the signal intensity increases.

Figure 3Figure 3
1H NMR diffusion-weighted spectra of MbO2 from perfused rat heart under KCl-induced arrest at 22°C

A plot of the natural logarithm of the MbO2 signal intensity from the myocardium (n = 5) as a function of the square of the gradient strength applied along x, y and z reveals a linear relationship (Fig. 4; r > 0.99). Gradients applied along x, y or z yield a similar translational diffusion coefficient: 4.12 ± 0.40 (x), 4.51 ± 0.38 (y) and 4.08 ± 0.19 (z) × 10−7 cm2 s−1. The average diffusion coefficient is therefore 4.24 × 10−7 cm2 s−1.

Figure 4Figure 4
Plot of the natural logarithm of the MbO2 Val E11 peak intensity from perfused heart as a function of b

Figure 5 shows the relative contribution from Mb and free O2 in transporting O2 in the cell. The straight lines depict the contribution from free O2 diffusion. The O2 flux contribution from free O2 diffusion reveals a linear dependence on PO2 and has a slope that reflects the two values reported in the literature for the Krogh's diffusion constant (K0) of 2.52 and 4.28 × 10−5 ml O2 cm−1 min−1 atm−1. The Mb-facilitated O2 flux shows a concentration-dependent response based on the experimentally determined DMb value of 4.24 × 10−7 cm2 s−1. As Mb concentration increases from 0.19 to 0.42 mm, the Mb contribution to the overall O2 flux increases correspondingly. Altering the P50 from 1.5 to 2.3 mmHg produces a modest change in the Mb-dependent O2 flux. The intersection of the free O2 and Mb-facilitated O2 diffusion marks the equipoise diffusion PO2, where Mb and free O2 contribute equally to the O2 flux. Below the equipoise diffusion PO2, the Mb contribution dominates. Table 3 summarizes the equipoise diffusion PO2 values at different Mb concentrations and values of P50 and K0.

Figure 5Figure 5
Plot of free O2 flux versus Mb-facilitated O2 diffusion as a function of PO2 at 22°C
Table 3Table 3
Equipoise diffusion PO2 in tissue with different Mb concentration
Discussion

NMR signal of cellular MbO2
With NMR, the detectable Val E11 MbO2 signal in myocardium and skeletal muscle presents an opportunity to determine the endogenous Mb diffusion in the cell with pulsed-field gradient methodology. Control experiments confirm that the NMR-determined diffusion coefficients of solution Mb (11.6 × 10−7 cm2 s−1) and Hb (7.53 × 10−7 cm2 s−1) agree closely with values reported in the literature. In perfused myocardium, Mb diffusion in the cell drops by 37% from 11.6 to 4.24 × 10−7 cm2 s−1.

A comparative study has shown that the 1H NMR spectral analysis and biochemical assay yield matching values for the Mb concentration in the perfused rat myocardium. No significant bound pool of Mb exists in the cell, and the NMR Mb Val E11 signal reflects the total cellular Mb pool (Kreutzer et al. 1993). Moreover, the line shape of the Mb Val E11 signal in the cell versus in solution shows no significant deviation, consistent with freely diffusing Mb pool in the cell. Any significant compartmentalization or restricted diffusion of Mb would yield disparate NMR versus biochemical assay results and contrasting solution versus cellular Mb line shapes.

Under normoxic conditions, the perfused myocardium model in the study also reveals no sign of O2 heterogeneity, which would give rise to a regional distribution of partially saturated MbO2 (Kreutzer & Jue, 1995). Experiments with infused high affinity CO yield a dynamically matching MbCO and MbO2 Val E11 signal intensity. The MbCO signal intensity never exceeds the MbO2 signal intensity, and the sum of the MbCO and MbO2 signal remains constant (Glabe et al. 1998; Chung et al. 2006). Any O2 heterogeneity would yield a higher MbCO signal intensity.

Comparison of translational diffusion coefficients
The literature contains reports of DMb ranging from 1.2 to 23 × 10−7 cm2 s−1 (Riveros-Moreno & Wittenberg, 1972; Federspiel, 1986; Papadopoulos et al. 1995). Many models have predicted on the premise that the Mb concentration in terrestrial mammalian muscle does not exceed 0.5 mm and the cellular environment contains enzymes as well as metabolites that increase the viscosity. As a consequence, the DMb of an 18 g dl−1 Mb solution (5–7 × 10−7 cm2 s−1 at 20°C) has served as a key starting point for mathematical modelling of intracellular O2 transport (Riveros-Moreno & Wittenberg, 1972; Federspiel, 1986). To mimic the cellular environment, tissue homogenates have been used. In rat skeletal muscle homogenate, Fe (+3) Mb-H2O (metMb) has a DMb of 1.5 × 10−7 cm2 s−1 at 20°C (Moll, 1968). Homogenates, however, do not necessarily reflect the cellular milieu. Indeed, the literature has documented, such as the case with ADP, that homogenates and the cell do not exhibit matching free metabolite and enzyme pools (Iles et al. 1985).

Nevertheless, studies following the diffusion of microinjected metMb into Mb-free frog muscle have found a similar DMb of 1.6 × 10−7 cm2 s−1 at 22°C (Baylor & Pape, 1988). Similarly, recent fluorescence recovery after photobleaching (FRAP) experiments have followed the diffusion of microinjected dye-conjugated metMb in isolated muscle fibre from heart and skeletal muscle tissue and have obtained a DMb of 1.2 × 10−7 cm2 s−1 at 22°C, which is about 10 times slower than dilute Mb diffusion (Papadopoulos et al. 2001). Because of the uncertain contribution of metMb reaction kinetics with Mb reductase, the non-physiological nature of an isolated fibre model, and boundary condition assumptions, questions have been raised about the validity of the observed DMb as a reflection of endogenous Mb diffusion in respiring tissue (Groebe, 1995). In particular, invasive microinjection procedure requires 4–6 h of post-injection recovery to minimize cell trauma (Seksek et al. 1997). The present NMR study shows that the endogenous Mb diffusion in respiring myocardium has a DMb 2.7 times slower than dilute Mb solution, but about 2.7–3.5 times faster than the diffusion coefficient determined by Mb microinjection-based experiments.

Mb versus free O2 contribution to O2 flux
A key element of the Mb-facilitated diffusion theory pivots about the translational diffusion of Mb in the cell. The intracellular O2 transport depends upon the O2 flux from Mb and free O2, FOMb2 and equation M3, (eqns (47)). A relatively low diffusion coefficient of Mb in the cell cannot support a significant role for Mb in facilitating O2 diffusion, as Mb cannot compete effectively with free O2 diffusion.

The contribution from free O2 flux depends linearly upon PO2 and K0. K0 values ranging from 2.52 to 4.28 × 10−5ml O2 cm−1 min−1 atm−1 have been reported (Bentley et al. 1993). With a K0 of 2.52 × 10−5 ml O2 cm−1 min−1 atm−1, a P50 of 1.5 mmHg and an Mb concentration of 0.19 mm, the NMR-determined translational diffusion coefficient of 4.24 × 10−7 cm2 s−1 yields an equipoise diffusion PO2 of 1.77 mmHg, where Mb and free O2 have equal contribution to the O2 flux. Below a PO2 of 1.77 mmHg, the Mb-dependent contribution to the O2 flux begins to dominate. Increasing the concentration of Mb from 0.19 to 0.42 mm shifts the equipoise diffusion PO2 to 5.7 mmHg, well above the Mb P50. In essence, as Mb concentration rises, its role in facilitated O2 diffusion also increases.

In terrestrial mammalian muscle, the Mb concentration range from 0.19 mm in heart muscle to 0.42 mm in soleus muscle indicates a higher poise for Mb-facilitated O2 diffusion in skeletal muscle than in myocardium (Wittenberg, 1970). In marine mammalian muscle, Mb concentration in muscle can rise to 25–70 g (kg tissue)−1 (approximately 1.4–4 mm) (Dolar et al. 1999; Wright & Davis, 2006). At 1.4–4 mm Mb, the equipoise diffusion PO2 increases to 12–38 mmHg at 37°C. Mb-dependent O2 diffusion predominates even under resting conditions.

In vivo NMR experiments have shown that in the basal state of muscle, sufficient O2 exists to saturate Mb > 90% and to keep the PO2 well above 10 mmHg. Even as myocardial respiration increases with workload, the O2 level does not fall enough to produce a detectable deoxy-Mb signal (Zhang et al. 1999; Kreutzer et al. 2001). No transient fluctuation in MbO2 saturation appears in a cardiac contraction cycle (Chung & Jue, 1999). Moreover, spontaneously beating heart with 77% of Mb inactivated with CO suffers no impairment in respiration, contractile function or high energy phosphate state, even under conditions that would accentuate the purported role of Mb in O2-facilitated diffusion (Glabe et al. 1998; Chung et al. 2006). Mb does not appear to play a significant role in regulating myocardial respiration.

In contrast, as skeletal muscle begins to contract, Mb desaturates within 30 s to reach a deoxygenated steady state that depends upon workload, even though the cell has abundant O2 to drive oxidative phosphorylation (Mole et al. 1999; Chung et al. 2005). MbO2 responds to a transient rather than a steady-state change in energy demand.

As the Mb P50 rises, however, the equipoise diffusion PO2 declines. In particular, during muscle contraction, the muscle temperature rises and will increase the Mb P50 (Schenkman et al. 1997). If Mb P50 rises from 1.5 to 2.3 mmHg, the equipoise diffusion PO2 decreases from 1.77 to 0.97 mmHg in tissue with 0.19 mm Mb. At 0.42 mm Mb, the equipoise diffusion PO2 shifts from 5.72 to 4.92 mmHg. As muscle contraction proceeds and generates heat, the cell reduces its reliance on Mb-facilitated O2 diffusion.

Isotropic versus anisotropic diffusion
In solution, Mb exhibits isotropic diffusion; in myocyte, Mb can exhibit anisotropic diffusion, as the longitudinal myofibril dimension exceeds the radial dimension by a factor of 10. In particular, the different fibre orientations in the myocardium could lead to a macroscopic volume-averaged determination of the components of the apparent diffusion tensor. Indeed, de Graaf et al. (2000) have hinted at anisotropic diffusion of PCr and ATP in the sarcoplasm. For Mb, however, the translational diffusion in the cell shows no orientation preference. In the x, y and z directions, Mb diffuses at 4.12 ± 0.40, 4.51 ± 0.38 and 4.08 ± 0.19 × 10−7 cm2 s−1, respectively.

The isotropic motion of Mb agrees with the independent rotational diffusion analysis. Because paramagnetic molecules can exhibit field-dependent relaxation, the deoxy-Mb proximal histidyl NδH signal has served to assess Mb rotational diffusion time in respiring muscle tissue. Under the assumption of unrestricted, isotropic diffusion, the observed rotational correlation time of 13.6 ± 1.3 × 10−9 s leads to a calculated translational diffusion coefficient of 4–6 × 10−7 cm2 s−1 (Wang et al. 1997). The calculated and measured translational diffusion values are in excellent agreement. Mb diffusion does not distinguish between the radial versus axial direction and shows an apparent isotropic motion.

Estimated root mean square (RMS) displacement
Previous studies have used the O2 off-rate constant for MbO2 and the translational diffusion coefficient to estimate the RMS displacement (Wittenberg & Wittenberg, 2003). For Mb, the rate determining O2 off-rate has served as a basis to estimate the O2 residence time. Beyond the RMS displacement, Mb will lose half of its O2 load. At 20°C, the MbO2 dissociation constant of 12 s−1 leads to a half-time (t½) of approximately 58 ms, the time required to dissociate half of the O2 from MbO2 (Gibson et al. 1986). Given the measured DMb of 4.24 × 10−7 cm2 s−1, the Einstein-Smoluchowski equation of the mean square displacement, [left angle bracket] r2 [right angle bracket] = 6Dt, yields a RMS displacement of [left angle bracket] r [right angle bracket] = 3.8 μm (Wittenberg & Wittenberg, 2003). As muscle cells have a typical dimension of 10 μm × 100 μm, a RMS displacement of Mb represents a small portion of the cell. Electron microscopy analysis reveals that many mitochondria cluster near the capillary and form a reticulum. A 3.8 μm Mb RMS displacement poses no apparent limitation of O2 delivery to the mitochondria reticulum (Kirkwood et al. 1986).

Cellular architecture
The Mb diffusion coefficients also yield insight into the cellular environment and architecture. Field-dependent relaxation measurement of the paramagnetic proximal histidyl NδH Mb signal reveals an Mb rotational correlation time about 1.4 times longer in the myocardium cell than in solution and an estimate of the translational diffusion coefficient (4–6 × 10−7 cm2 s−1) (Wang et al. 1997). Independent pulsed-field gradient method confirms that indeed Mb diffuses in the myocardial cell at 4.24 × 10−7 cm2 s−1. Both measurements point to a local cellular environment that slows Mb diffusion by about 40% relative to solution Mb (1.8 mm). Calibrating the diffusion against the water or Mb solution viscosity of 0.95 cP (centipoise) at 22°C leads to a cardiac myocyte viscosity of 2.6 cP, 2.74 times larger than solution viscosity (Lide & Frederikse, 1990). Indeed, the NMR and FRAP portrayal of the cellular architecture shares similar features. FRAP experiments have determined a cellular viscosity in the 2–3 cP range, in excellent agreement with the values derived from NMR rotational and translational diffusion measurements (Mastro et al. 1984). The translational diffusion of large solutes in cytoplasm and nucleus slows only 3–4 times relative to water diffusion and indicates an unrestricted diffusion distance of ~4 μm in the cell (Kao et al. 1993). The NMR-determined Mb diffusion provides then another perspective and experimental means to assess any impact of cellular crowding on enzyme reactivity (Welch & Marmillot, 1991).

Conclusion
This study has applied pulsed-field gradient NMR methods to determine the endogenous Mb diffusion in perfused rat myocardium. Mb diffuses with a translational diffusion coefficient of 4.24 × 10−7 cm2 s−1 and shows no orientation preference over an estimated RMS displacement of 3.8 μm. The translational diffusion coefficient matches precisely the value predicted by previous rotational diffusion measurements. Comparing the flux contribution from free O2versus Mb reveals an equipoise diffusion PO2 of 1.77 mmHg in rat myocardium and 5.72 mmHg in rat skeletal muscle. In marine mammalian muscle, the equipoise diffusion PO2 can increase to 67 mmHg. The different equipoise diffusion PO2 values arise largely from a variation in Mb concentration. Altering the P50 induces only a modest change. For terrestrial mammals, Mb can contribute to the O2 flux only if intracellular PO2 falls significantly, especially with increased energy demand.

Acknowledgments

We gratefully acknowledge funding support from NIH GM 58688 (T.J.), Philip Morris 005510 (T.J.) and American Heart Association Western States Affiliate 0265319Y (U.K.) and the invaluable technical assistance of Drs Jeff Walton and Jeff de Ropp.

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