1 Scaling of post-contractile phosphocreatine recovery in...

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Scaling of post-contractile phosphocreatine recovery in fish white muscle: effect of intracellular

diffusion

Albert C. Nyack1, Bruce R Locke2, Alejandro Valencia2, Richard M. Dillaman1, Stephen T. Kinsey1*

1 Department of Biology and Marine Biology, University of North Carolina Wilmington,

Wilmington, NC 28403-5915

2 Department of Chemical and Biomedical Engineering, FAMU-FSU College of Engineering,

Tallahassee, FL 32310-6046

*Corresponding author

Running head: Diffusion limitation of PCr recovery

Contact information:

Stephen T. Kinsey

Department of Biology and Marine Biology

University of North Carolina Wilmington

Wilmington, NC 28403-5915

e-mail: [email protected]

Work: (910) 962-7398

Fax: (910 962-4066

of 50Articles in PresS. Am J Physiol Regul Integr Comp Physiol (January 25, 2007). doi:10.1152/ajpregu.00467.2006

Copyright © 2007 by the American Physiological Society.

mailto:[email protected]

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ABSTRACT

In some fishes hypertrophic growth of white muscle leads to very large fibers. The

associated low fiber surface area to volume (SA:V) and potentially long intracellular diffusion

distances may influence the rate of aerobic processes. We examined the effect of intracellular

metabolite diffusion on mass-specific scaling of aerobic capacity and an aerobic process,

phosphocreatine (PCr) recovery, in isolated white muscle from black sea bass (Centropristis

striata). Muscle fiber diameter increased during growth and was >250 µm in adult fish.

Mitochondrial volume density and cytochrome-c oxidase activity had similar small scaling

exponents with increasing body mass (-0.06 and -0.10, respectively). However, the mitochondria

were more clustered at the sarcolemmal membrane in large fibers, which may offset the low

SA:V, but leads to greater intracellular diffusion distances between mitochondrial clusters and

ATPases. Despite large differences in intracellular diffusion distances, the post-contractile rate of

PCr recovery was largely size independent, with a small scaling exponent for the maximal rate (-

0.07) similar to that found for the indicators of aerobic capacity. Consistent with this finding, a

mathematical reaction-diffusion analysis indicated that the resynthesis of PCr (and other

metabolites) was too slow to be substantially limited by diffusion. These results suggest that the

recovery rate in these fibers is primarily limited by low mitochondrial density. Additionally, the

change in mitochondrial distribution with increasing fiber size suggests that low SA:V and

limited O2 flux are more influential design constraints in fish white muscle, and perhaps other

fast-twitch vertebrate muscles, than is intracellular metabolite diffusive flux.

Keywords: hypertrophy, fish, diffusion, creatine kinase, mitochondria

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INTRODUCTION

Studies of the scaling of metabolism with increasing body mass historically have focused

on rates of whole animal O2 consumption (reviewed in 4, 41). At the tissue level, the scaling of

the activity of aerobic and anaerobic enzymes has been well studied in fish muscle (5, 12, 36, 43,

44). While these studies yield indices of tissue metabolic capacity, the processes that are

powered by aerobic energy metabolism have been largely neglected. While it may be assumed

that aerobic capacity and aerobic processes scale in parallel, changes in cellular dimensions and

metabolic organization with increasing body mass may cause these metabolic rate indicators to

scale independently.

Divergence in the scaling of the rate of energy metabolism and the processes it supports

might be particularly prevalent in fish white muscle fibers, which can greatly exceed the size

range adhered to by most vertebrate muscle fibers. For the majority of fish species, axial white

muscle comprises most of the body mass (12, 32, 45) and increases in fish muscle mass occur by

both hyperplasia and hypertrophy (25, 37, 45, 48). In some species of fish, notably in

Notothenioids, axial white muscle hypertrophy can proceed until fiber diameters greatly exceed

100 µm (1, 11, 19). Large fiber size leads to a low fiber surface area:volume (SA:V), which may

limit O2 flux, and potentially to great intracellular diffusion distances between mitochondria.

However, the impacts of developing large muscle fibers on metabolism are not well understood

(3, 13, 18, 20, 22, 23).

The burst contractile function of muscle is an anaerobic process that relies on endogenous

fuels, and therefore is not dependent on oxygen flux across the cell membrane or net intracellular

metabolite diffusive flux. In fish white muscle, phosphocreatine (PCr) is the initial source of

high-energy phosphates during burst contraction (e.g., 7, 8, 14, 38, 42). The creatine kinase

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PCr + ADP + αH+ Cr + ATP

CK

(CK) reaction buffers the ATP concentration during contraction via the reversible transfer of a

phosphoryl group from PCr to ADP, forming ATP:

where α represents a partial proton and Cr is creatine. During recovery from contraction,

however, ATP and PCr resynthesis occurs aerobically in fish muscle (7), and the majority of

high-energy phosphate flux from the mitochondria to the rest of the cell is again mediated by the

CK reaction, with PCr as the dominant diffusing species (10, 29, 31). Thus, the recovery rate of

PCr is tightly coupled to both the aerobic production of ATP at the mitochondria and the

diffusive flux of PCr and Cr.

The intracellular domain within muscle fibers is crowded with both soluble proteins and

fixed structures such as mitochondria, sarcoplasmic reticulum (SR), and myofilaments, and these

obstacles reduce the diffusive flux of small metabolites (16, 17, 21, 22). Further, we have

previously shown that the diffusion coefficient for radial motion, Dr, which is the direction of

diffusive flux relevant to energy metabolism, is time-dependent in skeletal muscle, and

mathematical modeling indicated that the impedance at greater diffusion times is principally

caused by the sarcoplasmic reticulum (SR) (21, 22). Thus, at the short intracellular diffusion

distances characteristic of small cells, Dr is greater than that at the long diffusion distances that

may be prevalent in large cells. The time-dependent reduction of radial diffusive flux, coupled

with potentially extreme diffusion distances in large fibers of fish white muscle, may impact how

the rate of post-contractile PCr recovery scales with body mass.

We have previously hypothesized that diffusion constraints are the cause underlying the

recruitment of anaerobic metabolism following burst contractions in the very large muscle fibers

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of adult crustaceans (3, 13, 18, 22, 23). The anaerobic muscle fibers in the swimming leg of the

blue crab, Callinectes sapidus, increase from < 60 µm in small crabs to > 600 µm in adults, and

mitochondrial distribution shifts during growth from a uniform intracellular distribution to one

that is predominantly subsarcolemmal (SS) (3). This mitochondrial shift appears to be in

response to limited O2 flux due to a low fiber SA:V, but occurs at the expense of increased

intracellular diffusion distances between mitochondrial clusters and sarcoplasmic ATPases,

which may limit aerobic processes (3, 18). Kinsey et al. (23) tested this hypothesis by

comparing the scaling with body mass of post-contractile recovery rates of arginine phosphate

(AP) to a mathematical reaction-diffusion model of aerobic metabolism. They concluded that

intracellular metabolite diffusion did not limit the rate of AP recovery in large fibers, and

suggested that SA:V and the associated constraints on O2 flux exert more influence over

intracellular metabolic fluxes and metabolic organization. However, this study was conducted

using an in vivo exercise protocol, where large fiber size could lead to limited metabolic flux due

to extreme intracellular diffusion distances, low SA:V, or a combination of both factors.

The present study was an examination of the scaling with body mass of post-contractile

PCr recovery rate in isolated white muscle preparations from black sea bass, Centropristis

striata. The use of isolated muscle fiber bundles superfused in a high PO2 environment removed

the potential effects of low fiber SA:V on O2 flux, allowing an examination of only the effects of

intracellular metabolite diffusion. Muscle fiber diameter, aerobic capacity, and changes in

mitochondrial distribution also were measured over a large range in body mass. We hypothesized

that there would be an increase in SS mitochondrial clustering during fiber growth, resulting in

greater radial diffusion distances between mitochondrial clusters. Further, the rate of post-

contractile PCr resynthesis was expected to diverge from indices of aerobic capacity in muscle as

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a consequence of increased diffusion distances associated with hypertrophic fiber growth. To

rigorously test this latter hypothesis, a mathematical reaction-diffusion model was used to

determine whether the observed rate of PCr recovery was high enough to be limited by

intracellular metabolite diffusion.

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MATERIALS AND METHODS

Animal Care

All animal maintenance and experimental procedures were approved by the UNCW

IACUC. Centropristis striata from three size classes were obtained from the UNCW

Aquaculture Facility at Wrightsville Beach, NC. While at the aquaculture facility, fish were

reared in controlled environments (22-25 °C, pH 7.8-8.3, salinity >30 parts per thousand),

maintained on a 14:10 h light-dark cycle, and fed a diet of pellets containing 45% protein 6% fat.

At least 24 h before experiments, fish were transported in large coolers to tanks at UNCW’s

main campus and maintained under the same conditions until use.

Muscle Preparation

The following general protocol was used to prepare epaxial white muscle tissue for the

fiber size, mitochondrial distribution, and phosphocreatine recovery (PCr) experiments, with

specific alterations described in each section. To avoid muscle PCr depletion due to handling

stress, animals were individually sequestered for at least 1 h prior to sacrifice in covered and

aerated opaque containers with minimal water volume to limit movement. Animals were

tranquilized with concentrated MS-222 (tricaine methanesulfonate; Argent Laboratories,

Redmond, WA) that was gently diluted to 500 mg·L-1 (final volume) in the container’s seawater

via a small hole in the container cover to minimize disturbance of the fish. Fish remained in the

container until they were non-responsive to gentle prodding and/or they lost equilibrium control.

Fish body mass and total length (TL) was recorded, and anesthetized animals were

sacrificed via cervical dislocation to minimize neural-muscular contractions during dissection.

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Scales were quickly removed from both sides of the animal’s anterior dorsolateral body surface,

dorsal to the operculum and just below and anterior to the dorsal fin. Two rectangular sections of

skin in the scaled region were quickly cut and reflected posteriorly. Strips of epaxial white

muscle were excised parallel to the fiber long axis and maintained ex vivo in saline solution

(composition in mM·L-1: 133.5 NaCl, 2.4 KCl, 11.3 MgCl2, .47 CaCl2, 18.5 NaHCO3, 3.2

NaH2PO4, pH 7.4) aerated with a mixture of 99.5% O2 and 0.5% CO2. Muscle samples were

trimmed to 1-1.5 mm thick bundles in aerated saline parallel to the fiber long axis and fastened at

each end using 5-0 surgical silk. Fiber bundles were then stretched and held at 110% of resting

length by dental wax affixed to a wood dowel (for fiber morphometry and TEM), or in a Petri

dish containing aerated saline solution (for ex vivo PCr recovery experiments). For examining

COX activity, white muscle was excised contralateral to that removed for the PCr experiments,

frozen in cryo-tubes in liquid nitrogen, and stored at -80ºC until processed.

Fiber Size

Frozen sections from fiber bundles from the left side of the fish were collected as

described previously (Boyle et al. 2003). Frozen mounts were sliced in 12 µm thick sections

from an arbitrary starting point on a Reichert-Jeung Cryocut 1800 cryostat (Leica Microsystems

Inc., Bannockburn, IL) and stained using Groat’s variation for Weigert haemotoxylin stain for 3-

5 min followed by staining in eosin for 60 s. Stained slides were viewed under an Olympus BX-

60 microscope (Olympus America, Inc, Melville, NY) and digitized with a Diagnostic

Instruments Spot RTke camera (Diagnostic Instruments, Sterling Heights, MI). Polygons of

fibers were traced from the micrographs in Adobe Photoshop v7.0. Cell diameters were

determined using Image-Pro Plus (IPP) v4.1.0.9 software. The average diameter of the polygon

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traces through the centroid was calculated in 2-degree increments around the circumference of

the cell.

Mitochondrial Distribution

Mitochondrial fractional volumes and distributions were examined using transmission

electron microscopy (TEM). All six small fish and five of the six large fish used for this section

were also used for fiber size. Muscle from the right side of the fish was excised, tied and

stretched in the same manner described above. Preparations were fixed at room temperature in

2.5% glutaraldehyde with 0.2 M sodium cacodylate buffer (pH 7.4 and 300 mOsm) for at least

24 h, rinsed twice (15 min each) in cacodylate buffer, and placed in a secondary fixative of OsO4

for 2 h. Embedding and systematic random thin-sectioning methods followed those described

previously (3, 18). Sections were examined on a Philips CM-12 TEM (Philips Research,

Briarcliff Manor, NY) and micrographs were taken by a systematic random sampling method for

each grid (15). This method was executed by magnifying the first section observed on a TEM

grid under low magnification 3000x, 5000x, or 8000x, after which the first micrograph was then

taken and utilized as an arbitrary starting point for two subsequent micrographs. The field of

view was then moved up by a distance equal to three times the field of view. A second

micrograph was collected at this new position and the process was repeated once more, for a

total of three micrographs per grid (15 micrographs per tissue preparation). If any position was

obstructed by a TEM grid bar, or was no longer on a section, the previous viable field of view

was reestablished and a new field of view was sought three fields of view right from this position

(or to the left if an obstruction was again encountered). If no viable field of view could be found,

the grid was repositioned under low magnification and a different section was utilized as the

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arbitrary starting point. Micrographs were then developed and digitized using a Microtek

Scanmaker 4 (Microtek Lab, Inc., Carson, CA).

Digitized micrographs were viewed in Adobe Photoshop v7.0 and a stereological point-

counting method was applied to calculate mitochondrial fractional volume (15). A point grid was

applied to the images, and all points touching extracellular space were subtracted from the total

number of points per micrograph. Points that landed on mitochondria were tallied as either

subsarcolemmal (SS) if the mitochondrion lay between the sarcolemmal membrane and the

myofibrils, or intermyofibrillar (IM) if they were located among myofibrils, regardless of

proximity to the sarcolemmal membrane. The sums of either SS or IM points from all

micrographs taken for each fish were divided by the sum of points hitting cellular space to

determine fractional volume (FV). Total mitochondrial fractional volume (TMFV) was

calculated as the sum of SS mitochondrial fractional volume (SSFV) and IM mitochondrial

fractional volume (IMFV).

Cytochrome-c Oxidase (COX) Activity

COX activity was determined spectrophotometrically using an enzyme assay kit

purchased from Sigma-Aldrich (St. Louis, MO). Frozen tissues were homogenized in a ten-fold

dilution of ice-cold enzyme extraction buffer (50 mM imidazole, 50 mM KCl, and 0.5 mM

dithiothreitol, pH 7.4) and sonicated on ice for three 10-s bursts with a Fisher Scientific

(Pittsburg, PA) 60 sonic dismembranator. Up to one ml of homogenate was centrifuged at 12,000

g for 15 min at 4 °C. Assays were performed on an Ultrospec 4000 spectrophotometer at 20 °C,

maintained by an Isotemp 3016 recirculating water bath (Fisher Scientific, Pittsburg, PA).

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Phosphocreatine Recovery

Muscle tissue was excised and prepared as described above and small, rigid plastic rings

were tied to the end of each trimmed bundle with 5-0 surgical silk. Fiber bundles were allowed to

recover from dissection perturbation for at least 30 min for small fish or 45 min for medium and

large fish before use (time needed for recovery was determined experimentally). Similar post-

dissection recovery has been described by other researchers who performed nearly identical

procedures on fish muscle (33).

Isolated muscle preparations were suspended between glass hooks that were attached to

the thin plastic rings. The lower hook was secured to the frame of the stimulation system

(Radnoti Glass Technologies, Inc., Monrovia, CA) and the upper hook, made from a thin glass

fiber, connected the tissue to an isometric force transducer (Harvard Apparatus, South Natick,

MA). Once suspended and stretched to 110% resting length, muscle preparations were

submerged in a ten ml water-jacketed, glass chamber with built-in electrodes (Radnoti Glass

Technologies, Inc., Monrovia, CA) containing aerated saline maintained at 20° C by an Isotemp

3016S recirculating water bath. The fiber bundle was then field-stimulated using a Grass S88

physiological stimulator (Astro-Med, Inc., West Warrick, RI) to elicit a short tetanus every 150

ms (70 V, 70 Hz, 3 ms pulse duration, 6 pulses per tetanus) for 120 s. The voltage signal from

the force transducer was digitized using a Biopac MP100 data acquisition system and recorded

on a PC using Acqknowledge v.3.5.7 software (Biopac Systems, Inc., Santa Barbara, CA).

Following stimulation, fiber bundles were allowed to recover for 0, 5, 10, 15, or 30 min. Bundles

were then freeze-clamped in liquid nitrogen cooled tongs, transferred to small tubes, and stored

temporarily (no more than a few hours) in liquid nitrogen until extraction. Unstimulated bundles

were used to determine resting [PCr] and were freeze clamped at the end of the post-dissection

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recovery period. Frozen samples were then extracted in perchloric acid as previously described

(13, 23).

The relative [PCr] and [Pi] in muscle extracts was determined using 31P nuclear magnetic

resonance (NMR). The relatively broad ATP peaks were not consistently well resolved and were

not included in the analysis. NMR spectra were collected at 162 MHz on a Bruker 400 MHz

DMX spectrometer (Bruker Biospin Corporation, Billerica, MA) using a 45° excitation pulse

(2.5 µs) and a 0.6 s relaxation delay. Four hundred scans were collected for a total acquisition

time of five min. A 0.5 Hz line broadening exponential multiplication was applied prior to

Fourier transformation. The area of each peak was integrated and expressed as a fraction of the

total integral for all peaks.

To ensure that O2 delivery to the fiber bundle core was adequate to support mitochondrial

respiration, the critical PO2 where diffusion of O2 would become limiting was calculated from

the solution for concentric diffusion in a Krogh cylinder as described previously (29, 31). The

rate of O2 consumption in the bundle was estimated from the PCr recovery curves, where the

NMR peak areas were normalized to a peak from a standard PCr sample of known concentration

to yield a recovery rate in units of µmoles•min-1•g-1. The rate of O2 consumption was estimated

from the maximal rate of PCr recovery immediately following contraction using a P:O ratio of 3.

For our maximal bundle diameter of 1.5 mm, the critical PO2 in the bath was 550 torr, which is a

value similar to that from prior analyses (6), and so our experiments were conducted with a bath

PO2 well above this limit (>720 torr).

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Reaction-Diffusion Model

The reaction-diffusion model used in the present study was as described in Kinsey et al.

(23), with parameters adjusted to comply with fish white fibers and data collected in the present

study. In brief, the model consists of Michaelis-Menten expressions for a mitochondrial

boundary reaction (ADP + Pi→ATP) with a rate dependant on the ADP concentration, a myosin

ATPase bulk reaction (ATP→ADP + Pi) that is only active during contraction, and a basal

ATPase bulk reaction that is always active. An appropriate kinetic expression for creatine kinase

(CK) was also included in the bulk phase (34) and Dr values were used that accounted for the

time-dependence of radial diffusion (21, 22). The diffusion and reaction of ATP, ADP, PCr, Cr,

and Pi were modeled in a one-dimensional system that extended from the surface of a

mitochondrion to a distance (λ/2) equal to half of the mean free spacing between clusters of

mitochondria. Temporally- and spatially-dependent concentration profiles of metabolites were

calculated according to a molar-species continuity equation (2). The bulk reactions catalyzed by

CK, myosin ATPase and basal ATPase were assumed to occur homogenously throughout the

domain 0 ≤ x ≤ λ/2, where x is the distance from the mitochondrial surface.

Simulations of a burst-contraction recovery cycle were generated using the finite element

analysis software, FEMLAB (Comsol, Inc., Burlington, MA, USA). Parameter values used in the

model are presented in Table 2. The resting metabolite concentrations were from data gathered

during this study and from (16). The Dr for each metabolite was based both on direct

measurements from fish white fibers (21) and from the relationship of molecular mass and Dr in

muscle (22). Intracellular diffusion distances (λ/2) were estimated in two ways in order to

bracket the range of possible distances: (1) assuming an exclusively SS distribution of

mitochondria, λ/2 was determined from fiber radius data, and (2) assuming a uniform

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distribution of IM mitochondria, λ/2 was determined as described previously (3). A Km for the

mitochondrial reaction (Kmmito) for ADP was used that is appropriate for fast-twitch skeletal

muscle (27). The basal ATPase consumed ATP at a constant rate (Vbas) that balanced the rate of

mitochondrial ATP production at rest. CK dissociation constants (K, Ki, and KI) were obtained

from (34), the maximal velocity for the forward reaction (VmCKfor) (in the direction of ATP

formation) and in the reverse direction (VmCKrev) were taken from measurements in fish white

muscle (35). The myosin ATPase maximal velocity (Vmmyo) and Km (Kmmyo) for ATP were the

same as in (16).

While the model generated temporally and spatially resolved concentrations of

metabolites, our experimental measurements yielded values that were spatially averaged across

the fiber. In order to compare the model results to the experimental data, the model data was

mathematically volume averaged. The duration of myosin ATPase activation was then adjusted

so that the simulated decrease in [PCr] was comparable to that in the observed data, and the

maximal velocity of the mitochondrial boundary reaction (Vmmito) was adjusted so that the PCr

recovery curve predicted by the model approximated the measured recovery rate. This approach

allowed us to analyze whether the observed rate of PCr recovery was limited by intracellular

metabolite diffusion.

Statistical Analysis

One-way analysis of variance (ANOVA) was used to test for significant effects of size

class, and where significant size effects were detected Tukey’s HSD test was used for pairwise

comparisons. A two-way ANOVA was implemented to examine the interaction between size

class and recovery time on [PCr]. All statistical tests were analyzed with JMP software version

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7.0.2 (SAS Institute, Cary, NC). In all cases, P<0.05 was considered significant. Linear

regression analysis of COX activity and TMFV data on body mass were conducted using Sigma

Plot version 8.02 (SPSS Inc., Chicago, IL).

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RESULTS

Fish Body Mass and Fiber Size

The present study used fish ranging in body mass from 1.5 to 4496 g and in total body

length from 45 to 544 mm (Table 1). This corresponds to a mass range of nearly 3000-fold and a

12-fold increase in length. Figure 1 demonstrates hypertrophic growth exhibited by epaxial white

muscle in C. striata during ontogeny, leading to large fibers in adults. The fiber diameters ranged

from 5.3 to 80.4 µm (348 fibers) in the small fish, 16.4 to 152.5 µm (245 fibers) in the medium

fish, and 74.1 to 465.4 µm (239 fibers) in the large animals (Fig. 2). The distribution of muscle

fiber diameters noticeably broadened during growth. One-way ANOVA indicated a significant

effect of size class on mean fiber diameter (F=2.35, d.f.=2, P<0.001) and pair-wise comparisons

indicated that each size class was significantly different from the other two (Fig. 2 inset; Tukey’s

HSD, P<0.05). The mean diameter of the small and medium size class differed by only two-fold

despite a nearly 32-fold difference in mean body mass, while the difference in mean fiber

diameter was 3.5-fold between the medium and large size classes, which corresponded to a 45-

fold difference in body mass.

Mitochondrial Distribution

Representative TEM micrographs showing mitochondrial distribution are presented in

Fig. 3. Mitochondrial density scaled negatively with body mass and the total mitochondrial

fractional volume (TMFV), was significantly higher in the small fish than the large (Fig. 4A;

Tukey’s HSD, P<0.05). Both IMFV and SSFV decreased with increasing body mass, but there

were no significant differences between size classes in either category (Fig. 4A). To determine

whether SS mitochondria were clustered more densely in large fibers than in small (3), the SS

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mitochondrial volume per sarcolemmal membrane area (SSMV/SA) was calculated by dividing

SSFV by the mean fiber SA:V. Since the same fish used in determining fiber diameter were also

used to measure mitochondrial fractional volume, the fiber SA:V could be accurately calculated.

A significant increase in the SSMV/SA was found (Fig. 4B; Tukey’s HSD, P<0.05), indicating a

greater clustering of mitochondria at the sarcolemmal membrane in the fibers of large fish.

Cytochrome-c Oxidase Activity

A line was fitted to the mass specific COX activity according to the scaling relationship:

COX activity = aMb, where M is animal mass, a is a constant, and b is the scaling exponent (41).

The mass specific COX activity of epaxial white muscle from 39 fish scaled negatively with

body mass with a b of -0.10 (Fig. 5; r2= 0.11). This scaling exponent is similar to the value for

TMFV of -0.06 obtained using the data in Fig. 4 (graph not shown).

Metabolite Dynamics and Reaction-Diffusion Analysis

Model input parameters are detailed in Table 2. A typical simulation of volume-averaged

changes in metabolite concentrations are shown in Figure 6. The near-equilibrium status of the

CK reaction is reflected by the nearly perfect buffering of [ATP] during a contraction-recovery

cycle. Experimentally measured changes in [PCr] and [Pi] and volume-averaged model

approximations of the measurements during a contraction-recovery cycle are shown in Figure 7.

The resting values of both metabolites were significantly different from those immediately post-

contraction in all size classes (Tukey’s HSD, P<0.05). Aerobic recovery for all size classes was

slow, and complete recovery required approximately 30 min. Two-way ANOVA revealed no

significant interaction of size class and recovery time on [PCr] or [Pi] (PCr: F=0.40, d.f.=10,

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P=0.95; Pi: F=0.39, d.f.=10, P=0.95), indicating no differences in the rate of PCr or Pi recovery

between size classes. To compare the scaling with body mass of the measured maximal rate of

PCr recovery to that found for mitochondrial volume density and COX activity, the rate of

recovery during the first 5 min post-contraction was analyzed using the scaling equation

described above. The PCr recovery rate scaling exponent (b = -0.07) was very similar to that for

mitochondrial density and COX activity (see above).

Figure 7B-D and F-H shows that the volume averaged model simulations reasonably

approximated the measured rates of PCr and Pi recovery, thus permitting us to draw conclusions

about diffusion limitation in the fibers. Figure 8 is an expansion of these model results to include

spatially, as well as temporally, resolved profiles of [PCr] and [Pi] during contraction-recovery

cycles in each size class. The other high energy phosphate molecules yield similar results as

shown previously (23). The simulations are for the case with exclusively SS mitochondria, which

yields larger diffusion distances and the highest likelihood for diffusion limitation of PCr

recovery (the cases with a uniform distribution of mitochondria are not shown but yielded

recovery rates that were only slightly higher). There were only very shallow intracellular

concentration gradients in all of the high energy phosphates in the small (Fig. 8A, D) and

medium (Fig. 8B, E) size classes, indicating essentially no control of metabolic flux by

intracellular diffusion (these small gradients are not readily visible on the concentration scale

used, since the gradients are a tiny fraction of the total concentration). The concentration

gradients in the largest fibers were more substantial than in the other two size classes, but despite

the extreme diffusion distances were still barely perceptible for each metabolite (Fig. 8C, F),

indicating that diffusive flux is fast compared to the rate of metabolite recovery.

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The maximal concentration gradients observed occurred in the largest fibers immediately

after burst contraction ceased (when oxidative phosphorylation was maximally stimulated by the

high [ADP]) (Figure 9). For each metabolite, the spatial variation in concentration is shown as

absolute concentration gradients (Figure 9A) and as gradients relative to the total metabolite

concentration (Figure 9B). The magnitude of the gradients for all metabolites was extremely

small and represented a tiny fraction of the total concentration for most metabolites. The small

gradients in [ADP] constituted a larger fraction of total ADP pool (about 13%) due to the low

concentration of ADP in muscle. However, the lack of a difference in recovery rates between

size classes and the negligible effect of simulating a reduced diffusion distance on recovery rate

(by assuming a uniform distribution of mitochondria) indicate that the measured processes were

too slow to be limited by intracellular metabolite diffusion. This conclusion is further supported

by the fact that the initial velocity of post-contractile recovery (Vo) is proportional to the volume-

averaged rate of ATP production at the mitochondria (Vmmito, in mmoles l-1 s-1) at all diffusion

distances (Fig. 10). If diffusion were substantially limiting metabolite recovery, then Vo would

be lower relative to Vmmito at large diffusion distances, leading to a steep, negative slope for each

metabolite in Fig. 10.

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DISCUSSION

The major findings of the present study were (1) hypertrophic growth of white muscle

fibers occurred during ontogeny, and this growth is associated with small, negative scaling

exponents for both mitochondrial density and COX activity, (2) a significant increase in the

amount of sarcolemmal membrane occupied by mitochondria occurred during fiber growth, (3)

the time course of PCr recovery was independent of fish body mass (and therefore fiber size),

and the maximal rate of recovery immediately post contraction had a body mass scaling

exponent similar to that for the measured indicators of aerobic capacity, and (4) the rate of post-

contractile PCr recovery (and other metabolites) was too slow to be substantially limited by

intracellular diffusion.

Fish white muscle fibers are typically characterized as having lower oxidative capacity

and larger diameters relative to other types of fish skeletal muscle (26, 30), and there are

examples of white fibers attaining very large dimensions (11, 19, 48). However, the white

muscle fibers in many fish species do not grow to particularly large sizes (30, 37, 48). For

example, species such as carp (Cyprinus carpio; 24) and white sea bass (Atractoscion nobilis;

49), which attain body masses as adults that are similar to, or greater than, the adult C. striata

used in this study, exhibit much smaller mean white muscle fiber diameters. The present study

was not designed to broadly address the determinants of fiber size. However, it is likely that the

widely varying relationship between body mass and muscle fiber diameter in different species of

fishes (and other organisms) results from a complex interplay of developmental programs, body

mass range, reaction-diffusion constraints, behavior, and evolutionary history.

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The TMFV (Fig. 4A) was within the range reported in white muscle of other temperate

fish species (9, 26, 47). Also, the negative scaling exponent of COX activity (b = -0.10)

corresponds fairly well with that of TMFV (b = -0.06). The finding that SSFV was greater than

IMFV in both small and large fibers may reflect low rates of O2 supply to the muscle due to

sparse vascularization, which is typical of teleost white muscle (9, 26). The large and significant

increase in the amount of sarcolemmal membrane occupied by mitochondria in adult C. striata

(Fig. 4B) may help counteract the very low SA:V in the large fibers. This finding is similar to the

shift in mitochondria observed during hypertrophic growth in the large white fibers of C.

sapidus, which was attributed to low fiber SA: V (3, 23). Mainwood and Rakusan (29) showed

mathematically that the capillary PO2 required to supply sufficient O2 to the fiber was

considerably less for a SS distribution of mitochondria than when mitochondria were evenly

distributed over the entire fiber. One interpretation of the change in mitochondrial distribution

with increasing fiber size is that mitochondria are simply produced in regions of the cell that

have adequate O2 (in large fibers, near the membrane). Alternatively, when less surface area is

available for O2 flux in large fibers, a SS mitochondrial distribution may serve to facilitate O2

flux across the sarcolemmal membrane. In this case, the rapid consumption of O2 by

mitochondrial clusters would reduce the intracellular PO2 inside the sarcolemma, and would

enhance the transmembrane PO2 gradient leading to increased flux. Therefore, in both adult C.

striata and adult C. sapidus the predominantly SS mitochondrial distribution may help offset the

effects of low SA:V, but it also leads to increased intracellular diffusion distances between

mitochondrial clusters and sites of ATP utilization, which may limit rates of aerobic metabolism

(3, 13, 18, 21, 22, 23).

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Post-contractile PCr recovery is powered exclusively by aerobic metabolism in fish white

muscle (7), and the rate of recovery is assumed to define the rate of O2 supply and substrate

utilization in skeletal muscle (28). Kinsey et al. (23) analyzed in vivo post-contractile recovery

rates of AP in the white swimming muscle of C. sapidus, which attain greater fiber diameters

than C. striata, using a mathematical reaction-diffusion model of aerobic metabolism similar to

that used in the present study. They concluded that diffusion did not greatly limit aerobic AP

recovery in large fibers, and suggested that SA:V exerted more influence over metabolic fluxes

and mitochondrial organization. However, that study utilized an in vivo exercise and recovery

protocol, so both intracellular metabolite diffusion and/or low SA:V and limited O2 flux may

have constrained aerobic metabolism. The present study used superfused muscle fiber

preparations in a solution with high PO2 similar to the study of Curtin et al. (7), which

maximized the oxygen gradient across the fiber bundle and, thus, removed the effect of fiber

SA:V on metabolic recovery. This approach allowed an examination of the effect of intracellular

metabolite diffusion on recovery in isolation, without the confounding effects of fiber-size

dependent limitations on O2 flux as in our previous work (3, 13, 18, 23).

PCr and Pi recovered slowly in all size classes, and there was no significant interaction

between size class and recovery time on post-contractile concentration, indicating that recovery

rate did not differ significantly among size classes (Fig. 7). The rate of PCr recovery observed in

the present study is comparable to that found in isolated white muscle from dogfish, Scyliorhinus

canicula (7), and to in vivo rates of recovery in white muscle of rainbow trout, Oncorhynus

mykiss (42), tilapia, Oreochromis mossambicus, (46), and Pacific spiny dogfish, Squalus

acanthias (38). Additionally, the observed rates are similar to that of AP recovery in C. sapidus

anaerobic muscle (23), which also has large fibers and a similar mitochondrial density to C.

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striata. The size class independence of metabolite recovery in C. striata occurred despite

significant differences in fiber diameter and mitochondrial organization, suggesting that the large

fibers are not greatly limited by intracellular metabolite diffusion. This is consistent with the

finding that the maximal rate of PCr recovery immediately following contraction had a scaling

exponent (-0.07) that did not diverge from that found for TMFV (-0.06) or COX activity (-0.10).

This conclusion is further supported by the reaction-diffusion mathematical analysis, which

demonstrated that the observed rate of metabolite recovery in the present study was too slow to

be substantially diffusion limited (Figs. 7-9) and that the rate of recovery was essentially

controlled by the fiber’s aerobic capacity (Fig. 10).

Our findings contrast with the reaction-diffusion analysis of fish white muscle by Hubley

et al. (16), which demonstrated large gradients in high-energy phosphate compounds. However,

this prior study assumed perfect buffering of ATP concentration at the mitochondria (i.e., an

infinite rate of ATP supply), whereas the present study used realistic rates of mitochondrial ATP

production that were derived from the observed rate of PCr and Pi recovery. Further, Hubley et

al. (16) only modeled contraction, where rates of ATP demand are very high, while the present

study examined the more realistic condition of burst contraction and post-contractile recovery,

the latter of which is exclusively aerobic and occurs with a much lower ATP demand in fish

white muscle. The differences between the study of Hubley et al. (16) and the present study

illustrate the interaction between ATP turnover rates and diffusive flux on aerobic recovery.

Thus, the results from the present study support our prior assertion that in fast-twitch muscles

SA:V and O2 flux may exert more control over cellular organization and aerobic process rates

than intracellular metabolite diffusion (13, 23). The effect of SA:V on aerobic rates may be

direct (particularly in large fibers), by limiting rates of O2 flux during maximal demand, or

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indirect, by limiting mitochondrial density and therefore aerobic capacity. Despite the findings

of the present study, simulations of energetics in aerobic muscle fibers during steady-state

contraction indicate that intracellular diffusive flux may exert substantial control over metabolic

flux if the rate of ATP turnover is high, even when diffusion distances are short (13).

The notion that intracellular diffusion limits aerobic metabolism in systems without long

diffusion distances has been proposed previously for cardiac myocytes (40). These authors

suggested that aerobic muscle fibers are composed of discrete intracellular energetic units, and

that metabolite diffusion (particularly ADP) within these units is locally restricted.

Mathematical modeling indicated that this structural organization induces heterogeneity of ADP

diffusion in permeabilized aerobic fibers where diffusion coefficients are locally reduced by 1-2

orders of magnitude, and these low rates of diffusion lead to the limitation of oxidative

phosphorylation in these experimental preparations (40). In contrast, the present study assumed

that sarcoplasmic metabolite diffusion occurred as in other porous media, which is consistent

with previous measurements and modeling of diffusion in fast-twitch muscle (21, 22). Further,

as pointed out in (40), fast-twitch muscles are not thought to contain the functional energetic

units that they described for cardiac myocytes. Rather, the present study focused on the effect of

widely varying diffusion distances between mitochondria on a relatively slow aerobic metabolic

process, and found that the effects of diffusive flux (including ADP) were negligible.

In fish that undergo a large increase in body mass, prolonged muscle hypertrophy may be

the default developmental strategy if there are no selective pressures against large fiber size.

Although the experimental approach used here eliminated the effects of SA:V, the expectation is

that the low SA:V of the large fibers would lead to slow PCr recovery in vivo in the large fish. In

the wild, the low rate of PCr recovery would mean that bouts of high power contractions would

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be followed by a relatively protracted recovery period before a similar bout of contractions could

occur. The fish in this study had no discernable medial-lateral red muscle, which has been

observed in other fishes (12). The lack of red muscle in C. striata suggests that swimming at

higher speeds is powered almost exclusively by white muscle, whereas routine locomotion is

slow and relies largely on labriform swimming (AC Nyack, unpublished observations). Black sea

bass therefore appear to be capable of extended periods of very slow aerobic swimming, or short

bursts of high velocity swimming, but they are not well equipped for sustained periods of

swimming at intermediate velocities. Since C. striata is a benthic fish associated with hard

bottom communities, and is often in close proximity to cover (39), a protracted recovery

following burst swimming may not have negative consequences. That is, aspects of the animal’s

behavior may make large fiber size a relatively unimportant functional constraint.

It is also possible that there is positive selection for the presence of large fibers in fish

white muscle. Johnston et al. (20) proposed that the cost of maintaining cellular ion balance is

relatively high, and since a large amount of the body mass in most teleosts is white muscle, ion

homeostasis within this tissue contributes considerably to whole animal metabolism. Thus, the

low SA:V in tissues comprised of large fibers would lead to less membrane leak, and therefore

fewer ion pumps would be required to maintain ion balance. This hypothesis could also be

applied broadly, in the sense that many types of muscle fibers may have selective pressure to be

as large as possible, within the constraints of the muscle’s function. At present, however, it is

unclear whether very large cells arise as a natural consequence of hypertrophic growth in species

with a large body mass range and behavioral patterns that obviate the need for rapid metabolic

recovery, or whether there is selection in favor of large cells in order to lower energetic costs

associated with ion homeostasis.

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In summary, this study characterized the epaxial white musculature in C. striata and

investigated the effects of hypertrophy on post-contractile PCr recovery, which is the product of

an aerobic process. White muscle fibers grew very large during ontogeny, and the proportion of

the sarcolemmal membrane occupied by mitochondria was significantly greater in large fibers

than in small fibers. This change in mitochondrial distribution may help facilitate diffusion of O2

into the large fibers. The scaling with body mass of the maximal rate of PCr recovery paralleled

that of indicators of aerobic capacity, despite the extreme dimensions attained during

hypertrophic white muscle growth, and the rate of PCr recovery was too slow to be greatly

limited by intracellular metabolite diffusion. It is therefore likely that low mitochondrial density

is primarily responsible for the slow rate of PCr recovery, and fiber SA:V may be a more

important factor than intracellular metabolite flux on metabolic design in fish white muscle

fibers, and perhaps in other vertebrate fibers as well.

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ACKNOWLEDGEMENTS

We thank Dr. Wade Watanabe for generously providing the animals used in this study, Mr. Mark

Gay for his assistance with microscopy, and Dr. D. Ann Pabst and Dr. Thomas Lankford for their

valuable insights on the manuscript.

GRANTS

This research was funded by National Science Foundation grants to S.T.K. (IBN-0316909) and

B.R.L. (IBN-0315883) and a National Institutes of Health grant to S.T.K. (R15-AR052708-01A1).

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FIGURE LEGENDS

Figure 1. Typical cross-sections of C. striata white muscle fibers from small (A), medium (B), and large

fish (C) at 20x magnification.

Figure 2. Epaxial white muscle cross-sectional fiber diameter distribution and mean by size class (inset)

from small, medium, and large fish. The fiber cross-sectional diameters, shown as percent frequency, are

binned in 10 µm increments. The * indicates that each size class is significantly different from the other

two (inset). Values are means ±SEM.

Figure 3. Examples of micrographs from small (left) and large (right) fish taken at a magnification of

3000x. The white dots mark the location of individual mitochondria. Both the sarcolemmal and the bulk

of the intermyofibrillar spaces are visible in the two examples from the small size class fish (A and B).

The fibers from the large size class were too large to show a comparable percentage of the cell, as a

result (C) shows a large region of the sarcolemma and SS mitochondria, while (D) shows primarily the

intermyofibrillar region with typical low densities of IM mitochondria, as well as a small section of the

sarcolemmal with part of a SS mitochondrial cluster in the lower right corner. Scale bar = 5 µm.

Figure 4. (A) Total mitochondrial fractional volume (TMFV; filled circles), sub-sarcolemmal

mitochondrial fractional volume (SSFV; inverted triangles), and intermyofibrillar mitochondrial

fractional volume (IMFV; filled squares). The * indicates that only TMFV is significantly different

between the two size classes. (B) The SS mitochondrial volume/sarcolemmal surface area (SSMV/SA)

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in the small and large size classes. The * indicates that the means are significantly different. Values

shown are means ± SEM.

Figure 5. Scaling with body mass of cytochrome-c oxidase activity from epaxial white muscle of C.

striata. The line is described by the equation, COX activity = 0.1M-0.1 (r2 = 0.11, P < 0.05), where M is

body mass.

Figure 6. Representative simulation of changes in volume-averaged metabolite concentrations during a

burst contraction and recovery in muscle from a small fish. The change in [ATP] during contraction is

too small to be resolved due to temporal buffering of [ATP] by the CK reaction.

Figure 7. PCr (A-D) and Pi (E-H) recovery curves in isolated white fiber bundles. In (A) and (E) the

fractional [PCr] and [Pi] are presented for all size classes. To achieve an approximate fit of the reaction-

diffusion model to the data, the experimental values were converted to absolute concentrations of PCr

(B-D) and Pi (F-H) by assuming a resting [PCr] of 30.9 mM. The absolute [PCr] and [Pi], as well as the

volume averaged approximations of the recovery rate from the reaction-diffusion analysis (solid line),

are shown for small (B and F), medium (C and G) and large fish (D and H). Each time point within each

size has n ≥ 5 and values shown are means ± SEM.

Figure 8. Reaction-diffusion simulation of spatial and temporal profiles of [PCr] and [Pi] during a

contraction recovery cycle in isolated white muscle from small (A, D), medium (B, E) and large fish (C,

F). The distance axis refers to the distance from the mitochondrial boundary (at zero microns) to the

center of the fiber (assuming only subsarcolemmal mitochondria). In large fish muscle, concentration

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gradients are barely perceptible immediately after contraction ends (indicated by arrows). The recovery

rates were derived from the volume averaged approximations of the experimental data presented in

Figure 7.

Figure 9. Simulation of the maximal concentration gradients observed for all metabolites, which

occurred in the large fish size class immediately after burst contraction ended. The absolute magnitude

of the gradients is shown in (A), where concentration difference was determined by subtracting the

concentration at the mitochondrial boundary from the concentration at each distance from the

mitochondria (e.g., PCr and ATP concentration is lower further from the mitochondria). The magnitude

of the gradient relative to the total concentration of each metabolite is shown in (B), where the

concentration was normalized to a value of zero at the mitochondrial boundary.

Figure 10. Simulated fractional initial velocities (Vo/Vmmito) during the first 5 min of post-contractile

recovery as a function of diffusion distance for each metabolite. Vo/Vmmito is nearly constant despite the

large differences in diffusion distances, which would be expected if diffusion were not substantially

limiting recovery in the large fibers. Regression equations: (ADP) Vo/Vmmito = –5.2 x 10-6 x (distance) +

0.0039, r2 = 0.88, p = 0.23; (ATP) Vo/Vmmito = –6.5 x 10-6 x (distance) + 0.0034, r2 = 0.94, p = 0.16; (Cr)

Vo/Vmmito = –8.7 x 10-4 x (distance) + 0.54, r2 = 0.96, p = 0.12; (PCr) Vo/Vmmito = –6.6 x 10-4 x (distance)

+ 0.50, r2 = 0.99, p = 0.04; (Pi) Vo/Vmmito = –6.9 x 10-4 x (distance) + 0.51, r2 = 0.99, p = 0.03;

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Table 1. Body size characteristics of fish and n-values used for each type of experiment.

Values for mean body mass are mean ±SEM. In some cases, multiple strips of epaxial white

muscle were isolated from a single fish and were used in multiple experiments.

Fiber Size Mitochondrial Distribution COX Phosphocreatine Recovery

Size

Class n

Mean body

mass (g)

Body mass

range (g) n

Mean body

mass (g)

Body mass

range (g) n

Mean body

mass (g)

Body mass

range (g) n

Mean body

mass (g)

Body mass

range (g)

Small 7 2.4±0.8 1.5–5.8 6 1.9±0.2 1.5–2.2 12 6.2±1.1 1.6–14.2 26 10.8±0.8 3.3–20.8

Medium 7 77.0±2.3 46.7–181.8 -- -------- -------- 15 87.9±11.2 43.5–196.9 14 299.4±55.7 56.6–765.1

Large 6 3531.5±60.32413.2-

4496.5 6 3166.4±667.0

2413.2–

4496.5 12 2332.1±297.1

948.5-

3668.3 18

2507.93

±315.85

948.5-

4159.4

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Table 2. Parameters used in reaction-diffusion model.

See text for definitions and source information.

Parameter type Parameter Small Medium Large Units

Initial concentrations PCr 30.9 30.9 30.9 mmol l-1

Cr 3.6 3.6 3.6 mmol l-1

Pi 14.3 17.0 16.5 mmol l-1

ATP 5.5 5.5 5.5 mmol l-1 ADP 0.003 0.003 0.003 mmol l-1

Diffusion DrPCr 1.9 x 10-6 1.9 x 10-6 1.9 x 10-6 cm2/sDrCr 2.39 x 10-6 2.39 x 10-6 2.39 x 10-6 cm2/sDrPi 2.81 x 10-6 2.81 x 10-6 2.81 x 10-6 cm2/s

DrATP 1.22 x 10-6 1.22 x 10-6 1.22 x 10-6 cm2/sDrADP 1.33 x 10-6 1.33 x 10-6 1.33 x 10-6 cm2/sλ/2 18.9 35.4 124.4 µm

Mitochondrial boundary reaction

Vmmito 5.07 x 10-16

(0.0268)9.17 x 10-16

(0.0259)3.17 x 10-15

(0.0255)mmol µm-2 s-1 (mmol l-1 s-1)

Kmmito 20 20 20 µmol l-1

Basal ATPase Vbas 0.62 0.62 0.62 µmol l-1 s-1

Creatine kinase VmCKfor 105 105 105 mmol l-1 s-1 VmCKrev 26.1 26.1 26.1 mmol l-1 s-1 KATP 0.48 0.48 0.48 mmol l-1 KCr 6.1 6.1 6.1 mmol l-1 KPCr 2.9 2.9 2.9 mmol l-1 KADP 0.05 0.05 0.05 mmol l-1 KiATP 1.34 1.34 1.34 mmol l-1 KiCr 19 19 19 mmol l-1 KiPCr 8.6 8.6 8.6 mmol l-1 KiADP 0.17 0.17 0.17 mmol l-1 KIATP 3.5 3.5 3.5 mmol l-1 KICr 17 17 17 mmol l-1 KIPCr 21 21 21 mmol l-1 KIADP 0.12 0.12 0.12 mmol l-1

Myosin ATPase Vmmyo 6.92 6.92 6.92 mmol l-1 s-1

Kmmyo 0.15 0.15 0.15 mmol l-1

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