A REACTION-DIFFUSION ANALYSIS OF CELLULAR DESIGN AND FUNCTION IN SKELETAL MUSCLE

Kristin M. Hardy

A Dissertation Submitted to the University of North Carolina Wilmington in Partial Fulfillment

of the Requirements for the Degree of Doctor of Philosophy

Department of Biology and Marine Biology

University of North Carolina Wilmington

2009

Approved by:

Advisory Committee __________Dr. Richard Dillaman______ __________Dr. Bruce Locke__________ ____________Dr. Ann Pabst__________ __________Dr. Robert Roer___________ __________Dr. Richard Satterlie_______ _________Dr. Stephen Kinsey_________ Chair

Accepted by

__________________________________ Dean, Graduate School

TABLE OF CONTENTS

ACKNOWLEDGMENTS ................................................................................................. iv

DEDICATION.................................................................................................................. vii

LIST OF TABLES........................................................................................................... viii

LIST OF FIGURES ........................................................................................................... ix

CHAPTER 1- DOES INTRACELLULAR METABOLITE DIFFUSION LIMIT POST-

CONTRACTILE RECOVERY IN BURST LOCOMOTOR MUSCLE?...........................1

Abstract ...................................................................................................................2

Introduction .............................................................................................................4

Materials and Methods ............................................................................................8

Results ...................................................................................................................17

Discussion .............................................................................................................25

References .............................................................................................................33

CHAPTER 2- A REACTION-DIFFUSION ANALYSIS OF ENERGETICS IN LARGE

MUSCLE FIBERS SECONDARILY EVOLVED FOR AEROBIC LOCOMOTOR

FUNCTION .......................................................................................................................38

Abstract .................................................................................................................39

Introduction ...........................................................................................................41

Materials and Methods ..........................................................................................44

Results ...................................................................................................................54

Discussion .............................................................................................................63

References .............................................................................................................71

ii

CHAPTER 3- A SKELETAL MUSCLE MODEL OF EXTREME HYPERTROPHIC

GROWTH REVEALS THE INFLUENCE OF DIFFUSION ON CELLULAR

DESIGN.............................................................................................................................74

Abstract .................................................................................................................75

Introduction ...........................................................................................................76

Materials and Methods ..........................................................................................78

Results and Discussion..........................................................................................93

References ...........................................................................................................116

CHAPTER 4- A PHYLOGENETIC APPROACH TO UNDERSTANDING THE

INFLUENCE OF DIFFUSION ON CELLULAR ORGANIZATION IN SKELETAL

MUSCLE .........................................................................................................................122

Abstract ...............................................................................................................123

Introduction .........................................................................................................125

Materials and Methods ........................................................................................130

Results .................................................................................................................139

Discussion ...........................................................................................................149

References ...........................................................................................................159

iii

ACKNOWLEDGEMENTS

When I was young, my Mom sat me down and told me – in no uncertain terms –

that I was going to do something important with my life; not successful, per se, but

something significant and meaningful. This document exists because of that poignant

piece of advice. Thank you, Mom, for pointing me in the right direction and helping me

to keep my eyes open.

To my large, immediate family – littered with last names as you are – I am

extremely fortunate for your love, encouragement and support. I realize the countless

sacrifices you have each made to help provide me with an exceptional education and,

even more, to foster in me a deep appreciation for that gift. Your own years of experience

and hard-work were an inspiration to me along the way. Mom, thank you for having a

will that can keep up with my own. It was you who taught me how to use my powers for

good. Ken, thank you for acting as my guide down the road-less traveled. I realize you

didn’t actually sign up for this. Dad, thank you for being so proud of me. It was always

encouraging to know there was someone in my corner, even if that corner was all the way

in Mississippi. Jennifer, thank you for being my friend. It just isn’t as much fun to drink

wine and gossip in the hot tub with your dad. And lastly, Michelle – I am not sure I can

even pinpoint what I have to say here. Thank you for your dogged, unwavering,

relentless, unfettered, non-judgmental support. You have been the oars on my rowboat.

To my many friends, thank you for immersing me in your perspective. In your

own way, you have each made me question what it means to live purposefully in this

world. In particular, I am overwhelmingly grateful to have found, and thereafter affixed

iv

myself to, Leah Wilhelmsen and Dan Bonné. Leah, whose contagious energy and

boundless sense of adventure left me with no choice but to follow suit. Thank you for

forcing me to wrestle against my will. Dan, who never let me forget that I am good.

Thank you for letting me into your playground and showing me where “it” is. I am a

better, happier person because of you both.

To my past and present lab mates, who have patiently coped with my vociferous

disposition, it has been a joy to work alongside of you. Jennifer Berting Krohn, your

propensity for Type A behavior makes you ever more loveable. Thank you for sharing

that responsibility with me. Jessica Burpee, for three straight years now you have sat by

my side, both literally and figuratively. Thank you for picking me up when I was down,

for helping me down when I was too far up, and for everything else in between. The two

of you have been my family here – without you, the lab would have merely been a

workplace and not the home it turned out to be.

To my committee, your guidance and support has proven invaluable. Dr. Richard

Dillaman, you have been so much more to me than a committee member. Thank you for

being so involved in my project and in my life; I know this may have come at somewhat

of a price to your eardrums. Dr. Ann Pabst, your uninterruptable enthusiasm is a treasure.

Thank you for all of your encouraging words and wisdom. Dr. Richard Satterlie, your

caffeine intake would be cause for concern if it didn’t render you so emphatically

cheerful. Thank you for making a place for creativity in science. Dr. Robert Roer, I am

convinced your laugh has healing powers. Thank you for being such an approachable

Dean. And Dr. Bruce Locke, you have given me the ability to use the phrase “reaction-

v

diffusion mathematical model” with confidence. Thank you for teaching me how to speak

your language.

To the additional faculty and staff who have played a part in this story, thank you

for keeping your doors open to me. Mark Gay, your technical expertise and infallible

patience have made you an absolutely indispensable figure in the Biology and Marine

Biology department. I cannot thank you enough for the countless hours you spent

de-frustrating me. I am also graciously indebted to Dr. Sean Lema for ushering me into

the world of molecular biology and phylogenetics. Thank you for tolerating my

unfashionably late hours and sharing with me that refrigerator you call a lab.

Finally, to my advisor, Dr. Stephen Kinsey. Your keen ability to raise my spirits

by relentlessly “pushing my buttons” is remarkable. I can honestly say that my

experience at this university was made immeasurably more wonderful by having you as

my advisor. Thank you for your guidance, both as an academic mentor and as a friend. I

hope to one day show my own students the same patience and dedication that you have

shown to me.

This research was made possible by the financial support of the National Science

Foundation, National Institutes of Health, Sigma Xi, as well as the generous contributions

of the UNCW Biology and Marine Biology Department, GSA, Biology GSA, UNCW

Graduate School, and the UNCW Alumni Association.

vi

DEDICATION I would like to dedicate this manuscript to my sister, Michelle. I can only hope to

swing so gracefully on my own trapeze of life.

vii

LIST OF TABLES

CHAPTER 1 Page

1. Parameters used in reaction-diffusion model.........................................................14

CHAPTER 2

1. Size classes of crabs...............................................................................................46

2. Parameters used in reaction-diffusion model.........................................................52

3. Absolute resting values of AP, Pi, ATP and glycogen in small and large dark

levator fibers ..........................................................................................................58

CHAPTER 3

1. Influence of mitochondrial distribution and fiber dimensions on the effectiveness

factor as predicted by a reaction-diffusion mathematical model .........................102

viii

LIST OF FIGURES

CHAPTER 1

1. Representative 31P-NMR spectra from large light levator muscle fibers that

demonstrate changes in relative concentrations of AP and Pi during a contraction-

recovery cycle ........................................................................................................18

2. Relative changes in AP (A) and Pi (B) concentrations in light levator fibers during

a contraction-recovery cycle ..................................................................................19

3. Model output for small (A,C) and large (B,D) light levator fibers........................21

4. Measured AP recovery compared to the volume averaged model of AP recovery

in small (top) and large (bottom) light fibers.........................................................23

5. The effect of increasing the rate of mitochondrial ATP production in large light

fibers on the temporal and spatial concentration profiles of AP (left panels) and

ATP (right panels)..................................................................................................24

CHAPTER 2

1. Schematic of the reaction-diffusion mathematical model .....................................50

2. Representative 31P-NMR spectra from large dark levator muscle fibers that

demonstrate changes in relative concentrations of AP and Pi during a contraction-

recovery cycle ........................................................................................................56

3. Relative changes in AP (A) and Pi (B) content and absolute changes in ATP (C)

and AP+ Pi+ATP (D) content in dark levator fibers during a contraction-recovery

cycle .......................................................................................................................57

ix

4. Relative changes in glycogen content in dark levator fibers during a contraction-

recovery cycle ........................................................................................................59

5. Measured AP recovery compared to the volume averaged model of AP recovery

in small (A) and large (B) dark fibers....................................................................61

6. The effect of increasing the rate of mitochondrial ATP production and myosin

ATPase activity during steady-state contraction in small fibers on the temporal

and spatial profiles of AP (left panels) and ATP (right panels).............................62

CHPATER 3

1. Schematic of the reaction-diffusion mathematical model .....................................87

2. Levator swimming muscle from C. sapidus (adult)...............................................94

3. Mitochondrial distribution in juvenile (left panels) and adult (right panels)

anaerobic light fibers..............................................................................................96

4. Nuclear distribution in juvenile (A) and adult (B) anaerobic light fibers..............97

5. Changes in mitochondrial and nuclear distribution during growth in anaerobic

light fibers. .............................................................................................................99

6. Correlation between nuclear number per millimeter and fiber cross-sectional area

(A) and the resulting conservation of myonuclear domain during fiber growth (B)

in anaerobic light fibers. ......................................................................................100

7. Effect of changes in nuclear distribution on the rate constant for nuclear

processes ..............................................................................................................105

8. Aerobic dark fiber organelle distribution and perfusion......................................107

x

9. Pattern of hemolymph perfusion of the aerobic dark (A,C) and anaerobic light

(B,D) levator fibers ..............................................................................................109

10. Immediate post-bleach images of dark (A,C) and light (B,D) levator fibers during

fluorescence recovery after photobleaching (FRAP)...........................................112

11. Innervation patterns in the dark (A,B) and light (A,C) levator fibers..................114

CHAPTER 4

1. Method of estimating mitochondrial density from intensity profiles of muscle

cross-sections stained for succinic dehydrogenase (SDH) activity. ....................134

2. Phylogenetic relationship among several brachyuran species (family Portunidae

(circles), Xanthidae (square), and Cancridae (triangle)) based on 16S rDNA

sequences. ............................................................................................................140

3. Representative images of muscle cross-sections stained for mitochondria with

SDH (A) and nuclei with DAPI (B,C) .................................................................141

4. Fiber and subdivision sizes in the anaerobic light fibers (left panels) and aerobic

dark fibers (right panels)......................................................................................143

5. Differences in mitochondrial and nuclear distribution with size for anaerobic light

fibers (○) and aerobic dark fiber subdivisions (●) ...............................................145

6. Relationship between total average SDH staining intensity and body mass for

anaerobic light fibers (○) and aerobic dark fiber subdivisions (●) ......................147

7. Differences in mitochondrial density, from total average SDH intensity, (A) and

myonuclear domain (B) with size, as well as the relationship between

xi

mitochondrial density and myonuclear domain (C) for anaerobic light fibers (○)

and aerobic dark fiber subdivisions (●) ...............................................................148

xii

CHAPTER 1

DOES INTRACELLULAR METABOLITE DIFFUSION LIMIT POST-

CONTRACTILE RECOVERY IN BURST LOCOMOTOR MUSCLE?

Prepared in the style of The Journal of Experimental Biology

ABSTRACT

Post-metamorphic growth in the blue crab entails an increase in body mass that

spans several orders of magnitude. The muscles that power burst swimming in these

animals grow hypertrophically, such that small crabs have fiber diameters that are typical

of most cells (<60 μm) while in adult animals the fibers are giant (>600 μm). Thus, as

the animals grow their muscle fibers cross and greatly exceed the surface area to volume

(SA:V) and intracellular diffusion distance threshold that is adhered to by most cells.

Large fiber size should not impact burst contractile function, but post-contractile recovery

may be limited by low SA:V and excessive intracellular diffusion distances. A number

of changes occur in muscle structure, metabolic organization and metabolic flux during

development to compensate for the effects of increasing fiber size. In the present study,

we examined the impact of intracellular metabolite diffusive flux on the rate of post-

contractile arginine phosphate (AP) resynthesis in burst locomotor muscle from small and

large animals. AP recovery was measured following burst exercise, and these data were

compared to a mathematical reaction-diffusion model of aerobic metabolism. The

measured rates of AP resynthesis were independent of fiber size, while simulations of

aerobic AP resynthesis yielded lower rates in large fibers. These contradictory findings

are consistent with previous observations that there is an increased reliance on anaerobic

metabolism for post-contractile metabolic recovery in large fibers. However, the model

results suggest that the interaction between mitochondrial ATP production rates, ATP

consumption rates and diffusion distances yield a system that is not particularly close to

being limited by intracellular metabolite diffusion. We conclude that fiber SA:V and O2

2

flux exert more control than intracellular metabolite diffusive flux over the

developmental changes in metabolic organization and metabolic fluxes that characterize

these muscles.

3

INTRODUCTION

The net rate of metabolic processes in cells depends on the competition between

the reactivity of the system and the diffusive flow of substrates to the reaction center

(Weisz, 1973). For instance, aerobic metabolism depends on the kinetic properties of the

mitochondrial enzymes involved in oxidative phosphorylation, and on the diffusive flux

of substrates such as ADP to the mitochondria. However, most work on aerobic energy

metabolism in skeletal muscle has focused only on the catalytic aspects of cellular

enzyme systems. This simplification has been based on the reasoning that cellular

dimensions tend to be modest (muscle fibers generally range from 10-100 μm in

diameter; Russell et al., 2000), and intracellular diffusion distances between mitochondria

are typically very short in both aerobic and anaerobic skeletal muscle (e.g., Tyler and

Sidell, 1984). Thus, diffusion is assumed to be rapid relative to the catalytic capacity of

the mitochondria, leading to minimal intracellular gradients in the concentration of

metabolites. This approach has been effectively employed to describe some of the major

processes of energy metabolism in muscle, and a variety of kinetic models have been

developed that closely match experimental data (e.g., Meyer, 1988; Jeneson et al., 1995;

Vicini and Kushmerick, 2000; Korzeniewski, 2003).

While the value of purely kinetic analyses of muscle energy metabolism is readily

apparent, the conditions under which diffusive flux may be important in either limiting

the net rate of aerobic processes or influencing the evolution of metabolic pathways are

unresolved (Suarez, 2003). The principal hurdle to understanding the role of diffusion

and metabolic organization is that most metabolic measurements constitute weighted-

4

averages over an entire cell or tissue, making it difficult to observe localized intracellular

events or concentration gradients. However, several studies that employed reaction-

diffusion mathematical modeling of aerobic metabolism found theoretical evidence for

concentration gradients in high-energy phosphate molecules during steady-state

contraction in muscle (Mainwood and Rakusan, 1982; Meyer et al. 1984; Hubley et al.

1997; Aliev and Saks, 1997; Kemp et al., 1998; Vendelin et al., 2000; Saks et al., 2003).

The intracellular diffusive flux of high-energy phosphates is largely mediated by

phosphagen kinases, such as creatine kinase (CK) and arginine kinase (AK), although the

mechanistic details are still the subject of study (reviewed by Walliman et al., 1992;

Ellington, 2001).

In an effort to understand the role of diffusion and metabolic organization on the

control of metabolism, we have been examining metabolic processes in an extreme

anaerobic muscle model system. The muscles that power burst swimming in the blue

crab, Callinectes sapidus, grow hypertrophically, and during post-metamorphic

development the diameter of fibers increases from <60 μm in juveniles to >600 μm in

adults (Boyle et al., 2003). Moreover, the distribution of mitochondria changes

dramatically during development. In small anaerobic fibers mitochondria are uniformly

distributed throughout the cell, whereas in large fibers the mitochondria are largely

clustered at the sarcolemmal membrane forming an oxidative cylinder at the periphery of

the cell (Boyle et al. 2003). Thus, the average distance between mitochondria in small

fibers is several microns, while in large fibers there may be hundreds of microns between

mitochondrial clusters. The potentially limiting rate of diffusive flux of metabolites over

such large distances is exacerbated by intracellular barriers in muscle that lead to a time-

5

dependent reduction in metabolite diffusion coefficients for movement in the direction

perpendicular to the fiber axis (D⊥) (Kinsey et al., 1999; De Graaf et al., 2000; Kinsey

and Moerland, 2002). This means that over the short diffusion distances characteristic of

small anaerobic fibers, the D⊥ is about 2-fold higher than D⊥ for the long diffusion

distances that typify large fibers. While the burst contraction function of these muscles

should not be impacted by intracellular diffusion, the aerobic recovery process may be

compromised by the extreme size of the fibers in adult animals. There are, in fact,

substantial, size-dependent differences in the recovery of the anaerobic fibers following

burst contraction. Small anaerobic fibers accumulate lactate and modestly deplete

glycogen during burst contraction, and both of these metabolites recover to resting levels

relatively quickly following an exercise bout (Boyle et al., 2003; Johnson et al., 2004).

The large fibers similarly accumulate lactate and deplete glycogen during contraction, but

following exercise they continue to accumulate large amounts of lactate and further

deplete glycogen. Full aerobic recovery of these metabolites requires several hours in

adult blue crabs (Milligan et al., 1989; Henry et al., 1994; Boyle et al., 2003; Johnson et

al., 2004).

We have previously hypothesized that anaerobic metabolism is recruited

following burst contractions in the large anaerobic fibers to accelerate certain key phases

of recovery that would otherwise be overly slow due to intracellular diffusion constraints

(Kinsey and Moerland, 2002; Boyle et al., 2003; Johnson et al., 2004). In the present

study we tested this hypothesis by examining the fiber size-dependence of the rate of

post-contractile arginine phosphate (AP) resynthesis, and these data were compared to a

mathematical reaction-diffusion model of aerobic metabolism in crab fibers. The

6

phosphagen, AP, is the initial energy source used during burst contraction, and its rapid

resynthesis following an initial exercise bout allows subsequent high-force contractions.

We predicted (1) that the measured rate of AP resynthesis would be independent of fiber

size, (2) that the predicted rate of AP resynthesis by aerobic metabolism would be fiber

size-dependent, with a considerably lower rate in large fibers than in small fibers, and (3)

that the contributions of anaerobic metabolism would offset intracellular diffusive flux

limitations on AP recovery in the large fibers, which would account for the expected

contradictory results of (1) and (2) above. Our results were consistent with these

predictions, with the exception that intracellular metabolite diffusion does not appear to

be a substantial limiting factor of AP recovery rate in large fibers. This suggests that the

low fiber surface area:volume (SA:V), which may limit oxygen flux, is a more important

determinant of metabolic rate and/or metabolic design in the large fibers.

7

MATERIALS AND METHODS

Animals

Juvenile blue crabs were collected by sweep netting in the basin of the Cape Fear

River Estuary, NC, USA. Adult crabs were obtained from baited crab traps set out on

Masonboro Sound, NC, USA or purchased from local fisherman (Wilmington, NC,

USA). Crabs were maintained in full-strength filtered seawater (35‰ salinity, 21°C) in

aerated, recirculating aquariums. They were fed bait shrimp three times weekly and kept

on a 12h:12h light:dark cycle. All animals were acclimated for at least 72 h and starved

for 24 h before experimental use. Animals were sexed, weighed, and their carapace

width and body mass was measured prior to use. Only animals in the intermolt stage

were used as determined by the rigidity of the carapace, the presence of the membranous

layer of the carapace, and the absence of a soft cuticle layer developing beneath the

existing exoskeleton.

Exercise Protocol

Crabs were induced to undergo a burst swimming response as described

previously (Boyle et al., 2003; Johnson et al., 2004). Crabs were held suspended in the

air by a clamp in a manner that allows free motion of the swimming legs and small wire

electrodes were placed in two small holes drilled into the mesobranchial region of the

dorsal carapace. A Grass Instruments SD9 physiological stimulator (Astro Med, Inc.,

West Warwick RI, USA) was used to deliver a small voltage (80 Hz, 200 ms duration, 10

V/cm between electrodes) to the thoracic ring ganglia, which elicited a burst swimming

8

response in the 5th periopods for several seconds following the stimulation. A single

pulse was administered every 30s until the animal was no longer capable of a burst

response, which was evident when it responded by moving its legs at a notably slower

rate. Immediately following exercise, animals were returned to aerated full-strength

seawater for a recovery period of 0, 15, 30, or 60 min.

Metabolite Measurement

At the end of the recovery period crabs were rapidly cut in half along their sagittal

plane in order to minimize spontaneous burst contraction of the swimming legs that

typically occurs during sacrifice. The dorsal carapace, reproductive and digestive organs

were removed and the basal cavity which houses the muscles of the fifth periopod was

exposed. The light levator muscle was rapidly isolated by cutting away the surrounding

muscle and freeze-clamped while still intact within the animal. The time elapsed from

sacrifice to freeze clamping the muscle was 60-90 s. Tissue samples were immediately

homogenized in a 6-35 fold dilution of chilled 7% perchloric acid with 1mM EDTA

using a Fisher Powergen 125 homogenizer, and then centrifuged at 16,000 x g for 30 min

at 4°C. The supernatant pH was neutralized with 3 M potassium bicarbonate in 50 mM

PIPES, stored on ice for 10 minutes, and centrifuged at 16,000 x g for 15 min at 4°C.

The supernatant was immediately analyzed by 31P nuclear magnetic resonance (NMR)

spectroscopy. NMR spectra were collected at 162 MHz on a Bruker 400 DMX

spectrometer to determine relative concentrations of AP and inorganic phosphate (Pi).

Spectra were collected using a 90° excitation pulse and a relaxation delay of 12s, which

ensures that the phosphorus nuclei were fully relaxed and peak integrals for the

9

metabolites were proportional to their relative concentrations. Forty-eight scans were

acquired for a total acquisition time of 10 min. The area under each peak was integrated

using Xwin-NMR software to yield relative concentrations of each metabolite. Two-way

analysis of variance (ANOVA) was used to analyze the post-contractile metabolite

concentrations for the interaction between size class and recovery time. All metabolite

data are presented as means ± s.e.m.

Mathematical Modeling

The general modeling approach was the same as that described in Hubley et al.

(1997), with parameters adjusted to comply with blue crab fibers, and the addition of a

mitochondrial reaction boundary condition, a basal rate of ATP consumption, an

appropriate kinetic expression for the phosphagen kinase (AK), and D⊥ values from

crustacean anaerobic fibers that incorporated the time-dependence of diffusion (Kinsey

and Moerland, 2002). The diffusion and reaction of ATP, ADP, AP, arginine (Arg), 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

mitochondria or between clusters of mitochondria. Reactions catalyzed by AK, myosin

ATPase and basal ATPase were assumed to occur homogenously throughout the domain

0 ≤ x ≤ λ/2, where x is distance from the mitochondrial surface. A burst contraction-

recovery cycle was modeled in the anaerobic, light levator fibers (so named because they

lack the high density of mitochondria that give the aerobic, dark levator its characteristic

pigmentation; Tse et al., 1983) using conditions appropriate for a small (100 μm)

diameter fiber from a juvenile animal and a large (600 μm) diameter fiber from an adult.

10

Simulations were generated using the finite element analysis software, FEMLAB

(Comsol, Inc., Burlington, MA, US).

Temporally- and spatially-dependent concentration profiles of ATP, ADP, AP,

Arg and Pi were calculated according to the molar-species continuity equation:

ii

ii R

xC

Dt

C+

∂∂

=∂∂

⊥ 2

2

(1)

where Ci is the molar concentration of species i (ATP, ADP, AP, Arg, Pi) and t is time.

Ri is the sum of the reaction rates in the intermitochondrial “bulk” space in which species

i participates and includes the basal ATP consumption, myosin ATPase and AK. The

initial conditions were Ci = Ci0 over the domain 0 ≤ x ≤ λ/2 at t = 0, where Ci

0 is the

resting concentration of species i.

The mitochondrial boundary conditions at x = 0 balance the fluxes of ATP and

ADP into the bulk phase with the rates of formation and consumption at the

mitochondria, and are modeled using Michaelis-Menten kinetics with ADP activation

(Meyer et al., 1984):

ADPmmito

ADPmmitoATPATP

mitoATP CK

CVdx

dCDR+⋅

== ⊥ (2)

ADPmmito

ADPmmitoADPADP

mitoADP CK

CVdx

dCDR+⋅

−== ⊥ (3)

where and are the boundary reaction rates for ATP and ADP, respectively,

V

mitoATPR mito

ADPR

mmito is the maximal velocity (Vmax) of the boundary reaction, and Kmmito is the Michaelis

constant for ADP for the boundary reaction. While there is considerable evidence for

more complex control of mitochondrial ATP production (e.g., Korzeniewski, 2003), even

11

when considering ADP as the sole activating species (Jeneson et al., 1996), we have used

the simplified approach described here because the mitochondrial reaction will be

functioning near Vmmito during most of recovery, making a detailed kinetic mechanism

describing oxidative phosphorylation (which is lacking for crustacean muscle)

unnecessary to achieve our objectives. There are no fluxes of Arg, AP or Pi into the bulk

phase since these species do not participate in the mitochondrial reaction:

0===dx

dCdx

dCdx

dC PiArgAP (4)

A basal ATPase rate in the bulk phase was modeled using an equation of the same form

as for the mitochondrial boundary reaction (Eq. 2), and the basal reaction values for Vmbas

and Kmbas were adjusted to maintain Ci0 constant over time in inactive fibers and to

promote a return to the initial steady state following metabolic recovery. No-flux

boundary conditions (dCi/dx=0) were also applied for all species at x = λ/2 to provide

symmetry about this boundary.

AK catalyzes the reversible phosporyl-transfer reaction, AP + ADP ↔ Arg +

ATP, and intracellular AP serves as the initial energy source used during burst

contraction in crustacean muscle. The reaction proceeds by a rapid equilibrium, random

mechanism and was modeled according to the kinetic expression of Smith and Morrison

(1969):

iADPIArg

ADPArgmArgiATP

iAPIATP

ArgATPmArgiATP

iADPiAP

ADPAPmArgiATP

iADP

ADPmArgiATP

iAP

APmArgiATPArgATPATPmArgArgmATPmArgiATP

ADPAPiADPmAP

iArgiATPmAKforArgATPmAKrev

AKATP

KKCCKK

KKCCKK

KKCCKK

KCKK

KCKK

CCCKCKKK

CCKKKK

VCCVR

+++

+++++

−=

(5)

12

where VmAKfor and VmAKrev are Vmax values in the forward (ATP formation) and reverse

direction, respectively, Km values are Michaelis constants for ternary complex formation,

Ki values are free enzyme-substrate complex dissociation constants, KI values are

dissociation constants relevant to the formation of dead-end complexes and

. AKArg

AKAP

AKADP

AKATP RRRR =−=−=

Myosin ATPase was modeled using Michaelis-Menten kinetics (Pate and Cooke,

1985; Hubley et al., 1997):

ATPmmyo

ATPmmyomyoATP CK

CVR

+⋅

−= (6)

where Vmmyo is the Vmax, Kmmyo is the apparent Michaelis constant for ATP and

. myoPi

myoADP

myoATP RRR −=−=

For each simulation, myosin ATPase was activated for 7 s at 10 Hz to simulate

burst contraction and was then deactivated during the post-contractile recovery period,

whereas the basal ATPase was active throughout the entire contraction-recovery cycle.

Small fibers (100 μm diameter) were modeled assuming a uniform distribution of

mitochondria, whereas large fibers (600 μm diameter) were assumed to have only

mitochondria at the periphery of the fiber (subsarcolemmal mitochondria) as described in

Boyle et al. (2003). Large fibers were also modeled assuming a uniform distribution of

mitochondria in order to assess the consequences of the extreme diffusion distances (300

μm) associated with an exclusively subsarcolemmal distribution.

Model input parameters are detailed in Table 1. The resting metabolite

concentrations for crustacean anaerobic locomotor fibers were obtained from a

combination of the data in Head and Baldwin (1986), 31P-NMR spectra collected by

13

Table 1. Parameters used in reaction-diffusion model. See text for additional details and source information.

Parameter type Parameter Value Small Fiber

Value Large Fiber

Units

Initial concentrations

AP 34.3 34.3 mmoles/L

Arginine 0.47 0.47 mmoles/L Pi 4.88 4.88 mmoles/L ATP 8.6 8.6 mmoles/L ADP 0.01 0.01 mmoles/L

Diffusion D⊥AP 2.20 x 10-6 1.00 x 10-6 cm2/s D⊥Arg 2.79 x 10-6 1.27 x 10-6 cm2/s D⊥Pi 3.56 x 10-6 1.62 x 10-6 cm2/s D⊥ATP 1.54 x 10-6 0.70 x 10-6 cm2/s D⊥ADP 1.75 x 10-6 0.79 x 10-6 cm2/s λ/2 2.73 300 μm

Mitochondrial boundary reaction

Vmmito 3.40 2.22 μmoles/L/s

Kmmito 20 20 μmoles/L

Basal ATPase Vmbas 11.75 11.75 μmoles/L/s Kmbas 100 100 mmoles/L

Arginine kinase reaction

VmAKfor 611 611 mmoles/L/s

VmAKrev 39 39 mmoles/L/s KATP 0.32 0.32 mmoles/L KArg 0.75 0.75 mmoles/L KAP 3.82 3.82 mmoles/L KADP 0.40 0.40 mmoles/L KiATP 0.34 0.34 mmoles/L KiArg 0.81 0.81 mmoles/L KiAP 0.26 0.26 mmoles/L KiADP 0.024 0.024 mmoles/L KIATP 2.43 2.43 mmoles/L KIArg 3.45 3.45 mmoles/L

Myosin ATPase Vmmyo 6.92 6.92 mmoles/L/s Kmmyo 0.15 0.15 mmoles/L

14

Kinsey and Ellington (1996), and calculations using the AK equilibrium constant (Teague

and Dobson, 1999). The resting metabolite concentrations were the same in small and

large fibers (Baldwin et al., 1999). The D⊥ values for each metabolite were based both

on direct measurements from crustacean anaerobic fibers and calculations from the

relationship of molecular mass and D⊥ in these fibers (Kinsey and Moerland, 2002). The

D⊥ used for the short diffusion distances characteristic of small fibers was higher than

that for the long distances found in large fibers due to the time dependence of radial

diffusion in muscle (Kinsey et al. 1999; Kinsey and Moerland, 2002). Intracellular

diffusion distances (λ/2) were estimated from the total mitochondrial fractional area,

which was 0.026 in small fibers and 0.017 in large fibers (recalculated from data

collected by Boyle et al. 2003) and the mean area/mitochondrion, which was 0.608 μm2

(Boyle et al., 2003) using the relationship λ/2 = π1

././

⋅areacellareamito

mitoarea . The Vmmito

values were estimated from rates of aerobic post-contractile phosphagen resynthesis from

white muscle fibers with a mitochondrial density comparable to blue crab light levator

muscle. Data from small prawn anaerobic tail muscle that would not be expected to have

large fibers (Thébault et al., 1987) and from isolated dogfish white muscle, which

resynthesizes phosphocreatine (PCr) using only aerobic metabolism and has a

mitochondrial fractional area of about 0.01 (Curtin et al. 1997) yielded very similar

estimates for Vmmito. This approach was necessary due to an absence of suitable

measurements of maximal oxygen consumption or ATP production rates from isolated

crustacean anaerobic fibers, and because estimates of Vmmito derived from mammalian

studies (corrected for differences in mitochondrial density) yielded AP recovery rates that

15

were several-fold higher than observed in the literature or presented herein. This is

consistent with the fact that PCr recovery rates in mammalian muscle (e.g., Vicini and

Kushmerick, 2000) are >10-fold higher than rates in crustacean muscle (Thébault et al.,

1987). Rates of mitochondrial ATP production per cell volume were converted to rates

of flux per mitochondrial surface area using a mitochondrial SA:V of 6.81 and the

mitochondrial fractional area data for small and large levator fibers (Boyle et al. 2003).

A Kmmito value for ADP of 20 μM was used, which is within the range for fast skeletal

muscle (Meyer et al., 1984). AK dissociation constants were obtained from Smith and

Morrison (1969), VmAKrev was taken from Zammitt and Newsholme (1976) and VmAKfor

was calculated from the AK Haldane relationship from Smith and Morrison (1969) using

an equilibrium constant for AK of 39 (Teague and Dobson, 1999). Values for Vmmyo and

Kmmyo were the same as in Hubley et al. (1997).

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, some of

the model data was mathematically volume averaged over the domain from x = 0 to

x=λ/2:

2/

),()(

2/

0

λ

λ

∫=

=>=<

x

xi

i

dxtxCtC (7)

For model simulations that were volume averaged, the duration of myosin ATPase

activation was adjusted so that the decrease in [AP] was comparable to that in the

observed data, in order to facilitate comparison of AP recovery measurements with the

model.

16

RESULTS

Arginine Phosphate Recovery

Crab body mass for the small size class had a median value of 1.6 g and a range

from 0.7 to 3.5 g (N = 40), while the large size class had a median of 184.5 g and a range

from 89.0 to 285.0 g (N = 53). This corresponds to an estimated median fiber size in the

light levator muscle of the small size class of 131 μm with a range from 54 to 221 μm,

and in the large size class a median of 607 μm with a range from 433 to 770 μm (fiber

sizes estimated from data summarized in Boyle et al., 2003). The crab stimulation

procedure elicited a burst exercise response that was qualitatively similar among the two

size classes, as reported previously (Boyle et al., 2003; Johnson et al., 2004). While the

frequency of swimming leg movement was higher in the juvenile animals, the duration of

swimming was greater in the adult animals. However, the AP depletion (see below),

glycogen depletion (Boyle et al. 2003), and lactate accumulation (Johnson et al. 2004)

during exercise were identical in muscle fibers from the juvenile and adult crabs,

indicating that the metabolic effects of exercise on the muscle were the same in both size

classes.

Examples of 31P-NMR spectra from perchloric acid muscle extracts demonstrate

the reciprocal change of AP and Pi during a burst exercise-recovery cycle that results

from the stoichiometric coupling of cellular ATPases (including myosin ATPase) and the

AK reaction (Fig. 1). The time course of relative changes in AP and Pi concentrations is

shown in Fig. 2, where the NMR peak integrals at each time point have been normalized

17

AP

Pi ATP

Sugar phosphate

Rest

0 min recovery

60 min recovery

30 min recovery

Figure 1. Representative 31P-NMR spectra collected from perchloric acid extracts of large light levator muscle fibers that demonstrate the changes in relative concentrations of AP and Pi during a contraction-recovery cycle. Spectra were collected from crabs at rest, and after 0, 30 and 60 min of recovery from burst exercise. Chemical shifts are in units of parts per million.

18

Time (min)

0 10 20 30 40 50 60 70

Rel

ativ

e [A

P]

0.2

0.4

0.6

0.8

1.0

1.2

1.4

small fiberlarge fiber

Time (min)

0 10 20 30 40 50 60 70

Rel

ativ

e [P

i]

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

small fiberlarge fiber

A

B

Figure 2. Relative changes in (A) AP and (B) Pi concentrations in small (filled symbols) and large (open symbols) light levator fibers during a contraction-recovery cycle. N ≥ 5 for every point.

19

to the mean resting integrals to allow direct comparison of the rate of recovery in small

and large animals. A rapid depletion of AP (and increase in Pi) is followed in small and

large fibers by a slow recovery that is complete in about 60 min. Despite the large

differences in body mass and fiber size between the small and large animals, the rate of

recovery was essentially the same for both groups and there was no significant interaction

between size class and recovery time for AP (F=0.63, DF=3, P=0.60) or Pi (F=1.78,

DF=3, P=0.16).

Reaction-Diffusion Analysis of Contraction and Recovery

Since the size-independence of post-contractile AP resynthesis described above

presumably arises from anaerobic contributions to recovery in the large fibers (Boyle et

al. 2003; Johnson et al. 2004), the reaction-diffusion analysis allows us to test whether

this pattern results from diffusive constraints on the aerobic component of recovery. The

spatially- and temporally-resolved concentrations of high-energy phosphate molecules

are presented in Fig. 3. The rate of recovery was somewhat faster in the small than in

large fibers, and there were no intracellular gradients in small fibers, as expected.

However, there were only mild gradients present in the large fibers, indicating that

diffusive flux is fast relative to the mitochondrial reaction (Fig. 3). This result is not

consistent with intracellular diffusive flux limiting aerobic metabolism during post-

contractile recovery, even though metabolite diffusion in the large fiber was modeled

over a distance of 300 μm. Thus, the relatively small differences between the small and

large fibers in Fig. 3 result almost exclusively from differences in mitochondrial density

20

3366

100133

02.8

5

35

1.40

25

15

[AP]

(mM

)

Distance (μm) Time (min)

3366

100133

02.8

7.8

8.8

1.40

8.5

8.2[ATP

](m

M)

Distance (μm) Time (min)

66 100

133

0300

6

1500

9

7.5[A

TP] (

mM

)

Distance (μm) Time (min) 33

66

133

0300

0

1500

20

10[AP]

(mM

)

Distance (μm) Time (min)

30

33

B A

C D

Figure 3. Model output for small (left panels) and large (right panels) light levator fibers using parameters in Table 1. The small fibers were modeled assuming a uniform distribution of mitochondria while the large fibers were modeled assuming only subsarcolemmal mitochondria (Boyle et al. 2003). The temporally- and spatially-resolved concentrations of AP and ATP during a contraction-recovery cycle are shown. The arrows indicate where mild gradients exist in the large fibers. For AP the gradients are not obvious due to the scaling of the concentration axis, but they are of a magnitude similar to that seen in ATP. ADP, Arginine and Pi are not shown, but the concentrations change in reciprocal fashion to that of AP.

21

(Table 1). The model results were also volume-averaged to allow a comparison of the

observed and simulated recovery rates. The observed and modeled AP recovery data are

in agreement for the small fibers, but in the large fibers it is clear that aerobic

metabolism alone could not account for the relatively high observed rate of post-

contractile recovery (Fig. 4). Thus, anaerobic metabolism appears to accelerate AP

recovery in the large fibers, but in the context of the present model this simply serves to

offset the mass-specific decrease in aerobic capacity that typifies metabolic scaling in

general (Schmidt-Nielson, 1984), and not to compensate for diffusion limitations.

If recovery in the large fibers is not substantially constrained by diffusion, then

how close are the fibers to being limited by intracellular diffusive flux? Fig. 5 shows the

effect of incremental increases in the rate of the mitochondrial boundary reaction. It can

be seen that doubling the Vmmito leads to the formation of only slightly steeper

concentration gradients, which means that there is a minimally increased control of

aerobic flux by intracellular diffusion, and the concentration gradients grow more

substantial as Vmmito is further increased. However, it is also clear that the metabolic

recovery rate increases in proportion to the increases in Vmmito. Only when unrealistically

high rates of Vmmito are used do steep concentration gradients appear, indicating diffusion

limitation of recovery rate. Thus, the mitochondrial reaction rate used in the model fits

our data well (Fig. 4) and is considerably below that which would lead to substantial

diffusive limitations of aerobic flux in large fibers (Fig. 5).

In the simulations of the large light levator fibers, we have assumed that all of the

mitochondria are subsarcolemmal, which is consistent with the dramatic shift of

mitochondrial distribution toward the fiber periphery during development (Boyle et al.

22

Time (min)0 20 40 60 80 100 120 140

[AP

] (m

M)

10

20

30

40

Time (min)0 20 40 60 80 100 120 140

[AP

] (m

M)

10

20

30

40

Small fiber

Large fiber

Small Fiber

Large Fiber

Time (min)

Time (min)

[AP]

(mM

) [A

P] (m

M)

A

B

Figure 4. Measured AP recovery (symbols) compared to the volume averaged model of AP recovery (solid line) in small (top) and large (bottom) fibers. The measured AP data has been normalized to a resting concentration of 34.3 mM to coincide with that of the model. In the model, the myosin ATPase was activated long enough to cause a decrease in AP that was comparable to the measured data. The dotted line indicates the resting concentration.

23

66 100

133

0 300

8

150 0

8.6

8.3

[ATP

] (m

M)

Distance (μm) Time (min) 33

2X

10X

100X

66 100

133

0 300

0

150 0

30

20

[AP]

(mM

)

Distance (μm) Time (min)

10

33 66

100

0 300

6.5

150 0

7.5

[ATP

] (m

M)

Distance (μm)

8.5

133

Time (min) 33

66 100

133

0 300 150

0

30

20

[AP]

(mM

)

Distance (μm) Time (min)

10

33 66 100

133

0 300

7

150 0

9

8[A

TP] (

mM

)

Distance (μm) Time (min) 33

66 100

133

0 300 150

0

30

20

[AP]

(mM

)

Distance (μm) Time (min)

10

33

A

B

C

Figure 5. The effect of increasing the rate of mitochondrial ATP production in large fibers on the temporal and spatial concentration profiles of AP (left panels) and ATP (right panels). All parameters are the same as in Fig. 3 (right panels), except that the Vmmito has been increased over the value used in Fig. 3 by 2-fold (A), 10-fold and (B), and 100-fold (C).

24

2003). To assess the impact of this reorganization of mitochondria during development,

we also analyzed the large fibers assuming a uniform distribution of mitochondria,

similar to that seen in the small fibers. The average λ/2 value calculated from the total

mitochondrial fractional area from large fibers was 3.4 μm, which is only slightly greater

than in small fibers (Table 1) but nearly two orders of magnitude less than for the

exclusively subsarcolemmal distribution assumed in Figs. 3-5. Despite the large

difference in diffusion distance, the rate of metabolic recovery assuming a uniform

distribution of mitochondria was almost identical to that shown in Fig. 3 (slightly higher),

and no concentration gradients were observed (data not shown). This result is also

consistent with a very limited control of metabolic flux by intracellular diffusion.

DISCUSSION

The principal findings of the present study were (1) that AP recovery following

burst contraction was independent of body mass and fiber size, (2) that the predicted rate

of aerobic metabolism was insufficient to account for the relatively high rate of recovery

in the large fibers, which is consistent with the hypothesis that anaerobic metabolism

contributes to AP recovery to a greater extent as fibers grow, and (3) that intracellular

diffusive flux does not appear to limit metabolic recovery in large fibers, despite the fact

that diffusion must occur over hundreds of microns. Rather, the fibers appear to have an

aerobic capacity that is considerably below that which would lead to substantial diffusion

limitation (Fig. 5).

25

It is well-established that some crustacean muscles produce lactate following

contraction, and it has been speculated that this leads to an increased rate of metabolic

recovery (Ellington, 1983; Head and Baldwin, 1986; Kamp, 1989; Henry et al., 1994;

Baldwin et al., 1999; Morris and Adamczewska, 2002; Johnson et al., 2004). We first

described the fiber size-dependence of post-exercise glycogen depletion (Boyle et al.,

2003) and lactate production (Johnson et al., 2004) in crustacean muscle and attributed

the observed pattern to the long intracellular diffusion distances and/or the low SA:V

associated with the large developmental increase in fiber size. While the studies cited

above suggested that post-contractile recovery was accelerated by anaerobic metabolism,

the present study is to our knowledge the first demonstration in crustacean muscle of a

metabolic recovery process (AP resynthesis) that is faster in the large fibers as a result of

anaerobic contributions.

In our view, the patterns of recovery reported previously (Boyle et al. 2003;

Johnson et al. 2004) and herein are clearly related to fiber size. It was therefore

surprising that the model results did not indicate a limitation of aerobic flux by

intracellular metabolite diffusion, considering that AP and arginine, which are the key

diffusing species (Ellington and Kinsey, 1998), can traverse the λ/2 distance in small

fibers in <30 ms, while needing 16,000 times longer (nearly 8 min) to cover the distance

modeled in large fibers (Kinsey and Moerland, 2002). Implicit in this finding is that

kinetic expressions alone (no diffusion component) would have been nearly sufficient to

simulate the differences between small and large fibers in Fig. 3. This is at odds with

some previous reaction-diffusion mathematical analyses in burst anaerobic muscle.

Hubley et al. (1997) found substantial concentration gradients for PCr and the free energy

26

of ATP hydrolysis (ΔGATP) in fish white muscle during contraction, while Boyle et al.

(2003) applied the reaction-diffusion model of Mainwood and Rakusan (1982) to blue

crab light levator muscle and likewise found dramatic concentration gradients for AP and

ΔGATP. However, both of these models assumed higher rates of steady-state ATP demand

and perfect buffering of high-energy phosphate concentrations at the mitochondrial

membrane, which means that rates of ATP chemical flux were always high relative to the

rates of diffusive flux. In contrast, the present study used a simple kinetic expression for

the mitochondrial boundary reaction and reasonable maximal rates of ATP production.

Further, no additional ATP demand was applied during recovery beyond the

thermodynamic drive to restore the resting steady-state metabolite concentrations.

It could be argued that we underestimated the Vmmito and post-contractile ATP

demand, and therefore misjudged the effect of diffusion. Thus, the approach used herein

represents a conservative analysis of the potential for diffusion limitation in these muscle

fibers. It should be noted, however, that the model results for AP recovery paralleled our

observations in the small fibers (Fig. 4), which rely exclusively on aerobic metabolism

for recovery (Boyle et al., 2003; Johnson et al., 2004), and the low Vmmito values are

consistent with observations that complete aerobic recovery from exercise in blue crabs

occurs over many hours (Booth and McMahon, 1985; Milligan et al., 1989; Henry et al.,

1994; Boyle et al. 2003; Johnson et al., 2004). Our results are also consistent with the

generalized analysis of diffusion limitation described by Weisz (1973), which relates the

observed rate of the catalytic process to rates of diffusive flux. Applying this approach to

the present case we can conclude that even if Vmmito and post-contractile ATPase rates

27

were underestimated, the observed rate of AP recovery is simply too slow to be limited

by diffusive flux (Weisz, 1973).

There are other possible size-dependent effects that could confound our analysis.

For instance, size-dependent differences in AP hydrolysis during dissection, freeze

clamping or perchloric acid extraction could conceivably bias our AP recovery curves.

However, in resting animals the AP/Pi ratios in extracts were always similar to previous

values observed in intact, superfused crustacean white muscle (Kinsey and Ellington,

1996), and there were no significant differences in the AP/Pi ratios between size classes

(data not shown). Therefore, AP hydrolysis during the dissection and/or extraction was

minimal and not size-dependent. It is also possible that differences in intracellular pH

(pHi) or free Mg2+ between large and small animals could alter the AK equilibrium

constant and therefore the AP recovery rate. While lactate accumulation during

contraction is the same in both size classes, post-contractile lactate accumulation is

greater in the large fibers (Johnson et al. 2004), and this could lead to a reduced pHi in

large fibers that would slow AP recovery. In addition, the low SA:V in large fibers may

hinder compensatory acid/base equivalent exchange and exacerbate cellular acidosis,

again leading to slower AP recovery. However, it should be noted that both the post-

contractile lactate production and potential effects of SA:V still fall within the realm of

fiber size effects, which is consistent with our conclusions. In addition, intracellular

buffering capacity in white muscle of crustaceans is greater in larger animals (Baldwin et

al. 1999), which may offset the pHi effects described above.

The findings in the present study are somewhat paradoxical. If it is assumed that

a relatively rapid post-contractile recovery in burst muscle is beneficial, which is

28

apparently the case since large fibers use anaerobic metabolism to speed up recovery, and

if intracellular diffusive flux does not limit recovery, then why do the large fibers not

simply increase the mitochondrial density to accelerate recovery rather than relying on

anaerobic processes that put them further in oxygen debt? It is clear from Figs. 3 and 5

that doubling the mitochondrial density leads to a near doubling of recovery rate, with

only mild limitation by diffusion. We propose that in blue crabs the low SA:V associated

with large fiber size is more important in limiting aerobic metabolism and/or driving

metabolic design than is intracellular metabolite diffusion. The most compelling

evidence in support of this argument is the dramatic shift in the distribution of

mitochondria toward the periphery of the fiber as the light levator muscle fibers grow

(Boyle et al., 2003). This distributional change places more mitochondria at the

sarcolemmal membrane near the source of O2 at the expense of increased intracellular

diffusion distances. In our model analysis, there was a very slight advantage associated

with a uniform, instead of subsarcolemmal, distribution of mitochondria in the large

fibers (data not shown). However, the fact that the developmental shift in mitochondria

occurs anyway indicates that O2 flux (which was not included in the model) drives

mitochondrial distribution more than intracellular diffusive flux. This view has been

suggested previously to explain mitochondrial clustering at the sarcolemma in non-giant

mammalian (Mainwood and Rakusan, 1982) and crustacean muscle (Stokes and

Josephson, 1992).

In addition to the above argument, the partial pressure of oxygen (PO2) in

crustacean blood (including blue crabs) is low relative to that of muscle from active

vertebrate species (Gannon and Wheatly, 1995; Forgue et al., 2001). This leads to

29

relatively shallow PO2 gradients across the sarcolemma that, when coupled to the low

SA:V of large fibers, would be expected to promote very low rates of O2 flux into the

fiber. The lack of myoglobin (Mb) in the light levator muscle amplifies this effect, since

Mb-less fibers require a higher extracellular PO2 to support a given rate of O2

consumption compared to muscles with Mb (Groebe and Thews, 1990). This view is

consistent with recent observations in isolated Xenopus laevis skeletal muscle fibers,

which are also relatively large and lack Mb, that low intracellular PO2 limits the rate of

NAD(P)H oxidation by the electron transport system during steady-state contraction

(Hogan et al., 2005). Further, the modeled differences between the recovery rate in small

and large fibers are modest, due to the relatively small differences in oxidative potential

(Figs. 3 and 4; Table 1), but the measured differences in post-contractile lactate

production among size classes are dramatic; far greater than would be necessary to

accelerate AP resynthesis by the relatively small amount indicated in Fig. 4 (Johnson et

al. 2004). If fiber SA:V limits aerobic metabolism then the size-dependence of aerobic

recovery may be much more substantial than shown in Fig. 3, which would explain the

strong size-dependence of post-contractile lactate production.

While intracellular diffusive fluxes of high-energy phosphate metabolites do not

appear to exert substantial control over the rate of aerobic metabolism in blue crab giant

anaerobic fibers, based on our current one-dimensional model, there may be other cell

types where diffusion is limiting. These likely include systems with relatively high rates

of ATP production/consumption and distant sites of ATP utilization, such as in some

muscle fibers with a higher aerobic capacity than examined here (Meyer et al. 1984;

Stokes and Josephson, 1992; Vendelin et al., 2000; Saks et al., 2003; Suarez, 2003) or in

30

the flagellum of spermatozoa, which has been the subject of many reaction-diffusion

analyses (e.g., Nevo and Rikmenspoel, 1969; Tombes and Shapiro, 1985; Van Dorsten et

al., 1997; Ellington and Kinsey, 1998). However, it is possible that in most cases neither

intracellular metabolite diffusion nor sarcolemmal O2 flux limit aerobic metabolism per

se, but even if this is true it is still likely that the interaction between diffusive processes

and ATP demand has shaped the evolution of cellular design. For instance, if there are

advantages to having large fibers then the principles of symmorphosis (Taylor and

Weibel, 1981) dictate that other metabolic properties, such as mitochondrial density and

distribution, would be adjusted to match rates of O2 and substrate delivery, thereby

avoiding diffusion limitation.

What then are the potential advantages associated with large muscle fibers?

Rome and Lindstedt (1998) have characterized the manner in which muscle fiber volume

is devoted to metabolic or contractile machinery in relation to muscle function. It is

possible that a burst contractile muscle composed of relatively few large fibers may yield

a greater percentage of total muscle volume that is devoted to myofibrils, and therefore

improve contractile force, compared to muscle with a much larger number of small

fibers. Johnston et al. (2003; 2004) proposed that in certain cold-water fishes white

muscle fibers attain a size that is just below that which would be diffusion-limited in

order to minimize sarcolemmal surface area over which ionic gradients must be

maintained, thus lowering metabolic rates. A similar argument could be made for blue

crab anaerobic fibers, with the additional consideration that a low mitochondrial content

may also constitute an energy saving strategy to avoid the costs of mitochondrial

biogenesis and the maintenance of electrochemical gradients across the inner membrane.

31

Forgue et al. (2001) have made complimentary arguments that the low blood PO2 in

crustaceans limits resting metabolic rate to reduce costs during periods of inactivity.

These proposed energy saving measures are linked; if the capacity to produce ATP is

strategically lowered, then there is no negative consequence to the low SA:V and long

diffusion distances associated with large fibers. Similarly, if SA:V is lowered to

minimize ionic transport costs, then there is no further consequence to lowering aerobic

capacity, since high rates of mitochondrial respiration would be limited by low O2 flux in

large fibers.

The implication of the hypothesis that selective pressure to lower maintenance

costs favors large fiber size is that the benefits of a rapid aerobic recovery following a

burst contraction are outweighed by long-term energetic savings. Blue crabs have large

chelipeds and highly effective defensive behavior, and they also have the capacity to

rapidly bury themselves to avoid predators. These characteristics may obviate the need

for additional high-force contractions following an initial bout of burst swimming, and

may explain why the juvenile crabs do not also employ anaerobic metabolism to

accelerate recovery. Large fibers might be particularly important in reducing metabolic

costs in cases where anaerobic muscle constitutes a large fraction of the total body mass

and is used infrequently, but must maintain a polarized sarcolemma at all times.

Additional examples may include lobster abdominal muscle that is used for tail-flip

escape maneuvers, or fish white muscle in species that infrequently undergo burst

swimming. At present, however, the benefits of large fiber size, if any, in crustaceans

and other groups are not known.

32

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Schmidt-Nielsen, K. (1984). Scaling: why is animal size so important? New York: Cambridge University Press.

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Stokes, D.R. and Josephson, R.K. (1992). Structural organization of two fast, rhythmically active crustacean muscles. Cell Tiss. Res. 267, 571-582. Suarez, R.K. (2003). Shaken and stirred: muscle structure and metabolism. J. Exp. Biol. 206, 2021-2029. Taylor, C.R. and Weibel, E.R. (1981). Design of the mammalian respiratory system. Respir. Physiol. 44, 1-164.

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CHAPTER 2

A REACTION–DIFFUSION ANALYSIS OF ENERGETICS IN LARGE MUSCLE

FIBERS SECONDARILY EVOLVED FOR AEROBIC LOCOMOTOR FUNCTION

Prepared in the style of The Journal of Experimental Biology

ABSTRACT

The muscles that power swimming in the blue crab, Callinectes sapidus, grow

hypertrophically, such that juvenile crabs exhibit cell diameters of <60 μm, while fibers

of the adult crabs often exceed 600 μm. Thus, as these animals grow, their muscle fibers

cross and greatly exceed the surface area:volume (SAV) and intracellular diffusion

distance limits adhered to by most cells. Previous studies have shown that arginine

phosphate (AP) recovery in the anaerobic (light) fibers, which demonstrate an increasing

reliance on anaerobic processes following contraction, is too slow to be restricted by

intracellular metabolite diffusive flux, in spite of the fiber’s large size. In contrast, the

aerobic (dark) fibers have evolved an intricate network of intracellular subdivisions that

maintain an effectively small “metabolic diameter” throughout development. In the

present study, we examined the impact of intracellular metabolite diffusive flux on the

rate of post-contractile AP resynthesis in the dark muscle, which has a much higher

aerobic capacity than the light muscle. AP recovery was measured for 60 min in adults

and 15 min in juveniles following burst-contractile activity in dark fibers, and a

mathematical reaction-diffusion model was used to test whether the observed aerobic

rates of AP resynthesis were fast enough to be limited by intracellular metabolite

diffusion. Despite the short diffusion distances and high mitochondrial density, the AP

recovery rates were relatively slow and we found no evidence of diffusion limitation.

However, during simulation of steady-state contraction, an activity more typical of the

dark fibers, there were substantial intracellular metabolite gradients, indicative of

diffusion limitation. This suggests that high ATP turnover rates may lead to diffusion

39

limitation in muscle even when diffusion distances are short, as in the subdivided dark

fibers.

40

INTRODUCTION

The muscles that power swimming in the blue crab, Callinectes sapidus, grow by

increasing the diameter of individual fibers (hypertrophy), rather than by increasing fiber

number (hyperplasia), and during post-metamorphic development fiber diameters

increase from <60 μm in juveniles to >600 μm in adults (Boyle et al., 2003). This

contrasts with muscle fibers of most organisms, which generally have a size range of 10-

100 μm. Presumably, fiber size is governed by the fundamental need to carry out aerobic

metabolic processes, which rely on oxygen flux across cell membranes (Kim et al.,

1998), and ATP diffusive flux from mitochondria to sites of ATP-demand (Mainwood

and Rakusan, 1982). Thus, a likely functional consequence of excessive cell size is a

reduced capacity for oxidative metabolism (Boyle et al., 2003; Johnson et al., 2004;

Kinsey et al., 2005).

The swimming muscles of C. sapidus are composed of 3 distinct types of fibers:

light fibers that power anaerobic burst swimming, dark fibers that power aerobically

fueled endurance swimming, and a small number of fibers intermediate to the light and

dark fibers (Tse et al., 1983). The anaerobic light fibers rely on endogenous fuels such as

arginine phosphate (AP) and glycogen during contraction, not oxygen influx, so

contractile function should not be impacted by an increase in fiber size. However,

aerobically driven processes, such as post-contractile recovery, may be limited in the

largest light fibers because low cell surface area:volume (SAV) may constrain oxygen

flux into the cell and intracellular diffusion distances may become excessive (Kinsey and

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Moerland, 2002; Boyle et al., 2003; Kinsey et al., 2005). These cell level limitations may

therefore have behavioral costs by extending the recovery time required between

successive bursts of high velocity swimming needed for predator escape.

While the dark fibers reach the same large dimensions as the light fibers, their

aerobic contractile function should favor small size throughout development. To

accommodate the conflicting demands for hypertrophic growth and small fiber size, dark

fibers have evolved small mitochondria-rich subdivisions (Tse et al., 1983) that increase

in number and maintain a constant size during development, as well as promote intra-

fiber perfusion to facilitate O2 delivery to the subdivisions (Johnson et al., 2004). Thus,

blue crab dark fibers are unusual in having metabolic functional units (fiber subdivisions)

that retain small dimensions throughout development, while their contractile functional

units (fibers) appear to grow hypertrophically to extreme proportions.

Anaerobic light fibers are therefore characterized by large cell size and low ATP

demand, while dark fibers remain effectively small (via subdivisions) throughout

development, but have the capacity for much higher rates of ATP turnover. We have

previously hypothesized that anaerobic glycogenolysis is recruited following burst-

contractions in large anaerobic fibers to accelerate certain key phase of recovery that

would otherwise be slowed by size-related limitations to the rate of aerobic ATP

synthesis (Kinsey and Moerland, 2002; Boyle et al., 2003; Johnson et al., 2004; Kinsey et

al., 2005). This hypothesis is supported by observations that the rate of post-contractile

AP resynthesis, which is potentially increased by anaerobic metabolism, is size-

independent in blue crab anaerobic fibers (Kinsey et al., 2005). Further, significant post-

contractile glycogen depletion (Boyle et al., 2003) and increased post-contractile lactate

42

accumulation (Johnson et al., 2004), both anticipated consequences of anaerobic

glycogenolysis, were found in the anaerobic fibers from adult animals, but not juveniles.

It is unlikely, however, that this strategy is implemented in the large dark fibers because

intracellular subdivisions maintain the small effective diameter necessary to permit

aerobic metabolism during recovery. Thus, it is reasonable to expect that differences in

the rate of post-contractile AP recovery in dark fibers from adult and juvenile crabs are

not related to fiber size, but result from “normal” metabolic scaling with body mass

(Schmidt-Neilson, 1984). Furthermore, if anaerobic glycogenolysis is not being

exploited in the large aerobic fibers, post-contractile glycogen depletion and lactate

accumulation should be minimal and size independent.

Johnson et al. (2004), however, reported significant post-contractile lactate

accumulation in the highly subdivided dark fibers of adult crabs (although the levels were

significantly lower than seen in light fibers). The authors reasoned that this was a likely

consequence of close proximity of the dark muscle to the much larger mass of lactate

producing light fibers, as well as net diffusive flux into the dark fibers from the lactate-

laden hemolymph, but not the result of post-contractile anaerobic glycogenolysis

occurring within the dark fibers. The absence of size-dependent glycogen depletion in

dark fibers would be consistent with the conclusions of Johnson et al. (2004).

These past observations provide strong evidence for fiber size effects in blue crab

light muscle fibers, which are likely mediated through excessive intracellular diffusive

distances and/or low cell SAV. The dark fibers have the aforementioned structural

modifications that appear to offset the constraints of large fiber size, but these fibers also

have high rates of ATP turnover that make them more susceptible to diffusion limitation.

43

The present study examined the fiber size dependence of post-contractile recovery in the

dark muscle fibers of juvenile and adult blue crabs. The objectives were to (1) measure

the rate of AP recovery, (2) apply a mathematical reaction-diffusion model to determine

whether the rate of AP recovery is limited by intracellular metabolite diffusive flux, and

(3) measure post-contractile glycogen depletion. We hypothesized that (1) differences in

the rate of post-contractile AP recovery in dark fibers are principally the result of

differences in mass specific aerobic capacity due to metabolic scaling (Schmidt-Neilson,

1984), (2) intracellular metabolite diffusive flux does not limit the rate of AP recovery,

and (3) there is no size-dependent post-contractile depletion of glycogen in dark aerobic

fibers because anaerobic metabolism is not recruited during recovery in the large fibers of

the adults.

MATERIALS AND METHODS

Animals

Juvenile blue crabs (Callinectes sapidus, Rathbun) were collected by sweep

netting in the basin of the Cape Fear River Estuary, NC, USA. Adult crabs were obtained

from baited crab traps set in Masonboro Sound, NC, USA or purchased from local

fisherman (Wilmington, NC, USA). Crabs were maintained in full-strength filtered

seawater (35‰ salinity, 21°C) in aerated, recirculating aquariums. They were fed bait

shrimp three times weekly and kept on a 12h:12h light:dark cycle. All animals were held

under these conditions for at least 72 h before experimentation. Animals were sexed, and

44

45

their carapace width and body mass were measured prior to use (Table 1). Only animals

in the intermolt stage were used as determined by the rigidity of the carapace, the

presence of the membranous layer of the carapace, and the absence of a soft cuticle layer

developing beneath the existing exoskeleton (Roer and Dillaman, 1984).

Exercise Protocol

Crabs were induced to undergo a burst swimming response as described

previously (Boyle et al., 2003; Johnson et al., 2004; Kinsey et al., 2005). Crabs were

held suspended in the air by a clamp in a manner that allows free motion of the

swimming legs and small wire electrodes were placed in two small holes drilled into the

mesobranchial region of the dorsal carapace. A Grass Instruments SD9 physiological

stimulator (Astro Med, Inc., West Warwick, RI, USA) was used to deliver a small

voltage (80 Hz, 200 ms duration, 10 V/cm between electrodes) to the thoracic ring

ganglia, which elicited a burst swimming response in the 5th periopods for several

seconds following the stimulation. A single pulse was administered every 20-30s until

the animal was no longer capable of a burst response, which was evident when it

responded by moving its legs at a notably slower rate. During exercise, animals were

exposed to the air for a period of only 3-4 min, which is sufficiently short to avoid

compromised gill oxygen transport due to changing scaphognathite activity, lamellar

clumping or lactate accumulation (deFur et al., 1988). Immediately following exercise,

animals were returned to aerated full-strength seawater and allowed to recover. Animals

assayed for AP were sampled at 0, 15, 30, or 60 min (adults) and 0, 5, 10, or 15 min

Table 1. Size classes of crabs used in this study based on body mass and light levator fiber diameter data from Boyle et al. (2003). Arginine phosphate use and recovery Glycogen use and recovery

Size class

N

Carapace width (mm)

Body mass (g)

Body mass range (g)

N

Carapace width (mm)

Body mass (g)

Body mass range (g)

Small 41 28.3±0.5 2.0±0.1 1.0-3.6 60 29.0±0.4 2.2±0.1 1.1-3.6 Large 36 139.2±1.9 187.0±6.7 89.0-254.1 60 142.7±1.3 182.2±4.6 136.2-284.5

46

(juveniles) post-contraction, while animals assayed for glycogen were sampled at 0, 30,

60, 120, or 240 min post-contraction.

Metabolite Measurement

At the end of the recovery period crabs were rapidly cut in half along their sagittal

plane in order to minimize the spontaneous burst contraction of the swimming legs that

typically occurs during sacrifice. The dorsal carapace, reproductive and digestive organs

were removed and the basal cavity that houses the muscles of the fifth periopod was

exposed. The dark levator muscle was rapidly isolated by cutting away the surrounding

muscle and freeze-clamped using tongs cooled in liquid nitrogen while still intact within

the animal. The time elapsed from sacrifice to freeze clamping the muscle was 60-90 s.

After tissue extraction, samples being analyzed for glycogen were stored at -80ºC until

further evaluation. Samples assayed for AP were immediately homogenized in a 6-35

fold dilution of chilled 7% perchloric acid with 1mM EDTA using a Fisher Powergen

125 homogenizer, and then centrifuged at 16,000 x g for 30 min at 4°C. The supernatant

pH was neutralized with 3M potassium bicarbonate in 50 mM PIPES, stored on ice for 10

min, and centrifuged at 16,000 x g for 15 min at 4°C. The supernatant was immediately

analyzed by 31P nuclear magnetic resonance (NMR) spectroscopy. NMR spectra were

collected at 162 MHz on a Bruker 400 DMX spectrometer (Bruker Instruments, Billerica,

MA, USA) to determine relative concentrations of AP, inorganic phosphate (Pi), and

ATP. Spectra were collected using a 90° excitation pulse and a relaxation delay of 12 s,

which ensures that the phosphorus nuclei were fully relaxed and peak integrals for the

metabolites were proportional to their relative concentrations. Forty-eight scans were

47

acquired for a total acquisition time of 10 min. The area under each peak was integrated

using Xwin-NMR software to yield relative concentrations of each metabolite.

Previously frozen tissue samples were analyzed for glycogen based on the method

of Keppler and Decker (1974). Samples were homogenized in a 5-31 fold dilution of

3.6% perchloric acid then divided into two pools: a blank aliquot for measuring free

glucose, and a sample aliquot for measuring total glucose content (free glucose +

glycogen). The total glucose sample aliquot was neutralized with 1M potassium

bicarbonate and incubated at 40ºC for two hours in an amyloglucosidase solution

(14units/mL in 0.2 M acetate buffer, pH 4.8) while undergoing constant shaking. After

incubation was complete, the reaction was stopped by the addition of 3.6% perchloric

acid and both the glucose blank and the total glucose sample were centrifuged at 16,000 x

g for 15 min. Before being assayed, supernatants from both pools were neutralized with

1M KHCO3. Both aliquots were then added to a solution containing 1 M ATP, 0.9 mM

β-NADP, 15.6 units glucose-6-phosphate dehydrogenase, 0.3 M triethanolamine

hydrochloride, and 4.05 mM MgSO4 at pH 7.5. The reaction was started by the addition

of 15.8 units of hexokinase. The amount of glucose in each pool is proportional to the

increase in NADPH, which is measured spectrophotometrically at a wavelength of 340

nm. Subtraction of the free glucose in the blank from glucose hydrolyzed from glycogen

in the total glucose sample aliquot yielded glycogen content in units of μmols of glucosyl

units per gram of tissue.

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Mathematical Modeling

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

et al. (2005), with parameters adjusted to comply with blue crab dark levator fibers. In

brief, the model calculated the diffusion and reaction of ATP, ADP, AP, arginine (Arg),

and Pi 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,

which were assumed to be distributed at the periphery of each subdivision (Fig. 1). Four

kinetic expressions were used to determine reaction rates, and these expressions were

either boundary reactions (i.e., the production of ATP at the mitochondrial membrane), or

bulk reactions (those reactions that occur throughout the cytoplasm). Michaelis-Menten

expressions were used for the mitochondrial boundary reaction (ADP + Pi→ATP) with a

rate dependent 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. In addition, a complete kinetic expression for arginine kinase (AK) was included

in the bulk phase (Smith and Morrison, 1969). Diffusion coefficients for radial motion

(perpendicular to the fiber long axis; D⊥) incorporated the time-dependence of diffusion

found in skeletal muscle (Kinsey et al., 1999; Kinsey and Moerland, 2002). Temporally

and spatially dependent concentration profiles of metabolites were calculated using

molar-species continuity equations for all five metabolites (Bird et al., 1960).

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

element analysis software, FEMLAB (Comsol, Inc., Burlington, MA, USA). The myosin

ATPase was activated at 10 Hz for several seconds, while the basal ATPase was active

49

Dark fiber subdivision

Mitochondrial clusters

λ/2

λ /2 (half the distance between mitochondrial clusters )

Mitochondrial cluster (boundary reaction) Reactions homogenous across fiber:

• Basal ATPase • Myosin ATPase • Arginine kinase

Figure 1. Schematic of the reaction-diffusion mathematical model. Metabolite concentrations during a contraction-recovery cycle in dark levator fibers were modeled over the length λ/2, which represents half of the distance between mitochondrial clusters.

50

throughout the entire contraction-recovery cycle. Model input parameters are detailed in

Table 2. The resting metabolite concentrations for crustacean aerobic locomotor fibers

were obtained from data gathered during this study and calculations using the AK

equilibrium constant (Teague and Dobson, 1999). Metabolite data collected in units of

μmol g-1 were converted to units of mmol l-1 by assuming that intracellular water

accounted for 68% of the wet weight in blue crab dark levator muscle (Milligan et al.,

1989). Resting arginine concentrations were set at a reasonable, but arbitrary value (Beis

and Newsholme, 1976). The D⊥ values for each metabolite were based both on direct

measurements from crustacean anaerobic fibers and calculations from the relationship of

molecular mass and D⊥ in these fibers (Kinsey and Moerland, 2002). Intracellular

diffusion distances were estimated according to Johnson et al. (2004), who found a mean

subdivision diameter of 35.6 μm and a primarily subsarcolemmal distribution of

mitochondria in the subdivisions of both small and large fibers in the dark muscle. A Km

for the mitochondrial reaction (Kmmito) for ADP of 50 μM was used, which is within the

range for slow-twitch skeletal muscle (Kushmerick et al., 1992). The basal ATPase

maximal velocity (Vmbas) and Km (Kmbas) for ATP were estimated so as to maintain

constant resting concentrations over time in an inactive fiber and to promote a return to

the initial steady state following contraction, and these values are similar to basal ATPase

rates estimated for skeletal muscle (Vicini and Kushmerick, 2000). AK dissociation

constants were obtained from Smith and Morrison (1969), the maximal velocity for the

reverse reaction (VmAKrev) was taken from measurements in blue crab dark levator muscle

(Holt and Kinsey, 2002), and the maximal velocity for the forward reaction (VmAKfor) was

calculated from the AK Haldane relationship from Smith and Morrison (1969) using an

51

Table 2. Parameters used in reaction-diffusion model. See text for additional details and source information.

Parameter type Parameter Small fiber Large fiber Units

Initial concentrations AP 26.9 43.97 mmol l-1

Arginine 0.5 0.5 mmol l-1

Pi 21.37 19.56 mmol l-1

ATP 10.79 11.13 mmol l-1

ADP 0.0045 0.00285 mmol l-1

Diffusion D⊥AP 1 x 10-6 1 x 10-6 cm2/s D⊥Arg 1.27 x 10-6 1.27 x 10-6 cm2/s D⊥Pi 1.62 x 10-6 1.62 x 10-6 cm2/s D⊥ATP 0.7 x 10-6 0.7 x 10-6 cm2/s D⊥ADP 0.79 x 10-6 0.79 x 10-6 cm2/s λ/2 17 17 μm Mitochondrial boundary reaction

Vmmito 6 x 10-17 1.97 x 10-17 mmol μm-2 s-1

Kmmito 50 50 μmol l-1

Basal ATPase Vmbas 7 7 μmol l-1 s-1

Kmbas 10 10 mmol l-1

Arginine kinase reaction

VmAKfor 373 373 mmol l-1 s-1

VmAKrev 23.5 23.5 mmol l-1 s-1

KATP 0.32 0.32 mmol l-1

KArg 0.75 0.75 mmol l-1

KAP 3.82 3.82 mmol l-1

KADP 0.40 0.40 mmol l-1

KiATP 0.34 0.34 mmol l-1

KiArg 0.81 0.81 mmol l-1

KiAP 0.26 0.26 mmol l-1

KiADP 0.024 0.024 mmol l-1

KIATP 2.43 2.43 mmol l-1

KIArg 3.45 3.45 mmol l-1

KIAP 1.46 1.46 mmol l-1

Myosin ATPase Vmmyo 3.81 3.81 mmol l-1 s-1

Kmmyo 0.15 0.15 mmol l-1

52

equilibrium constant for AK of 40 (Teague and Dobson, 1999). The myosin ATPase

maximal velocity (Vmmyo) and Km (Kmmyo) for ATP were the same as used for aerobic

muscle in Hubley et al. (1997).

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, some of

the model data was mathematically volume averaged to remove the spatial dependence in

concentration while retaining the temporal variation. (Note that since the model is one-

dimensional, this averaging process required integration only over that one dimension.)

For model simulations that were volume averaged, the duration of myosin ATPase

activation was adjusted so that the decrease in [AP] was comparable to that in the

observed data and the values for the maximal velocity of the mitochondrial reaction

(Vmmito) values were adjusted so that the AP recovery curve predicted by the model

approximated the measured recovery rate. This approach facilitated the analysis of

diffusion limitation of the rate of AP recovery. Since the dark levator muscle is active

during sustained aerobic swimming, steady-state contractions, in which myosin was

continuously active, were also simulated, and Vmmito and Vmmyo were adjusted to model

different rates of ATP turnover. These latter simulations were arbitrarily modeled in the

small fibers, due to the similarity in the model parameters between the large and small

fibers and because the higher rate of oxidative phosphorylation in the small fibers make

them more likely to be influenced by intracellular metabolite diffusion.

53

Analysis

Measurements of AP during recovery were not collected at the same time points

for both small and large animals, so a t-test was used to compare the fractional recovery

at 15 min post-exercise, a recovery time point that was shared between size classes. For

other metabolite data, a one-way ANOVA was used to test for the main effects of

recovery time. Where significant differences were detected, Tukey’s HSD tests were used

to compare post-contractile recovery time points to the resting value. All metabolite data

are presented as means ± s.e.m with a significance accepted at p<0.05.

RESULTS

Metabolite Recovery

Size classes were defined based on the relationship between animal mass and light

levator fiber size determined by Boyle et al. (2003) (Table 1), where the mean fiber size

in the small and large animals was approximately 150 μm and 600 μm, respectively. In

these experiments, as in previous studies (Boyle et al., 2003; Johnson et al., 2004; Kinsey

et al., 2005), the crab stimulation procedure elicited a burst-escape response that was

qualitatively similar for both size classes. While the frequency of leg beats during burst-

swimming was higher in the juveniles, the duration of the movement was greater in the

adults and both size classes required approximately the same number of stimulations to

reach fatigue. Additionally, glycogen depletion (Boyle et al., 2003), lactate accumulation

(Johnson et al., 2004), and AP depletion (Kinsey et al., 2005; see below) during exercise

54

were identical in muscle fibers from juvenile and adult crabs, indicating a uniform

metabolic response to stimulated exercise.

During a burst exercise-recovery cycle there is a reciprocal change in AP and Pi

that results from the stoichiometric coupling of cellular ATPases and the AK reaction.

Contraction results in a rapid depletion of AP, and corresponding increase in Pi, which is

followed by a slow recovery to pre-contractile levels. This pattern is demonstrated in

examples of the 31P-NMR spectra collected from perchloric acid extracts of dark muscle

(Fig. 2). Table 3 shows the absolute concentrations of metabolites collected at rest, and

the time course of relative changes in the AP and Pi content during a contraction-recovery

cycle are shown in Fig. 3. In the large fibers total recovery takes about 60 min, while the

small fibers completely recover in about 15 min A comparison of the percent AP

recovery at 15 min post-exercise revealed a significant difference (t-test, p<0.05) between

size classes (mean values for small and large fibers were 100.94±10.14% and

46.27±8.9% of the resting value after 15 min of recovery, respectively). During the

course of a contraction-recovery cycle ATP content and the sum of AP, Pi, and ATP

remained constant in both large and small fibers, as expected (Fig. 3).

The absolute value of glycogen at rest can be found in Table 3. The relative

glycogen values during a contraction-recovery cycle in both size classes are illustrated in

Fig. 4. The values at each time point have been normalized to the mean resting values to

allow a direct comparison of post-contractile glycogen changes in small and large

animals. In the large size class there was no significant depletion for up to 4h after

contraction, although there was a transient, non-significant, decrease in glycogen

55

15 10 5 0 -5 -10 -15 -20 -2515 10 5 0 -5 -10 -15 -20 -25

Figure 2. Representative 31P-NMR spectra collected from perchloric acid extracts of large dark levator muscle fibers that demonstrate the changes in relative concentrations of AP and Pi during a contraction-recovery cycle. Spectra were collected from crabs at rest, and after 0, 30 and 60 min of recovery from burst exercise. The same pattern of recovery is observed in the small dark fibers, however, complete AP resynthesis occurs in only 15

in. Chemical shifts are in units of parts per million. m

56

-10 0 10 20 30 40 50 60 70

Rel

ativ

e A

P (µ

mol

·g-1

)

-10-505

1015202530

Large FiberSmall Fiber

Time (min)

-10 0 10 20 30 40 50 60 70

Rel

ativ

e P i (

µmol

·g-1

)

-30-25-20-15-10-505

10

Large FiberSmall Fiber

-10 0 10 20 30 40 50 60 70

ATP

(µm

ol·g

-1)

02468

101214

Large FiberSmall Fiber

Time (min)

-10 0 10 20 30 40 50 60 70

AP

+ P i +

ATP

(µm

ol·g

-1)

20

40

60

80

Large FiberSmall Fiber

‡

‡

** *

*

*

*A

C D

B

Figure 3. Relative changes in AP (A) and Pi (B) content and absolute changes in ATP (C) and AP+ Pi+ATP (D) content in small (open symbols) and large (filled symbols) dark levator fibers during a contraction-recovery cycle. In (A) and (B), values at each time point have been normalized to the mean immediately after contraction to allow direct comparison of the recovery rate between the size classes (absolute resting values are in Table 3). Note how quickly AP and Pi levels are restored in the small fibers compared to the large fibers during recovery, as well as the relative stability in ATP and total high-energy phosphate content during contraction and recovery in both size classes. The arrow indicates when burst-contractile exercise was stimulated, the * indicates where values are significantly different from the resting value, and the ‡ indicates that AP levels in each size class were significantly different from each other at the common 15 min recovery time point. N ≥ 7 for every point.

57

Table 3. Absolute resting values of AP, Pi, ATP, and glycogen in small and large dark levator fibers.

Resting Values Small fiber Large fiber Metabolite Content (μmol g-1) Content (μmol g-1) AP 18.3±2.3 29.9±3.1 Pi 16.5±1.8 13.3±1.4 ATP 7.2±0.8 7.3±1.1 Glycogen 33.1±4.0 69.9±9.4

58

Figure 4. Relative changes in glycogen content in small (open symbols) and large (filled symbols) dark levator fibers during a contraction-recovery cycle. Values at each time point have been normalized to the mean resting value to allow direct comparison between the size classes (absolute resting values are in Table 3). The arrow indicates when burst-contractile exercise was stimulated. The * indicates where values are significantly different from the resting value. N ≥ 10 for every point.

59

immediately after exercise (F=0.7611, d.f=5 , p=0.5818). In the small size class,

however, there was a significant depletion of glycogen during recovery (F=6.38, d.f=5,

P=0.0001). Glycogen values at 60, 120, and 240 min after exercise were significantly

lower than values in animals at rest or immediately post-exercise.

Reaction-diffusion Analysis of Contraction and Recovery

The modeled rate of mitochondrial ATP production was adjusted to approximate

our measured AP recovery curve, thereby allowing us test whether the aerobic synthesis

of AP was limited by metabolite diffusion in the dark levator fibers. Here, the model

results were volume-averaged to allow a direct comparison of the observed and simulated

recovery rates. Figure 5 shows that the model and measured data for both size classes are

in close agreement, thus permitting us to draw conclusions about diffusion limitation in

the aerobic fibers. The spatially and temporally resolved concentrations of high-energy

phosphate molecules during a contraction-recovery cycle are also presented in Figure 5.

As expected, neither fiber exhibited intracellular concentration gradients, indicating that

diffusive flux is fast relative to the rate of ATP turnover.

While the contraction-recovery protocol used here is experimentally tractable, the

primary function of the dark fibers is to power sustained, steady-state contraction.

However, this is a condition we cannot replicate experimentally, so we used the model to

simulate steady-state contraction. Figure 6 shows the effect of incremental increases in

the rate of the mitochondrial boundary reaction and the myosin ATPase (i.e., turnover) on

[AP] and [ATP] during steady-state contraction. The initial simulation (Fig. 6A,B), in

which AP is depleted by roughly 50% during contraction, is a realistic depiction of a

60

Figure 5. Measured AP recovery (symbols) compared to the volume averaged model of AP recovery (solid line) in small (A) and large (B) dark fibers. In the model, the myosin ATPase was activated long enough to cause a decrease in AP that was comparable to the measured data. The dotted line indicates the resting concentration. Three dimensional graphs show the temporally- and spatially-resolved concentrations of AP for small (C) and large (D) dark levator fibers during a contraction-recovery cycle. This model output was generated using parameters in Table 2. Note the absence of concentration gradients.

61

Figure 6. The effect of increasing the rate of mitochondrial ATP production and myosin ATPase activity during steady-state contraction in small fibers on the temporal and spatial profiles of AP (left panels) and ATP (right panels). Metabolite concentrations during a typical steady-state contraction, where Vmmito= 1.00 x 10-14 mmol μm-2 s-1 and Vmmyo= 1 mmol l-1 s-1 (A and B), during steady-state with a 3-fold increase in Vmmito and Vmmyo (C and D), and during steady-state with a 7-fold increase in Vmmito and Vmmyo (E and F).

62

steady-state contraction in skeletal muscle (Meyer, 1988) and both the boundary reaction

and myosin ATPase values used in this simulation are reasonable estimates (Vicini and

Kushmerick, 2000). There are obvious AP gradients across the cell, indicating that at the

high rate of ATP turnover characteristic of steady-state contraction, diffusion is limiting.

As the mitochondrial boundary reaction and myosin ATPase activity are increased to

simulate higher intensity swimming, a much greater AP depletion is observed, which

reduces the cell’s ability to buffer [ATP], leading to substantial intracellular ATP

gradients (Fig. 6C-F). While aerobic dark fibers may not be limited by diffusive flux

during recovery from burst-contraction, it appears that they are limited during sustained

steady-state exercise.

DISCUSSION

The principal findings of the present study were (1) that the rate of AP recovery

following exercise in the aerobic dark fibers was dependant on body mass, with

differences somewhat greater than that expected from normal metabolic scaling, (2) that

intracellular diffusive flux does not appear to limit aerobic AP recovery after burst-

contraction, but it does appear to limit aerobic flux during steady-state contraction, and

(3) that there was no significant glycogen depletion during post-contractile recovery in

the large fibers, which is consistent with our hypothesis that intracellular subdivisions

alleviate the need for anaerobic contributions during recovery.

Post-contractile AP resynthesis in anaerobic light fibers from both juvenile and

adult blue crabs has been shown to occur in about 60 min, despite large differences in

63

body mass and fiber size (Kinsey et al., 2005). This size independence appears to result

from anaerobic contributions to recovery in large fibers (Johnson et al., 2004). Post-

contractile AP resynthesis in the aerobic fibers, however, should be much faster owing to

a nearly 10-fold greater mitochondrial content and a 2-fold greater citrate synthase

activity than light fibers (Boyle et al., 2003; Johnson et al., 2004). This is supported by

our observation that AP recovery in the small dark fibers was complete 15 min after

exercise, a rate of recovery roughly four times faster than found in the light fibers.

However, the dark fibers of adults recovered at the same rate as previously observed for

the light fibers. Further, the relatively fast AP recovery rate in the small dark fibers was

still several fold lower than typical recovery rates in mammalian skeletal muscle with a

similar mitochondrial content (e.g. Meyer, 1988; Vicini and Kushmerick, 2000; Hancock

et al., 2005). Thus, the AP recovery rate appears to be influenced by both size-dependent

and size-independent factors.

In the large dark fibers, intracellular subdivisions serve to create metabolic

functional units with the same small diameter as the juvenile fibers, thereby permitting

sustained aerobic contraction. Additionally, mitochondria represent the same total

fractional volume (23-25%) in both small and large dark fiber subdivisions (Johnson et

al., 2004). Thus, we expected to see a rapid AP recovery in the dark fibers from both size

classes, with differences between size classes attributable to body mass specific

metabolic scaling. The mass-specific scaling exponent (b) for CS activity in blue crab

aerobic fibers is relatively small (b= -0.19) (Johnson et al., 2004), whereas in many

mammalian systems measurements of basal rates of O2 consumption typically yield b

values near -0.25 (Brody, 1945), although b may be as high as -0.33 (White and

64

Seymour, 2003). Using this range of scaling exponents we calculated that small dark

fibers should recover 2 to 4 times faster than large dark fibers due to scaling alone. In the

present study, AP recovery in the adults took around 60 min, which is roughly 4 times

longer than in juveniles. While the observed size-dependence of AP recovery lies at the

upper range of that expected from mass-specific metabolic scaling, the low scaling

exponents for CS activity and mitochondrial density in blue crab fibers suggests that

scaling does not fully account for the difference in the rate of AP recovery between

juvenile and adult crabs.

What then can account for residual differences between size classes, and why do

the aerobic fibers recover more slowly than expected? The resynthesis of phosphagens

following contraction is a proton producing process. It has been shown in vertebrate

systems that changes in intracellular pH (pHi) are responsible for altering the creatine

kinase (CK) equilibrium constant and hence, the phosphocreatine (PCr) recovery rate

(Sahlin et al., 1975; Harris et al., 1976; Meyer et al. 1986; van den Thillart et al., 1993;

McMahon and Jenkins, 2002). Similarly, experimental reductions in pHi in invertebrate

muscle lead to a reduction in AP concentration (Combs and Ellington, 1995).

Considering that our exercise protocol leads to substantial lactate production in all size

classes (Johnson et al., 2004), and since pH recovers with a time course similar to AP in

blue crab dark muscle (Milligan et al., 1989), it is possible that a reduced pHi in the dark

fibers induces a transient shift in the AK equilibrium constant and slows the rate of AP

recovery in both small and large fibers. However, it is unlikely that cellular acidosis can

explain the differences in the rate of AP recovery between the small and large fibers,

since in adult animals the dark levator pHi recovers to resting levels much faster than

65

extracellular pH or lactate concentration, despite the fact that anaerobic metabolism

continues after contraction (Milligan et al., 1989). On the other hand, the processing of

accumulated lactate may contribute to the differences between size classes. There is

evidence that gluconeogenesis occurs in swimming muscle of blue crabs, and since there

is no known designated site for lactate processing in crustaceans comparable to the

mammalian liver, there is no Cori cycle (Milligan et al., 1989; Lallier and Walsh, 1991;

Henry et al., 1994). Thus, lactate diffusing into the dark fibers of adult crabs may be used

as a substrate for gluconeogenesis. Since gluconeogenesis and glycolysis are reciprocally

controlled, aerobic AP recovery may be slowed in the large fibers because they are

supplied with lactate, while the small fibers are not.

An unexpected finding of Johnson et al. (2004) was that there was significant

post-contractile lactate accumulation in the dark fibers of the adult crabs, since it was

assumed that their subdivisions alleviate the need for anaerobic contributions during

recovery. They reasoned that this accumulation was likely a consequence of the dark

fiber’s close proximity to lactate producing light fibers and net diffusive flux into the

dark fibers from the lactate-laden hemolymph, and not a result of post-contractile

anaerobic glycogenolysis occurring within the dark fibers. This supposition is supported

by our observation that large dark fibers have no significant post-contractile glycogen

depletion (Fig. 4). This is in contrast to large light fibers, which produce copious lactate

and significantly deplete glycogen post-contraction (Boyle et al., 2003; Johnson et al.,

2004).

Though the large fibers did not exhibit any significant post-contractile glycogen

depletion, we did observe a sharp, yet non-significant decrease in glycogen immediately

66

after exercise. This depletion may result from anaerobic glycogenolysis, which

increasingly powers burst contractions in these fibers as AP is depleted, although a

similar contraction induced decrease was not observed in small fibers despite producing

an identical amount of lactate. This same pattern of post-contractile glycogen depletion

was observed by Henry et al. (1994) in adult blue crab dark fibers following vigorous

exercise, indicating that this may be a typical response to burst-contractile activity. While

we did not observe any significant post-contractile glycogen depletion in the large fibers

as expected, we did see an unexpected depletion of glycogen during recovery in the small

fibers. Boyle et al. (2003), who measured post-contractile glycogen dynamics in blue

crab light fibers, reported no significant glycogen depletion during recovery in the

juveniles. However, immediately after exercise and before sacrifice the animals in their

study were fed, potentially restoring depleted glycogen pools during the several hours of

recovery. In our study, animals were not provided with a food source during recovery.

We speculate that with no glycogen storing organ (van Aardt, 1988; Lallier and Walsh,

1991; Henry et al., 1994), as in the mammalian liver, and with no new source of glucose

from a food supply, glycogen pools diminished by aerobic glycogenolysis during

recovery could not be replenished to resting levels.

Kinsey et al. (2005) used the same mathematical reaction-diffusion model used in

the present study to investigate whether diffusion was limiting to AP recovery in the blue

crab anaerobic light muscle; a fiber with extreme proportions, but a relatively low aerobic

capacity (and hence low rate of ATP production). They found only small intracellular

concentration gradients of high-energy phosphates during simulations of AP recovery.

However, gradients became more substantial as the mitochondrial reaction rate was

67

increased, which illustrated the interaction between diffusion limitation and ATP

turnover rates. While intracellular diffusive flux does not appear to exert substantial

control over AP recovery in the blue crab giant light fibers, there may be other cell types

where diffusion is limiting. These are likely to include systems with a relatively high rate

of ATP production/consumption such as the blue crab dark fibers, which have a 10-fold

higher mitochondrial density than the light fibers. However, our reaction-diffusion

analysis revealed no intracellular concentration gradients of high-energy phosphates

during a burst-contraction recovery cycle at the rates of AP recovery determined for the

dark fibers (Fig. 5). This is not surprising considering that AP recovery rates in dark

fibers were similar to those found previously for light fibers (Kinsey et al., 2005),

although it is likely that a less intense exercise protocol may have allowed higher

recovery rates in dark fibers by reducing lactate production (see above). In fact, in prior

simulations where the mitochondrial rate was increased to yield AP recovery rates that

were comparable to that observed in aerobic mammalian muscle, substantial gradients

were observed (Kinsey et al., 2005). Nevertheless, even the fast rate of recovery that was

observed in the dark fibers of the small animals was too slow to be limited by

intracellular metabolite diffusion, which is consistent with the analysis of light fibers by

Kinsey et al. (2005).

Although post-contractile AP recovery in the dark fibers does not appear to be

limited by diffusion, these aerobic fibers normally power steady-state contraction during

sustained swimming. Under these conditions, ATP turnover rates are much higher than

they are during post-contractile recovery. Using a myosin ATPase rate that was 25% of

that used for burst-contraction and a Vmmito that is comparable to that of prior studies (see

68

Vicini and Kushmerick, 2000), we observed substantial concentration gradients in AP

and ATP, as well as other metabolites, during simulated steady-state contraction. As

expected, the gradients became more substantial as the ATP turnover rate was increased

(Fig. 6). The ATP buffering role of AK is apparent since at relatively low rates of

demand ATP gradients are minimal, but as AP is depleted ATP gradients become severe.

Thus, it appears that AP recovery in blue crab dark fibers is not limited by diffusion at the

low rates of ATP turnover that seem to characterize our burst-contraction recovery

protocol, but despite the short intracellular diffusion distances due to fiber subdivisions,

the high rates of ATP turnover observed during steady-state contraction result in

substantial metabolite gradients.

In summary, the patterns of recovery that have been observed in blue crab

locomotor muscles previously (Boyle et al., 2003; Johnson et al., 2004; Kinsey et al,

2005) and herein suggest that there are effects of fiber size on aerobic metabolism.

Although the aerobic dark fibers are as large as the anaerobic light fibers, the selective

pressure to power aerobic swimming has promoted the evolution of an intricate network

of mitochondria-rich, highly perfused subdivisions. These subdivisions allow the fibers to

retain a small metabolic functional unit while apparently developing a large contractile

functional unit during growth, thereby eliminating the need for anaerobic contributions to

recovery in adult animals. Our reaction-diffusion analysis, in conjunction with observed

AP recovery data, suggests that intracellular diffusion does not limit aerobic recovery in

blue crab levator fibers, as expected. However, the rates of AP recovery in the dark fibers

were considerably lower than expected, considering the high mitochondrial density of

these fibers, and this was likely due to metabolic inhibition. During simulated steady-

69

state contraction, intracellular metabolite diffusion did limit aerobic metabolism,

suggesting that diffusion may exert substantial control over aerobic flux even in small

fibers if the ATP turnover rate is high.

70

REFERENCES

Beis, I. and Newsholme, E. A. (1975). The contents of adenine nucleotides, phosphagens and some glycolytic intermediates in resting muscles from vertebrates and invertebrates. Biochem. J. 152, 23-32. Bird, R. B., Stewart, W. E. and Lightfoot, E. N. (1960). Transport phenomena. New York: Wiley. Boyle, K. L., Dillaman, R. M. and Kinsey, S. T. (2003). Mitochondrial distribution and glycogen dynamics suggest diffusion constraints in muscle fibers of the blue crab, Callinectes sapidus. J. Exp. Zool. 297A, 1-16. Brody, S. (1945). Bioenergetics and Growth. New York: Reinhold. Combs, C. A. and Ellington, W. R. (1995). Graded intracellular acidosis produces extensive and reversible reductions in the effective free energy change of ATP hydrolysis in a molluscan muscle. J. Comp. Physiol. B. 165, 203-212. deFur, P.L., Pease, A., Siebelink, A. and Elfers, S. (1988). Respiratory responses of blue crabs, Callinectes sapidus, to emersion. Comp. Biochem. Physiol. A. 89A, 97-101. Hancock, C. R., Brault, J. J., Wiseman, R. W., Terjung, R. L. and Meyer, R. A. (2005). 31P-NMR observation of free ADP during fatiguing, repetitive contractions of murine skeletal muscle lacking AK1. Am. J. Physiol. Cell Physiol. 288, C1298-C1304. Harris, R. C., Edwards, R. H. T., Hultman, E., Nordesjö, L. O., Nylind, B. and Sahlin, K. (1976). The time course of phosphorylcreatine resynthesis during recovery of the quadriceps muscle in man. Pfluegers. Arch. 367, 137-142. Henry, R. P., Booth, C. E., Lallier, F. H. and Walsh P. J. (1994). Post-exercise lactate production and metabolism in three species of aquatic and terrestrial decapod crustaceans. J. Exp. Biol. 186, 215-234. Holt, S. M. and Kinsey, S. T. (2002). Osmotic effects on arginine kinase flux in muscle from the blue crab. J. Exp. Biol. 205, 1775-1785. Hubley, M. J., Locke, B. R. and Moerland, T. S. (1997). Reaction-diffusion analysis of effects of temperature on high-energy phosphate dynamics in goldfish skeletal muscle. J. Exp. Biol. 200, 975-988. Johnson, L. K., Dillaman, R. M., Gay, D. M., Blum, J. E. and Kinsey, S. T. (2004). Metabolic influences of fiber size in aerobic and anaerobic muscles of the blue crab, Callinectes sapidus. J. Exp. Biol. 207, 4045-4056.

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Keppler, D. and Decker, K. (1974). Glycogen determination with amyloglucosidase. In Methods of Enzymatic Analysis, vol.3 (ed. H.U. Bergmeyer), pp.1127-1131. New York: Academic Press, Inc.

Kim, S. K., Yu, S. H., Jeong-Hwa, S., Hübner, H. and Buchholz, R. (1998). Calculations on O2 transfer in capsules with animal cells for the determination of maximum capsule size without O2 limitation. Biotech. Letters. 20, 549-552. Kinsey, S. T. and Moerland, T. S. (2002). Metabolite diffusion in giant muscle fibers of the spiny lobster, Panulirus argus. J. Exp. Biol. 205, 3377-3386. Kinsey, S. T., Penke, B., Locke, B. R. and Moerland, T. S. (1999). Diffusional anisotropy is induced by subcellular barriers in skeletal muscle. NMR Biomed. 11, 1-7. Kinsey, S. T., Pathi, P., Hardy, K. M., Jordan, A. and Locke, B. R. (2005). Does metabolite diffusion limit post-contractile recovery in burst locomotor muscle? J. Exp. Biol. 208, 2641-2652. Kushmerick, M. J., Meyer, R. A. and Brown, T. R. (1992). Regulation of oxygen consumption in fast- and slow-twitch muscle. Am. J. Physiol. 263, C598-C606. Lallier, F. H. and Walsh, P. J. (1991). Metabolic potential in tissues of the blue crab, Callinectes sapidus. Bull. Mar. Sci. 48, 665-669. Mainwood, G. W. and Raukusan, K. (1982). A model for intracellular energy transport. Can. J. Physiol. Pharmacol. 60, 98-102. Meyer, R. A. (1988). A linear model of muscle respiration explains monoexponential phosphocreatine changes. Am. J. Physiol. 254, C548-C553.

Meyer, R. A., Brown, T. R., Krilowicz, B. L. and Kushmerick, M. J. (1986). Phosphagen and intracellular pH changes during contraction of creatine-depleted rat muscle. Am. J. Physiol. 250, C264-C274. McMahon, S. and Jenkins, D. (2002). Factors affecting the rate of phosphocreatine resynthesis following intense exercise. Sports Med. 32(12), 761-784. Milligan C. L., Walsh P. J., Booth C. E. and McDonald D. L. (1989). Intracellular acid-base regulation during recovery from locomotor activity in the blue crab, Callinectes sapidus. Physiol. Zool. 62, 621-638.

Roer, R. and Dillaman, R. (1984). The structure and calcification of the crustacean cuticle. Amer. Zool. 24, 893-909. Sahlin, K., Harris, R. C. and Hultman, E. (1975).Creatine kinase equilibrium and

72

lactate content compared with muscle pH in tissue samples obtained after isometric exercise. Biochem. 152, 173-180. Schmidt-Nielsen, K. (1984). Scaling: Why is animal size so important? New York: Cambridge University Press.

Smith, E. and Morrison, J. F. (1969). Kinetic studies on the arginine kinase reaction. J. Biol. Chem. 244(15), 4224-4234.

Teague, W. E. and Dobson, G. P. (1999). Thermodynamics of the arginine kinase reaction. J. Biol. Chem. 274(32), 22459-22463.

Tse, F. W., Govind, C. K. and Atwood, H. L. (1983). Diverse fiber composition of swimming muscles in the blue crab, Callinectes sapidus. Can. J. Zool. 61, 52-59. van Aardt, W. J. (1988). Lactate metabolism and glucose patterns in the river crab, Potamonautes warreni Calman, during anoxia and subsequent recovery. Comp. Biochem. Physiol. 91A, 299-304. van den Thillart, G. and Waarde, A. V. (1993). The role of metabolic acidosis in the buffering of ATP by phosphagen stores in fish: an in vivo NMR study. In Surviving Hypoxia: Mechanisms of Control and Adaptation. (ed. P.W. Hochachka, P.L. Lutz, T. Sick, M. Rosenthal and G. van den Thillart), pp. 237-252. Orlando: CRC. Vicini, P. and Kushmerick, M. (2000). Cellular energetics analysis by a mathematical model of energy balance: estimation of parameters in human skeletal muscle. Am. J. Physiol. Cell Physiol. 279, C213-C224. White, C. R. and Seymour, R. S. (2003). Mammalian basal metabolic rate is proportional to body mass. Proc. Natl. Acad. Sci. 100, 4046-4049.

73

CHAPTER 3

A SKELETAL MUSCLE MODEL OF EXTREME HYPERTROPHIC GROWTH

REVEALS THE INFLUENCE OF DIFFUSION ON CELLULAR DESIGN

Prepared in the style of the American Journal of Physiology

ABSTRACT

Muscle fibers that power swimming in the blue crab, Callinectes sapidus, are <80μm in

diameter in juveniles, but grow hypertrophically, exceeding 600μm in adults. Therefore,

intracellular diffusion distances become progressively greater as the animals grow, and in

adults vastly exceed those seen in most cells. This developmental trajectory makes C.

sapidus an excellent model for characterizing the influence of diffusion on fiber structure.

The light fibers, which power burst-swimming, undergo a prominent shift in organelle

distribution with growth. Mitochondria, which require oxygen and rely on the transport of

small, rapidly diffusing metabolites, are evenly distributed throughout the small fibers of

juveniles, but in the large fibers of adults are located almost exclusively at the fiber

periphery where oxygen concentrations are high. Nuclei, which do not require oxygen but

rely on the transport of large, slow-moving macromolecules, have the inverse pattern;

they are distributed peripherally in small fibers, but are evenly distributed across the large

fibers, thereby reducing diffusion path lengths for large macromolecules. The dark fibers,

which power endurance swimming, have evolved an intricate network of

cytoplasmically-isolated, highly-perfused subdivisions that create the short diffusion

distances needed to meet the high aerobic ATP turnover demands of sustained

contraction. However, fiber innervation patterns are the same in both the dark and light

fibers. Thus, the dark fibers appear to have disparate functional units for metabolism

(fiber subdivision) and contraction (entire fiber). Reaction-diffusion mathematical models

demonstrate that diffusion would greatly constrain the rate of metabolic processes

without these developmental changes in fiber structure.

75

INTRODUCTION

Cellular metabolism is carried out through a network of reactions with individual

rates that depend on the relationship between catalytic capacity and molecular diffusion

(70). Across the animal kingdom intracellular reaction rates and diffusion distances vary

over several orders of magnitude, and diffusion would be expected to play a more critical

role as either of these properties increase (34,41,42,71). In muscle cells growth often

occurs hypertrophically (increase in fiber size rather than fiber number) and diffusive flux

may progressively exert more control as intracellular diffusion path lengths increase and

fiber surface area:volume (SAV) decreases with growth. For example, increasing fiber

size may compromise aerobic metabolism by reducing O2 flux to the mitochondria and

increasing diffusion distances for small metabolites (e.g., ADP, ATP and phosphagens).

It may be expected that during fiber growth the cellular distribution of mitochondria is

governed by the need for both sufficiently short diffusive path lengths between the blood

and the mitochondria and between adjacent mitochondria (6,14,26,32). Similarly, fiber

hypertrophy may impede net protein synthesis and turnover since these processes rely on

diffusive transport of large, slow-moving macromolecules (e.g., tRNA, mRNA, rRNA,

nuclear proteins and ribosomal subunits; 22,60). Thus, diffusion may play a major role in

shaping the evolution of basic cellular design and function.

Since the influence of diffusion on aerobic processes becomes greater as reaction

fluxes increase (24,34,47,71), diverse muscle fiber types may be impacted differently

based on their metabolic demands and ATP turnover rates. For instance, burst locomotor

fibers power contraction anaerobically and maximal aerobic metabolic rates are important

76

only during post-contractile recovery, which is often associated with relatively low ATP

demand (16,40). In contrast, aerobic fibers rely on mitochondrial ATP production to

support the high rates of ATP turnover associated with sustained contractile activity

(15,39). Anaerobic fibers may therefore tolerate comparatively long intracellular

diffusion distances (38), which is consistent with the observation that anaerobic fibers

tend to be larger than aerobic fibers. This argument is supported by reaction-diffusion

model analyses of experimental data, which indicated that the low rate of post-contractile

phosphocreatine (PCr) or arginine phosphate (AP) recovery in large anaerobic fibers is

not substantially limited by diffusion, despite the presence of extremely large diffusion

distances (29,38,49). However, intracellular ATP and AP concentration gradients

(indicative of diffusion limitation) were present in aerobic fibers at the high rates of ATP

turnover characteristic of steady-state contraction (24).

To understand how diffusion influences cellular design, we have examined two

metabolically distinct muscle fiber types (anaerobic light fibers and aerobic dark fibers)

that undergo extreme hypertrophic growth in the blue crab, Callinectes sapidus. Since the

effects of diffusion should be more pronounced in fibers that undergo large changes in

cellular dimensions, this model system enables us to reveal influences of diffusion likely

present in many muscle fibers, but not easily observed. The use of reaction-diffusion

mathematical models and previously measured rates of ATP turnover allowed us to

evaluate the functional role that developmental changes in cell structure have in

moderating the diffusion constraints imposed by hypertrophic fiber growth.

77

MATERIALS AND METHODS

Animals

Juvenile blue crabs (Callinectes sapidus, Rathbun) were collected by sweep netting in the

Intracoastal Waterway behind Wrightsville Beach, NC, USA, while adult crabs were purchased

from commercial fisherman. Animals were maintained in full-strength, filtered seawater (35‰

salinity, 21°C) in aerated, recirculating aquariums and fed shrimp three times weekly. Carapace

width and body mass were measured prior to use in all experiments. Only animals in the

intermolt stage were used as determined by the rigidity of the carapace, the presence of the

membranous layer of the carapace, and the absence of a soft cuticle layer developing beneath the

existing exoskeleton (56).

Exercise Protocol

Crabs were induced to undergo a burst swimming response as described previously

(6,24,30,38). Briefly, crabs were held suspended in the air by a clamp in a manner that allowed

free motion of the swimming legs and small wire electrodes were placed in two small holes

drilled into the mesobranchial region of the dorsal carapace. A Grass Instruments SD9

physiological stimulator (Astro Med, Inc., West Warwick, RI, USA) was used to deliver a small

voltage (80 Hz, 200 ms duration, 10 V/cm between electrodes) to the thoracic ring ganglia,

which elicited a burst swimming response in the 5th pereiopods for several seconds following the

stimulation. A single stimulation train was administered every 20-30 s until the animal was no

longer capable of a burst response, which became evident when it responded by moving its legs

at a notably slower rate.

78

Dissection

Crabs were rapidly cut in half along the sagittal plane and the dorsal carapace, heart,

reproductive and digestive organs were removed from each section. The gills and other

supporting architecture were cut off to expose the basal cavity, which houses the levator muscles

of the 5th periopods (swimming legs).

Perfusion

To illustrate hemolymph perfusion of the large dark and light fibers, five adult blue crabs

injected with 125 μg of Alexa Fluor 594-labeled wheat germ agglutinin (WGA; Molecular

Probes) in filtered sea water (FSW) were induced to undergo a burst exercise bout as described

above, and then rested in FSW for 10 min. They were subsequently injected with 50 μL of a

suspension of 0.2 μm diameter carboxylated fluorescent FluoSpheres (Molecular Probes) in 200

μL of FSW and exercised again. After 10 min of rest in FSW, animals were sacrificed and

individual basal levator swimming muscle fibers were mechanically isolated and removed. Both

anaerobic (light) fibers that are used for burst swimming and aerobic (dark) fibers that are used

to power sustained swimming were examined (68). All image stacks and three-dimensional (3D)

reconstructions of the fibers were generated using an Olympus FluoView 1000 laser scanning

confocal microscope.

WGA is a lectin that binds to sialic acid and N-acetylglucosaminyl residues found on the

basement membrane of the fiber sarcolemma and the blood vessel endothelium (72). Fluorescent

microspheres, which behave as a solution at the relatively small size of 0.2 μm, completely fill

vessel spaces and lodge within the smallest microvasculature where they will remain throughout

79

histological sectioning (65). The cardiovascular system of C. sapidus differs from vertebrate

systems in that it is loosely defined as “partially closed”, rather than completely open (45). It has

a system of arteries that branch into arterioles and ultimately form capillary-like structures.

However, only a few of these small vessels form complete capillary beds; most have blind

endings through which hemolymph empties into sinuses that bathe organs. When injected into

the circulatory system of a blue crab, WGA percolates through the muscle tissue labeling the

sarcolemma of individual fibers (or subdivisions) thereby revealing regions that are in contact

with hemolymph, while the microbeads remain within the smallest perfused extra- or

intracellular spaces.

Histology

To describe the ontogenetic changes in mitochondrial and nuclear distribution in

light and dark fibers, fixed muscle fiber cross-sections from juvenile and adult animals

were labeled with the red-fluorescent mitochondrial probe MitoTracker Deep-Red 633

(Molecular Probes) and the blue-fluorescent nuclear probe DAPI (Molecular Probes).

Adult (N=5) and juvenile (N=5) animals were injected with approximately 0.1 mg of

Alexa Fluor 488 WGA to delineate fiber boundaries. Animals were exercised, allowed to

rest for 10 min in FSW and sacrificed. Dark and light levator muscles were removed,

fixed for 4-8 hrs in 4% paraformaldehyde in FSW, rinsed overnight in 25% sucrose, then

flash frozen in liquid nitrogen. Frozen sections were cut at 20 μm with a Leica Cryocut

1800. Sections were incubated for 10 min in 20 nM MitoTracker Deep-Red 633, rinsed in

PBS, incubated for 30 min in DAPI and then rinsed again for 3 min in PBS. Imaging and

80

3D reconstruction were performed with an Olympus FluoView 1000 confocal

microscope.

Fluorescence Recovery after Photobleaching (FRAP)

FRAP experiments were used to measure intracellular diffusion for the purposes

of characterizing cytoplasmic connectedness within the fibers. Isolated light and dark

fiber bundles from adult animals (N=4) were arranged lengthwise across a rectangular

Vaseline well formed on a slide. Fibers were maintained at resting length, and anchored

beyond the edges of the well. Fibers in the well were incubated for 1h with 100 μM

Calcein AM (Molecular Probes) in FSW. Calcein, a membrane permeable probe, is

colorless and non-fluorescent until inside of a cell where endogenous esterases hydrolyze

the calcein rendering it fluorescent and negatively charged (thus, membrane

impermeable). The Vaseline well was covered with a coverslip while taking care to avoid

flattening the fibers. FRAP measurements were then immediately performed with an

Olympus FluoView 1000 confocal microscope.

Prior to running each FRAP experiment, 3D reconstructions were collected to

ensure adequate dye distribution and homogeneity throughout the fiber. Based on these

images, a uniformly fluorescent optical slice of muscle, at least 30 μm from the fiber

surface, was chosen for each experiment. Diffusion coefficients were measured in both

the longitudinal (D║) and radial (D⊥) directions from each light and dark fiber examined

(n=4 per fiber type). The slide was rotated 90º when switching from a longitudinal to a

radial measurement to assure that the time required to bleach the fiber was the same in

both directions. The 488 nm laser was used at 1% intensity to take pre-bleach and post-

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bleach images of a 206 X 176 pixel (501 X 427 μm) region of the fiber. Five pre-bleach

images, which provided average baseline fluorescence intensity, and 120 post-bleach

images, which were sufficient to chart complete recovery of the bleach region, were

collected at 1.2 s intervals at a resolution of 10 μs/pixel. The laser was used at 100%

intensity to bleach a 150 X 5 pixel (360 X 12 μm) rectangular region of interest (ROI).

The bleached ROI was substantially longer than wide to ensure that recovery was only

due to the diffusion of calcein in the direction of interest (i.e. longitudinally or radially).

The bleached ROI was scanned ten times at a rate of 200 μs/pixel to ensure proper

bleaching (25 to 50% of pre-bleach intensity) and images were collected at 1.2 s

intervals.

Post-bleach fluorescence images were aligned and Olympus FluoView v. 1.6a

software was used to extract a one-dimensional fluorescence intensity profile for a one

pixel wide line perpendicular to the bleached ROI whose ends reached sufficiently far

outside the ROI as to incorporate a non-bleached intensity baseline. This line series data

describing the change in the bleaching profile over time was analyzed based on the

approach described by Mullineaux et al. (48) in which the one-dimensional diffusion

equation is:

2F

FF

xCD

tC

∂∂

=∂∂ (1)

where CF is the fluorophore concentration, t is time, x is distance and DF is the diffusion

coefficient of the fluorophore. Post-bleach intensity values for all points along the line

were subtracted from their corresponding average pre-bleach intensity values yielding a

one-dimensional bleaching profile to which a Gaussian curve was fit (assuming the

bleach profile to be normal and the width of the bleach to be very narrow compared to the

82

length of the fiber). JMP v. 4.0.4 (SAS institute Inc.; Cary, NC, USA) was used to

perform an iterative curve-fitting procedure in which the fluorescence intensity was

estimated as a function of the linear position across the ROI, using the standard deviation

and mean as floating variables. The fitted Gaussian curve was used to determine bleach

depth, C, and the laser beam half-width, Ro, at an intensity of 1/e2. To calculate diffusion

coefficients, (C0/Ct)2 was plotted against time, t, where C0 is the bleach depth at time 0

(immediately post-bleach) and Ct is the bleach depth at time t. This yields a linear plot

with a slope equal to 8DF/R02 (48).

Immunohistochemistry

To describe the pattern of neuromuscular innervation in the dark and light fibers

immunohistochemistry was performed using an antibody to synapsin, a pre-synaptic vesicle

associated phosphoprotein, using methods modified from Buchner et al. (11).

The levator swimming muscle group was removed from four adults, fixed for 4-8 hrs in 4%

paraformaldehyde in FSW, rinsed overnight in 25% sucrose, then flash-frozen in liquid nitrogen.

Frozen sections 12-15 μm thick were air dried for 15 min and then incubated at room

temperature for 2 h in blocking solution (2% goat serum, 1% bovine serum albumin (BSA), 0.1%

Triton-X, 0.05% Tween 20, 0.05% sodium azide in PBS). They were then incubated overnight at

4ºC in the primary antibody (mouse monoclonal anti-Drosophila SYNORF1; Developmental

Studies Hybridoma Bank) at a dilution of 1:5 (7.4 μg/ml) in PBS containing 1% BSA and 0.05%

sodium azide. After three rinses in PBS containing 0.1% Triton-X, sections were incubated for 1

h at 37ºC in the secondary antibody (AlexaFluor 488-labeled goat anti-mouse; Molecular Probes)

at a concentration of 10 μg/ml in PBS containing 0.05% sodium azide followed by three PBS

83

washes. Controls included primary antibody, secondary antibody, or both being replaced with

PBS. All image stacks and 3D reconstructions were collected with an Olympus FV1000 confocal

microscope using the appropriate lasers and filters for the particular fluorochromes.

Transmission Electron Microscopy

Mitochondrial fractional volume was calculated from electron micrographs of adult

(N=3) and juvenile (N=3) light fibers collected using standard transmission electron microscopy

techniques. Isolated light fiber bundles were placed at resting length in a primary fixative

consisting of 1% glutaraldehyde and 4% paraformaldehyde in 0.063 M Sörenson’s phosphate

buffer, pH 7.38 (18, 53). The osmolarity of the fixative and all corresponding buffer rinses was

adjusted by the addition of 10% sucrose and a trace amount of CaCl2 to prevent changes in cell

volume. Tissues were held in primary fixative for a minimum of 24 h at room temperature and

then rinsed for 15 min in Sörenson’s phosphate buffer. This process was followed by a secondary

fixation in 1% osmium tetraoxide in Sörenson’s phosphate buffer for 2-3 h. Samples were then

dehydrated with an ascending series (50%, 70%, 95%, 100%, 100%) of acetone and embedded in

Spurr’s epoxy resin (66; Electron Microscopy Sciences). Samples were sectioned at 90 nm with

a diamond knife on a Reichert Ultracut E and collected using a systematic random sampling

method (27) to ensure complete representation of the mitochondria throughout the muscle.

Sections were stained with 2% uranyl acetate in 50% ethyl alcohol and Reynolds’ lead citrate

(55) and then examined with a Philips CM-12 TEM operated at 80 kV. One section per grid was

randomly chosen from each of five grids per animal and one micrograph was taken from each of

these sections. Negatives were digitized using a Microtek Scanmaker 4 negative scanner and

processed with Adobe Photoshop version 7.0.

84

A stereological point-counting method was applied to the micrographs to determine the

fractional volume of SS and IM mitochondria (27,49). A point grid was superimposed on each

image, and all points touching extracellular space were subtracted from the total number of

points per micrograph. Points that landed on mitochondria were recorded as either

subsarcolemmal (SS), if the mitochondrion or mitochondrial cluster was between the

sarcolemmal membrane and the myofibrils, or intermyofibrillar (IM), if the mitochondrion was

located among the myofibrils regardless of its proximity to the sarcolemmal membrane. The total

number of SS and IM mitochondria was respectively divided by the total number of points that

fell within intracellular space to determine subsarcolemmal fractional volume (SSFV) and

intermyofibrillar fractional volume (IMFV).

Calculation of Myonuclear Domain and Nuclear Number Volume

Single optical slices of DAPI-labeled 20 μm cross-sections of light fibers from

three adult and five juvenile WGA-injected animals (see above) were collected with the

confocal microscope and nuclei were counted and scored as either SS or IM as described

above for mitochondria. Intracellular SS nuclei were difficult to distinguish from nuclei

in the extracellular space and in adjoining fibers, but differential interference contrast

(DIC) images and nuclear shape helped us to determine if peripherally located nuclei

were truly intracellular. Fiber margins were traced using Adobe Photoshop and resultant

polygons were analyzed with Image Pro Plus (IPP) version 6.1 to calculate fiber cross-

sectional area (CSA), circumference and mean diameter, as well as nuclear CSA and

diameter (from fiber cross-sections) and nuclear lengths (from longitudinal sections). The

85

number of nuclei per millimeter of fiber (X) was calculated as described in Schmalbruch

and Hellhammer (61), using the equation:

X=(NL)/(d+l) (2)

where N is the number of myonuclei in a fiber cross-section, L is the desired length of segment

(i.e. 1 mm), d is the thickness of the section and l is the mean length of a muscle nucleus. “L”

was set at 1000 μm, “d” was the optical thickness of each image (0.9-8.5 μm) and “l” was 13.0

μm and 16.8 μm for juveniles and adults, respectively. From this X value, we calculated the

myonuclear domain (i.e., the volume of cytoplasm per myonucleus; Y) using the equation from

Rosser et al. (58):

Y=(CL)/X (3)

where C is the cross-sectional area of the muscle fiber, L is the length of the fiber segment and X

is the number of myonuclei per millimeter of fiber determined from equation (2). To estimate

number volume (number of nuclei per volume of fiber), we calculated the inverse of the

myonuclear domain, Y, for SS and IM nuclei respectively. Both nuclear and mitochondrial

stereological data were analyzed using student’s t-tests.

Reaction-Diffusion Mathematical Model

Reaction-diffusion models were developed to evaluate the influence of

developmental changes in muscle structure on muscle metabolic function. The

mathematical model used to evaluate aerobic metabolism was developed from that

described in Jimenez et al. (29) and extended for the system shown in Figure 1 where

oxygen is supplied at a fixed concentration, C0, and diffuses through a membrane with a

fixed resistance, 1/kmt, and it includes mitochondrial reactions at the fiber boundary as

86

Figure 1. Schematic of the reaction-diffusion mathematical model showing a one- dimensional spatial domain where the position in the cell, x, ranges from x=0 (sarcolemma) to x=L (fiber center). Oxygen is supplied at a fixed concentration (7.85 μM) and is transported through a membrane (gray area) with a fixed resistance, 1/kmt. Oxygen supplies both a bulk population of mitochondria uniformly distributed throughout the region from x=0 to x=L and a boundary population of mitochondria clustered at the fiber’s edge, x=0. The myosin ATPase reaction is distributed uniformly through the spatial domain from x=0 to x=L.

87

well as throughout the fiber. Oxygen is consumed by a pseudo homogeneous second

order reaction at the mitochondria with six moles of ADP forming six moles of ATP for

every mole of oxygen by the overall reaction:

O2 + 6ADP 6ATP (4)

There are two populations of mitochondria considered, which allows the influence of

mitochondrial distribution to be examined. One population (IM) is assumed to be

uniformly distributed throughout the region from x=0 to x=L and the rate constant for

this reaction reflects an averaged value accounting for the density of the mitochondria.

The second population of mitochondria (SS) is clustered at the boundary of the cell at

x=0 and the rate constant for this reaction accounts for the density and activity of the

mitochondria at this boundary. The ATP formed by the mitochondria is consumed by a

cellular ATPase by a first order reaction:

ATP ADP + Pi (5)

The ATPase is also assumed to be uniformly distributed through the domain from x=0 to

x=L. The one-dimensional molar species balances for ADP, ATP, and oxygen valid in the

region from x=0 (boundary of cell with hemolymph in the extracellular space) to x=L

(center of cell) are given by:

88

TADPATP

OADPO

O

OADPATPATP

ATP

CCC

CCkdxCd

D

CCkCkdxCdD

=+

=

−=

2

2

2

2

)6/( 22

2

212

2

(6)

where D is the diffusion coefficient, C is the concentration, k1 is the rate constant

governing the ATPase reaction, and k2 is the rate constant for ATP production at the

mitochondria. The boundary conditions for these equations are:

( )

Lxdx

dCD

xCCkCCkdx

dCD

Lxdx

dCD

xCCkdx

dCD

OO

OADPwOmtO

O

ATPATP

OADPwATP

ATP

==−

=−−=−

==−

==−

0

06/)(

0

0

2

2

22

2

2

2

20

2

(7)

where k2w is the rate constant for ATP production at the fiber boundary and kmt is the

mass transfer coefficient for transport of oxygen from the hemolymph through the cell

membrane. The first boundary condition reflects the fact that ATP is formed by the

mitochondria at the boundary and the second reflects symmetry about the center of the

cell. The third boundary condition describes the transport of oxygen across the cell

membrane by diffusion with a linear driving force, where C0 is the concentration of O2 in

the hemolymph, and the consumption of oxygen to form ATP by the mitochondria

clustered at the boundary. This boundary condition can be derived for the case of

interfacial reaction and transport. The last boundary condition indicates that the oxygen

89

distribution is symmetric with respect to the center of the cell. The above system of

equations is solved using MATLAB v. 7.5.0.342 (Mathworks, Inc., Lowell, Ma) to

determine the spatially dependent concentrations and to determine the flux at the

boundary, x=0, as well as the average concentrations of oxygen and ATP defined by

∫

∫

=

=

L

ATPATP

L

OO

dxCL

C

dxCL

C

0

0

1

122

(8)

The effectiveness factors (η) are determined following the methods discussed in

Locke and Kinsey (41). The effectiveness factor is defined as the rate of the reaction in

the presence of diffusion to the rate of the reaction in the absence of diffusion, and it can

range from 1 (no limitation of reaction flux by diffusion) to 0 (complete limitation of

reaction flux by diffusion). In the absence of diffusion, equations (6) and (7) can be

shown to give

( )( ) )1(1

1

1222

2111

wowowo

wowowo

CCCCCC

−=−Ω−=Ω

(9)

where

90

2

2

2

/

/

//

/)/]/([

)/()/(6

/

02

1

0

0222

22

21

21

222

22

211

Omt

Owo

TATPwo

TR

OATPR

ATPw

ATP

RR

DLk

CCC

CCCCCC

DDDDCLLkk

DLkCD

=

=

==

=+=

=

=Ω

=Ω

γ

φ

φ

φγ

φφ

(10)

Equation (9) leads to a quadratic equation which can be easily solved for the non-

dimensional ATP and oxygen concentrations in the absence of diffusion, C1wo and C2wo,

respectively. All roots of the quadratic are real, however only one root is within the

physical domain of the problem. The reaction rates in the cases without and with

diffusion, respectively, are determined from

1511 10*60)( woTwo CCkr = (11)

152 10*60)/)0(1(6)/(2 ⎥

⎦

⎤⎢⎣

⎡=−= oO

RRTATP CxC

CDLCDr γ (12)

where the units of k1 are in s-1, those for CT are mmoles/μm3 and the rate is given in

mM/min. In all calculations for this paper the following parameters are fixed

91

DATP = 70 μm2/s

DO2 = 1160 μm2/s

CT = 10-14 mmoles/μm3

kmt = 1100 μm/s

Co = 7.85 μM

The effectiveness factor for mitochondrial function was determined by the ratio of

Equation (12) to Equation (11). The concentration in Equation (12) is determined by the

numerical solution of equations (6) and boundary conditions (7) in MATLAB. The first

set of calculations was determined using Equations (9) to find the concentrations in the

absence of diffusion for various values of k1, k2, and k2w. The resulting rates were

determined by Equation (11). Similar analysis was conducted in the case with diffusion

whereby the numerical solution of Equation (6) was used with Equation (12). Since it

was found that a range of combinations of k1 and k2 can give the same reaction rate,

another set of calculations for the cases in the presence of diffusion was performed to

determine the value of k2 for various fixed values of k1 that would match the

experimentally determined reaction rate. In this set of computations, the value of k1 was

set at fixed values from the smallest value that would satisfy the rate and a root finding

method was used to determine the value of k2 that would give the desired experimental

rate. This procedure led to the maximal possible effectiveness factor that could be

attained for any combination of rate and diffusion distance. The average concentrations

of oxygen and ATP were determined in each of these cases (with fixed rate) using

Equation (8). Since a range of k1 and k2 can satisfy the rate, it is important to note that the

92

average ATP and oxygen concentrations change; i.e., the average ATP concentration

drops with increasing k1.

To characterize the influence of diffusion on nuclear distribution, we evaluated an

existing derivation of η with spherical geometry (19; Equation 12-32) for a range of

diffusion coefficients and reaction rates. Here, we assumed a boundary source of nuclear

products (e.g., RNA and proteins) and a uniform rate constant defining “consumption”

across the myonuclear domain, which varied in distance from 14.5 μm (observed radius

of myonuclear domain) to 300 μm (radius if there were only SS nuclei in a large light

fiber.)

RESULTS AND DISCUSSION

Basal Locomotor Muscle

The blue crab has a number of anatomical modifications that give it an

exceptional capacity for both burst and steady-state swimming (64). Principal among

these are the flattened, oar-like 5th pereiopods and the massive, basal locomotor

musculature that powers the rotary motion of these appendages. Crustacean muscle

fibers, like those in vertebrates, are distinctive in that they are multinucleated, post-

mitotic and syncytial. During post-metamorphic development fiber diameters in these

muscles grow hypertrophically, increasing from <80 μm in juveniles to >600 μm in

adults (6). The basal muscles are composed of three distinct fiber types: light fibers that

power anaerobic burst swimming, dark fibers that power aerobically fueled endurance

swimming, and a small number of intermediate fibers (68; Fig. 2). The light fibers have

93

Figure 2. Levator swimming muscle from C. sapidus (adult) stained for endogenous peroxidase activity with a Vectastain Elite ABC kit (PBS buffer; PK-6100; Vector Laboratories, Inc.). This muscle is comprised of aerobic light fibers (L) and highly subdivided anaerobic dark fibers (D). There is a small fraction of moderately subdivided intermediate fibers (I) that create a transition zone between the dark and light fibers.

94

very low mitochondrial densities, leading to a slow, aerobic recovery following

anaerobic, burst contraction (6,38). In contrast, the dark fibers have a network of

mitochondria-rich subdivisions (68) that promote high rates of aerobic metabolism during

sustained swimming. The subdivisions increase in number, but maintain a constant,

relatively small size (~35 μm), during fiber growth (30).

Anaerobic Light Fibers

Mitochondrial and nuclear distribution in the anaerobic light fibers changes

dramatically during growth. In small fibers from juveniles mitochondria are uniformly

distributed throughout the intermyofibrillar (IM; Fig. 3A,C) and subsarcolemmal (SS;

Fig. 3A,E) regions of the cell, but in the large fibers from adults mitochondria are found

clustered almost exclusively at the sarcolemma (Fig. 3B,D,F). This pattern change was

first noted qualitatively in blue crab muscle by Boyle et al. (6), and more recently was

found in fish white muscle fibers that attain large sizes (49). Nuclei, on the other hand,

show the opposite pattern during fiber growth. In the smallest juvenile fibers nuclei were

located exclusively in the SS region of the cell (Fig. 4A), but as fiber size increased

nuclei had SS, as well as an abundance of IM nuclei (Fig. 4B). The nuclear distribution in

the large fibers from adults is in striking contrast to the pattern in vertebrate skeletal

muscle, where nuclei are typically found exclusively at the sarcolemma (e.g., 9), although

a similar response to hypertrophic growth has been observed in fish white muscle (S.T.

Kinsey, unpublished observations).

Stereological analyses revealed that the mitochondrial SS fractional volume

(SSFV) increased significantly while the IM fractional volume (IMFV) decreased

95

Figure 3. Mitochondrial distribution in juvenile (left panels) and adult (right panels) anaerobic light fibers. Cross-sections of fixed light fibers from WGA injected juveniles (A) and adults (B) were labeled with the red-fluorescent probe MitoTracker Deep Red, specific for mitochondria. Green-fluorescent WGA labeling indicates where perfusion is occurring, which in the light fibers concurrently delineates fiber boundaries. TEM micrographs depicting mitochondrial distribution in the subsarcolemmal (E,F) and intermyofibrillar regions (C,D) of juvenile (C,E) and adult (D,F) anaerobic light fibers. Mitochondria are marked with white circles. Note that in the small fibers of the juvenile, there is homogenous distribution of intermyofibrillar mitochondria and subsarcolemmal mitochondria, while in the large fibers of the adult there is a high density of subsarcolemmal mitochondria and sparse intermyofibrillar mitochondria.

96

Figure 4. Nuclear distribution in juvenile (A) and adult (B) anaerobic light fibers. Cross-sections of fixed light fibers from WGA injected animals were treated with DAPI, a blue-fluorescent probe for nuclei. Green-fluorescent WGA staining identifies the fiber sarcolemma. Note that in the small fibers of the juvenile, nuclei are found almost exclusively at the fiber edge, while in the large fibers of the adult there is a high density of both subsarcolemmal and intermyofibrillar nuclei.

97

significantly during fiber growth (Fig. 5A). In contrast, nuclear SS number volume

(SSNV) decreased significantly, while the IM number volume (IMNV) increased

significantly during fiber growth (Fig. 5B). Neither the total (IM + SS) mitochondrial

fractional volume (TMFV) nor the total nuclear number volume (TNNV) was

significantly different between the juveniles and the adults. The unchanging TMFV is

consistent with the minimal negative allometry of aerobic capacity with body mass in the

blue crab light fibers (6). The constancy of TNNV reflects a direct relationship between

the number of nuclei per mm of fiber and fiber cross-sectional area (Fig. 6A), and a

myonuclear domain (the volume of cytoplasm in a cell that is serviced by a single

nucleus; 13) that is not significantly different between juvenile (24,583.23±1,412 μm3)

and adult fibers (24,356±768 μm3)(Fig. 6B). While the nuclear distribution was quite

different from that seen in vertebrate skeletal muscle, the myonuclear domain in muscle

from blue crab was comparable to that of chicken (58), rat (3) and human (50) muscle. It

is possible that our estimates of myonuclear domain are slightly in error due to the

difficulty of classifying nuclei adjacent to the sarcolemma as intracellular myonuclei

versus extracellular satellite cell nuclei (23). However, this potential source of error does

not alter our general findings, and misidentified nuclei likely comprise a small percentage

of the total number of SS and IM nuclei (61).

We suggest that mitochondria and nuclei undergo opposite patterns of

redistribution during fiber growth as a result of contrasting diffusion constraints.

Mitochondria require adequate diffusive flux of both O2 to mitochondria and small

metabolites between mitochondria and cytosolic ATPases. Thus, the shift in mitochondria

toward a SS distribution during fiber growth reflects the need to minimize diffusion

98

Figure 5. Changes in mitochondrial and nuclear distribution during growth in anaerobic light fibers. (A) Subsarcolemmal fractional volume (SSFV) and intermyofibrillar fractional volume (IMFV) of mitochondria in adult and juvenile light fibers. SSFV (black) increases significantly (p<0.047) and IMFV (gray) decreases significantly across size classes (p<0.0001). (B) Subsarcolemmal number volume (SSNV) and intermyofibrillar number volume (IMFV) of nuclei in adult and juvenile light fibers. SSNV decreases significantly (p<0.0001), while IMFV increases significantly across size classes (p<0.0001). Asterisks indicate values that are significantly different across size class. Values shown are means±S.E.M.

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Figure 6. Correlation between nuclear number per millimeter and fiber cross-sectional area (A). Nuclear number per mm increases significantly with fiber CSA (y=669.79+0.035x, r2=0.80, p<0.0001), resulting in the conservation of myonuclear domain during fiber growth (B). Values shown are means±S.E.M.

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101

distances for O2, at the expense of larger diffusion distances for small metabolites.

Nuclear function, on the other hand, is not directly dependent on O2 supply, but relies on

the diffusion of slowly moving macromolecules between the nucleus and the cytosol that

it serves. The increase in IM nuclei during fiber growth likely indicates a strategy to

minimize transport distances for RNA and proteins in large diameter fibers, although this

constitutes a striking departure from the usual skeletal muscle paradigm of an exclusively

SS nuclear distribution (9).

Reaction-diffusion models allow us to assess the influence of organelle

distribution on cellular function. By varying the percentage of ATP production of the SS

and IM mitochondrial population we were able to evaluate the effect of changing

distribution on ATP turnover rates. Using previously measured maximal rates of aerobic

metabolism in the light fibers (38), we found that the small, light fibers (with diffusive

length scale, L= 40 μm) had a high η when 48% of the ATP production was assumed to

occur via SS mitochondria (observed case) and when we assumed all ATP production

was carried out by the IM mitochondria (no SS mitochondria; Table 1). Thus, there was

no effect of changing mitochondrial distribution from the near uniform distribution that

we observed to a truly uniform, hypothetical distribution over the short diffusion

distances that characterize small light fibers. In contrast, the large light fibers (L= 300

μm) had a high η (little diffusion limitation) when 88% of ATP production was supplied

by the SS mitochondria (observed case), whereas a greatly reduced η and a 3-fold lower

rate of ATP turnover was observed when we assumed a uniform distribution with only

IM mitochondria (Table 1). Therefore, in the large fibers that have longer maximal

intracellular diffusion distances, clustering mitochondria at the sarcolemma permits a

Table 1. Influence of mitochondrial distribution and dark fiber subdivision on the effectiveness factor (η), average non-dimensional oxygen, <O2>=<CO2>/Co, and ATP, <ATP>=<CATP>/CT, concentrations, and k1 (ATPase rate constant) and k2 (oxidative phosphorylation rate constant) for small and large fibers based on experimentally determined diffusion path lengths and phosphagen recovery rates (6,24,30,38). Output was obtained at the lowest values of k1 that would satisfy the observed rate, which maximized η. The ATP turnover rate is fixed in the observed case (SS mitochondrial fraction= 48, 88 or 75%) and the values of k1 and k2 from these cases are used in the hypothetical cases with only IM mitochondria (SS mitochondrial fraction= 0).

Fiber type

Length (μm)

SS fraction

(%)

k1 (s-1)

k2 (mM-1 s-1)

<O2>

<ATP>

Effectiveness factor (η)

ATP turnover rate

(mM min-1) 40 48 0.0009 0.86 0.94 0.86 0.99 0.47 40 0 0.0009 0.86 0.90 0.86 0.99 0.46 300 88 0.005 0.186 0.55 0.16 0.77 0.47

Light

300 0 0.005 0.186 0.20 0.05 0.26 0.16

17.5 75 0.005 1.10 0.96 0.61 0.99 1.84 17.5 0 0.005 1.10 0.92 0.59 0.98 1.80 300 75 0.012 14.9 0.065 0.25 0.32 1.84

Dark

300 0 0.012 14.9 0.027 0.13 0.17 0.98

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much higher rate of ATP turnover than does a uniform mitochondrial distribution. To our

knowledge, this is the first demonstration that rates of aerobic flux can be enhanced

simply by changing the position, but not the number, of mitochondria to offset diffusion

limitation. However, it is also clear that there are limits on the extent to which the

ontogenetic shift in distribution is effective, indicated by the reduced (but still high) η

seen at the previously measured rates of ATP turnover. That is, the combination of fiber

size, mitochondrial distribution and blood PO2 in adult animals appears to allow a

maximal ATP turnover rate in the large light fibers that is very close to the observed rate.

The redistribution of mitochondria observed in the light fibers leads to decreased

diffusion path lengths for O2, but at the expense of increasing intracellular diffusion

distances for small metabolites like ATP and ADP. Although O2 is a relatively small,

rapidly-diffusing molecule, it is found in low concentrations in the hemolymph around

the basal muscle due to the low blood O2 partial pressures characteristic of blue crabs

(20,43). Also, blue crabs lack myoglobin, which would increase the solubility of O2 in the

sarcoplasm and enhance diffusive flux to the mitochondria (51). Relocating mitochondria

to the fiber periphery therefore appears to limit O2 gradients across the cell (42,67), and

leads to enhanced aerobic ATP flux (Table 1). This is consistent with our previous

finding that post-contractile phosphagen recovery is not substantially limited by

metabolite diffusion in the anaerobic light fibers (38). The effect of mitochondrial

distribution is dependent on both metabolic rate and diffusion distance, and it seems

likely that the processes that govern the relative density of SS and IM mitochondria in

blue crab muscles are also found in organisms that do not necessarily have large fibers

(see 33,42,49,67).

103

Nuclei (and their associated synthetic apparatus) are involved in the simultaneous

transcription, translation and diffusive flux of a variety of molecules ranging in size from

small metabolites, to larger macromolecules, and potentially membrane bound vesicles.

To determine whether the distribution of nuclei in the anaerobic fibers was influenced by

diffusion limitations we modeled a simpler, existing derivation of the effectiveness factor

(19) at varying reaction rates for molecules with a range of diffusion coefficients

(indicating a range of sizes). Figure 7 demonstrates that, at any specific η changing the

nuclear distribution during fiber growth and thereby reducing diffusion distances

enhances the permissible rate constant for a given nuclear process by three orders of

magnitude. This relationship holds for processes that entail diffusion coefficients

characteristic of small molecules, macromolecules, or membrane vesicles. While the

high density of IM nuclei in large light fibers has not, to our knowledge, been seen in

other organisms, it should be noted that extensive hypertrophy can lead to the occurrence

of IM nuclei in vertebrate muscle as well (31,58). Thus, diffusion constraints may govern

both the spacing of SS nuclei (9,10), and the emergence and spacing of IM nuclei once

fibers reach a threshold size.

Myonuclear domain size is thought to remain constant during the life of a muscle

fiber (2,3,7,8,12,17,21), as nuclear number changes in response to hypertrophy (9,28,31,

44,57,59,62) and/or atrophy (1,25,50,69). This domain conservation can be achieved with

more than one arrangement of nuclei. By increasing nuclear density only at the fiber

periphery during growth, as is typical in vertebrate systems, myonuclear domains can be

conserved without changing nuclear distribution. However, in cells that get as large as the

anaerobic light fibers, implementing this strategy may inhibit gene expression or protein

104

Figure 7. Effect of changes in nuclear distribution on the rate constant for nuclear processes. A diffusion distance of 14.5 μm (observed radius of myonuclear domain; A) is compared to a distance of 300 μm (hypothetical case with only SS nuclei in an adult fiber; B). Note that if the population of IM nuclei did not increase during light fiber hypertrophic growth there would be a three order of magnitude smaller rate constant that could be attained at a given value of η (for any diffusion coefficient).

105

synthesis by drastically increasing diffusion distances. By increasing the number of

intermyofibrillar nuclei (as opposed to SS nuclei) with growth, as we observed in the blue

crab light fibers, short diffusion distances can be conserved within each nuclear domain.

We propose that it is not the myonuclear domain, per se, but rather a small maximal

diffusion distance within that domain that is being conserved with growth. We found that

the mean distance between any two myonuclei is 29.0±0.5 and 28.6±0.4 μm in juvenile

and adult light fibers, respectively, which is consistent with nuclear spacing in mouse

skeletal muscle with an exclusively SS distribution (9). Furthermore, Bruusgaard et al.

(9,10) have used novel myonuclear labeling techniques and mathematical analyses to

convincingly demonstrate that SS nuclei are not positioned randomly within a mouse

muscle fiber, but approximate an evenly spaced distribution, presumably to minimize

transport distances.

Aerobic Dark Fibers

The capacity for aerobic swimming in the blue crab presumably entailed the

evolution of the highly-subdivided dark fibers from giant light fiber precursors, which

had diffusion distances that were too great to support the high O2 and metabolite diffusive

flux needed for sustained swimming behavior (24,30). Figure 8 is a micrograph of a dark

fiber that is representative of both juveniles and adults. Here, the WGA probe for

sarcolemmal glycoproteins revealed intrafiber perfusion around each subdivision. This

was further supported in muscle fibers from animals injected with both WGA and

fluorescent microspheres, where it is clear that hemolymph circulates between fiber

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Figure 8. Aerobic dark fiber organelle distribution and perfusion. Transverse section of fibers labeled with WGA to indicate perfusion pathways (green), DAPI to label nuclei (blue) and MitoTracker Deep Red to label mitochondria (red). Note that the nuclei are found exclusively at the subdivision edges, while mitochondria are located at the edge and core of each subdivision. Intrafiber perfusion is indicated by complete WGA staining around each individual subdivision. The pattern is the same in small and large fibers.

107

subdivisions in the dark fibers, but does not penetrate inside the adjacent light fibers (Fig.

9). Nuclei are located exclusively at the periphery of each subdivision, while

mitochondria are primarily, but not exclusively, at the subdivision periphery (Fig. 8). The

pattern of organelle distribution within a dark fiber subdivision is reminiscent of

mammalian skeletal muscle fibers (9,33), which share similar dimensions, and therefore

similar diffusion constraints. Unlike the light fibers, however, the dark fibers do not show

any dramatic changes in organelle distribution during growth. This is consistent with the

observation that as these fibers grow hypertrophically, new subdivisions form and the

effective diffusion distances do not change (30).

We evaluated the interaction of metabolic organization and metabolic fluxes, as

described above, in both a subdivided and a hypothetical, non-subdivided aerobic fiber.

We incorporated rates of aerobic metabolism experimentally determined for the dark

fibers (24). A high η was found for a single fiber subdivision (L=17.5) in which 75% of

the ATP production occurred via SS mitochondria (observed case; 30), as well as when

only uniformly distributed, IM mitochondria were present (Table 1). Therefore, at these

short diffusion distances the experimental reaction rate can be attained with either

mitochondrial distribution. However, the influence of mitochondrial distribution on η

becomes sizable when the ATP turnover rate increases to values characteristic of other

aerobic muscles. Our measurements of aerobic metabolism were based on post-

contractile phosphagen resynthesis rates that likely underestimate maximal metabolic rate

in the dark fibers for reasons described elsewhere (see 24). However, even at these

relatively low rates of ATP turnover the influence of subdividing the fiber is readily

apparent. If subdivisions were not continuously formed during growth, which would

108

Figure 9. Pattern of hemolymph perfusion of the dark (A,C) and light (B,D) levator fibers. Live animals were injected with a red-fluorescent Alexa594 conjugated WGA and 0.2μm yellow-green fluorescent microspheres. WGA binds to sarcolemmal (and vessel endothelial) glycoproteins, while the microspheres become lodged in the smallest microvasculature of the muscle. A and B represent 3D reconstructions (stacks) of whole fiber bundles, while C and D are digitally reconstructed images of A and B, respectively, viewed in cross-section. Fibers appear slightly flattened due to pressure from the coverslip. Note the intense WGA staining and substantial accumulation of microspheres inside of the dark fibers, indicating a high-degree of intrafiber perfusion. This contrasts with the light fibers, which have very faint WGA staining and a lower abundance of microspheres (B, D), both of which occur primarily at the fiber edge. Beads that appear to be lodged inside of the light fibers are likely located within fiber clefts.

109

result in a diffusion distance of approximately 300 μm, aerobic fibers would yield a η of

only 0.32 when the SS mitochondrial population was 75%. Thus, in the absence of

subdivisions, dark fibers cannot sustain even this modest rate of ATP turnover. As in the

light fibers, both the η and ATP turnover rate decreased even further (0.17 and 0.98 mM

min-1, respectively) when there was no SS mitochondrial population (Table 1). Similarly,

the distribution of nuclei throughout the fiber (at the periphery of each subdivision) again

reduces diffusion distances and enhances nuclear reaction fluxes. The effective diffusion

distance between nuclei in the dark subdivided fibers (17.5 μm) is similar to that for IM

nuclei in the light fibers discussed above (14.5 μm). Therefore, we can again examine

Figure 7 to demonstrate that nuclear reaction rate constants for the observed short

diffusion distances in the dark fibers are much higher than the hypothetical, unsubdivided

case with only SS nuclei.

The subdivided structure of dark muscle raises the question: What constitutes a

fiber? A fiber is typically considered to share a common cytoplasm. We therefore

compared intracellular diffusion coefficients (of the small dye molecule calcein) between

the dark, subdivided fibers and light, non-subdivided fibers as a probe for cytoplasmic

connectedness between subdivisions using the FRAP method. Intracellular diffusion

coefficients for calcein could be calculated for movement in both the longitudinal

direction (D║; parallel to the fiber or subdivision) and the radial direction (D⊥;

perpendicular to the fiber or subdivision). By comparing D⊥ between the two fiber types,

we intended to determine whether intracellular diffusion in the dark fibers was to any

extent impeded by the subdivision walls or whether the membrane permitted completely

free cytoplasmic exchange.

110

In the light fibers, D⊥ (0.33 ± 0.06 X 10-6 cm2 s-1) was significantly lower than D║

(1.31 ± 0.16 X 10-6 cm2 s-1; p<0.0001), indicating an orientation dependence of diffusion

in these fibers, and D|| in the dark fibers (0.89 ± 0.093 X 10-6 cm2 s-1) was lower than in

the light fibers. These results are consistent with previous measurements of metabolite

diffusion using pulsed-field gradient nuclear magnetic resonance (PFG-NMR) in

crustacean and fish muscle, which showed that subcellular barriers inhibit mobility in the

radial direction more substantially than in the axial direction (34,35,36,37). While this

anisotropy has been demonstrated before by PFG-NMR methods, this is to our

knowledge the first time this phenomenon has been observed using FRAP experiments.

The measurement of D⊥, however, yielded an unexpected result. The long, thin

rectangular bleached region was invariably encapsulated within a single dark fiber

subdivision, and the subdivisions appeared to be completely isolated from one another

(Fig. 10A). This pattern contrasts with that in the light fibers, which show a much faster

recovery of fluorescence in the bleached region, indicative of rapid, unconstrained

diffusion (Fig. 10B). Thus, diffusion of the fluorescent probe within the small volume of

a dark fiber subdivision led to rapid equilibration, such that the entire subdivision became

bleached. Further, there was no detectable movement of unbleached fluorophore due to

radial diffusion from adjacent subdivisions. It therefore appears that the membranes

separating individual subdivisions do not allow free cytoplasmic exchange.

These findings suggest that each subdivision functions as an independent

metabolic unit, complete with mitochondria, nuclei and thorough perfusion. From this

perspective the subdivisions would appear to constitute a fiber. However, fibers have

both metabolic and contractile functions. What then is the contractile functional unit: the

111

Figure 10. Immediate post-bleach images of dark (A,C) and light (B,D) fibers during fluorescence recovery after photobleaching (FRAP). Fibers were incubated in the membrane permeable dye Calcein, which fluoresces green when hydrolyzed by intracellular esterases, then subjected to a series of high-intensity bleach treatments. Dark (A) and light (B) fiber post-bleach images from a FRAP experiment measuring radial diffusion coefficients (D⊥). In the dark fibers the Calcein flurophore (green) is thoroughly bleached within a single subdivision and there is no radial diffusion into this bleached region, indicating cytoplasmic isolation. In contrast, the light fibers already exhibit some post-bleach recovery via radial diffusion, indicative of cytoplasmic continuity throughout the fiber. Images from measurements of axial diffusion coefficients (D║) show that the pattern of recovery in the bleached region is similar between the dark (C) and light (D) fibers indicating unhindered cytoplasmic exchange along the longitudinal axis in both fiber types. Subsequent images (not shown) demonstrate complete recovery of fluorescence in the bleached region.

112

subdivision or the fiber? There are approximately 70 subdivisions per large dark fiber in

an adult animal, and if the subdivisions are the contractile unit we would expect a much

greater neuromuscular synapse density in the dark fibers than the light fibers (an

approximately 70-fold increase if the innervation per fiber is constant). However, no such

difference was observed (Fig. 11). Synapses were located in comparable densities at the

sarcolemmal surface and within clefts that penetrate the interior of both the light and dark

fibers. Crustacean muscle is often multi-terminally innervated (reviewed in 4,5) and

motor axons travel deep into the sarcolemmal clefts to terminate in more central positions

within the fiber (63). In addition, crustacean muscle fibers, unlike mammalian muscle

fibers, often exhibit electrical continuity (52, 54) and can propagate membrane potentials

via cytoplasmic connections between adjacent fibers (46). This quality makes it difficult

to use electrophysiological techniques to determine whether subdivisions are able to

contract independently, but it also makes it more likely that all of the fibers within a

subdivision contract in unison, making the whole fiber the contractile functional unit.

The above evidence suggests that aerobic dark fibers evolved from the anaerobic

light fiber precursors by effectively separating the metabolic functional unit (fiber

subdivision), from the contractile functional unit (whole fiber). The subdivisions

therefore circumvent diffusion constraints associated with aerobic metabolic processes,

and can be considered a distinct metabolic unit. Contraction, on the other hand, which is

not constrained by diffusive processes, is presumably carried out by the fiber as a whole

due to electrical continuity between subdivisions.

113

Figure 11. Innervation patterns in the dark (A,B) and light (A,C) levator fibers. Anti-SYNORF1 was used to label the pre-synaptic vesicle associated phosphoprotein synapsin. In both fiber types synapses were visualized at the fiber sarcolemma (arrows) and inside the fiber core (within sarcolemmal clefts) and between subdivisions (arrowheads). Note that synapse density is not higher in dark fibers (left side of image in A) than the light fibers (right side of image in A), which would be expected if subdivisions were independent contractile units.

114

Summary

The light and dark fibers of C. sapidus swimming muscles both grow

hypertrophically and reach dimensions in adult animals that are atypical of most cells.

The two fiber types have evolved in fundamentally different ways to compensate for the

changing role that diffusion plays during fiber growth. It is currently not known whether

the ontogenetic changes in fiber design are controlled by diffusive processes per se, or

whether they represent part of a fixed developmental program. Nevertheless, it seems

clear that the changes in fiber structure during development are a response to diffusion

constraints, and they ameliorate many of the consequences of hypertrophic growth.

While the use of an extreme model system has revealed diffusion control of cell design

that would be difficult to observe in traditional models, it is likely that similar rules apply

to other muscle fiber types.

115

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hypertrophy and work-induced hypertrophy. Am J Anat 145: 459-465, 1976.

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63. Selverston A. Structure and function of the transverse tubular system in crustacean muscle fibers. Am Zool 7: 515-525, 1967.

64. Spirito CP. An analysis of swimming behaviour in the Portunid crab Callinectes sapidus.

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67. Stokes DR, Josephson RK. Structural organization of two fast, rhythmically active crustacean muscles. Cell Tiss Res 267: 571-582, 1992.

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muscles in the blue crab, Callinectes sapidus. Can J Zool 61: 52-59, 1983.

69. Viguie CA, Lu D-X, Huang S-K, Rengen H, Carlson BM. Quantitative study of the effects of long-term denervation on the extensor digitorum longus muscle of the rat. Anat Rec 248: 346-354, 1997.

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CHAPTER 4

THE EFFECT OF DIFFUSION ON SKELETAL MUSCLE FIBER DESIGN: A

COMPARATIVE ANALYSIS OF THE BRACHYURAN FAMILY PORTUNIDAE.

Prepared in the style of Marine Biology

ABSTRACT

Skeletal muscle fiber design in the blue crab, Callinectes sapidus (F. Portunidae), is

substantially influenced by intracellular diffusion constraints and the cellular responses to

these constraints ultimately facilitated the evolution of swimming behavior in these

animals. We investigated the influence of diffusion on muscle fiber design in several

representative swimming and non-swimming brachyuran crab species. The swimming

muscles in these animals are composed of both anaerobic light fibers, which power burst-

swimming and aerobic dark fibers, which power sustained swimming. Here we show that

sustained swimming behavior was facilitated by subdividing the aerobic dark fibers into

metabolically small functional units. This creates the short intracellular diffusion

distances needed to meet the high ATP turnover demands of endurance swimming. This

was true for all swimming species including Ovalipes ocellatus, which has apparently

evolved swimming behavior independently of the other portunids. In addition, we

observed that differences in the pattern of organelle distribution over a range of light fiber

and dark fiber subdivision sizes from these species mirrored the ontogenetic changes

previously observed in C. sapidus. Mitochondria, which rely on oxygen to function, were

found evenly distributed in the small fibers, but were preferentially clustered at the

sarcolemma in the larger fibers. The inverse was true for nuclei, which are not oxygen

dependent. Nuclei were found only at the fiber periphery in small fibers, but are located

both in the fiber core and adjacent to the sarcolemma in the large fibers. This preserves

short diffusion distances for large RNA and protein macromolecules. A phylogenetically

independent contrast analysis revealed that this relationship between organelle

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distribution and fiber/subdivision size was independent of phylogeny. Our results

demonstrate that the cellular response to diffusion is uniform across many species, and

likely represents rules of diffusion control that can be broadly applied to all muscle

fibers.

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INTRODUCTION

The potential limitations caused by excessive intracellular diffusion distances

have long been hypothesized as one of the primary reasons that cells maintain relatively

small sizes (typically within an order of magnitude of 10 μm) (Koch 1996; Russell et al.

2000; Teissier 1939; Thompson 1917). Rapid intracellular diffusion of oxygen and small

metabolites [i.e. ATP, arginine phosphate (AP), and inorganic phosphate (Pi)] is critical

to maintaining high rates of aerobic metabolism (Kim et al. 1998; Mainwood and

Rakusan 1982) and the diffusion of larger RNA and polypeptide molecules is important

for protein turnover (Fusco et al. 2007; Russell and Dix 1992). Thus, diffusion has the

potential to play a major role in shaping the evolution of basic cellular design and

function, and this role becomes greater as intracellular diffusion distances and/or aerobic

metabolic rates become larger.

The basal muscles that power swimming in the blue crab, Callinectes sapidus,

grow hypertrophically and during post-metamorphic development fiber diameters

increase from <60 μm in juveniles to >600 μm in adults (Boyle et al. 2003). At these

sizes intracellular diffusion distances begin to limit certain processes critical to normal

cell function (Hardy et al. 2006; Kinsey et al. 2005), thereby providing selective pressure

for the modification of cellular design. The basal swimming muscles are composed

primarily of two fiber types: light fibers that power anaerobic burst swimming and dark

fibers that power aerobic endurance swimming (Tse et al. 1983). The light fibers rely on

maximal rates of aerobic metabolism only during post-contractile recovery, which is

associated with low ATP turnover rates, while the dark fibers use aerobic processes to

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support the high rates of ATP turnover associated with sustained contractile activity. We

previously demonstrated that diffusion has a considerable impact on cellular organization

in the basal swimming muscles of the blue crab and these effects were distinctly different

between the anaerobic light fibers and aerobic dark fibers as a result of their

fundamentally different metabolic requirements (Boyle et al. 2003; Hardy et al. 2009;

Johnson et al. 2003).

During hypertrophic growth, the anaerobic fibers of C. sapidus appear to maintain

cellular function by redistributing certain organelles in a way that minimizes intracellular

diffusive path lengths. Mitochondria, for example, are homogenously scattered

throughout each fiber in juvenile animals so that there are nearly equal numbers of

mitochondria in the fiber interior (intermyofibrillar or IM mitochondria) and at the fiber

periphery (subsarcolemmal or SS mitochondria). However, during growth mitochondria

begin to cluster near the sarcolemma, and in the adults virtually no mitochondria occur

within the fiber core (Boyle et al. 2003; Hardy et al. 2009). This rearrangement

effectively reduces transport distances for oxygen to the mitochondria. Nuclei follow the

inverse pattern. In the small juvenile fibers, myonuclei are located exclusively at the

sarcolemma (the characteristic pattern in vertebrate fibers), but during growth begin to

occupy more centrally located positions within the fiber as well. This shift results in

reduced intracellular transport distances for the large, slowly-diffusing protein and RNA

products required by the fiber for the turnover of metabolic and contractile machinery

(Hardy et al. 2009).

The aerobic fibers, on the other hand, have to meet much higher ATP demands

during steady-state contraction and high reaction-rates can result in a diffusion limiting

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environment even in fibers with small diameters. To satisfy the opposing demands for

hypertrophic growth and short diffusion path lengths, the dark fibers have developed a

network of highly-perfused, mitochondria-rich subdivisions (Johnson et al. 2004; Tse et

al. 1983) that increase in number, but maintain a constant size (~35 μm) with growth

(Johnson et al. 2004). In this way the aerobic fibers preserve an effective metabolic

diameter throughout development that is well within the range of cellular dimensions

typical of aerobic muscle from other animals. The perfused subdivisions result in greatly

reduced diffusion distances and increased oxygen availability to the mitochondria. As

such, nuclei and mitochondria do not undergo the ontogenetic shift in organelle

distribution observed in the anaerobic fibers. In both the adult and juvenile animals

mitochondria are found predominantly at the periphery of each subdivision and are also

present at lower density between the myofibrils, while nuclei are found exclusively at the

subdivision periphery.

Organelle distribution in adult skeletal muscle fibers is a plastic property.

Mitochondrial distribution and morphology have been shown to vary dramatically in

response to factors including temperature (Tyler and Sidell 1984), hypoxia (Hoppeler and

Vogt 2001), and exercise (Chilibeck et al. 2002; Howald et al. 1985; Kayar et al. 1986),

while nuclei have been reported to realign themselves with newly formed blood vessels

in skeletal muscle fibers subject to chronic stimulation following denervation (Ralston et

al. 2006). The processes by which organelles migrate and anchor inside of cells have

been extensively studied (Bitoun et al. 2005; Frederick and Shaw 2007; Milner et al.

1996; Ralston et al. 2006; Rube and van der Bliek 2004; Smirnova et al. 1998; Starr

2007; Starr and Han 2002). However, current understanding of how this movement is

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regulated is limited, and the signals that result in the relocation of mitochondria or nuclei

within an adult (or embryonic) muscle fiber are largely unknown.

There are many potential regulatory mechanisms that could dictate the

intracellular arrangement of organelles and these strategies are not necessarily mutually

exclusive. The distribution of organelles within a cell may simply be a product of

phylogenetic inertia. This term refers to the stability of a trait that results from the

influence of an ancestor on its descendant (for review see Blomberg and Garland 2002).

If there is no selective pressure to modify the placement of organelles in a fiber, then they

will likely share the same distribution as their ancestor. Alternatively, intracellular

organelle distribution may be the product of a genetic developmental program (Badrinath

and White 2003; van Blerkom 1991). A cell must be able to function normally over the

entire range of sizes it will span in its lifetime. If the terminal cell size or degree of

expected hypertrophy is encoded in the genome of an animal, then certain mechanisms

may be implemented early in development to prepare each cell for constraints that will

surface only after substantial growth has occurred. A third possibility is that the cellular

organization of organelles is the direct and immediate product of some prevailing

intracellular condition—in particular, diffusion constraints. For example, mitochondrial

distribution could be responsive to intracellular oxygen concentrations. During

hypertrophic growth oxygen gradients across the cell may steepen due to increasing fiber

size, and mitochondria may shift from areas of low to high oxygen concentration to

maintain rates of oxidative phosphorylation sufficient to preserve function in that fiber.

C. sapidus is a member of the family Portunidae, a group of brachyuran crabs

well-known for their swimming abilities (Feidler 1930; Judy and Dudley 1970; Spirito

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1972). Portunids exhibit a number of characteristic morphological adaptations that have

facilitated the evolution of swimming behavior. Most notably, the 5th pereiopods have

been modified into flattened, oar-like paddles and the carapace has been laterally

extended and dorso-ventrally compressed to increase hydrodynamic efficiency during

sideways swimming (Hartnoll 1971). The basal swimming musculature in particularly

adept swimming portunids is also generally enlarged and exhibits severe fiber

hypertrophy, most likely to fulfill the high power requirements of swimming (Cochran

1935).

Within the portunid family, however, there is considerable variation in the extent

of these specializations and hence, the range of swimming proficiency. In some animals

swimming behavior only accompanies brief feeding or escape events, while others have

adopted an entirely pelagic lifestyle (Hartnoll 1971). Carcinus maenus, for example, is

particularly interesting because it is one of the only portunids whose 5th pereiopods have

retained their original walking leg characteristics. As such, it is a much weaker swimmer

than many of the other more modified portunids. Although this family is popularly

referred to as “swimming crabs”, there are representative species from at least 12 other

brachyuran families that also exhibit some capacity to swim (reviewed in Hartnoll 1971).

Previously we examined changes in cellular organization that occurred during

ontogenetic growth within a single species (Hardy et al. 2009). The present aim was to

investigate cellular organization across a similar range of fiber sizes spanned by adult

animals of many different species. This approach allowed us to take into account the

potential confounding effect of shared common ancestry on fiber design. In the current

study, we measured fiber/subdivision size, as well as mitochondrial and nuclear density

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and distribution in anaerobic light fibers and aerobic dark fibers from the homologous

basal muscles of six portunid and two non-portunid crabs. Using 16S rDNA sequences,

we generated a phylogeny for these species from which we performed a phylogenetically

independent contrast (PIC) analysis (Felsenstein 1985). The PIC analysis determines

whether an observed trait is the product of phylogenetic inertia (shared common

ancestry), and a trait that is found to be independent of phylogeny can be considered an

evolutionary adaptation. We used this analysis to try and discern the influence of

phylogenetic ancestry, as opposed to diffusion, on organelle distribution. We

hypothesized that all portunids evolved the ability to aerobically swim by subdividing

their dark fibers, and that higher aerobic swimming capacity is associated with smaller

subdivisions and higher mitochondrial densities. Additionally, we hypothesized that the

patterns in cellular design we previously observed during growth in C. sapidus light and

dark fibers would be broadly observable across a range of portunid (and non-portunid)

species, and that these patterns would be independent of phylogeny. Such an

independence from phylogeny would provide further evidence that intracellular organelle

distribution is an adaptation to prevailing diffusion conditions.

MATERIALS AND METHODS

Animals

Six species from the swimming crab family, Portunidae, were included in this

study: Callinectes sapidus, Portunus sayi, Portunus gibbesii, Portunus spinimanus,

Carcinus maenus and Ovalipes ocellatus. These species were chosen for their wide range

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of swimming abilities, appendage modifications and average adult sizes (as described by

Hartnoll 1971 and Williams 1974). Animals were also chosen with regard to their

phylogenetic relationships, which were recently resolved from 16S rRNA gene sequences

for many species of Portunids (Mantellata et al. 2007; Robles et al. 2007). In addition,

Cancer magister (F. Cancridae) and Menippe mercenaria (F. Xanthidae) were included

in this study as representative non-portunid, non-swimming crabs. Animals were obtained

locally (Wilmington, NC, USA) from inshore sweep netting, offshore trawling and

commercial fisherman, as well as purchased live from national commercial and marine

organism suppliers (Woods Hole Marine Biological Laboratories and Gulf Specimens

Marine Laboratories). Species identification, when necessary, was verified on the basis of

morphological characteristics (Rathbun 1930; Williams 1974) and only mature, adult,

intermoult animals were used, with no preference given to sex. Animals were maintained

in full-strength, filtered seawater (35‰ salinity, 21°C) in aerated, recirculating

aquariums, though in most cases, they were processed immediately upon arrival and did

not require long term housing. Prior to use in all experiments, animals were sexed, and

their carapace width and body mass measured.

Dissection

Crabs were first rapidly cut through the cerebral ganglion and then the dorsal

carapace, heart, reproductive and digestive organs were removed. The gills and other

supporting architecture were cut off to expose the basal cavity, which houses the basal

muscles of the 5th pereiopods (remoter, promoter, levator, depressor) (Cochran 1935).

The muscle group that originates on the median plate and inserts at the large tendon of

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the 5th pereiopods, which powers swimming (or walking) movement in the final pair of

legs, was carefully isolated and removed from each animal.

Cellular Dimensions and Mitochondrial Density

After being removed from the animal, the muscle (N=3 per species) was

subsequently frozen in isopentane cooled in liquid nitrogen, mounted in optimal cutting

temperature (OCT) compound and frozen again in cooled isopentane. Samples were

equilibrated to −18ºC and sectioned immediately. Muscle cross-sections were obtained

on a Reichert-Jung Leica Cryocut 1800 microtome (Leica Microsystems; Wetzler,

Germany) at 30 μm thickness in a systematic random sampling method to ensure

complete representation of mitochondrial and nuclear distribution throughout the muscle

(Howard and Reed 1998). Sections were picked up on room-temperature Superfrost

PLUS slides (12-550-15; Fisher Scientific) and allowed to air-dry for 30 min at room

temperature. Slides were then incubated in a succinic dehydrogenase (SDH) staining

solution [12.5% solution of nitro-blue tetrazolium (NBT) in equal volumes of 0.2 M

sodium succinate and 0.2M phosphate buffer (pH 7.6)] (Presnell and Screibman 1997) at

37 ºC for 1h while gently agitating every five minutes. Muscle fibers with a high

oxidative capacity, and hence high mitochondrial content, had increased SDH staining.

At this incubation duration the high resolution of SDH staining allowed individual

mitochondria and mitochondrial clusters to be distinguished. After incubation, slides

were rinsed in phosphate buffered saline (PBS) for 1 min at room temperature, and then

fixed for 1h in a 10% formalin/10%NaCl solution. Slides were dehydrated in ethanol

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(70%, 95%, 100% for three minutes each), cleared in toluene for 3 min, and mounted

with Permount.

Stained sections were viewed using an Olympus BH-2 light microscope and

digital images were captured using a Diagnostic Images, Inc. Spot RT camera. Fiber and

subdivision margins were traced using Adobe Photoshop v7.0 and resultant polygons

were analyzed with Image Pro Plus (IPP) v4.1.0.9 to calculate fiber and subdivision

cross-sectional area (CSA), circumference and mean diameter. To determine relative

mitochondrial densities, intensity profiles were collected from images of both light fibers

and dark fiber subdivisions. Using IPP, a straight, one pixel-wide line was drawn

randomly across the entire width of an individual fiber/subdivision cross-section (Fig. 1a)

and a relative intensity value (on a scale from 0 to 255, where 0 is pure white and 255 is

pure black) was assigned to each pixel of the image crossed by the line. These values

corresponded to the relative SDH staining intensity, which is indicative of mitochondrial

density. To determine the relative difference in mitochondrial density between the SS and

IM regions of the fiber, intensity profile data was first exported to Microsoft Excel and

plotted against position in the fiber (Fig. 1b). Two SS and two IM regions were then

defined from these plots and the average intensity value was calculated for each region.

An SS region was defined as the portion of the line between the peak of the intensity

curve and the point where the slope first becomes zero, while each IM region was

demarcated as half of the portion of the line between flanking SS regions. The two SS

and two IM intensity values in each radial profile were averaged together providing one

final SS and IM value per fiber/subdivision. In addition, a total average intensity value

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Position (μm)0 100 200 300 400 500 600

Inte

nsity

Val

ue

0

50

100

150

200

250

Total

SS-1 SS-2

IM-1 IM-2

a

b

Fig. 1 Method of estimating mitochondrial density from intensity profiles of muscle cross-sections stained for succinic dehydrogenase (SDH) activity. (a) Representative image of an anaerobic light fiber (here from M.mercenaria) that has been stained for SDH. A horizontal line is placed across the diameter of an entire fiber and an intensity value (from 0 to 255) is calculated by the IPP software for each pixel of the image crossed by the line. (b) The intensity value for each pixel is plotted against position, creating a profile of the staining intensity for that individual fiber. Shown here is a typical intensity profile from a light fiber, demonstrating intense mitochondrial staining near the sarcolemma and very faint staining in the interior of the fiber. From this profile two SS regions and two IM regions are defined and an average intensity value is calculated for each of these defined ranges. Additionally, a total average intensity value is calculated across the entire fiber (from peak to peak), to represent the total mitochondrial density of that fiber.

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was calculated across the entire diameter of the fiber/subdivision to reflect total relative

mitochondrial density.

Calculation of Nuclear Number Volume and Myonuclear domain

Animals (N=3 per species) were injected with 100 μL of 1mg/ml AlexaFluor 488-

labeled wheat germ agglutinin (WGA; W11261; Molecular Probes). Injections were

given straight into the hemolymph through the arthroidial membrane between the

carapace and the coxa of the 5th pereiopod. WGA is a lectin that binds to glycoproteins on

the basement membrane of the fiber sarcolemma (Wright 1984) and is used here to

delineate fiber and subdivision boundaries. After injection, animals were provoked with a

stick while in a container filled with filtered sea-water (FSW) to elicit exercise and

stimulate blood flow. Animals were then rested for 10 min in FSW and sacrificed. The

basal muscles were removed and fixed for 4-8 hrs in 4% paraformaldehyde in FSW,

washed overnight in 25% sucrose, then flash frozen in liquid nitrogen. Frozen sections

were cut on a Reichert-Jung Leica Cryocut 1800 microtome at 20 μm thickness in a

systematic random sampling method to ensure complete representation of nuclear

distribution throughout the muscle (Howard and Reed 1998). Frozen sections were

picked up on room-temperature Superfrost PLUS slides, and rinsed in PBS. Sections

were incubated for 15 min in 300 nM of blue-fluorescent probe 4´,6-diamidino-2-

phenylindole (DAPI; D1306; Molecular Probes) to label nuclei, and then rinsed again for

3 min in PBS and mounted in 9:1 Tris:Glycerol (0.1M Tris, pH 7.4) mounting media. All

images were taken with the Olympus FV1000 confocal microscope as single optical

slices and included the 404 nm (DAPI), 488 nm (WGA) and differential interference

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contrast (DIC) channels. Images were viewed with Olympus Fluoview v. 1.6a software

and nuclei inside of each complete fiber cross-section were counted and tallied as either

SS, if they were in contact with the sarcolemma, or IM, if they were not in direct contact

with the sarcolemma. Intrafiber SS nuclei can be difficult to distinguish from nuclei in

cells in the extracellular space and in adjoining fibers. Information from the WGA and

DIC channels allowed us to more accurately determine which peripherally located nuclei

were truly inside the fiber. Fiber and subdivision cross-sectional area (CSA),

circumference and mean diameter, as well as nuclear CSA, diameter (from fiber cross-

sections) and length (from longitudinal sections) were calculated as above.

As described previously (Hardy et al. 2009), the myonuclear domain (volume of

cytoplasm per myonucleus) was calculated according to the formula used in Schmalbruch

and Hellhammer (1977) and the nuclear number volume (number of nuclei per volume of

cytoplasm) was calculated as the inverse of the myonuclear domain for SS and IM nuclei

respectively.

Isolation and sequencing of 16S ribosomal DNA

DNA extraction, amplification, and sequencing protocols followed Mantellato et

al. (2007) and Robles et al. (2007). Total genomic DNA was isolated from muscle tissue

in the chelipeds of O. ocellatus and in the walking legs of C. magister using a DNeasy

Kit (Qiagen, Inc., Valencia, CA). These were the only two species included in this study

for which a partial 16S rDNA sequence did not already exist on GenBank. Partial

fragments of the 16S ribosomal region of mtDNA (16S rDNA) were amplified by a

polymerase chain reaction (PCR) on a PTC-100 thermal cycler (MJ Research). Each PCR

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reaction was performed in 50 μl volumes containing 2 μl of DNA template (~150 ng), 25

μl GoTaq® Colorless Master Mix (Promega, Madison, WI), 21 μl nuclease-free H20, and

1 μl each of forward and reverse primer (50 μM). Our thermal profiles were carried out as

follows: initial denaturation cycle for 10 min at 95°C, followed by 42 cycles of 1 min at

95°C, 1 min at 46°C and 2 min at 72°C, with a final extension of 72°C for 10 min. For

these reactions we used the forward primer 16Sar (5´-CGC CTG TTT ATC AAA AAC

AT-3´) paired with the reverse primer 16Sbr (5´-CCG GTC TGA ACT CAG ATC ACG

T-3´), and the forward primer 16SL2 (5´-TGC CTG TTT ATC AAA AAC AT-3´) paired

with the reverse primer 1472 (5´-AGA TAG AAA CCA ACC TGG-3´) (for references on

primers see Palumbi et al., 1991; Schubart et al., 2000; Fratini et al., 2005). Both primer

pairs produced clear, single bands of approximately 560-bp on a 1.2% agarose gel with

ethidium bromide (Invitrogen, Corp., Carlsbad, CA). The resulting PCR products were

purified (QIAquick PCR Purification Kit, Qiagen, Inc.) and sequenced on an ABI PRISM

3100 Genetic Analyzer using the ABI Big Dye Terminator Cycle Sequencing Kit v3.1.

Consensus sequences for O. ocellatus and C. magister were assembled using Sequencher

v4.8 (Gene Codes, Corp., Ann Arbor, MI) and are available online (Genbank Accession

no. FJ716615 and FJ829795, respectively)

Tree construction

The 16S rDNA sequences obtained above for O. ocellatus and C. magister were

aligned with sequences from C. sapidus (Gen Bank Accession no. AJ298189), P. sayi

(DQ388053), P. spinimanus (DQ388056), P. gibbesii (DQ388057), C. maenas

(DQ079709), and M. mercenaria (U20749) using ClustalX v2.0.10 (Larkin et al. 2007).

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A phylogeny was constructed with the beta version of MEGA v4.1 (Kumar et al. 2008),

and a congruent topology was inferred by both maximum parsimony (MP) and neighbor-

joining (NJ) analyses. MP analysis was performed as a heuristic search with random

sequence addition and all sites, including gaps, were equally weighted. A maximum-

likelihood model of NJ analysis was performed with pairwise comparisons. Bootstrap

analyses for both MP and NJ used 1,000 replicates and only confidence values >50%

were reported.

Statistical and Phylogenetic Independent Contrast Analyses

To test for phylogenetic signal, we used Felsenstein’s (1985) method of

phylogenetically independent contrasts (PIC). The analysis was conducted with the

Phenotypic Diversity Analysis Program (PDAP; Midford et al. 2005) and the subset

package PDTREE (Garland et al. 1999; Garland and Ives 2000). The topology and

branch lengths generated by the MP analysis of 16S rDNA sequences were used in the

PIC analysis and a diagnostic test (plot between the absolute value of each standardized

contrast and the standard deviation showed no relationship) found these branch lengths to

be statistically acceptable after log-transformation (Garland et al. 1992). Standardized

phylogenetic contrasts were calculated from log-transformed branch lengths and

regressions (through the origin) were determined between pairs of standardized contrasts.

The absence of a significant relationship between the contrasts (denoted by a slope that

did not significantly differ from 0) was evidence of a phylogenetic signal in those data.

Linear regressions were fit to the data (raw and contrasts) based on the ordinary least

square (OLS) model and significance was accepted at p<0.05.

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Student’s t-tests were used to make pairwise comparisons between species, using

a Bonferroni correction for multiple tests where the significance level, α, was adjusted to

0.0064. All data are presented as means ± SEM.

RESULTS

Phylogenetic Analysis

We arrived at a congruent phylogeny based on MP and NJ analyses of 16S rDNA

sequences (Fig. 2). Based on this phylogeny, C. maenas and O. ocellates are likely not

portunids, as they group more closely with the xanthids and the cancrids. In addition, C.

magister (F. Cancridae) and M. mercenaria (F. Xanthidae) were more closely related to

the Portunidae than O. ocellatus and C. maenas in a 16S rDNA phylogeny that was

rooted with the Caribbean spiny lobster, Panulirus argus (data not shown).

Animal body mass and fiber size

The adult animals used in this study ranged in size from 2.5 g to 857.4 g. The

mean body mass per species was: 4.0 ± 0.12 g (P. sayi), 10.17 ± 0.08 g (P. gibbesii),

20.58 ± 0.42 g (P. spinimanus), 37.98 ± 0.61 g (C. maenas), 57.69 ± 1.59 (O.ocellatus),

163.05 ± 3.18 g (C. sapidus), 359.53 ± 3.8 g (M. mercenaria), and 778.04 ± 4.23 g (C.

magister). Figure 3 demonstrates the variability in fiber structure that existed among a

subset of the species examined in this study. Across all eight species cross-sectional

diameter of the anaerobic light fibers ranged from 73.89 to 1088.56 μm. Average light

fiber diameter was larger in species with higher body mass (r2=0.91; p=0.0002) (Fig. 4a),

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Fig 2 Phylogenetic relationship among several brachyuran species [family Portunidae (circles), Xanthidae (square), and Cancridae (triangle)] based on 16S rDNA sequences. A congruent topology was inferred by maximum parsimony and neighbor-joining analyses. Values above each line are bootstrap values (1,000 replicates) and values below are branch lengths in units of number of mutations per time, as obtained from the MP analysis. Species are broadly classified as either excellent swimmers (black) or non-swimmers (gray) (Hartnoll, 1971). Note that C. maenas and O. ocellatus, which are considered to be in the Family Portunidae, along with the genera Portunus and Callinectes, appear to be more closely related to the Family Xanthidae member, M. mercenaria. The * by C. magister indicates that the scale bar for this species is 300 mm, instead of 150 mm.

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Fig. 3 Representative images of muscle cross-sections stained for mitochondria with SDH (a) and nuclei with DAPI (b,c). These images demonstrate the variability in light fiber diameter and dark fiber subdivision diameter that exists among the species examined in this study. (Note that images from only a subsample of the species studied are shown here). (a) In the SDH stained muscle, aerobic fibers are characterized by very dense staining, while the adjacent anaerobic light fibers stain much less intensely. This contrast reflects the large difference in mitochondrial density typical of these two fiber types. (b) Nuclear staining in the anaerobic light fibers. These images demonstrate an increase in the total number of intermyofibrillar nuclei with fiber size, but a fairly conserved myonuclear domain (the volume of cytoplasm ‘serviced’ by a single nucleus) for each species, regardless of fiber size. (c) Nuclear staining in the aerobic dark fibers. Nuclei are located exclusively adjacent to the sarcolemma in the smaller subdivisions, but, as in the light fibers, nuclei begin to appear in the intermyofibrillar zone as subdivision diameter increases (arrowheads). Scale bar: 500 μm (a), 150 μm (b,c).

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and this relationship appeared to be generally independent of swimming ability (Fig. 4c).

(O.ocellatus and C. maenas were the only two species that did not significantly differ in

mean light fiber diameter.) This differed from the subdivisions of the aerobic dark fibers,

which had no relationship between mean cross-sectional diameter and body mass

(r2=0.25; p=0.2122) (Fig. 4b), but were significantly smaller in species possessing the

ability to swim well (Fig. 4d). (Those species pairs whose subdivision diameters did not

significantly differ were M. mercenaria and C. magister, C. sapidus and P. sayi, and P.

spinimanus and P. gibbesii.) Dark fiber subdivision diameter ranged from 15.13 to

486.00 μm across the eight species examined. A comparison of the phylogenetically

standardized contrasts revealed that light fiber diameter was still significantly correlated

with body mass (Fig 4a- inset), while subdivision diameter remained independent of body

mass (Fig. 4b- inset).

Mitochondrial and Nuclear Distribution

The relative distribution of mitochondria between the SS and IM regions of a

fiber can be described in terms of the ratio of SS mitochondrial density to IM

mitochondrial density (SS:IM intensity), as determined from the average intensity of the

SDH staining. Using this approach, we measured a SS:IM average intensity of 7.4 in the

light fibers of C. sapidus, which is consistent with a previous SS:IM calculation of 7.5

obtained using transmission electron microscopy and standard stereological

measurements of mitochondrial volume density in the same muscle (Hardy et al. 2009).

This indicates that the SDH staining method accurately reflects relative mitochondrial

distribution. A significant relationship between SS:IM intensity and fiber/subdivision

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Fig. 4 Fiber and subdivision sizes in the anaerobic light fibers (left panels) and aerobic dark fibers (right panels). Scatterplot of the mean cross-sectional diameter of the light fibers (a) and dark fiber subdivisions (b) plotted as a function of body mass. Insets show the relationship between the phylogenetically standardized contrast values for diameter and log-transformed body mass. In each case they describe the same relationship as the raw data. Mean cross-sectional diameter of the anaerobic light fibers (c) and aerobic dark fiber subdivisions (d) for each species. Species are arranged in order of increasing adult body mass and are categorized as either excellent swimmers (black) or non-swimmers (gray). Values shown are means±SEM (error bars in (a) and (b) are smaller than the symbols). See text for additional details.

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diameter indicates fiber size-dependant differences in the intracellular placement of

mitochondria. Across all eight species, we observed that the SS:IM intensity was higher

in both light fibers (r2=0.24, p<0.001) and dark fiber subdivisions (r2=0.50, p<0.001) with

larger diameters (Fig. 5a). Thus, there is a higher density of SS mitochondria relative to

IM mitochondria in larger fibers/subdivisions. Figure 5b shows the relationship between

the standardized contrasts for log-transformed SS:IM intensity and log-transformed

diameter. The significant positive relationship found for both fiber types in the raw data

was still present between the contrasts of the light fibers (p=0.025), though not the dark

fibers (p=0.255).

The relative distribution of nuclei can be examined in a similar way. By

examining the ratio between the SS nuclear number volume and the IM nuclear number

volume (SSNV:IMNV) it is possible to assess if nuclear position is different in

fibers/subdivisions of varying sizes. We observed a significant negative relationship

between SSNV:IMNV and diameter in both the light fibers (r2=0.55; p<0.0001) and the

dark fiber subdivisions (r2=0.28; p<0.001) (Fig. 5c). This trend indicates that there is a

lower relative density of SS nuclei than IM nuclei per volume of cytoplasm in larger

fibers. When the phylogenetically standardized contrasts were correlated, there was still a

significant negative relationship between SSNV:IMNV and diameter in the light fibers

(p=0.006), but no longer in the dark fibers (p=0.074) (Fig. 5d).

Mitochondrial and Nuclear Density

We evaluated the mass specific scaling of mitochondrial density (from the total

average SDH staining intensity) using the standard scaling equation, mitochondrial

density = aMb, where a is a coefficient, M is body mass and b is the mass-specific scaling

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Fig. 5 Differences in mitochondrial and nuclear distribution with size for anaerobic light fibers (○) and aerobic dark fiber subdivisions (●). (a) Scatterplot of raw data for the ratio of SS to IM average intensity value (SS:IM intensity) and diameter. The SS:IM intensity increases with diameter in both the light fibers (r2=0.24; p<0.001) and the dark fibers (r2=0.50; p<0.001). This reflects an increase in density of SS mitochondria and a decrease in density of IM mitochondria that occur as fibers get bigger. (b) Standardized independent contrast values of log-transformed SS:IM intensity plotted as a function of log-transformed diameter. The significant positive relationship observed in the raw data disappears in the dark fibers (p=0.255), but persists in the light fibers (p=0.025). (c) Scatterplot of raw data for SSNV:IMNV and diameter. The SSNV:IMNV decreases with diameter in both the light fibers (r2=0.55; p<0.0001) and the dark fiber subdivisions (r2=0.28; p<0.0001). This negative relationship results from a decrease in the SSNV and a constant IMNV with size (data not shown) (d) Standardized independent contrast values of log-transformed SSNV:IMNV plotted as a function of log-transformed diameter. The negative relationship observed in the raw data disappears in the dark fibers (p=0.074), but persists in the light fibers (p=0.006).

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exponent. The b values for the light and dark fibers based on total average intensity

values (Fig. 6) were consistent with b values from C. sapidus muscle for citrate synthase

activity and mitochondrial volume density, which are standard measures of total aerobic

capacity (Hardy et al. 2009; Johnson et al. 2004), again indicating that the SDH method

effectively represented relative mitochondrial density.

The total average SDH intensity was lower in larger fibers over the range of sizes

encompassing both the light fibers and dark fiber subdivisions (Fig. 7a). The dark fiber

subdivisions had a strong negative relationship between total intensity and subdivision

size (r2=0.60; p<0.001), while the light fibers showed a weaker, though still significant,

negative relationship (r2=0.06; p<0.001). Aerobic dark fibers are characterized by high

mitochondrial densities (~25% in C. sapidus; Johnson et al., 2004), while anaerobic light

fibers, have substantially lower mitochondrial densities (<1% in C. sapidus; Hardy et al.

2009). In combination, however, the dark and light fibers form a fairly continuous

spectrum of sizes with decreasing total intensity values with fiber/subdivision diameter

(Fig. 7a).

With respect to nuclei, the IMNV was independent of diameter for the light fibers

(r2=0.0013; p=0.3015) (data not shown). (Since the small aerobic subdivisions frequently

had no IM nuclei, the IMNV could not always be accurately calculated and so no

relationship to diameter could be provided for these fibers). These results contrast with

the SSNV, which was negatively related to diameter for both light fibers (r2=0.63;

p<0.0001) and dark fiber subdivisions (r2=0.24; p<0.0001) (data not shown). Combined,

the size effects on IMNV and SSNV resulted in a myonuclear domain that increased with

diameter for both light fibers (r2=0.43; p<0.0001) and dark fibers (r2=0.20p<0.0001) (Fig.

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Fig. 6 Relationship between total average SDH staining intensity and body mass for anaerobic light fibers (○) and aerobic dark fiber subdivisions (●). This graph shows the mass-specific metabolic scaling of aerobic capacity in each fiber type. The regression equation for the dark fibers is Total Intensity=2.38M – 0.15 (r2=0.547, p=0.001; M is body mass) and for the white fibers Total Intensity=1.46M – 0.03 (r2=0.018, p=0.58). See text for additional details

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Fig. 7 Differences in mitochondrial density, from total average SDH intensity, (a) and myonuclear domain (b) with size, as well as the relationship between mitochondrial density and myonuclear domain (c) for anaerobic light fibers (○) and aerobic dark fiber subdivisions (●). (a) Total intensity of SDH staining decreases with diameter in both light fibers (r2=0.06; p<0.001) and dark fiber subdivisions (r2=0.60; p<0.001). (b) Myonuclear domain increases with diameter in both the light fibers (r2=0.43; p<0.0001) and the dark fiber subdivisions (r2=0.20; p<0.0001), which results from a decrease in SSNV and a constant IMNV with size (data not shown) (c) Relationship between myonuclear domain and total average intensity in anaerobic light fibers and aerobic dark fiber subdivisions. Black lines connect the light and dark fiber values from the same species and are for visualization purposes only. Thus, myonuclear domain is significantly higher in fibers with lower aerobic capacity (i.e., light fibers) in all species except for O. ocellatus (*) and P. sayi (†).

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7b). That is, while the IMNV remained constant, the number of SS nuclei per volume of

fiber/subdivision was lower in larger fibers, which meant that each nucleus was

responsible for servicing a larger volume of cytoplasm.

Figure 7c shows the relationship between myonuclear domain and total aerobic

capacity, as indicated by total average intensity value from SDH staining, for all eight

species. We demonstrated that in each species except for one (O. ocellatus), the anaerobic

light fibers, which are characterized by a much lower aerobic capacity than the aerobic

dark fibers, exhibit smaller myonuclear domains. Only O. ocellatus and P. sayi did not

have significantly different myonuclear domains between the light and dark fibers.

DISCUSSION

Species of brachyuran crabs in the family Portunidae are characterized by their

exceptional swimming abilities. The blue crab, C. sapidus, for example, has been shown

to swim at peak burst speeds up to 0.5 m/s and maintain sustained speeds of ~0.1-0.2 m/s

during migratory swims (Carr et al. 2004; Zimmer-Faust et al. 1994). The evolution of

swimming in the portunids has been facilitated by a number of morphological adaptations

to their 5th periopods, carapace and basal swimming musculature (Hartnoll 1971).

Based on our 16S rDNA phylogeny (Fig. 2), Carcinus maenas and Ovalipes

ocellatus may be historically misplaced in the family Portunidae and are likely more

closely related to the Families Xanthidae (M. mercenaria) and Cancridae (C. magister).

This is consistent with other recent molecular phylogenies, which characterized Ovalipes

as the most distant genera within the Portunidae (in a 16S rDNA based phylogeny

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exclusively of portunids; Mantellato et al., 2007) and grouped Carcinus with the

Cancridae and not Portunidae (in a multi-family phylogeny of brachyurans based on the

gene for arginine kinase; Mahon and Neigel 2008). Differences in basic body shape and

swimming ability would also suggest that O. ocellatus and C. maenas are more closely

related to the xanthid and cancrid crabs. They both lack the prominent anterolateral

spines that typify most portunids and share a more oval/hexagonally shaped carapace that

is more characteristic of xanthids and cancrids. Furthermore, the 5th periopods in C.

maenas resemble unmodified walking legs, not oar-like paddles, and this species has an

extremely limited swimming capacity. However, the closely related O. ocellatus exhibits

the same flat, broadened 5th periopods as the other portunids and is also a proficient

swimmer (though not as good as members of Callinectes and Portunus) (personal

observation).

Our phylogeny suggests that swimming ability and some of the morphological

modifications associated with swimming have evolved multiple times within the

brachyurans: at least once by the portunids, as we classify them here, and once within the

genus Ovalipes, which is probably not a portunid. Sustained swimming is aerobically

powered by the dark fibers and requires high rates of ATP turnover, which necessitates

short intracellular diffusion distances (and hence a smaller diameter) (Crow and

Kushmerick 1982; Kushmerick et al. 1992). How then is sustained aerobic swimming

activity supported in the relatively large dark fibers and do all swimming crabs solve this

problem in the same way?

In C. sapidus, the dark fibers have evolved a network of highly-perfused,

mitochondria-rich subdivisions (Hardy et al. 2009; Johnson et al. 2004; Tse et al. 1983)

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that increase in number, but maintain a constant size (~35 μm) during fiber growth

(Johnson et al. 2004). The perfused subdivisions result in greatly reduced diffusion

distances and increased oxygen flux to the mitochondria. In this way the aerobic fibers

preserve an effectively small metabolic diameter throughout development. Reaction-

diffusion mathematical models have demonstrated that the high rate of ATP turnover

required of steady-state swimming activity in the blue crab dark fibers could not be

supported at the large sizes that would exist if they were not subdivided (~300 μm

diffusion distance) (Hardy et al. 2009; Kinsey et al. 2007). However, the same high

reaction rate could be achieved over the short diffusion distances characteristic of the

smaller subdivisions (Johnson et al. 2004). Thus, subdividing the dark fibers appears to

be essential to the evolution of sustained swimming behavior in C. sapidus.

In the current study, we observed that the dark fibers were highly subdivided in

all of the swimming species that we examined (P. sayi, P. spinimanus, P. gibbesii, O.

ocellatus, and C. sapidus) (see Fig. 2 for representative examples). It therefore appears

that all swimming crabs have evolved the ability to support high levels of sustained

aerobic activity in the same way, by dividing their dark fibers into metabolically smaller

functional units, while the contractile functional unit appears to be the entire fiber (see

Hardy et al. 2009). Presumably, these aerobic dark fibers have secondarily evolved from

anaerobic light fiber precursors, which in crustaceans can have very large diameters

(>600 μm) (Boyle et al. 2003; Hardy et al. 2009; Jimenez et al. 2008). This notion is

supported by the essentially non-subdivided morphology of the aerobic fibers in C.

maenas, a species that cannot swim, compared to the highly subdivided fibers in the

closely related O. ocellatus, a species well-adapted for swimming.

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Previous work has shown that modest increases in diameter or ATP turnover rate

result in substantial diffusion constraints to aerobic metabolic processes in C. sapidus

(Hardy et al. 2006; Kinsey et al. 2007). If the dark fibers evolved from the large

anaerobic light fiber precursors then the development of subdivisions resulted from a

unidirectional pressure to be smaller as sustained swimming behavior evolved. Thus,

dark fiber subdivisions are likely only as small as they need to be to support the rate of

ATP turnover required by aerobic swimming, but no smaller. Accordingly, we found that

species with efficient swimming abilities had smaller average subdivision sizes than

species that could not swim (Fig. 4B,D). This was true even for O. ocellatus, which

appears to have independently evolved the ability to swim. However, it is interesting that

subdivisions in O. ocellatus, while relatively small, are still significantly larger on

average than the other swimming portunids (P. sayi, P. gibbesii, P. spinimanus, and C.

sapidus). This may reflect the fact that O. ocellatus lacks some of the morphological

adaptations for swimming that are apparent in the other swimming crabs (e.g. a modified

carapace shape). Therefore, they may not be able to attain the sustained swimming

velocities characteristic of C. sapidus and the genus Portunus. In this case, ATP turnover

demands would likely be lower, and selective pressure for small subdivisions and high

mitochondrial densities would be lessened.

The non-swimming species (C. maenas, C. magister and M. mercenaria) also

possessed subdivided dark fibers (see Fig. 3), although subdivision of these fibers was far

less extensive than in the other swimming species (Fig. 4d). These species are generally

associated with the benthic environment and move by walking with a relatively low

frequency of limb motion. This mode of locomotion requires a much lower rate of ATP

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turnover than sustained pelagic swimming, which is powered by a high contraction

frequency. Hence, aerobic metabolic rates in the dark fibers of the non-swimming crabs

can be supported with larger subdivisions. These differences are consistent with

behavioral observations. In pilot experiments, we observed that C. maenas, when

suspended in the water column of an aquarium, was only capable of sustaining

continuous aerobic swimming for an average of 25 min, while some of the swimming

crabs (C. sapidus, P. spinimanus, O. ocellatus) were capable of continuously swimming

for >8 hr. It is interesting that the stone crab, M. mercenaria, has dark fibers that are

somewhat more poised for aerobic function (i.e., moderately subdivided), despite the fact

that these animals cannot swim. It is likely that the 5th periopods in these animals are

used for holding on tightly to rocky substrates for sustained durations, although the ATP

turnover rate required for this is clearly less than for swimming. Thus, fiber subdivision

is not exclusive to swimming behavior, and may also be important for sustained walking

and gripping behavior.

The light fibers, in contrast to dark fibers, power anaerobic burst-swimming and

only rely on maximal rates of aerobic metabolism during recovery from exercise (Curtin

et al. 1997; Kushmerick and Paul 1976). However, aerobically fueled, post-contractile

recovery requires much lower ATP turnover rates than steady-state swimming in the dark

fibers. As a result of the decreased metabolic demands, there is apparently little or no

selective pressure for small light fibers. Supporting this view was the direct relationship

between light fiber diameter and body mass (Fig. 4a), which suggests that each species

experiences relatively unconstrained hypertrophic growth during development. This

multispecies relationship was independent of phylogeny and consistent with previous

153

observations in C. sapidus, which undergo an ontogenetic increase in light fiber diameter

with body mass (Boyle et al. 2003; Kinsey et al. 2005). Thus, within a single species and

across many species, diffusion does not appear to limit light fiber diameter because the

rates of aerobic ATP turnover are so low. However, at least in C. sapidus, this is only the

case because the mitochondria undergo a dramatic shift in distribution as the fibers get

bigger. In small fibers from juveniles mitochondria are uniformly distributed throughout

the IM and SS regions of the cell, but in the large fibers from adults mitochondria are

found clustered almost exclusively at the sarcolemma (Boyle et al. 2003; Hardy et al

2009). Mitochondrial function is dependent on adequate diffusive flux of O2 from the

blood and small metabolites like ATP to cytosolic ATPases. Thus, a shift in mitochondria

toward a SS distribution during fiber growth reflects the need to minimize diffusion

distances for O2, at the expense of larger diffusion distances for small metabolites. Hardy

at al. (2009) used a reaction-diffusion mathematical model to demonstrate that the

measured rate of ATP turnover in the adult (large) light fibers in C. sapidus can only be

met when the mitochondria cluster at the sarcolemma, thus demonstrating the functional

rationale for this ontogenetic reorganization (Hardy et al. 2009).

If the above interpretation is correct, then we would expect to see the same fiber-

size specific differences in mitochondrial distribution between small and large light fibers

in the present study. In this case, however, the observed differences would not reflect

ontogenetic changes in distribution, but rather would represent variations in the relative

diffusion constraints in adult muscle of species with different maximum fiber sizes. We

found that the SS:IM average SDH intensity ratio was higher in larger fibers indicating

that there were more SS mitochondria relative to IM mitochondria as fiber size increased.

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We have now demonstrated in multiple species of crustaceans that mitochondrial

distribution changes in response to diffusion constraints. Nyack et al. (2007)

demonstrated that the same pattern exists during growth of fish white muscle.

Furthermore, we have shown that the same fiber size-dependant distribution occurs in

both the light fibers and the dark fibers, suggesting that this is an aspect of cellular design

adopted by multiple muscle fiber types.

While the positive relationship between SS:IM intensity and diameter was

significant in both the light and dark fibers in the raw (phylogenetically uncorrected) data

(Fig. 5a), a comparison of the phylogenetically standardized contrasts revealed that the

relationship was only independent of phylogeny in the light fibers (Fig. 5b). Thus,

mitochondrial distribution in the light fibers is not the product of phylogenetic inertia;

that is, it does not occur because of a shared common ancestry between these species.

This finding further supports the notion that mitochondrial distribution is a plastic

property that can change in response to prevailing diffusion conditions. The absence of a

relationship in the dark fibers indicates that a phylogenetic signal largely explains the

distribution of mitochondria in the subdivisions (see below).

Nuclei, unlike mitochondria, do not rely on oxygen directly, yet they (and their

associated synthetic apparatus) are involved in the simultaneous transcription, translation

and diffusive flux of a variety of molecules ranging in size from small metabolites, to

larger macromolecules, and potentially membrane bound vesicles. In C. sapidus, nuclei

had a pattern of redistribution during fiber growth that was the opposite of that seen for

mitochondria (Hardy et al. 2009). In the smallest juvenile fibers nuclei were located

exclusively in the SS region of the cell, but as fiber size increased nuclei had SS, as well

155

as an abundance of IM nuclei. A reaction-diffusion model revealed that without the size-

dependent shift in nuclear distribution, relevant rates of transcription/translation would

decrease by three orders of magnitude. We demonstrated the same relationship between

nuclear distribution and fiber size in both light and dark fibers in the eight species

examined in this study. The SSNV:IMNV ratio was always lower in larger fibers, which

reflected an increased number of IM nuclei relative to SS nuclei (Fig. 5c). Nuclei appear

to solve the problem of long intracellular diffusion distances in larger fibers by shifting

toward a more IM distribution. As seen for mitochondrial distribution, however, the

relationship between nuclear distribution and diameter was significant in a comparison of

the phylogenetically weighted contrasts only in the light fibers (Fig. 5d).

Why are the fiber/subdivision size specific differences in mitochondrial and

nuclear distribution independent of phylogeny only in the light fibers? Since the rate of

aerobic recovery in the light fibers is relatively low, there does not seem to be a limit on

fiber size and as we have shown, fiber size in the light fibers is not linked to phylogeny

(rather it is strongly related to body mass; Fig. 4a). Thus, patterns of cellular organelle

distribution, which are directly dependant on fiber size, are independent of phylogeny in

the light muscle. In contrast, subdivision size in the dark fibers is highly constrained by

aerobic demand and variation in ATP demand is strongly linked to behavior (i.e.,

swimmers versus non-swimmers/walkers). It is apparent from our phylogeny that the

eight species we examined group strongly according to their mode of locomotion (see

Fig. 2). Thus, organelle distribution is intrinsically linked to phylogeny, despite that fact

these patterns may not necessarily be the direct result of a shared ancestry.

156

Figure 7a demonstrates that mitochondrial density was inversely related to fiber

or subdivision size. These data support the generally accepted relationship between fiber

type, oxidative capacity and fiber size. Highly oxidative (aerobic) fibers have small

diameters and high mitochondrial densities, compared to glycolytic (anaerobic) fibers,

which are much larger in diameter and have very low mitochondrial densities. Like

mitochondrial density, nuclear density also decreased with size. However, nuclei are

typically characterized in terms of myonuclear domain, which is simply the inverse of

nuclear number volume (a measurement of nuclear density) (Fig. 7b). In both the dark

and light fibers, myonuclear domain was larger in fibers/subdivisions with an increased

diameter. Increases in domain with fiber size have also been reported during hypertrophic

growth in mammalian skeletal muscle (Bruusgaard et al. 2005; Cheek et al. 1971;

Giddings and Gonyea 1992).

Another interesting finding was that myonuclear domain was negatively related to

aerobic capacity. Figure 7c demonstrates that the domain size was significantly higher in

the light fibers than the dark fiber for each species, excluding P. sayi and O. ocellatus.

This is not completely surprising given that protein synthesis rates are generally

recognized to be higher in smaller slow-twitch oxidative (aerobic) fibers than larger fast-

twitch glycolytic (anaerobic) fibers (Bates and Millward 1983; Garlick et al. 1989;

Goldberg 1967; Kelly et al. 1984; Laurent et al. 1978). This finding is also consistent

with the work of Bruusgaard et al. (2003) who suggested that fast glycolytic fibers are

more stable than slow oxidative fibers, owing to much longer protein half-lives, which

may explain why these authors observed nuclear numbers in glyocolytic fibers that did

not vary in proportion to volume as in the oxidative fibers, but rather varied in proportion

157

to surface area. A lower protein turnover rate would allow each nucleus to efficiently

service a larger volume of cytoplasm and over potentially longer intracellular diffusion

distances.

It is generally proposed that nuclear numbers increase during hypertrophy in

skeletal muscle fibers to maintain a constant myonuclear domain size (Bruusgaard et al.

2003, 2006; Cheek 1971; Giddings and Gonyea 1992; Jaspers et al. 2006; Roy et al.

1999). However, we propose that it is the maximum diffusion distance within that

domain that needs to be kept small. Nuclear domain can be conserved during growth by

increasing nuclear density only at the fiber periphery or by increasing nuclear density

both in the SS region and in the IM region. During hypertrophic growth in fibers of C.

sapidus myonuclear domain is conserved by the latter approach (Hardy et al. 2009), and

Figures 3a,b and 5c,d indicate that the same pattern exists across multiple species. While

the myonuclear domain size is higher in larger fibers/subdivisions (Fig. 7b), the increased

IMNV means that intracellular diffusion distances for large proteins and mRNA

molecules will be much smaller than they would be if all nuclei were restricted to the

fiber periphery. Accordingly, we found that the mean distance between any two

myonuclei was fairly constant across species and between fiber types (regardless of fiber

diameter and nuclear distribution), ranging from 23.5 ± 0.34 to 36.3 ± 0.58 μm in light

fibers and 20.7 ± 0.73 to 29.5 ± 0.58 μm in the dark fibers, which is consistent with

nuclear spacing in mouse skeletal muscle with an exclusively SS distribution (Bruusgaard

et al. 2003).

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ACKNOWLEDGEMENTS

The authors are grateful for the helpful comments of Drs. Richard Dillaman, Ann Pabst,

Richard Satterlie and Robert Roer, as well as the technical assistance of Mark Gay and

Dr. Marcel van Tuinen. This research was supported by a National Science Foundation

grant to STK (IOS-0719123) and a National Institute of Health grant to STK (R15-

AR052708).

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