Controversy exists over the scaling of oxygen consumption with body mass in vertebrates. A combination of biochemical and structural analyses were used to examine whether individual elements influencing oxygen delivery and demand within locomotory muscle respond similarly during ontogenetic growth of striped bass. Mass-specific metabolic enzyme activity confirmed that glycolytic capacity scaled positively in deep white muscle (regression slope, b=0.1 to 0.8) over a body mass range of ∼20–1500 g, but only creatine phosphokinase showed positive scaling in lateral red muscle(b=0.5). Although oxidative enzymes showed negative allometry in red muscle (b=–0.01 to –0.02), mass-specific myoglobin content scaled positively (b=0.7). Capillary to fibre ratio of red muscle was higher in larger (1.42±0.15) than smaller (1.20±0.15)fish, suggesting progressive angiogenesis. By contrast, capillary density decreased (1989±161 vs 2962±305 mm–2)as a result of larger fibre size (658±31 vs 307±24μm2 in 1595 g and 22.9 g fish, respectively). Thus, facilitated and convective delivery of O2 show opposite allometric trends. Relative mitochondrial content of red muscle (an index of O2demand) varied little with body mass overall, but declined from ∼40% fibre volume in the smallest to ∼30% in the largest fish. However, total content per fibre increased, suggesting that mitochondrial biogenesis supported aerobic capacity during fibre growth. Heterogeneous fibre size indicates both hypertrophic and hyperplastic growth, although positive scaling of fibre myofibrillar content (b=0.085) may enhance specific force generation in larger fish. Modelling intracellular PO2distribution suggests such integrated structural modifications are required to maintain adequate oxygen delivery (calculated PO2 5.15±0.02 kPa and 5.21±0.01 kPa in small and large fish, respectively).

Numerous studies have shown that biological processes, from metabolic enzyme activity to O2 consumption of an animal, scale with body mass, for organisms of greatly differing maximum size and species relatedness(Burness et al., 1999; West et al., 2002). Structural and functional characteristics of the cardiovascular system also scale with body mass (Schmidt-Nielsen,1984), although both aspects are rarely examined in a single study. Cells are thought to be as small as possible, commensurate with their function, in order to minimise O2 and metabolite diffusion distances, e.g. aerobic skeletal muscle fibres used for sustained locomotion tend to be smaller than anaerobic fibres used for ballistic activity. Such scaling effects are known to be one of the most influential factors defining metabolic rate (Schmidt-Nielsen,1984). However, muscle fine structure may also be remodelled during ontogenetic growth to augment functional capacity. Interestingly,similar changes may also occur in response to lowered environmental temperature in fishes (Egginton, 1998a), suggesting similar adaptive responses may be invoked if a metabolic error signal is derived from a mismatch in either supply or demand.

The capacity for terminal oxygen delivery represented by tissue capillarity has been measured in fish muscle using a number of different indices of varying utility (Egginton,1992) and shown to be responsive to exercise(Sänger, 1992), cold acclimation (Egginton and Sidell,1989) and seasonal temperature acclimatisation(Egginton and Cordiner, 1997). However, little is known of the process during normal ontogenetic growth, and how it is controlled. Growth of new capillaries (angiogenesis) is thought necessary to increase oxygen supply in response to increased oxygen demand associated with physiological challenges and during development(Hudlická et al.,1992). It is probable that the mechanisms involved include either local biochemical cues such as growth factor release, or mechanical factors such as elevated shear stress (Egginton,2002). Changes in the microcirculation are often paralleled by changes in muscle fine structure, such as mitochondrial volume density,appearing to optimise the balance between oxygen supply and demand(Weibel et al., 1996). In addition, fibre hypertrophy (increased size) and hyperplasia (increased number) may accompany angiogenesis, and such remodelling of the host tissue can affect the distribution of blood vessels. For example, hypertrophy will increase intramuscular diffusion distances, with a proportional decline in oxygen tension within individual muscle fibres(Egginton, 1998), but the heterogeneity of capillary supply (i.e. variance of intercapillary distances)appears to be preserved irrespective of body mass by an adaptive angiogenic response (Degens et al.,2006).

Many studies have determined the interspecific allometric response of basal metabolic rate (BMR), and most recent studies agree that in mammals oxygen demand is proportional to body mass2/3(White and Seymour, 2005). Also of interest is the scaling exponent for structural and biochemical determinants of oxygen supply and demand in locomotory muscle, as this probably underlies an animals' behavioural repertoire. A complementary effect of organism size on indices of oxygen supply to that observed with BMR has been demonstrated in mammals (Hoppeler et al., 1981; West et al.,1997). However, there have been few estimates of the allometric response of oxygen supply in fish, the only studies known to the authors being on the relatively sluggish eels (Egginton,1992) and tilapia (Kisia and Hughes, 1992). By contrast, the allometric relationships among enzymes of intermediary metabolism in skeletal muscle have been studied in a number of fish species. Somero and Childress(Somero and Childress, 1980)proposed a positive allometry for glycolytic and a negative allometry for oxidative enzymes, which was subsequently confirmed in other species(Garenc et al., 1999; Norton et al., 2000; Walsh et al., 1989).

The present study provides the first integrative analysis of scaling in the structural limits to oxygen supply and demand, coupled with the metabolic profile of skeletal muscle, using a highly active fish species where these may be expected to limit locomotory performance. A mathematical model was used to predict changes in oxygen tension across red muscle fibres of average composition as a consequence of ontogenetic growth, and to explore the relative importance of different elements to this response.

Experimental animals and tissue collection

Eleven striped bass (Morone saxatilis Walbaum) were sampled, over a range of body mass (BM) between 22.9 g and 1595 g. This is an active species, migrating up the Eastern seaboard of the USA, which displays impressive muscle plasticity in the face of changing environmental temperature(Sidell and Moerland, 1989). Fish were held at the University of Maine under controlled photoperiod (12 h:12 h light:dark) in filtered, aerated tap water and kept at 15±1°C for a minimum of 4 weeks before sampling. Fish were killed by a blow to the head and severing the spinal cord. A strip of slow oxidative muscle from the hypaxial lateral line triangle just posterior to the first dorsal fin, and samples of fast glycolytic (white) muscle close to the spinal column at the same position were carefully dissected.

Biochemical assays

Measurements of maximal activities of phosphofructokinase (PFK) and cytochrome oxidase (COX) were performed on fresh tissue shortly after dissection. Tissue used in measuring the maximal activities of citrate synthase (CS), pyruvate kinase (PK) and lactate dehydrogenase (LDH) were quickly frozen in liquid nitrogen and stored at –70°C until assayed. Tissue was homogenised in a 10% w/v ice-cold buffer (40 mmol l–1 Hepes, 1 mmol l–1 EDTA, 2 mmol l–1 MgCl2, pH 7.8 at 15°C), except for tissues used for COX analysis (see below). Tissue was first minced on a chilled stage,then homogenised with two 10–15 s bursts with a Tekmar Tissuemizer,keeping the homogenate on ice between bursts. Homogenisation was completed by hand using a Tenbroeckground glass homogeniser. Dithiothreitol (DTT) was added(final concentration of 2 mmol l–1) for PFK and LDH assays. Background activities were measured in the absence of initiating substrate and subtracted from total activity in the presence of substrate. Maximal activities were determined using a thermostatted cuvette carrier-equipped spectrophotometer (Perkin-Elmer Lambda 6) by measuring the rate of oxidation or reduction of pyridine nucleotides at 340 nm for 5 min, except when noted differently, with assays performed in triplicate at 15±0.5°C. Details of assay conditions are described below, following modification from original protocols (Egginton,1986b; Norton et al.,2000), including the composition of the final reaction mixture,and the substrate/cofactor added to initiate the reaction.

Phosphofructokinase (PFK; EC 2.7.1.11): 7 mmol l–1MgCl2, 200 mmol l–1 KCl, 1 mmol l–1 KCN, 2 mmol l–1 AMP, 0.15 mmol l–1 NADH, 2 i.u. ml–1 aldolase, 10 i.u. ml–1 triosephosphate isomerase, 2 i.u. ml–1glycerol-3-phosphate dehydrogenase, 75 mmol l–1triethanolamine, pH 8.4 at 15°C; initiated by 2 mmol l–1ATP + 4 mmol l–1 fructose 6-phosphate.

Lactate dehydrogenase (LDH; EC 1.1.1.27): 0.15 mmol l–1NADH, 1 mmol l–1 KCN, 50 mmol l–1 imidazole,pH 7.7; initiated by 5 mmol l–1 pyruvate.

Pyruvate kinase (PK; EC 2.7.1.40): 150 mmol l–1 KCl, 1 mmol l–1 KCN, 10 mmol l–1 MgSO4,0.15 mmol l–1 NADH, 5 mmol l–1 ADP, 10 i.u. ml–1 LDH, 50 mmol l–1 imidazole, pH 7.1;initiated by 2.5 mmol l–1 phosphoenol pyruvate.

Creatine phosphokinase (CPK, EC 2.7.3.2): 10 mmol l–1MgCl2, 20 mmol l–1 glucose, 10 mmol l–1N-acetyl-cysteine, 1 mmol l–1ADP, 10 mmol l–1 AMP, 0.7 mmol l–1NADP+, 1 i.u. ml–1 hexokinase, 1 i.u. ml–1 glucose-6-phosphate dehydrogenase, 100 mmol l–1 imidazole, pH 7.7; initiated by 35 mmol l–1 creatine phosphate.

Citrate synthase (CS, EC 4.1.3.7): 0.25 mmol l–1 DTNB(Ellman's reagent), 0.4 mmol l–1 acetyl CoA, 75 mmol l–1 Tris-HCl, pH 8.2; initiated by 0.5 mmol l–1 oxaloacetate, and monitored by production of the reduced anion of DTNB at 412 nm.

Cytochrome oxidase (COX, EC 1.9.3.1): Tissue was homogenised in 50 mmol l–1KH2PO4/KH2PO4, 0.05% Triton X-100,pH 7.5. The assay medium consisted of 10 mmol l–1K2HPO4/KH2PO4, 0.65% (w/v) reduced(Fe2+) cytochrome c and 0.93 mmol l–1K3Fe(CN)6; initiated by the addition of homogenate and measured by oxidation of reduced cytochrome c at 550 nm.

Myoglobin: homogenates (10–15% w/v) were prepared using 2 mmol l–1 DTT, 50 mmol l–1 phosphate buffer, pH 7.4, sonicated 2×5 s, and supernatants from high-speed (10,000 g) centrifugation were taken for analysis. Spectrophotometric scans were taken between 620 and 490 nm, including the oxymyoglobin peaks at 581 and 543 nm, and absorbance calculated with baseline (nonspecific absorbance) subtracted. Overestimation of myoglobin content, because of contamination by haemoglobin, was estimated by gel permeation chromatography of red muscle homogenates, using a BioGel (BioRad, Hercules, CA, USA) P-100(15 mm×280 mm) column equilibrated with 1 mmol l–1 DTT,5 mmol l–1 EDTA, 50 mmol l–1 Tris pH 7.6 at 5°C. Concentrations were calculated from pooled fractions, using 4 cm path length cuvettes, and millimolar extinction coefficients of ϵmM 581=14.6 and ϵmM 543=13.6 (Egginton,1986b).

Muscle fixation

Samples were pinned at resting length on strengthened cork and immersed in a fixative consisting of 1% glutaraldehyde, 4% formaldehyde, 0.1 mol l–1 phosphate buffer, 10% sucrose and 0.2% CaCl2(pH 7.3 and vehicle osmolality 482 mOsm), then post-fixed in buffered 1%osmium tetroxide (Egginton and Cordiner,1997; Egginton and Sidell,1989). Two to four blocks were prepared per fish, and one chosen at random for examination. For light microscopy, semi-thin (0.5 μm)sections were cut and stained with 1% Toluidine Blue, then viewed under an Olympus BH-2 microscope with a drawing arm. For transmission electron microscopy, ultra-thin (∼80 nm) sections were cut and mounted on Formvar-coated copper grids, stained with 30% uranyl acetate and Reynold's lead citrate, then viewed under a Jeol 1200 electron microscope at an accelerating voltage of 60 kV.

Morphometry

Semi-thin (0.5 μm) sections were viewed at a magnification of ×500 to obtain estimates of capillary density (CD; mm–2) capillary to fibre ratio (C:F) and mean fibre area (f;μm2) using an unbiased sampling protocol(Egginton, 1990). Digital images (×500, Zeiss Axioskop 2 plus microscope, AxioCam MRc camera) were imported into ImageJ software (NIH, USA), individual fibres outlined to obtain area and perimeter, and fibre size distribution constructed.

The principles of stereology, an application of geometrical probability theory that permits extrapolation of structural information from n to n+1 dimensions [e.g. length to surface, area to volume(Weibel, 1979)] were used to quantify muscle fine structure from electron micrographs. Volume and surface densities represent the area and boundary length of any structure as a proportion of a reference cross-sectional area; surface to volume ratio and profile cross-sectional areas are calculated in a similar manner. A systematic random sampling regime was used to quantify muscle fine structure as volume density (Vv, volume of object per unit volume of reference; μm3 μm–3), surface density(Sv, surface area of object per unit volume of reference;μm2 μm–3), and surface to volume ratio(S/V; μm2 μm–3) of components relevant to oxygen delivery and consumption. Organelle content of muscle fibres was calculated as the product of volume density and fibre cross-sectional area. These results were analysed with respect to body mass using the allometric equation:
\[\ Y=aW^{b},\]
(1)
where Y is the parameter examined, a is a normalisation constant (the value of y-axis intercept), W is the body mass(g) and b is the scaling exponent (slope of the regression line)(Schmidt-Nielsen, 1984). The value of b will vary among organisms with different traits, and biological processes with different characteristics, and represents the sum of multiple influences on control. For whole body traits `positive allometry'means that the scaling slope is >1, whereas `negative allometry' means it is <1. However, for mass-specific traits, as used here, `positive allometry' means that the scaling slope is >0, whereas `negative allometry'means it is <0.

To illustrate the range of response associated with differences in body mass, a minimum of 20 capillaries from each of the two smallest and two largest fish were analysed at a final magnification of ×5400 to×12,934, to quantify microvessel structure and provide a nominal scoring of a range of angiogenic indices (Egginton et al., 2001). In addition, a montage containing 12 capillaries from each of the two smallest fish, and individual micrographs around 12 capillaries from each of the two largest fish (a montage was not possible at adequate resolution because of the lower capillary density) were taken at a magnification of ×2400. Volume density of mitochondria was calculated in four concentric annulae of equal area. The maximum radius of the outermost annulus was set at half the mean intercapillary distance, measured iteratively on the montage until a stable estimate of the mean was achieved. The median capillary radius was used as the value for the inner ring around the perimeter of the capillary (Egginton and Sidell,1989).

Mathematical modelling

The dimensionless Reynolds number was estimated for the smallest fish using the equation:
\[\ Re=(LU){/}{\nu},\]
(2)
where L is body length (116 mm for small fish), ν is the dynamic viscosity of water at 15°C (1.14 centistokes), and assuming a velocity, U, of 10 BL s–1 (BL, body lengths)as a reasonable estimate of cruising speed for striped bass of that size, at that temperature (Kerr,1953).
Capillary radius was used to estimate potential limits to microvascular blood flow (), according to the Hagan-Poiseuille equation:
\[\ {\dot{Q}}=({\pi}r^{4}\mathrm{MABP}){/}(8L{\eta}),\]
(3)
where r is vessel radius (μm), MABP is the mean arterial blood pressure, L is vessel length (mm) and η is blood viscosity (cP). Although values for these are not, to our knowledge, available for striped bass, MABP in rainbow trout is 3.2 kPa(Sandblom and Axelsson, 2005)and trout blood at the same temperature has a measured viscosity of 5.4 cP(Egginton and Rankin, 1998). Capillary length is an unknown so we performed two calculations, the first assuming individual vessel L varies proportionally with myotome length, and therefore body length, and the second assuming L is a constant in all body sizes. Total capillary length would then equate to(L×CD×muscle mass). Using a published regression equation for striped bass length vs BM(Rodnick and Sidell, 1995),and scaling of red muscle mass in trout as a guide to that in bass(Goolish, 1989), enabled calculation of upper and lower boundaries for changes in .

The combined effect of changes in fine structure on intracellular oxygen tension of slow muscle fibres was explored by means of a mathematical model of diffusion (Hoofd and Egginton,1997). Briefly, the potential oxygen delivery (determined by capillary supply) is distributed according to oxygen consumption (scaled according to mitochondrial volume), allowing for the diffusion distances involved (varying with fibre size) and oxygen permeability (given by the ratio of intracellular lipid to aqueous sarcoplasm), corrected for the kinetic effects of temperature (Q10), and partitioned among the distinct structural regions found in fish muscle fibres (subsarcolemmal and intermyofibrillar zones). For clarity the results are presented as wireframe three-dimensional plots.

Statistical analysis

Single-factor analysis of variance (ANOVA) was used for comparison of values, with Fisher's PLSD to estimate significance between groups. Sufficiency of sample size for stereological parameters was tested by determining the stability of population means on replicate analysis. Distribution analysis of fibre area used the Kolmogorov–Smirnow procedure and comparisons from Mann–Whitney U-tests. Data are presented as mean ± s.e.m. with number of fish (N) or observations (n) given in parentheses, as appropriate. For allometric relationships, the coefficient of determination (R2)corresponds to the amount of variation explained by the best-fit regression line, and the F-test was used to determine whether the slope was significantly different from zero (P<0.05).

Chemicals

All chemicals were of reagent grade or better quality (BDH or Sigma, Poole,Dorset, UK). Glutaraldehyde and Araldite resin were of EM grade (Agar Scientific Ltd, Stanstead, Essex, UK).

Enzyme activity

In white muscle, significant scaling effects were observed in mass-specific activities of PK, LDH and PFK (b=0.110, 0.342 and 0.105,respectively). Interestingly, the glycolytic enzyme CPK displayed strong positive allometry in both white and red muscle (b=0.824 and 0.528,respectively, R2=0.900 in both cases). The oxidative enzymes COX and CS demonstrated negative allometry in red muscle(b=–0.014 and –0.022, respectively), in contrast to the index of facilitated oxygen diffusion, mass-specific myoglobin content, which displayed positive allometry (b=0.745; Table 1).

Muscle histology

Representative muscle sections from large and small fish are shown in Fig. 1, illustrating the similar mitochondrial content, changes in fibre size and scaling of capillarity with body mass. Red muscle C:F increased with fish mass(R2=0.946), but mean fibre area, f, also increased (R2=0.760),hence decreasing CD (R2=0.929), with an apparent boundary between small and large size classes at 200–300 g BM(Fig. 2). A different fibre size distribution in small and large fish was evident(Fig. 3), being right-shifted in the latter (P<0.0001).

Muscle fine structure

The mitochondrial volume density of red muscle fibres, Vv(mit,f), showed little evidence for an established allometric relationship (b=–6.069×10–5, R2=0.255, n.s.; Fig. 4), reflecting the sum of changes in regional distribution for intermyofibrillar [Vv(mitimf,f), b=–1.340×10–5] and subsarcolemmal[Vv(mitss,f), b=–4.043×10–5] populations(Table 2). There was no significant change in total mitochondrial content of fibres, V(mit,f), given as the product of Vv(mit,f) and f (b=0.031, R2=0.233,n.s.; Table 3). Fibre hypertrophy associated with growth led to little change in the relative content of contractile material, Vv(myo,f). However, this was not simply a consequence of adjustments in other compartments(Fig. 4), as the product of Vv(myo,f) and f showed significant positive scaling (b=0.085, R2=0.799, P=0.001). Nuclei and intracellular lipid droplets occupied a constant, low proportion of muscle fibres(Table 3).

The extracellular space of red muscle showed a modest negative scaling response (b=–2.923×10–5, R2=0.561, P=0.020; Fig. 4), showing closer packing of fibres in large fish. Conversely, positive scaling was found for the volume of sarcoplasm in the intermyofibrillar zone(b=5.245×10–5, R2=0.819, P<0.001), although no significant relationship was found in the subsarcolemmal zone of muscle fibres(b=1.641×10–5, R2=0.112).

Vv(mit,f) decreased with increasing distance from the point of oxygen supply (capillary) in both large and small fish, when normalised as a percentage of the intercapillary distance (ICD), with the outer radius being 47% of the maximal ICD. In large fish there was a significant decrease in Vv(mit,f) as the ICD is approached(P<0.05), whereas for the smaller fish the reduction in radial distribution of mitochondria was more variable (n.s.), although at any relative distance from a capillary Vv(mit,f) was greater in the small than the large fish (Fig. 5). Consistent with the global analysis of muscle fine structure total mitochondrial content, given as the product of Vv(mit,f) and f, was greater in large than small fish (464±23 and 222±7 μm2,respectively; P<0.01).

Capillary fine structure

The lumen occupied a larger proportion of the capillary cross-sectional area during ontogenetic growth, following the trend for greater capillary area and lower S/V with increasing BM(Table 4). Other structural parameters known to vary with metabolic status showed little differences among the size classes (Table 4), and there were no significant differences in any of the angiogenic indices measured (Table 5). Consequently, estimates of theoretical maximum blood flow, (relative units), for individual vessels showed no significant difference between small and large fish under the boundary conditions that L does not vary with body size (small fish =2.362±0.123, large fish =2.062±0.038), or that it is reduced sixfold if L varies with body length(=2.062±0.141 and 0.383±0.010, respectively). Allowing for changes in capillary size, CD and red muscle mass, then microvascular volume in large fish is probably about fourfold greater than that in small fish, and with a similar MABP then the difference in would be at least as great.

Intracellular oxygen tension

Estimates of PO2 across a red muscle fibre of average composition suggest that oxygen tension is maintained during ontogenetic growth (mean PO2=5.148±0.016 kPa and 5.209±0.010 kPa for the smallest and largest fish,respectively). We used `in silico' analysis to explore the consequences of not undertaking the observed tissue remodelling. If fibre size varied inversely with body mass (i.e. hyperplasia rather than hypertrophy dominated) but all other influences were the same, then small fish modelled with fibre area appropriate for large fish show a reduced mean PO2 (3.791±0.024 kPa) as well as lower minimum PO2 (3.19 kPa vs 4.86 kPa with normal fibre size), whereas complementary changes applied to large fish made little difference to mean or minimum PO2(Fig. 6). Reversing the scaling of capillary cross-sectional area had a minor effect in fibres from small fish(mean PO2 increased to 5.263±0.015 kPa,minimum=4.97 kPa) or from large fish (mean PO2decreased to 5.084±0.011 kPa, minimum=4.84 kPa). However, a greater effect was seen by changing the number of capillaries around a fibre, with fibres from small fish modelled with capillary supply appropriate for large fish having a higher calculated mean and minimum PO2 (5.544±0.009 and 5.39 kPa,respectively). A reduction in mean PO2 to 4.559±0.018 kPa was calculated for a representative fibre from a large fish having the capillary supply of small fish, with the minimum PO2 reducing to 4.12 kPa. As there was very little difference in mitochondrial density between the two groups, the effects of reversing this were trivial, suggesting tight regulatory control.

Scaling considerations

The hydrodynamics of swimming in small organisms may be influenced by fluid viscosity. However, Reynolds number estimated for the smallest fish, Re=1.1×10–5, is well above the threshold for swimming to be affected by the inertial rather than the viscous regime,calculated to be around Re=300. Hence, even the smallest fish in the present study would be unaffected by the viscous effects of water(McHenry and Lauder, 2005). The present study also avoids really large fish where scaling effects appear to wane (Norton et al., 2000)such that the size range studied, spanning two orders of magnitude in body mass, appears to be optimal to explore the integrative nature of any ontogenetic scaling response.

Many recent studies have shown that the metabolic scaling exponent varies substantially among vertebrates, mostly between 2/3 and 1 (e.g. Glazier, 2005; White et al., 2006). Oxygen consumption has been reported to scale with an exponent of 0.793 in a survey of 69 fish species (Clarke and Johnston,1999). However, this reflects a range of ∼0.4–1.3 among species, with little obvious correlation with lifestyle or body form. Unfortunately, comparable data on scaling of O2 in striped bass are not available, although estimates of particular sized fish confirm that this is one of the more aerobic species, e.g. 150 mg O2h–1 kg–1 for 5075 g striped bass at 15°C [assuming an exponent of 2/3(Mitchell and Cech, 1994)]. In many vertebrates there is a non-linear (Type III) ontogenetic shift in scaling exponent, from isometric (b=1) in larval stages to negative allometry(b<1) in juveniles and adults(Bochdansky and Leggett, 2001). Such data do not exist for striped bass, but in spotted seatrout(Cynoscion nebulosus), which has a similar body form, a break in the allometric relationship occurs at 480 μg dry mass (∼2.4 g wet mass),from b=1.04 to b=0.78(Wuenschel et al., 2004). All the fish sampled in the present study may therefore be expected to lie on the same allometric curve.

The allometric dependence of metabolic rate on body size continues to be a controversial subject. Organisms exhibiting scaling exponents close to 3/4 for metabolic rate and close to 1/4 for internal times and distances, represent the theoretical maximal and minimal values for the effective surface area and linear dimensions for a volume-filling, fractal-like hierarchical branching vascular networks, respectively (West et al., 1999; White et al.,2007), suggesting that supply rates determine metabolic rates. However, the metabolic rate of isolated cells also declines with increasing body mass. In addition, the scaling exponent characterises the relationship between body mass and basal (resting) metabolic rate, when elements of the oxygen delivery pathway may be expected to display excess capacity. Another approach would therefore be to adopt a multiple-causes model of allometry(Suarez and Darveau, 2005),based on metabolic control theory that identifies multiple contributors to metabolic rate. This may be especially important at sub-maximal rates, but as the relevant input data are not available one may use maximal enzyme capacity as an index of potential energy flux through different pathways, with suitable caution. For oxygen supply and demand the situation is a little easier, since structure can only identify capacities, and substrate supply plays an increasing role in limiting whole animal O2. Therefore,the values for b in this study may be expected to differ from that for basal O2,and may better reflect O2max.

Finally, in a field where statistical significance is treated as essential to discussion about the possible mechanistic basis of scaling responses, we caution that this is not always helpful. Recall that P<0.05 is a value adopted by convention, but lacking any theoretical foundation, its biological relevance depending on both importance of the process (cf. blood pH vs body mass) and whether a parameter is viewed in isolation (cf. overall oxygen delivery and demand). The flux of oxygen is part of a cascade of events, each of which involves a resistance and capacitance term. Small differences in one element may still give rise to functionally important effects because of the multiplicative response of the system as a whole. We have previously shown this to be the case with thermal acclimatisation(Egginton et al., 2000) where between any two seasons a single morphometric parameter was difficult to identify as statistically significant, however, the integrated response was clearly season dependent. The negative scaling relationship in specific mitochondrial content we identify, with suitable caveats, as probably being important must be viewed as part of the integrative whole, e.g. these structural data are consistent with an independent estimate of oxidative capacity, that of enzyme activity.

Metabolism

Most studies on scaling of metabolic enzymes in fish have concentrated on white muscle because of its functional significance in rapid movements to avoid predation or capture food. The anaerobic enzymes PK and/or LDH showed a positive scaling exponent for mass-specific activity, potentially enabling a greater burst swimming performance in larger fish, with anaerobic enzymes in red muscle also contributing to power output(Somero and Childress, 1980). This interpretation was supported by a lack of scaling in inactive fish(Goolish, 1991) and in tissue not involved in locomotion (Childress and Somero, 1990). Subsequent studies have confirmed this general pattern, although interspecific differences are influenced by life history,activity levels and phylogenetic relationships(Childress and Somero, 1990). Hence, LDH and PK showed positive allometry (b>0) in white muscle of many fishes (Burness et al.,1999; Davies and Moyes,2007; Ewart et al.,1988; Martinez et al.,2000; Sullivan and Somero,1983; Torres and Somero,1988), whereas in striped bass positive scaling was found in small and medium, but not large (>1000 g) fish(Norton et al., 2000). The same trend was also demonstrated in the present study in which LDH scaled with a similar exponent (b=0.342) to that previously reported(b=0.31) (Norton et al.,2000), although PK had weaker positive allometry (b=0.110 and b=0.56, respectively). The different size ranges examined and sample sizes may explain this discrepancy, hence the overall scaling pattern may be weakened by values from larger fish. Although these enzymes may provide an index of sustained glycolytic capacity, whether or not they are rate-limiting, a better guide to burst activity may be derived from the capacity to re-phosphorylate the high-energy reservoir of phosphocreatine. Importantly, CPK also displayed positive allometry in trout white muscle(Burness et al., 1999) and in the present study, where the scaling exponent showed the strongest positive allometry (P<0.0001). By contrast, the oxidative enzymes COX and CS displayed negative allometry in fish white muscle(Davies and Moyes, 2007; Martinez et al., 2000; Torres and Somero, 1988; Tripathi and Verma, 2004). However, CS displayed no size dependence in other species(Burness et al., 1999; Torres and Somero, 1988). Again, such intraspecific differences in scaling may be attributed to variations in lifestyle (Sänger,1993), activity level (Burness et al., 1999) as well as diet, season and latitude(Sullivan and Somero, 1983). No size-dependence in COX or CS was found in white muscle in the present study, as previously reported for striped bass(Norton et al., 2000),suggesting recovery from exercise was not compromised by size.

There have been fewer studies on scaling of metabolic enzymes in fish red muscle. Importantly, this may provide an index of aerobic capacity during routine swimming, which for many species represents the majority of locomotory activity. In striped bass red muscle oxidative enzymes (CS and malate dehydrogenase, MDH) showed size independence, whereas glycolytic enzymes in the smallest size class had similar activity and positive scaling in both red and white muscle, suggesting that red muscle may contribute to anaerobic performance in small, but not large fish(Norton et al., 2000). Whether that reflects the poor differentiation among muscle type at that stage is unclear. In the present study, the only glycolytic enzyme to display significant scaling in red muscle was CPK, supporting the idea that in striped bass the red muscle may contribute to re-phosphorylation of phosphocreatine during burst swimming of larger fish. Consistent with this pattern is reduced activity of the oxidative enzymes, COX and CS, with increasing body mass.

Thus, the metabolic potential of skeletal muscle differs according to the requirement for O2, with the general size independence of aerobic enzyme activity suggesting a limitation met by positive scaling of glycolytic enzymes. Interestingly, there may be differential control of these responses,involving transcriptional regulation of anaerobic and post-translational regulation of aerobic enzyme activity(Davies and Moyes, 2007). In addition to enzymatic activity, aerobic capacity may also be determined by the structural limits to oxygen supply and demand (below). Indeed, there is compelling evidence that oxygen delivery is a limiting factor in aerobic metabolism with increasing cell size(Pörtner, 2002).

A decrease in activity of enzymes used in aerobic respiration with increasing body size is to be expected as mass-specific oxygen demand is inversely related to BM, and scaling patterns in aerobic enzymes may therefore be determined by capacity for oxygen transport(Schmidt-Nielsen, 1984). Enzyme activities are estimated under optimal conditions, so it is necessary to examine other aspects of the O2 delivery cascade to determine whether such capacity may be realised in vivo. Myoglobin concentration, [Mb], was found to be independent of size in white and cardiac muscle of sea raven (Ewart et al.,1988), a sluggish sculpin-like species, whereas cardiac [Mb]increased with body size in more active species such as tuna(Poupa et al., 1981) and salmonids (Ewart and Driedzic,1987). These data indicate a positive scaling of facilitated O2 diffusion in species with high aerobic enzyme capacity, as influenced by activity levels. This is supported by our data showing no allometric influence in white muscle (b=0.003) but positive scaling(b=0.745) in red muscle of a migratory piscivore, suggesting that decreased oxidative capacity is not a consequence of impaired facilitated O2 diffusion. To assess whether structural determinants of O2 supply and demand complemented these changes, we quantified the mitochondrial content and capillarity of red muscle.

Mitochondria

According to theory, natural selection may optimise both metabolic capacity and intracellular efficiency, by maximising the scaling of exchange surface areas and minimising the scaling of transport distances and times,respectively (West et al.,1999). However, as short diffusion distances facilitate rapid O2 flux to mitochondria and ATP flux to sites of demand, a large fibre size will probably reduce the aerobic capacity(Kinsey et al., 2007). Mitochondrial biogenesis accompanied growth in eel(Egginton and Johnston, 1982),but the higher Vv(mit,f) in the smallest fish on a radial distribution from a capillary suggests that oxygen delivery to support oxidative phosphorylation may decline with size in striped bass, possibly accentuated by an increase in average diffusion distances between mitochondria within growing fibres. Under steady-state, aerobic conditions it is generally agreed that the majority of cellular O2 is due to mitochondrial respiration. Oxidative enzymes show a similar negative allometric relationship (COX 52% and CS 66% reduction) to that of Vv(mit,f) (33% reduction) over the range of BM studied. Small differences between scaling of metabolic and structural indices of oxidative phosphorylation may be due to differences in allosteric modification in the former or remodelling within the latter, e.g. modifications in cristae surface area (Egginton et al.,2000; St-Pierre et al.,1998). A greater variance in mitochondrial content within the small fish indicates this size range occurs in a period of the life history of more active fibre hypertrophy, rapidly reducing Vv(mit,f)towards that found in larger fish. However, there was a twofold increase in the total mitochondrial content of individual fibres, V(mit,f),between small and large fish. Whether one views the lack of a significant allometric regression as complete compensation for changes in cell size, or the negative scaling exponent for Vv(mit,f) as a partial compensation, mitochondrial biogenesis during ontogenetic growth clearly supports the specific aerobic capacity of fibres.

The similarity of scaling patterns between Vv(mitimf,f) and Vv(mitss,f) indicate they are co-regulated despite their putatively different functions, providing ATP for contractile function or active ion transport, respectively. The greater proportion of subsarcolemmal than intermyofibrillar mitochondria for a given fish size is unlikely to also provide ATP for contractile function, as diffusion rates of the ATP analogue AMP-PNP were found to be lower than those for the hexose 2-deoxyglucose (0.81 vs 2.14 cm2 s–1,respectively, at 15°C) (Sidell and Hazel, 1987). Changes in the exchange surface available for transport of ATP, i.e. Sv(mit,f), were less than those in Vv(mit,f), indicating that with fibre hypertrophy the population consists of proportionally fewer, larger mitochondria. Thus, if the outer membrane area limits mitochondrial respiration, e.g. at maximal O2 consumption(O2max), the aerobic capacity may be further compromised(Weibel et al., 1996) in large fish. However, a large separation of mitochondria may be accommodated if the metabolic rate is low (Kinsey et al.,2007), emphasising the need for a more holistic view of the scaling phenomenon.

Other structural remodelling

An increase in volume density of intracellular lipid in red muscle of larger eels was considered an adaptation to a more migratory lifestyle, rather than an effect of allometry (Egginton,1986a), a conclusion supported by the lack of scaling in striped bass. Indeed, glucose-6-phosphate dehydrogenase activity showed negative scaling in Clarias batrachus(Tripathi and Verma, 2004),suggesting a reduction in NADPH production and hence hepatic lipogenesis, such that fuel preference may shift away from lipolysis in larger fish. However,this outcome may be dependent on diet, e.g. availability of carbohydrates, or response of other enzyme systems such as MDH.

In general, power requirements for swimming show positive allometry for both burst and sustained swimming(Goolish, 1989). Although maximising the capacity for rapid movement in small fish may be critical to their survival, as the power required for swimming varies with speed3 the absence of positive metabolic scaling in the largest fish may suggest they are unable to generate sufficient power(Norton et al., 2000). However, the allometric increase in mean fibre area was accompanied by only a small increase in relative myofibrillar content, Vv(myo,f), although total myofibrillar content, V(myo,f), increased significantly. This suggests a greater force development per fibre with age, as power generation is proportional to total myofibril cross-sectional area. Adjustments to fibre composition mean that although the intermyofibrillar zone expands as the fish grows, this is due to an increase in myofibrils rather than other organelles, and the tight packing of muscle cells in larger fish may further enhance specific power output. From a theoretical perspective, energy consumption per unit volume is expected to show negative allometry in all vertebrates, such that cell volume and cell metabolic rate cannot both remain constant(Savage et al., 2007). Striped bass would appear to adopt the latter option for red muscle, i.e. maintain a constant cell metabolic rate but increase cell size with increasing body mass during ontogeny, consistent with scaling exponents for mass-specific metabolic rate >0 for some fish species (Clarke and Johnston, 1999). The right shift in fibre size distribution is also consistent with a dominance of hypertrophy, although the heterogeneity in both sizes indicates fibre hyperplasia occurs throughout the size range examined, possibly aiding recovery by facilitating diffusive exchange of metabolites.

Microcirculation

Although Vv(mit,f) in mammals scales with O2max(Hoppeler et al., 1980), and varies with oxidative enzyme activity in fishes(Egginton, 1998; Guderley, 2004; Sänger, 1993), these potential fluxes cannot be fully exploited unless matched by microvascular delivery of O2. Hence, capillaries may satisfy demand for O2 up to O2max, but beyond this, glycogen stores need to be utilised to support glycolytic activity (Weibel et al.,1996). Although CD generally increases in parallel with Vv(mit,f) in vertebrates, there is considerable variability that can be attributed to the limitations of this measure of vascular supply as it is sensitive to fibre hypertrophy accompanying skeletal muscle growth (Hudlická et al.,1992). In fish, changes in skeletal muscle capillary supply are seen during development, and in response to exercise or thermal acclimation(Egginton, 1992). However,fish recruit fibre hyperplasia as well as hypertrophy during remodelling, with changes in fibre size distribution also leading to changes in C:F and oxygen supply to individual fibres that may be obscured when using global indices of capillarity, such as CD (Egginton,1992). In trout, modest changes in various structural parameters encompassing fibre remodelling, including mitochondrial proliferation and angiogenesis, ameliorate the potentially deleterious effects of low temperature in response to seasonal acclimatisation(Egginton et al., 2000). In the American eel, an increase in C:F indicated that angiogenesis in the developing fish served to maintain aerobic capacity, while CD remained unchanged with the transition from yellow (non-migratory) to silver(migratory) morphs due to the effects of fibre hypertrophy(Egginton, 1986a). In tilapia and eel, mean fibre area varies directly with BM, whereas in red muscle CD decreased (Egginton, 1992). Ontogenetic growth thus appears to require, at best, maintenance of peripheral O2 supply.

In striped bass, muscle fibre hypertrophy is accompanied by a compensatory angiogenesis (increasing C:F), although the compensation is incomplete(decreasing CD). Analysis of capillary structure suggests that the period of extensive developmental angiogenesis begins to wane at a body mass of around 20 g, with angiogenic indices such as endothelial sprouts(Egginton et al., 2001)showing little difference between large and small fish. Consequently,capillaries in juveniles and adults are structurally quite similar, although there was considerable variability in the data as random sampling means that capillaries can be viewed anywhere along their length, from the venular to the arteriolar side. Unlike the situation in eels(Egginton, 1992) the small increase in capillary cross-sectional area in larger striped bass was not statistically significant, similar to the situation in tilapia(Kisia and Hughes, 1992). Such changes may have important biological effects on blood flow, as resistance is proportional to the fourth power of the vessel radius, and a lower perfusion resistance due to larger lumen may offer partial compensation for vessel rarefaction in large fish. However, our calculations failed to show a significant difference in flow resistance between size classes, highlighting the need for an accurate quantification of the three-dimensional structure of the capillary bed and MABP in small fish to fully describe oxygen supply to tissue, and its adaptability.

Integrative response

The less aerobic nature of red muscle fibres in larger fish is consistent with positive scaling of glycolytic enzymes and negative scaling of oxidative enzymes. However, an increase in total mass of red muscle with size has been shown in rainbow trout (b=3.62)(Goolish, 1989) and tilapia(b=1.157) (Kisia and Hughes,1992). Although not quantified, this was also evident in striped bass on dissection. This, in conjunction with compensatory angiogenesis,suggests that at the tissue and organism level aerobic capacity may be relatively constant, consistent with a similar calculated mean and minimum PO2 for fibres of both small and large fish. The necessity of changing fibre composition with increasing size to maintain constant oxygenation is illustrated by the lower mean and minimum PO2 predicted if the fibre composition of small fish are applied to a fibre of equal size to that of large fish. If the opposite situation is modelled then the difference is small, indicating that the suite of changes accompanying fibre growth are regulated by feedback control to minimise any drop in intracellular oxygenation of larger fibres. In vivo, this is consistent with a hypoxia-driven stimulus for compensatory changes such as angiogenesis(Nikinmaa and Rees, 2004). Modelling a reduced capillary supply in large fish to that found in small fish decreased mean and minimum PO2, indicating that angiogenesis is a key factor in the maintenance of intramuscular oxygenation.

Conclusion

Although physical laws may dictate that structural capacities decline with increasing BM, there are many reasons why biochemical capacities vary among organisms. O2maxis an integrated outcome of disparate processes showing complementary responses, e.g. facilitated (myoglobin) and convective (capillary) delivery of O2 show opposite allometric trends, whereas functional (enzyme) and structural (mitochondria) indices of O2 consumption show parallel trends, suggesting a decrease of specific aerobic capacity with size. Nevertheless, as with changes in fibre size seen on temperature acclimatisation (Egginton et al.,2000), ontogenetic growth requires only modest changes to different elements in O2 supply and demand to maintain adequate aerobic capacity of locomotory muscle in an active fish species.

LIST OF ABBREVIATIONS

     
  • f

    mean fibre area (μm2)

  •  
  • b

    scaling exponent

  •  
  • BM

    body mass

  •  
  • CD

    capillary density

  •  
  • C:F

    capillary to fibre ratio

  •  
  • COX

    cytochrome oxidase

  •  
  • CPK

    creatine phosphokinase

  •  
  • CS

    citrate synthase

  •  
  • ICD

    intercapillary distance

  •  
  • LDH

    lactate dehydrogenase

  •  
  • MABP

    mean arterial blood pressure

  •  
  • PFK

    phosphofructokinase

  •  
  • PK

    pyruvate kinase

  •  
  • Re

    Reynolds number

  •  
  • Sv

    surface density

  •  
  • Vv

    volume density (volume of object per unit volume of reference)

  •  
  • Vv(mit,f)

    mitochondrial volume density of fibres

  •  
  • Vv(myo,f)

    myofibrillar volume density of fibres

This work was supported by the NERC and NSF. The authors are very grateful to Bruce Sidell (University of Maine, ME, USA) for generous provision of fish and facilities for biochemical analyses, and Jennifer Molloy (University of Birmingham, UK) for assistance in analysing fibre size distribution.

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