Skinned fibres have advantages for comparing the muscle properties of different animal species because they can be prepared from a needle biopsy taken under field conditions. However, it is not clear how well the contractile properties of skinned fibres reflect the properties of the muscle fibres in vivo. Here, we compare the mechanical performance of intact fibre bundles and skinned fibres from muscle of the same animals. This is the first such direct comparison. Maximum power and isometric force were measured at 25°C using peroneus longus (PL) and extensor digiti-V (ED-V) muscles from wild rabbits (Oryctolagus cuniculus). More than 90% of the fibres in these muscles are fast-twitch, type 2 fibres. Maximum power was measured in force-clamp experiments. We show that maximum power per volume was the same in intact (121.3±16.1 W l−1, mean±s.e.m.; N=16) and skinned (122.6±4.6 W l−1; N=141) fibres. Maximum relative power (power/FIM Lo, where FIM is maximum isometric force and Lo is standard fibre length) was also similar in intact (0.645±0.037; N=16) and skinned (0.589±0.019; N=141) fibres. Relative power is independent of volume and thus not subject to errors in measurement of volume. Finally, maximum isometric force per cross-sectional area was also found to be the same for intact and skinned fibres (181.9 kPa±19.1; N=16; 207.8 kPa±4.8; N=141, respectively). These results contrast with previous measurements of performance at lower temperatures where skinned fibres produce much less power than intact fibres from both mammals and non-mammalian species.
Skinned fibres are commonly used for comparing the muscle properties of different animal species. They are an attractive choice because they can be prepared from a needle biopsy – a minimally invasive procedure possible under field conditions – and skinned fibres can be stored for many months, allowing time for return to the laboratory and for testing. However, it is not clear how well the contractile properties of skinned fibres reflect the properties of the muscle fibres in vivo. At present, the best information about this question comes from comparing published data for skinned fibres with data for intact fibres from the same species of animal but from experiments performed in different laboratories.
Much of the published data, which we summarise in the Discussion, suggest that skinned fibres produce less power and force than intact fibres. However, these comparisons are not completely satisfactory for at least two reasons: (1) most experiments on skinned mammalian fibres have been done at 15°C or less, and it is unclear how relevant comparisons at these low temperatures are to in vivo function; (2) comparison of the data from studies made in different laboratories may not be reliable, since values measured under ostensibly similar experimental conditions vary widely. For example, the maximum specific isometric force reported for human Type 2A fibres at 12°C ranges from 22 to 250 kPa (Harridge et al., 1996; Larsson et al., 1997; see also Kalakoutis et al., 2014). Similarly, for this fibre type and temperature, the maximum power output ranges from 1.6 to 7.3 W l−1 (Bottinelli et al., 1996; He et al., 2000). Thus, for both force and power, the indications are that the details of the methods used in a particular laboratory have a strong influence on the quantitative results.
We report here the experiments designed to deal with, as far as possible, these two problems and thus give a more robust comparison of skinned and intact fibres. (1) The experiments were done at 25°C, a temperature closer to that in vivo than is often used. (2) We used skinned and intact fibres from the same two muscles, peroneus longus (PL) muscle and extensor digiti-V (ED-V). All fibres were from the same population of wild European rabbits (Oryctolagus cuniculus Linnaeus 1758) and in many cases, skinned and intact fibres from the same individual were used.
−1× asymptote of force of the force versus velocity relationship
adenosine 5′ triphosphate disodium salt hydrate
extensor digitorum longus
ethylene glycol-bis(2-aminoethylether)-N,N,N′,N′-tetraacetic acid
force during shortening
fitted force intercept of the power versus force relationship
force at maximum power
flexor hallucis brevis
standard fibre length
peroneus longus muscle
normalised maximum power
velocity during shortening
velocity intercept of the force versus velocity relationship
Intact fibre bundles
An example of a force-clamped contraction from a bundle of intact fibres from an ED-V muscle is shown in Fig. 1. The active force and stimuli are shown in Fig. 1A. Once force reached the chosen level, the force-clamp was started and the controller regulated motor velocity to maintain constant force. The record of shortening is shown in Fig. 1B. Power (Fig. 1C) was calculated as the product of active force and velocity. This protocol was repeated for several different levels of force-clamp and the results are summarised in Fig. 2A,B. The line in Fig. 2A was fitted through the power versus force data points using Hill's relationship (as described in the Materials and methods) and the force versus velocity curve in Fig. 2B was calculated with the parameters from the fit. This particular fibre bundle has a rather straight force versus velocity curve and a relatively large value of , the fitted intercept on the force axis.
Such experiments were done with fibre bundles from ED-V and PL muscles. Useable results were obtained from 16 fibre bundles (9 ED-V and 7 PL). In 5 cases, we used bundles from both of these muscles from the same rabbit. The mean values of isometric force and the parameters of the fitted curves were not significantly different (P>0.125) for the two muscles, so all the results were combined. Table 1 summarises the mean values for the 16 fibre bundles of isometric force, maximum power, force and velocity at which maximum power was produced, Vmax and ; all of these values, except isometric force, are from the fitted curves.
Since there is evidence that force per cross-sectional area (CSA) is greater for small than large fibres in human skinned fibres (Gilliver et al., 2009) and because we are aiming to compare the performance of skinned and intact fibres, we examined the dependence of force on CSA in both intact fibre bundles and skinned fibres (see below). Fig. 3A summarises the relation between isometric force and CSA of bundles of intact fibres from ED-V and PL. We fitted lines through the values for each of these muscles assuming proportionality, that is, with the intercept=0, and found that the slopes were not significantly different for the two muscles (P=0.87). Therefore the line fitted through all the data points is shown in the graph. Fig. 3B shows the analogous graph of maximum power versus volume of the bundles of intact fibres. Again the slopes were not different for fibres from ED-V and PL (P=0.78) and therefore a single line is shown.
Skinned fibre results
An example record from a single skinned fibre from an ED-V muscle is shown in Fig. 4. The fibre dimensions were measured and zero-force baseline set in relaxing solution at 25°C. From there, the fibre was transferred through the sequence: pre-activating solution, activating solution at low temperature (∼1°C), activating solution at 25°C. The fibre was then relaxed at 25°C. Note that the free Ca2+ concentration in the activating solution is sufficient to produce maximum force (Millar and Homsher, 1990). In this high-temperature solution, force develops to a plateau in about 1 s. At this point, the force-clamp was started and the controller adjusted motor velocity to hold force constant during shortening for about 20 ms. The lower part of the figure shows, on an expanded time scale, the force, length change, velocity and power during the period from just before to shortly after the force-clamp. During the first 5 ms of the force-clamp, the force is falling rapidly and the velocity and power are very high. During this time, the elasticity in series with the fibre is shortening with falling force and the series elasticity is delivering power. Once the force has become constant, the shortening and power are delivered overwhelmingly by the contractile component, i.e. by filament sliding driven by crossbridge cycles. This is the power we measured by averaging the recorded values over a period of about 10 ms (between the blue vertical lines). We also measured the isometric force just before shortening starts (between the red vertical lines).
In this experiment, the protocol was repeated for 7 different force-clamp levels. Fig. 5 shows how power and velocity varied with force. The curve was fitted through the power versus force points (see Materials and methods). The maximum power and the force and velocity at which maximum power is exerted were identified on the fitted curve. We calculated the velocity versus force curve from the fitted parameters.
Such experiments were done on skinned fibres from ED-V and PL muscles. In total, 141 fibres from 16 rabbits gave useable results. Table 1 shows the isometric force and the parameters of the power versus force fit for fibres from each of these muscles. The isometric force (FIM; kPa) and maximum power (W l−1) are significantly different between the two muscles, with ED-V fibres producing more force per CSA and more power per volume than those from PL.
We examined the dependence of force on CSA in our skinned fibres to see whether force per CSA is greater for small than large fibres, as has been reported for skinned fibres from humans (Gilliver et al., 2009). Fig. 6A summarises the relation for ED-V and PL, where lines were fitted through the values for the fibres from each of these muscles assuming proportionality, that is, with the intercept=0. The slopes were significantly different for the two muscles. Fig. 6B shows the residual errors, which do not indicate any deviation from proportionality, in other words force per CSA did not vary with CSA. Fig. 6C shows the analogous graph of maximum power versus volume of the skinned fibres. Again the slopes were different and the residual plot (Fig. 6D) supports proportionality.
None of the force versus velocity properties, normalised as shown in Table 1, was correlated with rabbit mass. However, the fibres from male rabbits produced 12% more isometric force per CSA than fibres from female rabbits [P=0.027, two-way ANOVA with anatomical muscle (ED-V, PL) and rabbit sex as the factors].
Comparison of bundles of intact fibres with skinned fibres
The comparison between intact and skinned force and power data is shown in Fig. 7A,B. The skinned fibres and intact fibre bundles are very different in size, so the values are plotted on a log–log scale to ensure that the individual points are visible. In each figure, the blue line was fitted through the results for skinned fibres from both ED-V and PL muscles and can be compared with the red line for the intact fibre bundles from ED-V and PL. In both graphs, the two lines are almost continuous with each other. The constants of proportionality for the skinned and for intact fibres (given in the figure legend) are not significantly different. Note that on this log–log plot the assumption of proportionality results in all the lines being at 45 deg and the constant of proportionality sets the vertical position of each line.
The results for skinned fibres from ED-V and PL are combined in Table 1 (weighted as described in the footnote) and Fig. 7, where they are compared with the intact fibre bundle results. The isometric force and maximum power are not significantly different between skinned and intact fibre preparations. However, the force at which maximum power is produced is significantly greater in intact fibre bundles than in skinned fibres. Also the force intercept of the power versus force curve is significantly greater for intact fibre bundles than for the skinned fibres.
The main aim of this study was to compare the mechanical performance of intact fibres and skinned fibres under as similar conditions as possible. Maximum power output and isometric force were chosen because they are aspects of mechanical performance particularly relevant to muscle function in vivo and whole animal performance. Both of the muscles we used, PL and ED-V, are composed largely of fast-twitch, type 2 fibres with less than 10% slow twitch, type 1 fibres (Curtin and Woledge, 2014). Thus, the results can be taken as mainly representative of the population of fast-twitch fibres.
We found that maximum isometric force produced by intact and skinned fibres is the same within the limits of experimental errors. This result is based on comparison of the combined results from ED-V and PL using the mean values of the simple ratio of force/CSA for each preparation (Table 1). It is worth noting here that the value of force/CSA for a group of preparations can be evaluated in other ways. Here, we report one such other method: the slope of the force versus CSA relationship (Fig. 3A, Fig. 6A and Fig. 7A) when we were testing whether smaller preparations have more force/CSA than larger ones. This method gives a value for the group of force and CSA values that is different from the mean of the ratios for the individual preparations. The difference arises because when the slope of force versus CSA is calculated, preparations with large CSA and/or large force have greater influence than smaller preparations. Whereas the mean of the simple force/CSA values is influenced equally by all preparations, we prefer this method as a summary of our findings and the basis for comparing skinned fibres with intact fibre bundles.
We found that the maximum power (W l−1) produced by intact and skinned fibres from wild rabbit muscle is the same within the limits of our errors. However, it is worth noting that the accuracy of such comparisons of power between intact and skinned fibres is limited by a number of factors. First, the methods used to estimate the amount of contractile material is different for intact and skinned preparations. For intact fibre bundles, volumes were obtained from the masses of the blotted muscle and the density of muscle (Mendez and Keys, 1960). Whereas, for skinned fibre segments the volumes were obtained from measurements under the microscope of width, depth and length. Second, each of these methods is an imperfect estimate of the amount of myofibrillar material. The volume of an intact fibre bundle includes extracellular space. Also damaged and non-excitable muscle fibres in the bundle add volume but do not produce power. Fibres swell during skinning and so have a volume greater after skinning than before. The amount of swelling is highly variable (Godt and Maughan, 1977). A better comparison between intact and skinned preparations might be achieved based on the mass of the contractile proteins. A possible method is to measure dry mass of the fibres or fibre segment after fixation in alcohol and washout of salts and use this as an estimate of mass of contractile proteins. We measured dry mass in this way for the intact fibre bundles in this study and found that the coefficient of variation (CV=s.d./mean) of the power output is reduced by 25% if the results are expressed as W mg−1 dry mass rather than based on W mm−3 volume. We have used this method successfully on large single skinned fibres from dogfish (West et al., 2005). However, the CSA of rabbit fibres is much smaller and we only used a short segment of fibre. The dry masses of the smallest skinned fibre segments used in the experiments reported here were estimated to be less than 1 µg, which is beyond the accuracy of the methods we use. Another possible method is SDS-PAGE with stain-free technology, which may provide accurate quantification of fibre protein content and thus the size of skinned fibre segments.
For the purpose of comparing maximum power output of skinned and intact fibres, we have also used power expressed in relative units, which is less subject to the problem of measuring the amount of contracting myofibrillar material. Our definition of relative power is the ratio, maximum power/maximum isometric force×standard fibre length (max power/FIMLo; units: W/N m = s−1). The relevant point here is that relative power does not require measurement of fibre CSA or bundle volume, but instead uses maximum isometric force as measure of the amount of contracting myofibrillar material per CSA. Thus, it is not surprising that the coefficient of variation of relative power is less than that of power in W l−1 for both skinned fibres and intact fibre bundles. CV for skinned fibres was 0.387 for power in relative units (s−1) and 0.446 for power in W l−1; for intact fibre bundles, the corresponding values were 0.229 and 0.530. Our conclusion that maximum power output by intact and skinned fibres from wild rabbit muscle is the same within the limits of the errors is supported by comparison of the maximum power expressed in relative units whether based on all results or on only those with isometric force above the rejection threshold of 75 kPa.
Other comparisons of intact and skinned fibre performance can be made on the basis of literature values. A maximum power of 166±8.9 W l−1 (mean±s.e.m.) at 30°C has been reported for Type 2 skinned fibres from the rat (Knuth et al., 2006). This value can be compared with 177±22 W l−1, measured with intact fibre bundles from rat flexor hallucis brevis (FHB) muscle, which is ∼90% type 2 fibres (Roots and Ranatunga, 2008) and 174±12 W l−1 calculated by Ranatunga (1998) from his earlier experiments (Ranatunga, 1982,, 1984) using whole extensor digitorum longus (EDL) muscle and intact fibre bundles from EDL; all at 30°C. Our results also show that skinned and intact fibres produce the same power at around 25°C, and provide stronger evidence on this point because our intact and skinned fibres were from the same animals and the experiments were undertaken in parallel in the same laboratory.
This agreement contrasts with results obtained at lower temperatures, where skinned fibres maintain their performance well enough that reliable measurements of maximum power can be made. Comparisons of published data show that intact fibre preparations consistently produce more power than skinned fibres from the same species. For white muscle fibres of the dogfish at 12°C (its normal physiological temperature), Curtin and Woledge (1988) found that intact fibres produce a maximum power 65% greater than the value reported for skinned fibres by Bone et al. (1986). As reviewed by West et al. (2013), intact fibres from frog muscle at ∼2°C produce about 45% more power than the skinned fibres investigated by Ferenczi et al. (1984). Similar large differences are seen also in mammalian muscle at low temperature. At 15°C, intact fibres from rat (Ranatunga, 1998; Roots and Ranatunga, 2008) produce 76% more power than rat skinned fibres (Knuth et al., 2006).
Thus, our results and the published data show that the large discrepancies between intact and skinned fibres that occur at low temperatures are not present in mammalian muscle at temperatures of 25°C and 30°C. This prompts the question of how the powers compare at even higher temperatures. There are no data from which the comparison could be made for the highest muscle temperatures achieved during exercise; both human and horse muscle reach up to 39°C during intense exercise (Saltin and Hermansen, 1966; Hodgson et al., 1993). However, there is extensive evidence that intact mammalian fibres maintain their contractile performance in vitro at temperatures between 30 and 37°C (Barclay, 1994; Close, 1964,, 1965; Close and Luff, 1974; Luff, 1981; McCrorey et al., 1966; Ranatunga, 1982) and lizard muscle performs well at 40°C (Curtin et al., 2005). In contrast, skinned fibre performance declines rapidly with repeated activation, which prevents reliable measurements of maximum power (Bottinelli et al., 1996; Stienen et al., 1996). We encountered the same problem in the current set of experiments with skinned rabbit fibres at 33°C. Taken together, these comparisons suggest that there is an unidentified factor(s) or mechanism(s) in the intact fibres that preserves their ability to produce force and power at low temperature and prevent deterioration at temperatures above 30°C. We speculate that the factor is lost, or the mechanism is inactivated in skinned fibres, thus compromising their ability to produce force and power at these higher temperatures.
The match between the performance of intact and skinned fibres that we find at 25°C strengthens confidence in results of skinned fibres in situations where, for example, only needle-biopsy material can be obtained as is the case for some wild and/or rare animals. Skinned fibres have some advantages over intact fibres; for example, effects of metabolite levels and Ca2+ sensitivity can be measured. However, it is important to recognise that the in vivo behaviour of muscle cannot be duplicated in skinned fibre experiments, at least with current methods. In particular, it is not possible to rapidly turn off contraction of skinned fibres. Intact fibres have a definite advantage in this context because at the end of electrical stimulation action potentials cease and contraction relaxes, as in vivo. Consequently, the normal cycles of length change with intermittent contraction that occur during most locomotion can be duplicated with intact, but not with skinned fibres.
MATERIALS AND METHODS
Wild rabbits were live-trapped on the Hawkshead Campus of the Royal Veterinary College with ethical approval from the Royal Veterinary College Ethics Committee. They were killed according to supplementary material Appendix 1 of Schedule 1 (revised 1997) of the Animals (Scientific Procedures) Act 1986. Eighteen rabbits were used (9 male and 9 female). Their mass ranged from 0.4 to 2.0 kg (mean 1.1 kg). Successful experiments were done on bundles of intact fibre from 11 rabbits. Skinned fibres were prepared from 16 rabbits. The ED-V and PL muscles were usually dissected from both legs and then a part of each muscle was prepared for experiments.
Intact fibre bundles
Fibre bundles [average length 12.3±0.5 mm (mean±s.e.m.) and average CSA 1.92±0.29 mm2] were dissected and kept in physiological saline (mmol l−1): NaCl 135, KCl 4.0, CaCl2 2.35, MgCl2 0.85, NaH2PO4 1, NaHCO3 20 and glucose 5.5 and equilibrated with 95% O2, 5% CO2. Experiments were done at 25°C. A fragment of tendon at each end of the fibre bundle was held in an aluminium foil clip. At one end, the clip was attached to a fixed hook and the other to the motor/force transducer (Series 300B Lever System, Cambridge Technology, Inc. Watertown, MA, USA). A MultiStim System D330, with modules D334, D332, D333 and D342 (Digitimer Ltd, Welwyn Garden City, UK) provided electrical stimulus pulses. Supra-maximal stimulus strength (V, 1.0 ms pulse−1) and Lo, the standard fibre length, were found for each fibre bundle at the start of the experiment. Lo is the fibre length at which maximum isometric active force is produced. Brief tetanic contractions (stimulus frequency 100 Hz) were used, either isometric or force-clamped to a predetermined level. Passive force (i.e. without stimulation) was recorded during movements matching those in each force-clamped contraction, and was subtracted from that recorded with stimulation to give the active force. The experiments were controlled by a custom-written LabView program which sent trigger pulses to the stimulator, provided appropriate force-control and length-control signals to the motor and acquired the data at 1 kHz.
At the end of the experiment, the fibre bundle was fixed in alcohol while pinned at Lo so that fibre length could be measured. Tendons were removed and the preparation was then blotted and weighed. Preparation volume was calculated from the blotted mass assuming a density of 1.064 (value for 25°C from Mendez and Keys, 1960).
Preparation of skinned fibres
Thin fibre bundles (4–5 mm in diameter) were permeabilised on ice in solution A (Table 2) containing 2% Triton X-100. For fibres from 10 of the 16 rabbits, this solution also contained 20 mmol l−1 BDM (2,3-butanedione monoxime). BDM is used to prevent contraction which can occur during skinning. We found part way through this set of experiments that such contractions do not occur in the absence of BDM under the conditions we used and therefore we discontinued using BDM. Exposure to BDM did not affect mechanical properties: maximum values of isometric force, power and shortening velocity were not significantly different between the groups (96 fibres with BDM, 45 fibres no BDM). After 30 min, the fibre bundles were transferred to solution A for a further 30 min to remove the Triton X-100. Fibre bundles that were to be used within 4 weeks were stored at −20°C in a 50% glycerol solution containing the components at the concentrations shown in Table 2. Fibre bundles to be stored for longer than 4 weeks were stored at −80°C in 0.5% glycerol solution containing the cryoprotectant trehalose (500 mmol l−1). In this case, a gradual transition from solution A was achieved by holding the skinned fibre bundles on ice for 30 min in the following solutions: (1) 50:50 mixture of solution A and 500 mmol l−1 trehalose in 0.5% glycerol; (2) 500 mmol l−1 trehalose in 0.5% glycerol. The bundles were then frozen in liquid nitrogen and stored in cryo-tubes at −80°C for up to 20 months. When needed, they were thawed in solution 2 above, then transferred to solution 1 and finally to a 50% glycerol solution containing the components at concentrations shown in Table 2. These thawed bundles were then stored at −20°C in this solution, and used for experiments within 4 weeks. Fibres used within 4 weeks of skinning (N=21) and those used between 4 weeks and 20 months of skinning (N=120) did not have different mechanical properties; maximum values of isometric force, power and shortening velocity were not significantly different between these groups.
Small segments of the skinned fibre bundles (2–3 mm long) were dissected and used to prepare several single fibres in solution A at 7–10°C on the thermostat stage of a dissecting microscope. Aluminium foil ‘T-clips’ (Photofabrication Ltd, St Neots, UK) were placed on the ends of fibre segments (length between 0.6 and 1.5 mm). Clips were attached to several single fibres at a time, and some were stored again at −20°C in the glycerol-based solution A (described above) for use within 3 days. Individual fibres were transferred to solution A, containing 0.5% Triton-X 100, on the Aurora 600A permeabilised fibre apparatus, where they were ‘set-up’ for activation. The 600A apparatus was positioned on the x,y moving stage of an inverted microscope.
While in relaxing solution at 25°C, the sarcomere length (SL) was set to 2.5–2.6 µm using either laser diffraction or by visualising the striation pattern (under 40× objectives) and using the Aurora 900B FFT imaging protocol. Lo, the standard length, is the fibre segment length at which SL is 2.5–2.6 µm. Lo was measured using the eye-piece graticule under low magnification (10×). Fibre depth and width were measured using the 900B camera software. The fibre depth was visualised by using a prism built in the bath of the 600A apparatus. Each value of depth and width was recorded as the mean of three separate measurements along the fibre length. CSA was calculated from the fibre width and depth assuming an elliptical cross-section. Skinned fibre CSA was correlated with the mass of the rabbits.
We did not make a correction to the CSA for swelling that may have occurred as a result of skinning for the following reasons. (1) We did not measure the extent of swelling. (2) Literature values for the extent of swelling are highly variable. The published values range from 20% (Moss, 1979) to 52% (Godt and Maughan, 1977) increase in diameter. (3) The published values are for frog fibres at low temperature (5°C) and may not be relevant to mammalian fibres at high temperature. The variability is likely to be dependent on factors such as sarcomere length (Matsubara and Elliott, 1972) and solution ionic strength (West et al., 2005).
Fibre activation and power measurement
The Aurora 600A apparatus was modified for ‘temperature-jump’ (T-jump) activation of fibre segments (Goldman et al., 1987; Bershitsky and Tsaturyan, 1989) using the solutions shown in Table 3. The low temperature (T) was 0–1°C and the high T was 25°C. For this protocol the fibre segment was immersed successively in: (1) pre-activating solution at low T for 45 s; (2) activating solution at low T for 3 s; (3) activating solution at high T for 1–2 s; and finally, (4) relaxing solution at high T; the baseline force at 0.8 Lo was recorded before changing length back to the original Lo.
While in solution 3, force developed to a plateau at constant length (isometric force) and then was clamped for 20 ms to a predetermined level (see Fig. 4 for an example record). The shortening velocity during the force-clamp was measured and used to calculate power output. To accumulate a data series with a range of shortening velocities, the T-jump activation was repeated on each fibre between 5 and 8 times, each time with force clamped to a different level.
Some of the intact fibre bundles and some skinned fibres produced low isometric forces, probably because of damage during dissection and mounting. We rejected the data from preparations of either type that produced isometric force less than 75 kPa. Out of 26 intact fibre bundles, 10 were rejected and from 143 skinned fibres, 2 were rejected. In skinned fibre experiments the isometric force in successive activations decreased at an average rate of 2.1% per activation. After the isometric force fell below 80% of the maximum value for that fibre, further records were not used.
Force values (in mN) were divided by the corresponding isometric force (FIM). Power values were divided by the product (FIM Lo); power normalised in this way has units of s−1. Velocity data was divided by Lo and also has units of s−1.
For examining the dependence of isometric force on CSA and of power on volume, we used the Model 2 regression method (York et al., 2004) in which the value of the slope is found by minimizing the errors in both the dependent and independent variable.
Curve fitting for maximum power
We thank Joanne Gordon, Luis Lamas and Richard Harvey for assistance with the animals.
A.M.W., R.C.W., N.A.C. and T.G.W. developed the concept. R.A.D., T.G.W., R.C.W. and N.A.C. performed experiments. R.C.W. and N.A.C. did data analysis, and wrote the manuscript with input from other authors.
This work was supported by the Biotechnology and Biological Sciences Research Council UK [BB/J018007/1 to A.M.W., R.C.W. and N.A.C.]; and the European Research Council [323041 to A.M.W.].
The authors declare no competing or financial interests.