The contractile efficiency of the mantle muscle of European common cuttlefish (Sepia officinalis) during cyclical contractions

Cephalopod molluscs can propel themselves during swimming by jet propulsion, drawing water into their mantle cavity and ejecting it via the funnel. Jet propulsion swimming is energetically expensive compared with undulatory swimming (Bartol et al., 2008; Wells and O'Dor, 1991), and this has been attributed to the theoretically lower efficiency resulting from expelling relatively high velocity jets comprising relatively small volumes of fluid (Alexander, 2002; Gladman and Askew, 2023). However, investigations into the fluid motions in the wake have demonstrated that whole-cycle propulsive efficiency in cephalopod molluscs can be relatively high (in excess of 0.85; Anderson and Grosenbaugh, 2005; Bartol et al., 2009a,b; Gladman and Askew, 2023; Neil and Askew, 2018) and higher than those of undulatory swimmers (Maertens et al., 2015); therefore, another explanation for the relatively high energetic cost of jet propulsion swimming in cephalopod molluscs is required.

In order to quantify muscle contractile efficiency, energy utilisation and mechanical work generation must both be measured, ideally simultaneously. Whilst the mechanical performance of cephalopod muscle has been quantified (Gladman and Askew, 2022; Kier and Curtin, 2002; Milligan et al., 1997; Rosenbluth et al., 2010; Thompson et al., 2014, 2023; Zullo et al., 2022), the simultaneous metabolic energy expenditure has not, and therefore the contractile efficiency of cephalopod mollusc muscle is currently unknown. The aim of this study was to determine the contractile efficiency of the mantle musculature of the European common cuttlefish (S. officinalis) during cyclical contractions which simulate jet propulsion swimming, in order to gain insights into the determinants of the high metabolic cost of transport in jet-propelled swimmers. We also investigated the relationship between mechanical power output, contractile efficiency and cycle frequency, and hypothesised that cycle frequency would impact contractile efficiency, with cycle frequencies observed in vivo, 1.39 Hz during escape responses (Gladman and Askew, 2022), expected to be the most efficient and to also generate the highest power output. The mechanical work that the muscles generate was measured during cyclical contractions using the work loop technique (Josephson, 1985), and the metabolic energy expenditure was determined by quantifying the changes in the concentrations of high-energy phosphates and end products of anaerobic metabolism (Feala et al., 2007; Lowry and Passonneau, 1972; Smith et al., 2005).

Juvenile European common cuttlefish (Sepia officinalis Linnaeus 1758) were reared from eggs taken as by-catch upon fishing gear by R. K. Stride, Christchurch, Dorset, UK, during May 2016 in the English Channel. Eggs and hatchlings were maintained as previously described (Gladman and Askew, 2022). Juvenile animals were housed in two recirculating artificial saltwater systems [Aqua One Reef synthetic, Kong's (Aust.) Pty Ltd, Sydney, NSW, Australia] of 358 l (length×width×height; 91×69×57 cm). The temperature and salinity were maintained at 15±1°C and 32±1 PSU during the first 3 months after animals hatched; this temperature was then gradually decreased (over 10 days) to 11±1°C. Animals were fed bi-daily on alternate days using live river shrimp (Palaemon varians; Aquatic Live fish foods, Woodford, London, UK). Cuttlefish were reared for 12 months under these conditions, with final group sizes consisting of up to 30 animals per tank.

Water quality was monitored to ensure suitable ranges were maintained; temperature and salinity were monitored twice-daily; pH (7.8–8.1) and nitrogenous compounds were monitored monthly (NH₄ ≤0.5 mg l⁻¹; NO₂ ≤0.2 mg l⁻¹; NO₃ ≤80 mg l⁻¹); 25% water changes were carried out twice per week. The maintained parameters for temperature and salinity fell within the natural range of animals in the English Channel (Cefas, 2012).

Prior to muscle dissection, cuttlefish (N=25) were euthanised in accordance with schedule 1 (Appendix D) of the UK Animals (Scientific Procedures) Act 1986 (amended 2012); animals were chilled to 4°C in artificial seawater before the brain, vertical and optical lobes were destroyed by pithing. Prior use of sedative or anaesthetic was avoided because of the distress and adverse reactions reported by its administration in cephalopods (Andrews et al., 2013; Roumbedakis et al., 2020). Muscle preparations were then dissected out in artificial seawater at 11±0.5°C from the central zone of the ventral mantle wall, approximately 40% of the mantle length measured from the tip of the ventral mantle. Dissected muscle preparations were pared down to select the central zone of the muscle (muscle preparation mass 125.4±7.3 mg; optimal length L₀ 14.65±0.43 mm).

A stainless-steel metal ring was attached to each end of the muscle preparation using suture thread (2-0 USP, black braided silk non-absorbable, non-sterile surgical suture, LOOK surgical specialities corporation, Reading, PA, USA). These stainless-steel rings were used to attach the preparation to a fixed hook at one end of a Perspex flow-through muscle chamber, and the arm of an ergometer (Aurora Scientific Dual-mode lever system model 300B-LR, Aurora Scientific Inc., Aurora, ON, Canada). Approximately 500 ml of artificial seawater at 11±0.5°C was recirculated through the muscle chamber.

Muscles were activated using 0.2 ms pulses delivered using a stimulus isolation unit (UISO model 236, Hugo Sachs Elektronik, March, Germany) via parallel platinum wire electrodes that ran the length of the muscle preparation. Muscle length was increased incrementally by 0.5 mm, and a series of isometric twitches were used to optimise length, to that which yielded the highest active twitch force (L₀). Using twitches rather than tetani to optimise length may mean that muscle preparations were not at the length that yields maximum tetanic force or maximum net work (e.g. the length for maximum twitch force is approximately 4% shorter than that for maximum tetanic force: see Thompson et al., 2014; however, in vertebrates a different relationship has been reported with the optimum length for maximum tetanic force and net work being shorter than that for twitches: see Askew and Marsh, 1997; Holt and Azizi, 2014). Muscle preparations (N=25) were subjected to sinusoidal cyclical length changes, symmetrically about L₀ using a strain amplitude of 0.075 L₀, at one of three frequencies: [0.8 Hz (N=9), 1.4 Hz (N=8) or 2 Hz (N=8)] using the work loop technique (Josephson, 1985). The range of cycle frequencies selected encompassed the jet cycle frequency observed during swimming (1.39 Hz; Gladman and Askew, 2022). To ensure metabolite changes could be detected, muscles were subjected to either 15 or 30 cycles: at cycle frequencies of 0.8 and 1.4 Hz, muscle preparations were subjected to 15 cycles; at 2 Hz, 30 cycles were used as force and net work continued to increase up to the 15th cycle (see Fig. S1). A stimulation frequency of 50 Hz (pulse width 0.2 ms) was used and the timing and duration of stimulation were set to those previously found to maximise net power output (Gladman and Askew, 2022; see Table S1).

Instantaneous power was determined as the product of the muscle's velocity and the force generated. Cycle-by-cycle net power was determined as the average of the instantaneous power over the cycle. Net work per cycle (the difference between the work done by the muscle during shortening and the work done on the muscle during lengthening) was calculated from the ratio of net power to cycle frequency. Total net work was calculated as the sum of the cycle-by-cycle net work. Muscle mass-specific work and power were calculated by dividing the work and power values by the blotted wet mass of the muscle preparation. The average net work that was used in the calculation of contractile efficiency was calculated as the mean over the 15 or 30 cycles. The net power output in cycles 3 and 4 in this study and in a previous study (Gladman and Askew, 2022; N=5) are compared in Fig. S2.

Following the cyclical contractions, muscles were immediately removed from the experimental chamber, weighed (blotted wet mass) and snap frozen in liquid nitrogen before being stored at −80°C. The weighing and freezing process took <30 s in total, with recovery expected to be minimal over this time [recovery of the phosphagen pool following exercise is slow in cuttlefish, with the process taking between 150 and 200 min (recovery rate of 0.05–0.06 μmol g⁻¹ min⁻¹ at 15°C) to return to levels recorded at rest; Melzner et al., 2006]. Each muscle preparation was paired with a control, non-exercised sample from the same animal. These control samples were treated in the same way as the experimental preparations. A total of 25 preparations (1 preparation per animal) were used, each being utilised for a single bout of cyclical contractions at one frequency: 0.8 Hz (N=8), 1.4 Hz (N=8) and 2 Hz (N=9).

Metabolites were extracted from tissues using a modification of the methods of Gäde et al. (1978). Frozen muscle preparations were placed in 2 ml micro tubes (Eppendorf, Hamburg, Germany) and homogenised in 6% perchloric acid (Honeywell Fluka, Honeywell International Inc., Morris Plains, NJ, USA) in 40% ethanol (Sigma-Aldrich, St Louis, MO, USA; ratio of one part muscle to two parts solution) maintained at −20°C for 20 min using a bead mill homogeniser (Qiagen TissueLyser LT, Qiagen, Hilden, North Rhine-Westphalia, Germany). The homogenised sample was transferred to 1.5 ml micro tubes and centrifuged at 10,000 g for 30 min at room temperature (Sigma 1-14 Microfuge, Sigma Laborzentrifugen GmbH, Osterode am Harz, Niedersachsen, Germany). The supernatant was collected and neutralised with 0.125 volumes 3 mol l⁻¹ potassium carbonate (Fisher Chemical, Pittsburgh, PA, USA) in 50 mmol l⁻¹ MES buffer (Alfa Aesar, Haverhill, MA, USA). Neutralised samples were centrifuged again at 10,000 g for 15 min and the final supernatant collected and stored at −80°C.

NADPH absorbs light at 340 nm, with the increase in absorbance being used to determine the content of ATP from the stoichiometry of the reactions.

The reaction mixture consisted of 25 mmol l⁻¹ Tris-HCl (Lonza, Castleford, West Yorkshire, UK), 1 mmol l⁻¹ magnesium chloride (Fluorochem Ltd, Hadfield, Derbyshire, UK), 0.5 mmol l⁻¹ dithiothreitol (DTT; Fluorochem Ltd), 1 mmol l⁻¹ glucose (Sigma-Aldrich), 0.5 mmol l⁻¹ NADP (Merck Chemicals Ltd, Darmstadt, Germany) and 50 µl neutralised homogenate in a final volume of 2 ml. The reaction was initiated by the simultaneous addition of 1 unit of G6PD and 1 unit of HK (Sigma-Aldrich). Prior to the addition of G6PD and HK, the absorbance was read at 340 nm, 1 cm light path (Ultrospec 2100 Pro UV/Visible spectrophotometer, Biochrom, Harvard Bioscience Inc., Holliston, MA, USA); 20 min after the addition of G6PD and HK, absorbance was re-read. A blank (cuvette containing the reaction solutions and 50 µl deionised water rather than muscle homogenate) was included in all runs as a background control, which was deducted from all measurements to correct for any absorbance associated with the reaction solutions and the cuvette itself.

NADPH absorbs light at 340 nm, with the decline in absorbance being used to determine the content of arginine from the stoichiometry of the reactions.

ArgP content was subsequently determined using the same reaction pathways, with ArgP dephosphorylated using 1 mol l⁻¹ hydrochloric acid (following Morris and Adamczewska, 2002; Fisher Chemical, Loughborough, Leicestershire, UK). Hydrochloric acid was added in the same ratio as muscle homogenate (i.e. 50 µl) and samples were heated for 90 s at 100°C. Samples were cooled before 50 µl of 1 mol l⁻¹ sodium hydroxide (Fisher Chemical) was added to neutralise the solution.

Reactions were carried out using the l-arginine assay kit (K-large, Megazyme Ltd, Wicklow, Ireland). Each assay was performed at room temperature, using the neutralised homogenate in a buffered solution [containing triethanolamine (TEA), polyvinylpolypyrrolidone (PVPP), α-ketoglutaric acid (α-KG), ADP, orthophosphoric acid, 2-oxoglutarate and sodium azide], and containing 0.10 ml 0.13 mmol l⁻¹ NADPH. Prior to any enzyme addition, the solution was gently mixed and left for 2 min; the absorbance was then measured at 340 nm, 1 cm light path using an Ultrospec 2100 Pro UV/Visible spectrophotometer (Biochrom, Harvard Bioscience Inc.). Next, 10 µl (7.8 U ml⁻¹) of the glutamate dehydrogenase solution was added, the cuvette inverted to mix, and the absorbance measured again after 5 min. Then, 25 µl (9.8 U ml⁻¹) urease solution was added and the cuvette inverted to mix; the absorbance was measured after 6 min. Finally, 10 µl (6 U ml⁻¹) arginase solution was added to the cuvette, the cuvette inverted to mix, and the absorbance measured after 7 min or until absorbance became stable. An internal background control was included in all runs and the reading deducted from all measurements.

The reaction mixture contained 100 mmol l⁻¹ 2-amino-2-methyl-1-propanol (Sigma-Aldrich), 50 mmol l⁻¹ hydrazine (Sigma-Aldrich), 12 mmol l⁻¹ EDTA (Sigma-Aldrich), 4 mmol l⁻¹ NAD⁺ (Cayman Chemical Company, Ann Arbor, MI, USA), and was adjusted to pH 9.2–9.3 using 1 mol l⁻¹ hydrochloric acid. Each reaction contained 50 µl of homogenate and was made up to a total volume of 300 µl within a 96 well plate. An internal blank was included containing 50 µl deionised water rather than homogenate; all reactions were initiated by the addition of 0.08 units of ODH. Absorbance was measured prior to enzyme addition, and hourly until stable using a Varioskan Flash microplate reader (ThermoFisher Scientific, Waltham, MA, USA) at 340 nm. NADH absorbs light at 340 nm, with the increase in absorbance being used to determine the content of octopine from the stoichiometry of the reactions.

Data were analysed using IBM SPSS Statistics 24 (International Business Machines Corporation, Armonk, NY, USA). All data were tested for normality and homogeneity prior to statistical testing; data that were not normally distributed were transformed via log transformation to meet the conditions of normality and tested using ANOVA with Tukey post hoc tests; data that were non-normally distributed and could not be transformed to meet these assumptions were analysed using non-parametric tests. Comparisons of muscular work and power output were carried out using Kruskal–Wallis tests with post hoc Mann–Whitney U-tests. Comparisons of the change in metabolite concentrations between cycle frequencies were achieved using ANOVA tests. Comparisons of ATP_total and derived parameters between cycle frequencies were determined using ANOVA tests. Statistical significance was defined by a threshold of 0.05; a correction for multiple testing (e.g. Bonferroni) was not applied because of paired tests not influencing other tests (following the recommendations of Armstrong, 2014), and to avoid the risk of increasing type II errors in subsequent tests.

The net work per cycle was 4.08±0.26 J kg⁻¹ at 0.8 Hz, 2.69±0.11 J kg⁻¹ at 1.4 Hz, and 1.99±0.10 J kg⁻¹ at 2 Hz. Net work output varied significantly with cycle frequency (H=8.43, d.f.=2, P=0.015), with significantly higher work at 0.8 Hz than at 2 Hz (U=9.9, d.f.=1, P=0.006), and significantly higher work at 1.4 Hz than at 2 Hz (U=8, d.f.=1, P=0.03); no significant differences were found between net work at 1.4 and 0.8 Hz (U=1.90, d.f.=1, P=0.60; Fig. 2). Power output differed significantly between cycle frequencies (F=3.88, d.f.=2, P=0.028; Fig. 3), with significantly higher power output at 1.4 Hz than at 0.8 Hz (Tukey post hoc, P=0.022).

The octopine formed and ATP utilised per cycle did not vary with cycle frequency (Fig. 4), where 0.34±0.11, 0.20±0.06 and 0.37±0.14 µmol g⁻¹ of octopine was formed at 0.8, 1.4 and 2 Hz (F=0.37, d.f.=2, P=0.69), respectively, and 0.34±0.12, 0.18±0.05 and 0.34±0.06 µmol g⁻¹ of ATP was utilised at 0.8, 1.4 and 2 Hz (F=3.382, d.f.=2, P=0.052), respectively. ArgP utilisation differed significantly between cycle frequencies (Fig. 4), where 0.73±0.35 µmol g⁻¹ was utilised at 0.8 Hz, 0.21±0.11 µmol g⁻¹ at 1.4 Hz and 0.46±0.07 µmol g⁻¹ at 2 Hz (F=7.299, d.f.=2, P=0.004), with significantly less use at 1.4 Hz than at both 0.8 Hz (Tukey post hoc, P=0.006) and 2 Hz (Tukey post hoc, P=0.014). The estimated ATP consumption rate was 1.97±0.40 μmol g⁻¹ s⁻¹ at 0.8 Hz, 0.49±0.12 μmol g⁻¹ s⁻¹ at 1.4 Hz and 0.67±0.11 μmol g⁻¹ s⁻¹ at 2 Hz; assuming a recovery rate of 0.05–0.06 μmol g⁻¹ min⁻¹ at 15°C, we estimated the percentage recovery to be 0.05±0.01–0.06±0.01% at 0.8 Hz, 0.35±0.20–0.42±0.24% at 1.4 Hz, and 0.14±0.02–0.17±0.02% at 2 Hz.

The total ATP equivalents (ATP_total; calculated from Eqn 3) consumed per cycle was 1.57±0.32 µmol g⁻¹ at 0.8 Hz, 0.69±0.16 µmol g⁻¹ at 1.4 Hz and 1.35±0.12 µmol g⁻¹ at 2 Hz. ATP use per cycle significantly differed between cycle frequencies (F=7.63, d.f.=2, P=0.003), with significantly lower ATP consumption at 1.4 Hz than at both 0.8 Hz (Tukey post hoc, P=0.004) and 2 Hz (Tukey post hoc, P=0.014). ATP consumption rates were significantly affected by cycle frequency (F=16.74, d.f.=2, P<0.001), with significantly higher rates at 0.8 Hz than at 1.4 Hz (Tukey post hoc, P<0.001) and 2 Hz (Tukey post hoc, P=0.003), where ATP consumption was 1.97±0.40 μmol g⁻¹ s⁻¹ at 0.8 Hz, 0.49±0.12 μmol g⁻¹ s⁻¹ at 1.4 Hz and 0.67±0.11 μmol g⁻¹ s⁻¹ at 2 Hz.

The contractile efficiency (η_c) of the cuttlefish mantle muscle was 0.27±0.03 at 0.8 Hz, 0.37±0.06 at 1.4 Hz, and 0.20±0.05 at 2 Hz, but there were no significant differences in relation to cycle frequency (F=2.61, d.f.=2, P=0.098; Fig. 5).

Cuttlefish mantle muscle generated both peak η_c and peak power (Gladman and Askew, 2022) at a cycle frequency of 1.4 Hz, which is the frequency used in vivo during escape swimming (Gladman and Askew, 2022). At cycle frequencies above and below that used in vivo, the muscle generated less power but η_c was similar. This is similar to previous work using mouse hindlimb and dogfish myotomal muscle, where the cycle frequency at which peak net power and enthalpy efficiency were obtained was similar, and where efficiency was found to be within 10% of the peak value across a wide range of cycle frequencies [1.5–4 Hz in soleus muscle; 4–14 Hz in extensor digitorum longus muscle (Barclay, 1994); 1.3–3.3 Hz in dogfish white muscle (Curtin and Woledge, 1993b); 0.6–1 Hz in dogfish red muscle (Curtin and Woledge, 1993a)]. Hence, we can conclude that under conditions that yield maximal net power output, cuttlefish CMP muscle fibres operate with maximal contractile efficiency.

The η_c value of 0.37 is similar to that measured in scallop adductor muscle (0.30 in Chlamys hastata and 0.37 in Argopecten irradians) in vivo during escape swimming using a similar biochemical estimate of metabolic energy expenditure to that used here (R. L. Marsh, personal communication). The enthalpy efficiency of vertebrate fast-twitch muscles [i.e. the ratio of net mechanical work to the sum of work and heat (enthalpy change); Barclay, 2015] is also similar to that reported in molluscs; for example, in the dogfish (Scyliorhinus canicula) white myotomal muscle η_c was 0.41 (calculated from net power; Curtin and Woledge, 1993b) and the mouse (Mus musculus) extensor digitorum longus muscle η_c was 0.34 (calculated from net power; Barclay, 1994). However, the enthalpy efficiency is not equivalent to the contractile efficiency reported here, as part of the free energy change is incorporated into entropy changes (2nd law of thermodynamics; Smith et al., 2005). Assuming ATP is supplied by anaerobic glycolysis with a ratio of total free energy change to enthalpy change of +1.5 (Wilkie, 1960) yields estimates of contractile efficiency of 0.27 and 0.23 for the dogfish and mouse muscles, respectively. Therefore, compared with vertebrate fast-twitch muscles, mollusc muscles appear to have a relatively high contractile efficiency.

η_c depends on the value selected for ΔG_ATP. Here, we selected ΔG_ATP of −45 kJ mol⁻¹, which has been measured in squid during submaximal but exhaustive swimming (Portner et al., 1996). In our experiments, muscles were subjected to cyclical contractions in which stimulation timing elicited maximal net work and resulted in a progressive decrease in net work, indicating that the muscles were fatiguing. Therefore, while ΔG_ATP was higher in squid swimming at slower speeds, we feel that the minimal value of −45 kJ mol⁻¹ measured in squid is the most appropriate value to use to estimate η_c (Portner et al., 1996).

Over the period during which cyclical work was generated, there was a reduction in the ATP concentration in the muscle. This suggests that ATP was not fully replenished through the anaerobic pathways during this period. The net reduction in available ATP, as well as the build-up of the end-products of fatigue, will limit an animal's ability to sustain locomotion. In cuttlefish, burst responses are not typically used over prolonged periods, instead being a last resort when camouflage is broken by predators (Helmer et al., 2017; Staudinger et al., 2013). These escape responses also involve the release of ink and animal colour changes (Staudinger et al., 2013); these behaviours disrupt pursuit by predators, allowing cuttlefish to minimise the number of jets required to evade predation. The limited capacity of cuttlefish to replenish ATP through anaerobic pathways probably reflects these behaviours, where burst responses are used in a limited manner with ATP recovered following escape. Although the η_c of fast-twitch muscle is generally lower than that of slow twitch fibres (Barclay, 1994; Curtin and Woledge, 1993a,b), and the muscles fatigue more rapidly, the ability to replenish ATP rapidly via anaerobic pathways enables these muscles to deliver a burst of high power output, which may be a key determinant of survival.

In the muscle preparations, the radial fibres were not removed. It is possible that these fibres could become activated during the cyclical contractions imposed on the muscle preparation, which could contribute to metabolic energy expenditure. However, in a similar muscle preparation to the one used here, it was demonstrated that sectioning the radial fibres during the dissection disables them and they do not contract (Thompson et al., 2008). In addition, the bulk of the mantle is composed of circular muscle fibres. Therefore, for these two reasons, it is unlikely that the radial fibres contributed significantly to the measured metabolic energy expenditure or impacted upon our calculation of η_c.

At each stage within the energy cascade that results in the transfer of chemical energy into useful hydrodynamic work, energy is lost through the inefficient transduction of energy from one step to the next as well as energy costs associated with processes that are required to sustain muscle contraction but that do not directly contribute to the mechanical output of the muscle (e.g. the costs associated with Ca²⁺ cycling; Fig. 1). The overall efficiency of jet propulsion swimming (η_loco) is determined by the efficiency of each of these underlying steps; i.e. by η_R, η_c and η_wc (Eqn 1; Fig. 1).

The efficiency of mitochondrial oxidative recovery (η_R) assuming a P/O ratio of 2.5 (Hinkle et al., 1991; reviewed in Hinkle, 2005) is approximately 0.61. In our previous paper, the whole-cycle propulsive efficiency (η_wc) in juvenile cuttlefish during jet propulsion swimming was found to be ∼0.75 (0.74–0.76 depending on swimming orientation; Gladman and Askew, 2023). Here, the η_c of CMP fibres was found to be 0.37, giving an estimate of the overall efficiency of jet propulsion swimming in cuttlefish of 0.17. This estimate of overall efficiency accounts for the mechanical work done during refilling of the mantle cavity, as this is incorporated into the calculation of η_wc (see eqn 2 in Gladman and Askew, 2023). The work done to accelerate the water during refilling is only ∼3% of the total hydrodynamic work done in juvenile cuttlefish (Gladman and Askew, 2023) and is thought to be done largely by the release of elastic strain energy from the collagen fibres in the mantle wall that are stretched by the circular muscles during jetting (Curtin et al., 2000). However, it is possible that the radial muscle fibres contribute to the refilling work, which therefore could be done by both the circular and radial muscle fibres. Rather than considering the η_c of the radial and circular muscle fibres separately, a single value (0.37 measured for the CMP fibres in this study) was used: we do not know if this is correct for the radial muscle fibres. However, if the mechanical work generated by the circular and radial muscle fibres is considered separately and assuming that the radial fibres do all of the refilling work (which is unlikely; see Curtin et al., 2000), an overall efficiency of 0.17 is still obtained for an assumed radial muscle η_c of 0.2 and higher. It seems highly likely that the radial muscle fibre η_c lies within this range and therefore that the estimate of overall efficiency of 0.17 is realistic.

Other estimates of the overall efficiency of locomotion range from 0.06 to 0.17 in animal flight [0.06–0.07 in hawkmoths (Casey, 1981; Ellington, 1999; Willmott and Ellington, 1997); 0.17 in starlings (Ward et al., 2001); 0.07–0.10 in cockatiels (Morris and Askew, 2010; Morris et al., 2010); 0.06–0.10 in bats (von Busse et al., 2014)] and from 0.24 to 0.27 in human-powered terrestrial and aquatic pedal vehicles (Capelli et al., 2008). Therefore, contrary to the perception that jet propulsion swimming is inefficient (O'Dor and Webber, 1991), these data suggest that in cuttlefish this mode of locomotion is broadly comparable to the overall efficiency of several other modes of locomotion. We suggest that the high energetic cost of jet propulsion swimming can be attributed to the relatively high mechanical power requirements, rather than by a relatively low efficiency.

Part of this work is reproduced from the PhD thesis of N.W.G. (Gladman, 2018). We are most grateful to Professor Rich Marsh (Brown University) who shared with us unpublished measurements of the contractile efficiency of scallop adductor muscle and provided helpful comments on a draft of our manuscript. The energy cascade figure was based on earlier versions produced by Professors Rich Marsh and Tom Roberts (Brown University). We thank The Centre for Plant Sciences and Cardiovascular and Exercise Sciences Research Group for access to facilities, which supported this work.