The length–force behavior and operating length range of squid muscle vary as a function of position in the mantle wall

Hollow, cylindrical muscular organs and bodies are common in animals, especially soft-bodied invertebrates. Such body plans are effective in providing mechanical support for many forms of locomotion and movement (e.g. Clark, 1964; Wainwright, 1988), but recent work showed that they experience significant non-uniformity in circumferential strain across the thickness of the muscular body wall (Thompson et al., 2008; Thompson et al., 2010a). This phenomenon can be illustrated as follows. Imagine a cross-section of the cylindrical body wall. As long as (1) the body wall remains essentially constant in volume during shortening of the circumferential (i.e. circular) musculature (a reasonable assumption given the high bulk modulus of animal tissue), (2) the length does not change significantly, and (3) the circular muscle fibers remain oriented in the plane of section (i.e. their long axes remain perpendicular to the long axis of the body wall), the body wall must increase in thickness as the circular muscles shorten. The circular fibers near the inner lumen surface thus shorten proportionately more than the circular fibers near the outer surface for a given decrease in the diameter of the body.

Thompson et al. (Thompson et al., 2010a) investigated this phenomenon in the mantle, a cylindrical muscular organ that meets the three criteria specified above, of Atlantic longfin squid, Doryteuthis pealeii, and oval squid, Sepioteuthis lessoniana. They found that circular muscle fibers along the inner surface of the mantle experience circumferential strains 1.3 to 1.6 times greater than fibers along the outer surface of the mantle during the same contraction. This transmural gradient of strain implies that muscle fibers from the inner surface may operate on a different region of the length–tension curve than those on the outer surface at any point in the contraction cycle. Thus, fibers from a given region of the mantle wall may produce different instantaneous forces than those in other regions. Such transmural differences in force output by the circular fibers could reduce the mechanical efficiency of the mantle during contraction (Shadwick and Syme, 2008; van Leeuwen et al., 2008).

Because the circular fibers from near the inner surface of the mantle have significantly greater excursion ranges in vivo than circular fibers from near the outer surface of the mantle, we predict that fibers from near the inner surface will spend a smaller fraction of the contraction cycle in the region of maximum force of the length–tension curve. Different length–force relationships of the circular fibers near the outer versus the inner surfaces of the mantle might reduce the impact of such transmural differences in operating length range and potentially allow all of the circular fibers to generate similar instantaneous forces during mantle contraction. We hypothesize, therefore, that the circular muscle fibers near the inner surface produce higher forces, relative to the peak isometric force (P₀), on the ascending and descending limbs of the length–tension curve; i.e. the length–tension curve for the circular fibers from near the inner surface will have ascending and descending limbs with lower slopes. Our hypothesis assumes that all of the circular muscle fibers in the mantle operate on roughly similar regions of the length–tension curve during the mantle contraction cycle (i.e. there

is no transmural staggering of resting sarcomere lengths). Testing the hypothesis, therefore, also requires investigation of the in vivo operating length ranges of the circular muscles.

We tested the hypothesis in the mantle of the Atlantic longfin squid, Doryteuthis pealeii (Lesueur 1821). We first used sonomicrometry to measure muscle fiber length changes in the central mitochondria-poor (CMP) (Preuss et al., 1997) circular fibers near the outer and inner surfaces of the mantle during a range of locomotory behaviors. We then investigated the length–force relationship of bundles of CMP circular muscle fibers near the inner and outer surfaces of the mantle, and also examined potential transmural differences in other contractile properties, including length dependence of activation, the effect of stimulus frequency on the length–force relationship, twitch:tetanus ratio and maximum isometric stress. Finally, we developed a method to superimpose the two sets of data in order to identify where along the length–tension curve the muscle fibers operate in vivo.

We obtained thorough sampling of the ascending limb of the length–twitch force relationship for CMP circular muscle preparations obtained from near the inner and outer surfaces of the mantle (Fig. 1A). We were unable, however, to sample the descending limb extensively at lengths beyond the force maximum region because preliminary studies revealed that preparations exhibited signs of damage, including an altered force–time trace (i.e. an approximate doubling of T_50%, the half relaxation time) and an inability to produce peak isometric twitch force (P_TW) when returned to L_TW (the preparation length that produced P_TW). Data from damaged preparations were excluded from the results we present here. We also were unable to explore the ascending limb at lengths <0.60L/L_TW. The preparations resisted compression and buckled when we attempted to adjust them below this length when relaxed, yet appeared to contract when stimulated, suggesting that the circular fibers might be able to shorten even more in vivo.

The length–twitch force relationships of the two preparation types differed. On the ascending limb of the length–tension curve, the preparations from near the inner surface of the mantle generated higher force relative to P_TW than the preparations from near the outer surface at a given preparation length (Fig. 1A). At preparation lengths ≤0.95L_TW, the ascending limbs were sufficiently linear to allow comparison of the slopes and y-intercepts of the two data sets. The circular muscle preparations from the inner surface of the mantle exhibited a significantly lower slope of the ascending limb (independent-samples t-test: t=3.84, d.f.=17, P=0.001) and higher y-intercept (t=−4.63, d.f.=17, P<0.001) than preparations from near the outer surface of the mantle (Fig. 1A). At a given length on the descending limb, the preparations from near the inner surface of the mantle also produced higher twitch force than the outer preparations. We were unable to explore the descending limb beyond 1.1L_TW, however, and thus at this point our conclusions about the relative forces on the descending limb are tentative.

At each preparation length, the passive force (Fig. 1B), normalized to P_TW, did not differ significantly between preparations from the outer or inner surfaces of the mantle (independent-samples t-tests: P>0.2 for all comparisons).

The length–tetanic force relationship of the two preparation types also differed on the ascending limb, with preparations from near the inner surface producing higher force relative to P₀ (the maximum isometric tetanic force) at a given length than preparations from near the outer surface (Fig. 2). The preparations from the inner surface exhibited a significantly lower slope of the ascending limb (≤0.95L₀, t=2.91, d.f.=9, P=0.017) and higher y-intercept (t=−2.40, d.f.=9, P=0.04) than preparations from near the outer surface.

When stimulated tetanically, the mean (±s.d.) maximum isometric stresses (P₀) at L₀ (the preparation length that yielded P₀) were 212±105 kN m⁻² (n=7) and 290±166 kN m⁻² (n=8) for the preparations from the outer and inner surfaces of the mantle, respectively. The means did not differ significantly (t=−1.1, d.f.=13, P=0.29).

The mean (±s.d.) twitch:tetanus ratios for the outer and inner preparations were 0.60±0.085 (n=10) and 0.58±0.10 (n=11), respectively. The means of the two preparation types did not differ significantly (t=−0.43, d.f.=19, P=0.67).

All of the muscle preparations exhibited two characteristics that differ from the cross-striated muscles of vertebrates and arthropods. First, the CMP circular muscles did not exhibit substantial length-dependent changes in contraction kinetics (i.e. length-dependent activation) when stimulated with a twitch stimulus. Both T_max (time from the onset of stimulation to the maximum force of the twitch) and T_50% increased slightly as preparation length increased (Fig. 3). The T_max increased from the shortest to the longest preparation lengths by (mean ± s.d.) 0.0057±0.0046 s (n=10) and 0.0069±0.0054 s (n=10) for the outer and inner preparations, respectively. The difference was not significant (t=0.688, d.f.=17, P=0.497). The T_50% increased from the shortest to the longest preparation lengths by 0.019±0.014 and 0.025±0.013 s for the outer and inner preparations, respectively (Fig. 3). The difference was not significant (t=1.32, d.f.=28, P=0.196). In addition, the slopes of the regressions of preparation length versus T_max and preparation length versus T_50% did not differ significantly between muscle preparations from the outer and inner surfaces of the mantle (T_max: t=−0.594, d.f.=17, P=0.563; T_50%: t=−1.781, d.f.=17, P=0.106). Furthermore, the y-intercepts of the regressions did not differ significantly (T_max: t=−2.1, d.f.=17, P=0.08; T_50%: t=−2.0, d.f.=17, P=0.085).

Second, L₀ was longer than L_TW for all preparations (Fig. 4A). For the outer (n=7) and inner (n=7) preparations, L₀ was 1.05±0.035 (mean ± s.d.) and 1.06±0.061 times longer, respectively, than L_TW (Fig. 4). We calculated the ratio of L_TW to L₀ for each preparation and found no significant difference between the means for the outer and inner preparations (t=−0.43, d.f.=13, P=0.68).

The squid exhibited a diverse repertoire of jetting behaviors, ranging along a continuum from low-amplitude and low-frequency ventilatory jets to relatively stereotyped rapid, large-amplitude escape jets, with more variable jets used during slow swimming (i.e. ≤1 mantle length s⁻¹) in between (Fig. 5; see supplementary material Movies 1 and 2 for videos that illustrate swimming behavior). Two squid operated in a more-or-less hyperinflated state [i.e. contraction of the radial muscle fibers expands the mantle radially beyond the resting position, thus filling the mantle cavity with more water (see Gosline et al., 1983)] for most of the swimming trials whereas other individuals hyperinflated only during escape jets and isolated jets used during slow swimming.

All of the CMP circular muscle fibers operated almost exclusively on the ascending limbs of the length–twitch force and length–tetanic force relationships for all jets (Fig. 2; see Table 1 for the mean muscle operating length ranges). For escape jets, there was no significant transmural difference in muscle length at the start of mantle contraction (t=0.62, P=0.54) though there was considerable variation, with some jets initiated with the circular fibers at lengths greater than 1.05L₀ (Fig. 2). The muscle lengths at the end of escape jet contraction were significantly shorter for the circular fibers near the inner lumen surface of the mantle than those near the outer surface (t=5.7, P<0.001; Fig. 2). The muscle lengths at the end of escape jet contraction were relatively consistent, which may reflect the degree of stereotypy of this behavior.

If the two squid that operated in a hyperinflated state for most of the jets are excluded, the mean operating length ranges of the circular fibers differed significantly at both the start and end of mantle contraction for escape jetting (see Table 1 for statistics).

The length–twitch force and length–tetanic force relationships of the CMP circular muscle fibers varied with radial position in the mantle wall. Consistent with our prediction, the fibers from near the inner surface of the mantle produced higher force, relative to P₀, at all points along the ascending and descending limbs of the length–tension curve than fibers near the outer surface of the mantle.

The mechanism responsible for the transmural difference in length force properties is unknown. Studies of cross-striated muscle fibers have demonstrated that the level of activation can affect the slope of the ascending limb of the length–tension curve (e.g. Rack and Westbury, 1969; Chapple, 1983), with greater activation leading to an increase in the length dependence of force generation (i.e. a steeper slope). We were careful to use a stimulation current that elicited the maximum force for all preparations. In addition, we also explored the possibility that the difference in length–force properties resulted from a difference in length-dependent changes in contraction kinetics of the circular fibers when given a twitch stimulus. Although both T_max and T_50% increased slightly with preparation length, there were no significant differences in length-dependent contraction kinetics between the two preparation types. Furthermore, all the circular fibers produced maximum isometric twitch force at a length slightly shorter than the length that produced maximum isometric tetanic force, with no significant differences between the inner and outer preparations. Thus, we conclude that the transmural changes in length–force behavior we report are not an artifact of our experimental approach but instead reflect inherent differences in the circular fibers themselves.

Ultrastructural differences between the CMP circular fibers from near the inner and outer surfaces of the mantle might explain the ability of the inner fibers to produce higher relative twitch force along the ascending and descending limbs of the length–tension curve. In many striated muscles, long thin and thick filaments and higher thin:thick filament ratios are correlated with higher force output (Jahromi and Atwood, 1969; Josephson, 1975; Granzier et al., 1991). Previous ultrastructural investigations of the circular mantle muscles of squid (Ward and Wainwright, 1972; Moon and Hulbert, 1975; Bone et al., 1981; Thompson and Kier, 2006; Thompson et al., 2008; Thompson et al., 2010b) did not identify transmural differences in myofilament dimensions or their arrangement, but this has not, to our knowledge, been explored in a systematic way.

Intrinsic differences in the CMP fibers might explain the transmural variation in length–force properties. For example, protein-kinase -A-induced phosphorylation of two myofilament lattice proteins (troponin I and myosin binding protein C) in the cardiac myocytes of rats alters the shape of the length–tension curve, increasing the slope of the ascending limb dramatically (Hanft and McDonald, 2010). Expression of different troponin isoforms can also affect force generation in cardiac fibers (Gordon et al., 2000). Recent work has also revealed that the length–force relationship depends on the radial distance between the thin and thick myofilaments (Williams et al., 2013). It is unclear, however, if similar mechanisms to those outlined above occur in the obliquely striated squid mantle muscles.

Squid modulate isometric force and shortening velocity by varying thick filament length, not by expressing different isoforms of myosin heavy chain (Kier and Schachat, 1992; Kier and Schachat, 2008; Thompson et al., 2010b; Shaffer and Kier, 2012). Although other myofilament lattice proteins have the potential to affect the length–force relationship as well (e.g. Hanft and McDonald, 2010), we are currently investigating the dimensions and arrangement of myofilaments in our search for the mechanism driving transmural differences in muscle mechanics. Because we found no significant transmural difference in the maximum isometric tetanic force, we hypothesize that transmural gradients of myosin heavy chain expression or thick filament length do not occur in the mantle CMP circular fibers.

The data are consistent with our hypothesis that the CMP circular muscle fibers near the inner surface produce higher relative forces (both isometric twitch and tetanus) at a given length than the fibers near the outer surface, but the question remains whether the differences in the ascending limb of the length–tension curve are sufficient to allow all of the circular fibers in the mantle to produce similar forces at a given instant during the exhalant phase of the jet. Thompson et al. (Thompson et al., 2010a) showed in D. pealeii that the inner surface of the mantle experiences 1.3 to 1.6 times greater circumferential strain than the outer surface at any time point during the exhalant phase of a jet. Because circular fibers are oriented in transverse planes of the mantle and also appear to follow a perfectly circumferential trajectory, there are no architectural specializations, such as those found in mammalian cardiac ventricle muscle (Lunkenheimer et al., 2004; Anderson et al., 2006; Anderson et al., 2009) or vertebrate skeletal muscles (Alexander, 1969; Rome and Sosnicki, 1991; Wakeling and Johnston, 1999; Azizi et al., 2008) that could permit all of the fibers to experience approximately the same range of strains during jetting. Thus, the transmural gradient of circumferential strain in the mantle may require muscle fibers from the inner surface to operate farther left on the ascending limb of the length–tension curve at any instant during mantle contraction. But if the length–tension curve for the fibers from near the inner surface has a lower slope and higher y-intercept than the fibers from the outer surface of the mantle, then all of the circular fibers might produce approximately the same force at a given instant in the contraction cycle. This assumes that all of the CMP circular fibers are activated to a similar extent, which has not yet been established. How different must the slope and intercept be to allow this to happen?

The question can be addressed as follows. First, Thompson et al. (Thompson et al., 2010a) recorded circumferential strain simultaneously from both the inner and outer surfaces of the mantle from 12 D. pealeii that were similar in size [mean ± s.d. dorsal mantle length (DML)=157±44 mm] to the ones used in the present study. We fit a linear regression to their circumferential strain data that allowed us to predict the circumferential strain experienced by the inner surface of the mantle for a given strain at the outer surface (Fig. 6). Next, we used the sonomicrometry data for the outer surface of the mantle from the present study with the regression equation (Fig. 6) to estimate the corresponding circumferential strain at the inner lumen surface. Finally, we normalized those calculated strain data for the inner surface of the mantle by L₀ and plotted them on the length–twitch force curve (from Fig. 1A) and length–tetanic force curve (from Fig. 2). This allowed us to estimate the operating length range of the inner circular fibers relative to the outer fibers at any single point on the length–tension curve and, thus, predict the twitch or tetanic force output required by the inner fibers to match that of the outer fibers at a given instant in time.

The results of this analysis are shown in Fig. 7. The predicted lengths of the circular muscle fibers (relative to L₀) near the inner surface of the mantle fall very close to the actual ascending limb of the length–tension curve for the inner muscle preparations. Thus, we hypothesize that the differences in slope and intercept between the two length–tension curves may allow all of the CMP muscle fibers in the mantle to produce approximately the same force at any instant in the contraction cycle. Unfortunately, we do not know how much stress the CMP circular fibers from each location produce in vivo and cannot test this hypothesis at this time. This analysis is also complicated by potential transmural differences in (1) fiber activation, (2) the force–velocity properties of the circular fibers, and (3) shortening velocity in vivo (see Thompson et al., 2010a). These issues will be the subjects of future studies. In addition, we intend to characterize the force–velocity relationships and measure work output in preparations subjected to simulated in vivo patterns of stimulation and length change.

The CMP circular muscle fibers operated primarily on the ascending limb of the length–tension curve. They functioned routinely over muscle lengths at which force output ranged from only 85% to 40% of P₀, and during escape jets from 100% to approximately 30% of P₀. The operating length range of the muscles does not, therefore, appear to optimize work output. Shifting the range of operating lengths 0.15L₀ to the right on the length–tetanic force curve would center the length ranges on the force maximum region and, for most jets, likely result in higher work output (see Burkholder and Lieber, 2001). This finding is suggestive of a trade-off, but the nature of that trade-off is not yet clear.

One strong possibility is that squid trade muscle work output for maximum force production during escape responses. Squid use both the mantle and the fins for locomotion: adult animals use their fins extensively for station-holding and slow swimming, combinations of the fins and jetting for slow swimming and faster cruising, and the jet exclusively for escape responses (Bartol et al., 2008; Bartol et al., 2009). In two other species of loliginid squid (D. opalescens and Lolliguncula brevis), the thin layers of superficial mitochondria-rich (SMR) circular fibers provide power for ventilation and slow swimming while the CMP circular fibers we investigated are used periodically to augment power during slow swimming and also provide power for the escape jets (Gosline et al., 1983; Bartol, 2001). Because they operate on the ascending limb, the hyperinflation that precedes most escape jets lengthens the circular fibers close to L₀, thus allowing them to produce maximum force at the onset of the escape response.

There are several other examples of animals whose muscles operate solely along the ascending limb of the length–tension curve while providing power for locomotion or the pumping of fluid, situations in which maximizing work output might seem to be favored. The cross-striated adductor muscle of the bay scallop Argopecten irradians operates almost entirely on the ascending limb during the valve clapping movements required for swimming (Olson and Marsh, 1993; Marsh and Olson, 1994), as does the synchronous wing depressor of the hawkmoth Manduca sexta during flight (Tu and Daniel, 2004) and the human soleus muscle during walking and running (Rubenson et al., 2012). The papillary muscles of mammals (Allen and Kentish, 1985; Layland et al., 1995) and the atrial trabeculae of frogs (Winegrad, 1974) also operate solely along the ascending limb.

Operating on the ascending limb allows cyclically active muscles to respond to a stretch by increasing their capacity to produce force, though at the cost of decreased work and power. Such a response is hypothesized to provide non-neuronal mechanisms for regulating muscle excursion lengths during cyclical contractions (Tu and Daniel, 2004; Rubenson et al., 2012). The circular mantle muscles of squid are similar to the cardiac, flight and adductor muscles in that they contract and elongate rhythmically during locomotion and ventilation, and the degree of muscle lengthening during mantle cavity refilling can vary widely. But the cardiac, flight and adductor muscles have much steeper ascending limbs than the mantle fibers of squid, and thus force output is much more sensitive to changes in muscle length. Thus, we hypothesize that the observed operating length range of the mantle fibers may be more important for maximizing thrust during the initial phase of the escape jet than for regulation of muscle excursion length.

Both the leftward shift in the peak of the length–tension curve as stimulus frequency increases and the length dependence of activation of cross-striated skeletal and cardiac fibers in an isometric twitch are well-known phenomena (e.g. Rack and Westbury, 1969; Malamud, 1989; Roszek et al., 1994; Brown et al., 1999) that are assumed to be characteristic of striated fibers. In length-dependent activation in vertebrate striated fibers, the time to maximum isometric twitch force and the 50% relaxation time both increase significantly as fiber length increases (Rack and Westbury, 1969). The mechanisms responsible are still debated, with evidence suggesting roles for Troponin C (Babu et al., 1988; but see McDonald et al., 1995), Troponin I (Arteaga et al., 2000), Titin (Fukuda et al., 2001; Fukuda et al., 2003; Terui et al., 2008), and lateral/radial spacing of the thick and thin filaments (McDonald and Moss, 1995; Williams et al., 2013).

The CMP circular muscles exhibited a rightward shift in the peak of the length–force relationship as stimulus frequency increased (Figs 2, 4). They also showed no evidence of length-dependent changes in contraction kinetics (i.e. length-dependent activation) in an isometric twitch (Fig. 3). These differences are intriguing and may imply fundamental differences in the intrinsic properties of the obliquely striated circular fibers compared with cross-striated skeletal and cardiac fibers. The muscles of many invertebrates, including squid, have myosin-linked regulation. In these muscles, initiation of crossbridge cycling occurs via binding of Ca²⁺ to the essential light chain of myosin (Xie et al., 1994; Fromherz and Szent-Györgyi, 1995; Houdusse et al., 1999; for a review, see Szent-Györgyi, 2007). If length-dependent activation in vertebrate striated fibers involves changes in a troponin- or titin-linked mechanism, myosin-linked regulation may explain the absence of length-dependent changes in contraction kinetics during isometric twitches in the mantle circular fibers.

Milligan et al. (Milligan et al., 1997) and Thompson et al. (Thompson et al., 2008) reported a threefold lower twitch:tetanus ratio for the CMP circular muscle fibers than we report here. A difference in excitation–contraction coupling between the species may account for this disparity in the case of Milligan et al. (Milligan et al., 1997) because they studied Alloteuthis subulata, but Thompson et al. (Thompson et al., 2008) also studied D. pealeii. We noted in the present study that P_TW dropped steadily as the preparations first started to fatigue, while P₀ remained constant. Monitoring preparation health through periodic isometric tetanic contractions, as Thompson et al. (Thompson et al., 2008) did, would not allow the decline in P_TW to be detected. Thus, we feel the twitch:tetanus ratio reported here for D. pealeii may be more reliable than that reported previously by Thompson et al. (Thompson et al., 2008).

Obliquely striated muscles, so-called because the dense bodies (i.e. Z-elements) are aligned at an oblique angle to the long axis of the cell, have been reported in members of at least 14 different invertebrate phyla: Annelida (e.g. Rosenbluth, 1968), Brachiopoda (Kuga and Matsuno, 1988), Bryozoa (Bouligard, 1966), Echinodermata (Candia Carnevali et al., 1986), Gastrotricha (Rieger et al., 1974; Teuchert, 1974), Gnathostomulida (Rieger and Mainitz, 1977); Mollusca (e.g. Amsellem and Nicaise, 1980; Matsuno and Kuga, 1989), Nematoda (e.g. Rosenbluth, 1965), Nematomorpha (Eakin and Brandenburger, 1974; Lanzavecchia et al., 1979) Nemertea (Norenburg and Roe, 1998), Platyhelminthes (MacRae, 1965; Ward et al., 1986), Rotifera (Bouligard, 1966), Sipunculida (DeEguileor and Valvassori, 1977) and Urochordata (Bone and Ryan, 1974). Obliquely striated fibers are ubiquitous in some of these phyla (e.g. Nematoda), but are restricted in their distribution in others (e.g. the Mollusca, Urochordata and Sipunculida). A careful analysis of the evolution of these muscles is needed, but mapping the distribution onto a recent eumetazoan phylogeny (Paps et al., 2009) suggests that oblique striation evolved independently several times.

Such putative parallel evolution implies that the mechanical properties of obliquely striated muscles may be much more diverse than has been assumed (for reviews, see Rosenbluth, 1972; Toida et al., 1975; Lanzavecchia, 1977). For example, Lanzavecchia and colleagues (Lanzavecchia and De Eguileor, 1976; Lanzavecchia, 1977; Lanzavecchia and Arcidiacono, 1981) proposed that obliquely striated fibers are specialized to produce relatively high forces at exceptionally long muscle lengths. Using leeches as a model, they provided morphological evidence that overlap between the thick and thin filaments of the longitudinal body wall muscles is maintained over a fivefold increase in body length. Gerry and Ellerby (Gerry and Ellerby, 2011) showed recently that the longitudinal fibers of the body wall of the medicinal leech (Hirudo verbena) operated solely on the descending limb of the length–tension curve at very long muscle lengths during swimming and feeding. In the presence of serotonin, the longitudinal fibers produced relatively high forces (≥0.5P₀) at muscle lengths of nearly 2.5L₀.

In contrast, the present study shows that the obliquely striated CMP mantle fibers of squid operate almost exclusively on the ascending limb of the length–tension curve. Moreover, investigations of the length–force relationships of obliquely striated muscles in earthworms (Hidaka et al., 1969; Tashiro and Yamamoto, 1971), the horse leech Haemopis sanguisuga (Miller, 1975), and squid and cuttlefish (Milligan et al., 1997; Kier and Curtin, 2002) showed that these muscles produce force over a moderate range of lengths in vitro (Table 2), observations inconsistent with the hypothesis that oblique striation is a specialization for producing relatively high forces at long muscle lengths.

Furthermore, it is likely that considerable undescribed mechanical diversity exists among obliquely striated muscles, not only among different animals but also among different muscles in the same individual. For example, the tentacles of D. pealeii are elongated by 80% or more during prey capture (Kier, 1982) and then shorten to bring the prey within grasp of the arms, thereby requiring the obliquely striated longitudinal muscle fibers (Kier, 1985) that retract the tentacles to operate over a wide range of muscle lengths. In contrast, the obliquely striated funnel retractor muscle in the same animal experiences only small changes in length (±5%) during jetting, and operates nearly isometrically during the exhalant phase of the jet (Rosenbluth et al., 2010). In addition, the obliquely striated transverse muscle fibers of the arms of two squid species (D. pealeii and Sepioteuthis sepioidea) experience virtually no change in length while providing support for bending movements (Kier, 1982). To better understand the evolution and functional implications of oblique striation, investigations of the contractile properties and in vivo operating length ranges of obliquely striated muscles both from a broader taxonomic range and also from functionally diverse muscles within individuals is needed.

The experiments were conducted over three consecutive summers, with data collection each summer focusing on different aspects of muscle physiology or in vivo muscle function. In the summer of 2011, we used sonomicrometry to measure circumferential strain of the inner and outer surfaces of the mantle during jet locomotion as the first step in the investigation of the in vivo operating length ranges of the circular muscles. As the second step in this investigation, and also to evaluate the hypothesis that the length–force relationships of the circular muscle fibers vary transmurally, we used in vitro tests to measure the length–twitch force relationship of the circular muscle. Although the CMP circular fibers that were the focus of our study appear to be stimulated in brief tetanus in vivo (Gosline et al., 1983; Bartol, 2001), we used a twitch stimulus because it greatly increased the longevity of the preparations (relative to tetanic stimulation) and improved the odds of a successful experiment. This was crucial because we needed both sonomicrometry and muscle mechanical data from the same individual in order to identify the operating length ranges of the circular fibers.

Using twitch stimulations for the muscle preparations required additional experiments to ensure that any transmural differences in the length–twitch force relationship we observed were not merely artifacts of our experimental approach. Thus, in the summers of 2012 and 2013 we investigated the possibility that length-dependent activation of the CMP circular muscle preparations differed transmurally. This step was necessary because the cross-striated fibers of vertebrates and at least some arthropods exhibit greater activation at long lengths when stimulated with a single pulse of current (e.g. Rack and Westbury, 1969; Malamud, 1989; Roszek et al., 1994). If the circular muscles of squid exhibited length-dependent changes in contraction kinetics, and if those kinetics varied transmurally, then our comparisons of the length–twitch force relationship would have been inappropriate. In 2012 and 2013 we also performed experiments to measure the length–tetanic force and length–twitch force relationships in the same CMP circular muscle preparations. These experiments allowed us to correlate the length–tetanic force relationship with the sonomicrometry results, which as described above, required twitch stimulation for the viability of the preparations. In addition, we measured the twitch:tetanus ratio of the CMP fibers.

We used squid jigs and cast nets to capture adult D. pealeii from lighted piers and docks in Boothbay Harbor and South Bristol, Maine, USA, during the summers of 2011 (Group 1 squid), 2012 (Group 2) and 2013 (Group 3). The animals were transported to the laboratory in 20 l buckets and maintained in a 500 l aquarium supplied with flow-through seawater. Water temperature in the aquarium was 15 to 17°C. The animals were fed small fish (Brevoortia tyranus and Menidia menidia) daily until used in the experiments. Most squid were maintained in the laboratory for only a few days.

Group 1 included 20 squid used for measuring both the in vivo operating length range and length–twitch force relationship of the circular muscles from near the outer surface (n=10, 143±37 mm, mean ± s.d. DML) and the inner surface (n=10, 161±37 mm) of the mantle. Group 2 was composed of 16 squid (194±34 mm DML) for measurements of the twitch:tetanus ratio of the circular fibers, and Group 3 included 10 squid (150±55 mm DML) for evaluating length-dependent changes in contraction kinetics, the twitch–tetanic force relationship, and maximum isometric stress of the circular fibers. Note that in some cases for the squid in Groups 2 and 3, we were able to measure the contractile properties of the circular fibers from the inner and outer surface from the same individual, while in other individuals we were able to measure the properties of fibers from only one surface. Thus, the sample sizes for the twitch:tetanus ratio, twitch–tetanic force relationship, length-dependent contraction kinetics and maximum isometric stress experiments do not necessarily equal the number of individuals in the two sample population groups. The sample sizes for each experiment are listed in the Results.

We used sonomicrometry to measure circumferential strain of the inner and outer surfaces of the mantle during jet locomotion. We anesthetized squid in cold seawater (3 to 5°C) (O'Dor and Shadwick, 1989; Bower et al., 1999) and surgically affixed 1 mm diameter sonomicrometry transducers (Sonometrics Corp., London, ON, Canada) to the mantle. The transducers were attached to the mantle within a single transverse plane approximately one-third of the DML from the anterior edge (Fig. 8A,B). We chose this location because it experiences the largest amplitude changes in diameter during jetting. For experiments that focused on the outer surface of the mantle, transducers a and c (Fig. 8B) were sutured (6/0 polypropylene) to the outer surface of the mantle at the dorsal and ventral midlines, respectively. For experiments that focused on the inner surface of the mantle, transducer a was sutured to the outer surface of the mantle at the dorsal midline and transducer b was glued to the inner lumen surface of the mantle at the ventral midline with a drop of cyanoacrylate (Vetbond, 3M, St Paul, MN, USA) (Fig. 8B). All of the leads were secured to the dorsal collar of the mantle with a surgical staple to reduce interference with the mantle and fins during swimming.

Following surgery, the squid were transferred to a narrow tank (1.3×0.3×0.3 m deep) filled with natural seawater at 15–17°C. Each animal recovered quickly and then swam mantle-first and arms-first at various speeds using combinations of jetting and fin movement. We recorded sonomicrometry data at 150 Hz during swimming. The most rapid escape jets we recorded had exhalant phases of approximately 0.15 s and inhalant phases of approximately 0.4 s; thus, the two phases were described by a minimum of 30 and 90 data points, respectively. We positioned a digital video camera (Flip Ultra HD, 1280×720 pixel resolution, 30 frames s⁻¹) to record lateral views of the squid as they jetted. We used the video records to help select appropriate sequences for analysis. The duration of most swimming trials was 10 min. At the end of the trial, we euthanized the squid and evaluated the alignment of the transducers.

The CMP circular fibers of squid provide power for the escape jet and are also active sporadically during slow swimming (Gosline et al., 1983; Bartol, 2001). We analyzed sequences only in which the squid performed vigorous escape jets.

The sonomicrometry transducers recorded changes in the diameter of the outer or inner surfaces of the mantle at a single transverse plane along the dorso-ventral midline (Fig. 8B). The diameter of the outer surface was measured directly from the sonomicrometry traces. Calculation of the diameter of the inner surface required that we take into account the thickness of the dorsal mantle wall. Because the mantle remains circular in cross-section during jetting (Ward, 1972; Gosline and Shadwick, 1983), we used the diameter data to calculate the instantaneous circumference of either the inner lumen or outer surface of the mantle. We corrected the sonomicrometry data to account for transducer diameter and their location on the surface of the mantle by subtracting 1.0 mm from, or adding 1.0 mm to, the diameters recorded for experiments that focused on the outer or inner surfaces of the mantle, respectively.

Immediately after the end of a sonomicrometry experiment, the animal was anesthetized in cold seawater, and then decapitated. We cut a transverse ring of mantle tissue that included the sonomicrometry crystals (Fig. 8A,B), removed the skin, and placed the ring in a bath of chilled (3.5°C) modified artificial seawater solution containing (in mmol l⁻¹): NaCl (450), MgCl₂·6H₂O (10), Hepes (10) and EGTA (10), pH adjusted to 7.8 with 2 mol l⁻¹ NaOH (Milligan et al., 1997). We assessed the accuracy of the sonomicrometry crystal placement, detached them, and then used a surgical pen to draw two widely spaced marks on the cut surface of the ventral side of the ring (Fig. 8C). We photographed the ring and used morphometrics software to measure the circumference of either the inner or outer surface of the mantle, depending on the placement of the sonomicrometry crystals. We also measured the arc length of the inner or outer surface between the reference marks (Fig. 8C). These measurements allowed us to relate the relevant arc length between the marks to the circumference of the inner or outer surface of the mantle ring.

We next removed the ventral region of the ring that included the two reference marks and glued it with Vetbond, outer surface or inner surface down (depending on the experiment), to the stage of a vibratome (Fig. 8D). Experiments on the inner surface and the outer surface were interspersed over time. The vibratome bath was filled with chilled modified artificial seawater and maintained at 3.5°C. We then pierced the slab with an insect pin, forming a series of small but visible holes in the following locations: (1) one hole at the location of each mark of the tissue pen and (2) two straight lines of evenly spaced holes (Fig. 8D). We took care to ensure that each line of holes followed the trajectory of a single band of circular fibers.

We used the vibratome to cut 300 μm thick sheets of mantle tissue. The vibratome sliced through the radial muscle fibers, thereby inactivating them (see Milligan et al., 1997; Thompson et al., 2008; Thompson et al., 2010b). We selected a sheet that was 300 μm away from the appropriate surface of the mantle (i.e. inner or outer, depending on the experiment). This position insured that no SMR circular muscle fibers (see Preuss et al., 1997; Bone et al., 1981; Mommsen et al., 1981), which occur in layers within approximately 200 μm of both the inner and outer surfaces of the mantle of D. pealeii (Thompson et al., 2008), were present in the preparations. Thus, our preparations were composed of the CMP (see Preuss et al., 1997) muscle fibers, and remnants of radial fibers and collagenous connective tissue fibers. We further dissected the sheet into a preparation 10–12 mm long by 4–5 mm wide, with the line of holes in the center of each preparation (Fig. 8D). The ends were glued to T-shaped aluminum foil clips with Vetbond (Fig. 8E). Each muscle preparation had two or three of the pinholes visible between the foil clips.

The muscle preparation was transferred to a bath filled with 100 ml of cold (3.5°C) standard artificial seawater solution containing (in mmol l⁻¹): NaCl (470), KCl (10), CaCl₂ (10), MgCl₂·6H₂O (50), glucose (20) and Hepes (10), pH adjusted to 7.8 with 2 mol l⁻¹ NaOH (Milligan et al., 1997). After 60 min in the bath, we transferred the preparation to a recirculating temperature-regulated bath filled with standard artificial seawater at 15°C and attached one end to a fixed hook and the other to a hook on a muscle lever system (300B, Aurora Scientific Inc., Aurora, ON, Canada).

The muscle preparations were subjected to a twitch stimulus with rectangular constant current pulses (0.002 s pulse width) via platinum foil electrodes that were of sufficient size to cover the preparation. Prior to starting the length–twitch force experiments, we first determined the current amplitude that activated the preparation maximally. Interestingly, supramaximal stimulation consistently caused a decrease in force output.

We began each length–force experiment with the preparation barely slack and lengthened it as the experiment continued. Each length–tension curve was composed of 13 to 15 points. At the end of the experiment, we adjusted the preparation length to L_TW (i.e. the preparation length at peak isometric twitch force), stimulated it again to ensure that peak isometric force was stable (if it decreased by more than 10%, the animal was excluded from the study), and then measured the distance between the pinholes (Fig. 8E). The distance between the pinholes at L_TW was used to relate length–force data to the sonomicrometry data (see below).

Estimating the operating length ranges of the muscle fibers in the mantle is challenging because, like many other soft-bodied invertebrates, there are no landmarks that can be used to relate muscle lengths to body or appendage kinematics. Measuring muscle strain directly by inserting sonomicrometry crystals into the tissue is similarly challenging because (1) the mantle is circular in cross-section and the crystals measure straight-line distances, and (2) the large changes in mantle circumference during jetting preclude close spacing of the crystals to help reduce errors due to mantle geometry. Therefore, we used the reference marks and pin holes described above (Fig. 8C–E) to relate L_TW to mantle circumferential strain as follows. First, we calculated the ratio of the arc length between the pen marks to the circumference for either the inner or outer surface (depending on the experiment) of the mantle rings. Next, we measured the spacing between the two pinholes on the slab that were located adjacent to the two pen marks (the spacing changed as we flattened the slab and glued it to the stage) and calculated the ‘slab circumference’ using the aforementioned ratio. Next, we divided the measured distance between the pinholes at L_TW by the measured distance between the same pinholes in the slab of mantle tissue glued to the vibratome stage. We referred to this as the L_TW/L_Slab ratio. By multiplying the ‘slab circumference’ by the L_TW/L_Slab ratio, we were then able to determine the circumference of the relevant surface of the mantle at L_TW. We then used that circumference to normalize the sonomicrometry data by L_TW.

In the striated fibers of vertebrates and arthropods, the degree of fiber activation varies with length when preparations are activated with a twitch stimulus (e.g. Rack and Westbury, 1969; Malamud, 1989; Roszek et al., 1994). Transmural differences in such length-dependent contraction kinetics, if present, might affect the length–twitch force relationship of the outer or inner CMP circular mantle fibers given that we used a twitch stimulus. Thus, we investigated potential differences in length-dependent contraction kinetics of the circular fibers in two ways as follows. From the length–twitch force data collected from the animals in Group 1, we first compared the time required (T_max) for force to rise from the onset of stimulation to the peak as preparations were lengthened from their shortest to their longest lengths. We made similar comparisons for the time required (T_50%) for force to fall from the maximum to 50% of the maximum. We then performed linear regressions of preparation length versus T_max and, separately, versus T_50%. We used independent-samples t-tests to compare the slopes and y-intercepts of the regressions between preparations from the outer and inner surfaces of the mantle.

We also examined length-dependent activation by comparing the preparation lengths that generated maximum isometric twitch force (L_TW) and maximum isometric tetanic force (L₀). We anesthetized the squid in Group 3 in chilled seawater and prepared muscle preparations as described for the length–twitch force experiments above, though we did not perforate the preparations with a pin. We determined the current amplitude needed to activate the preparations maximally and then performed length–twitch force experiments to determine the length–tension curve using a twitch (2 ms pulse width) stimulus. We adjusted the preparation length to 0.84L_TW and then performed length–force experiments using tetanic (0.002 s pulse width, 80 Hz, 0.1 s duration) stimulation.

Performing the twitch stimulation experiments before the tetanic stimulation experiments allowed us to find the zone of highest forces of the preparation more rapidly and with less fatigue, which was necessary for viability of the preparations. In several preparations we rechecked the twitch results following the tetanic stimulation series to confirm that the length–force relationship was unchanged. We thus do not believe that conducting the twitch stimulations first introduced a bias, but preparation viability did not allow us to reverse the order.

Following these experiments, we fixed (3.75% formaldehyde in seawater) the preparations at L₀, embedded them in glycol methacrylate plastic (GMA, Technovit 7100, Heraeus Kulzer GmbH, Wehrheim, Germany), cut 7 μm sections transverse to the long axes of the circular fibers, and stained the sections in Picrosirius modified for use in GMA (Cerri and Sasso-Cerri, 2003). GMA plastic was chosen because it minimizes dimensional changes during embedding and sectioning procedures. We then used morphometrics software (Sigma Scan, Systat Software, Inc., San Jose, CA, USA) to measure the physiological cross-section of the circular muscle fibers of the preparations from photomicrographs of the sections. The inactivated radial muscle fibers were excluded from the area measurement because they do not contribute to force production by the preparation. The physiological cross-section measurements allowed us to calculate the maximum isometric stress for both twitch (P_TW) and tetanic (P₀) stimuli. We used independent-samples t-tests to compare P₀ and also differences in L_TW versus L₀ for the preparations.

We anesthetized the squid in Group 2 in chilled seawater and decapitated them, as described above. We then removed large blocks (15×20 mm) of the mantle tissue near the ventral midline one-third to one-half of the DML from the anterior margin of the mantle and used the vibratome to prepare 300 μm thick preparations as described above. We determined the current amplitude needed to activate the preparations maximally with a twitch stimulus (2 ms pulse width) and then performed stimulus frequency–force experiments. In five animals, we determined that maximum tetanic force was produced at 80 or 100 Hz (0.002 s pulses, 0.1 s tetanus duration). In all subsequent experiments, we cycled our stimulation protocol from twitch to 80 to 100 Hz (with 5 min rest periods between stimulations) until the twitch and tetanic force stabilized. We reported the twitch:tetanus ratio only when the twitch force was stable for two consecutive trials. Remarkably, the twitch:tetanus ratio changed very little, even as the twitch force generated by a preparation increased over successive initial trials and then stabilized.

The data from each group of squid were distributed normally. We used independent-samples t-tests and linear regression analysis as noted in the Results. All statistical comparisons were performed with SPSS 19 (IBM, Armonk, NY, USA).

We thank Harry Perilstein and Natalie Friedman for help with the muscle mechanics and sonomicrometry experiments, Jessica Kurth for assistance with the histology and morphometrics, and Dr Kevin Eckelbarger, Timothy Miller and Linda Healy at the Darling Marine Center for providing housing, laboratory space and aquaria for the squid. We thank Cole Natale and Ian, Claire and Sophie Thompson for help in capturing and caring for the squid.