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Department of Biology, CB#3280 Coker Hall, University of North Carolina, Chapel Hill, North Carolina 27599-3280
* To whom correspondence should be addressed. E-mail: joethomp{at}email.unc.edu
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Abbreviations: DML, dorsal mantle length • IM-1, intramuscular fiber system 1 • IM-1SAG, sagittal component of IM-1 fiber angle • IM-1TAN, tangential component of IM-1 fiber angle • IM-2, intramuscular fiber system 2
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Introduction |
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TOPAbstractIntroductionMaterials and MethodsResultsDiscussionAppendixLiterature Cited |
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Squid mantle morphology
Squid are soft-bodied molluscs that combine a hydrostatic skeleton with an uncalcified, chitinous gladius (= pen) to provide shape and structural support for the mantle. The mantle lacks the large, fluid-filled spaces characteristic of the hydrostatic skeleton of many worms and polyps. Instead, the muscle fibers and connective tissue fibers of the mantle are packed into a dense, three-dimensional array. Water contained within the muscle fibers and the connective tissue fibers themselves serves as the incompressible fluid. In such a system of structural support, termed a "muscular hydrostat" by Kier and Smith (1985), the volume of the mantle remains constant, such that a change in one dimension must result in a change in at least one of the other dimensions of the mantle.
The mechanical support for the mantle arises from a complex, three-dimensional arrangement of muscle fibers, connective tissue fibers, and the gladius. The muscle fibers in squid mantle are arranged primarily in two orientations: circumferentially and radially. Contraction of the circumferential muscles decreases mantle circumference and expels water from the mantle cavity through the funnel during the exhalant phase of jet locomotion (Young, 1938). Contraction of the radial muscle fibers thins the mantle wall and increases the mantle circumference, filling the mantle cavity during the inhalant phase of jet locomotion (Young, 1938).
The fibrous connective tissues of the squid mantle are arranged into five networks (Fig. 1): the inner and outer tunics, which sandwich the circumferential and radial muscles, plus three networks of intramuscular collagen fibers (Ward and Wainwright, 1972; Bone et al., 1981). Intramuscular fiber system 1 (IM-1) consists of collagen fibers (Gosline and Shadwick, 1983b; MacGillivray et al., 1999) that originate and insert on the inner and outer tunics (Ward and Wainwright, 1972). Viewed in sagittal section, the IM-1 collagen fibers are arranged at a low angle (28° in Lolliguncula brevis) relative to the long axis of the mantle (Ward and Wainwright, 1972) (Fig. 1). In sections tangential to the surface of the mantle, the collagen fibers in IM-1 are also arranged at low angles (10° to 15° in Alloteuthis subulata) relative to the long axis of the mantle (Bone et al., 1981) (Fig. 1). Thus, the IM-1 fibers actually follow an oblique path through the mantle wall, relative to both tangential and sagittal planes.
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The final connective tissue fiber system in squid mantle is intramuscular fiber system 3 (IM-3). Collagen fibers (MacGillivray et al., 1999) in IM-3 are arranged parallel to the circumferential muscle fibers and are not attached to the tunics (Bone et al., 1981).
Mantle connective tissue function
The tunics and intramuscular collagen fibers serve important roles in controlling shape change in the mantle. The low fiber angles reported for tunic and IM-1 fibers in Lolliguncula brevis suggest strongly that the tunics and IM-1 help prevent mantle elongation during contraction of the circumferential muscles (Ward and Wainwright, 1972). This putative role is corroborated by Ward’s (1972) observation that mantle length in L. brevis does not change measurably during jetting, though Packard and Trueman (1974) report small (i.e., <5%) increases in Loligo vulgaris and Sepia officinalis.
The collagen fibers in IM-1 and IM-2 may resist the substantial increase in mantle thickness that occurs during circumferential muscle contraction. In addition, these collagen fibers are thought to store elastic energy during the exhalant phase of the jet and return that energy to help restore mantle shape and refill the mantle cavity (Ward and Wainwright, 1972; Bone et al., 1981; Gosline et al., 1983; Gosline and Shadwick, 1983a, b; Shadwick and Gosline, 1985; MacGillivray et al., 1999; Curtin et al., 2000). The IM-1 and IM-2 collagen fibers may also help restore mantle shape during the low-amplitude movements that occur during respiration (Gosline et al., 1983).
Specific problem addressed
Virtually all the published work on squid mantle morphology and function is on adult loliginid squid. The few studies of hatchling or juvenile loliginid squid reveal dramatic changes in mantle function during ontogeny. For example, the morphology and physiology of the mantle musculature in Photololigo sp. and Loligo opalescens (Moltschaniwskyj, 1994; Preuss et al., 1997) and the neuromuscular physiology underlying the escape response in L. opalescens (Gilly et al., 1991) change significantly during growth from hatchlings to adults. Importantly for this study, the range of mantle movement during jet locomotion in newly hatched L. opalescens and Loligo vulgaris is greater than in adult animals (Packard, 1969; Gilly et al., 1991; Preuss et al., 1997). Given the link between the mantle connective tissue arrangement and mantle kinematics, it is likely that the orientation, the mechanical properties, or both the orientation and mechanical properties of squid mantle collagen change during ontogeny. Here, we examine ontogenetic changes in the arrangement and amount of connective tissue in the mantle in the oval squid, Sepioteuthis lessoniana (Cephalopoda: Loliginidae). The effect of ontogenetic changes in the collagen fiber arrangement of the outer tunic, IM-1, and IM-2 on mantle kinematics and elastic energy storage during jet locomotion is also analyzed.
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Materials and Methods |
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Commencing at hatching, and at weekly intervals thereafter, live squid were sent via overnight express shipping from the NRCC to the University of North Carolina. The squid, which ranged from 5 mm to 70 mm in dorsal mantle length (DML), were killed by over-anesthesia in a solution of 7.5% MgCl2 mixed 1:1 with artificial seawater (Messenger et al., 1985). The MgCl2 solution relaxed the mantle musculature of nearly all of the squid. Animals in which the mantle musculature was contracted noticeably were not used for the histological study. The MgCl2 solution did not distort the shape of the mantle. The resting mantle diameter of an anesthetized squid was always 80% to 90% of the peak mantle diameter measured during jet locomotion in the same, unanesthetized animal (for details of the kinematics measurements, see Thompson and Kier, 2001).
Histology
The mantle tissue was examined using standard histological methods. Immediately after death, the squid were fixed whole in 10% formalin in seawater for 48 to 96 h at 20° to 23 °C. In the larger animals (>25 mm DML), the animal was decapitated to permit unrestricted flow of fixative into the mantle cavity. The mantles were fixed whole, rather than dissected into smaller blocks of tissue, to help minimize shape changes (e.g., curling or bending of the tissue block) that could affect connective tissue fiber angle.
Following fixation, the tissue was dehydrated in a graded series of ethanol and cleared in Histoclear (National Diagnostics, Atlanta, GA) or Hemo-D (Fisher Scientific, Pittsburgh, PA). There was no discernible scale-related distortion of the mantle during dehydration and clearing. After clearing, the mantle was dissected into smaller pieces and embedded in paraffin (Paraplast Plus, Oxford Labware, St. Louis, MO; melting point 56 °C). To minimize shrinkage artifacts, infiltration with molten paraffin was limited to a total of 90 min (30-min baths x 3 changes) instead of the 180 min (60-min baths x 3 changes) recommended by Kier (1992).
Following clearing, most of the squid smaller than 30 mm DML were sliced in half along the sagittal plane using a fine razor blade. One half of the animal was oriented in the embedding mold to permit the cutting of sagittal sections; the other half was oriented for cutting of transverse sections. Many of the smaller squid were sliced in half along the frontal plane. The dorsal and ventral halves were oriented in the embedding molds to allow grazing sections to be cut. For the squid larger than 30 mm DML, large blocks of tissue of about 5 mm by 3 mm by the thickness of the mantle were dissected from several locations along the length and around the circumference of the mantle. These tissue blocks were oriented in the embedding molds to permit the cutting of sagittal, transverse, and tangential sections.
The tissue blocks were sectioned using a rotary microtome. The sections were mounted on slides coated with Mayer’s albumin and stained with picrosirius stain (Sweat et al., 1964; protocol adapted from López-DeLeón and Rojkind, 1985). Other connective tissue stains were used successfully (e.g., Milligan trichrome, picro-ponceau, and van Gieson’s stain) but picrosirius stain provided the best contrast between the collagenous and non-collagenous components of the tissue sections and made identification of intramuscular collagen fibers straightforward.
Several additional attributes made picrosirius an excellent choice for this study. First, the sirius red F3B dye molecules attach with their long axes parallel to the long axes of the collagen fibrils, enhancing the natural birefringence of collagen fibers (Montes and Junqueira, 1988). Second, picrosirius is an outstanding stain for resolving the smallest collagen fibers and fibrils. The stain has been used previously to visualize the fine reticular collagen fibers present in embryonic mammalian skin and organs, the thin type-II collagen fibrils present in mammalian cartilage, and the extremely fine type-IV collagen fibrils present in mammalian basal laminae (Montes and Junqueira, 1988). Third, there is a strong correlation between the collagen volume fraction estimated from paraffin-embedded human liver sections using the picrosirius stain and the collagen volume fraction from the same tissue sections measured by hydroxyproline content analysis (López-DeLeón and Rojkind, 1985). Thus, picrosirius stain is ideal for both visualizing collagen fibers and making precise estimates of collagen volume fraction.
The stained sections were viewed using brightfield and polarized light microscopy. Fiber angles were measured from digital photomicrographic images using image analysis software (SigmaScan Pro, SPSS Science, Chicago, IL).
Initial survey
We made an initial survey of the mantle intramuscular fiber (IM) networks 1 and 2 in five squid (25 mm to 70 mm DML) to help develop a protocol for measuring IM fiber angles. In this survey, IM-1 and IM-2 fiber angles from different regions along the length and around the circumference of the mantle were examined. IM-1 and IM-2 fiber angles were measured at four positions along the length of the mantle (1/10, 1/4, 1/2, and 3/4 DML) and at three positions around the circumference of the mantle (ventral, lateral, dorsal). Given the potential for regional differences in IM fiber angle (see Results for details), all the comparisons among the squid were made at the same location: the ventral portion of the mantle between 1/3 and 2/3 DML.
IM-1 fiber angle measurements
IM-1 collagen fibers are arranged obliquely to the sagittal plane (Fig. 1). Therefore, to describe accurately the trajectory of these fibers, two fiber angles must be measured. The first angle, called IM-1SAG here, is the angle of IM-1 collagen fibers relative to the long axis of the mantle in the sagittal plane (Fig. 1). The second angle, which we call IM-1TAN, is the IM-1 fiber angle relative to the long axis of the mantle in a plane tangential to the outer surface of the mantle and perpendicular to the sagittal plane (Fig. 1).
IM-1SAG fiber angle measurements
IM-1SAG fiber angles were measured from sagittal sections (thickness 10–15 µm) of the mantle. Criteria were developed to ensure consistency across all squid in the ontogenetic series. First, all measurements of fiber angles were made from the ventral portion of the mantle between 1/3 and 2/3 DML. This eliminated errors due to variation in fiber angle along the length and around the circumference of the mantle.
Second, because the apparent fiber angle depends on the viewer’s perspective, IM-1SAG fiber angles were measured only from tissue sections in which the circumferential muscle fibers of the mantle were cut in nearly perfect cross section. This restriction ensured that the perspective was similar for all the squid examined. Adjusting the orientation of the tissue block relative to the microtome knife made it possible, through trial and error, to meet this criterion, and conformance was determined by examining test sections 20 µm thick.
Third, sagittal tissue sections contained IM-1 fibers of varying lengths. It was difficult to obtain accurate angle measurements of the shortest fibers in each section. Therefore, IM-1SAG fiber angle measurements were made only on IM-1 fibers longer than the width of one circumferential muscle band. A circumferential muscle band was defined as a region of circumferential muscle fibers bounded by radial muscle fibers (Fig. 1).
Fourth, in all animals larger than about 15 mm DML, IM-1SAG fiber angles were measured only from crossed IM-1 fibers. The angle between the two fibers was measured and the half angle reported as the IM-1SAG fiber angle (Fig. 1). In squid smaller than 15 mm DML, IM-1 fibers were so scarce that there were few instances of crossed fibers. In these small squid, IM-1SAG fiber angles were measured relative to the outer or the inner tunic (Fig. 1). In areas where the tunics were folded due to histological artifact, IM-1SAG fiber angles were not measured.
Finally, the fiber angle of every IM-1SAG fiber in a given microscope field that conformed to the criteria was measured. A minimum of 20 measurements was made from each squid larger than about 15 mm DML. Because IM-1 fibers were sparse in animals smaller than 15 mm DML, the minimum number of fiber angle measurements was eight in these animals.
IM-1TAN fiber angle measurements
IM-1TAN fiber angles were measured from relatively thick (10 to 15 µm) tangential sections of the mantle. To ensure consistency in fiber angle measurements among all squid, the criteria listed previously were used with two exceptions. First, IM-1TAN fiber angles were measured only in those sections in which the radial muscle fibers were cut in nearly perfect cross section (determined from 20-µm thick test sections). Second, for squid larger than about 15 mm DML, fiber angles were measured only from crossed IM-1 fibers. In the smallest squid (<15 mm DML), there were few IM-1 fibers and virtually no crossed fibers. In these squid, IM-1TAN fiber angles were measured relative to a band of radial muscle fibers. Subtracting the measured angle from 90° gave the angle of the IM-1TAN fiber relative to the long axis of the squid.
IM-2 fiber angle measurements
IM-2 fiber angles were measured from 5 µm thick transverse sections of the mantle. As with the IM-1 measurements, IM-2 fiber angles were measured only from the ventral portion of the mantle between 1/3 and 2/3 DML. Fiber angles were measured only from sections that were nearly perfect transverse sections of the mantle. Sections oblique to the transverse plane show circumferential muscle fibers in closely spaced bands separated by a few radial muscle fibers. Nearly perfect transverse sections exhibited uninterrupted circumferential muscle fibers. IM-2 fiber angle was measured only from crossed fibers (Fig. 1). Given the scarcity of IM-2 fibers in squid smaller than about 15 mm DML, it was not always possible to measure crossed fibers. In these small squid, IM-2 fiber angle was also measured relative to nearby radial muscle fibers. Finally, the fiber angle of every IM-2 fiber in the microscope field was measured. No fewer than 20 fiber angle measurements were made from each squid longer than about 15 mm DML. The relative paucity of IM-2 fibers in squid smaller than 15 mm DML reduced the minimum number of fiber angle measurements to eight per squid.
Outer tunic fiber angle measurements
Outer tunic fiber angles were measured from 5-µm-thick grazing sections of the mantle. Tunic fiber angles were measured only from the ventral portion of the mantle between 1/3 and 2/3 DML and only from crossed fibers. The half angle between the crossed tunic fibers, relative to the long axis of the squid, was reported as the fiber angle (Fig. 1). A minimum of 20 fiber angle measurements was made from each squid.
Stereology
Stereological methods were used to estimate the volume fraction of IM-1 and IM-2 collagen fibers relative to the volume of the mantle musculature. To obtain an accurate estimate of the volume fraction of a particular tissue component, stereology requires that the tissue of interest be sectioned in randomly oriented planes (Weibel, 1979). Because it is difficult to positively identify a collagen fiber in a random section plane as an IM-1 or IM-2 fiber, it was not possible to use random section planes. IM-1 collagen fiber volume fraction was therefore determined from sagittal sections of the ventral mantle in which fiber identity could be verified. Likewise, IM-2 collagen fiber volume fraction was measured from transverse sections of the ventral mantle. Although this violates an assumption of stereology, it allows accurate comparison of the relative volume fraction of collagen fibers among squid in the ontogenetic series. However, this method is inappropriate for estimation of the absolute volume fraction of collagen fibers in the mantle (Weibel, 1979).
The procedure for collagen volume fraction determination was similar for both IM-1 and IM-2. The ventral portion of the mantle between 1/3 and 2/3 DML was examined. A slide containing either sagittal (IM-1) or transverse (IM-2) 10-µm-thick tissue sections was placed on the stage of a compound microscope, and the tissue positioned under a 40x objective lens without observation through the oculars. The tissue section was brought into focus, and an image of the section was captured by a digital camera. The image was expanded to fill the screen of the monitor, and a transparent plastic overlay with a grid of 24 lines x 24 lines (Weibel, 1979) was taped to the screen. The intersection of a collagen fiber in IM-1 (sagittal sections only) or IM-2 (transverse sections only) with the junction of two lines (= a point; there were 24 lines x 24 lines = 576 points on the grid) was counted as a "hit." After the image was sampled, the microscope stage was moved haphazardly without observing the image through the microscope. In all cases, the stage was moved sufficiently far to ensure that the same portion of the mantle tissue was not examined twice. Another digital image was then captured, and the procedure was repeated at 2 or 3 different locations within the same tissue section and on between 3 and 10 different tissue sections per squid. The average volume fraction of collagen in IM-1 and IM-2 relative to the average volume of the mantle musculature was calculated by dividing the total number of hits by the total number of points counted for each squid (Weibel, 1979).
In stereology, both the acceptable standard error of the volume fraction estimate and the volume fraction of the item of interest determine the total number of points that must be counted (Weibel, 1979). The total number of points (PC) was determined by
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is the acceptable error probability (the chance that the true volume fraction will be outside the confidence interval), and VV is the volume fraction of the item of interest. To determine PC, the volume fraction (VV) of collagen in both IM-1 and IM-2 was estimated for four squid of various sizes (5 mm, 15 mm, 27 mm, and 69 mm DML) using the procedure outlined in the previous paragraph. Using the initial estimate of VV, an error probability of 5%, and a confidence interval of ±10%, the total number of points to be counted (PC) was calculated (Table 1). The VV of collagen was strongly correlated with squid size. Thus, the total number of points counted per squid varied with size. Note that the actual number of points counted per squid was much greater than the minimum required to obtain an error probability of 5% and a confidence interval of ±10%. Thus, the actual error probability and confidence interval were smaller than the predicted values.
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Nonparametric statistics were used for most of the analyses because the sample population was not normally distributed. For comparisons among the life-history stages, Kruskal-Wallis one-way analysis of variance on ranks was used with Dunn’s method of pairwise multiple comparisons (Zar, 1996). All statistical analyses were completed using SigmaStat 1.01 (SPSS Science).
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Results |
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TOPAbstractIntroductionMaterials and MethodsResultsDiscussionAppendixLiterature Cited |
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The majority of the mantle is composed of circumferential muscle fibers. These muscle fibers are bordered by the outer and inner tunics and are partitioned by regularly spaced bands of radial muscle fibers. Consistent with the trend for Photololigo sp. (Moltschaniwskyj, 1994), the circumferential muscle fibers increased in diameter during ontogeny from 2.5 µm ± 0.49 µm (mean ± standard deviation, n = 46 from four specimens) in newly hatched squid to 3.9 µm ± 0.66 µm (n = 43 from four individuals) in the largest animals examined. In addition, the ratio of mitochondria-rich to mitochondria-poor (Bone et al., 1981; Mommsen et al., 1981) circumferential muscle fibers decreased from 1:5 in newly hatched squid to 1:7 in young 2 stage squid. The number of mitochondria-rich fibers adjacent to the inner tunic is twice that of the mitochondria-rich muscle fibers adjacent to the outer tunic in S. lessoniana.
The inner tunic is adjacent to the mantle musculature and to the thin epithelial lining of the mantle cavity. The radial muscle fibers and the collagen fibers in IM-1 and IM-2 insert on the inner tunic.
Initial survey
An initial survey of the mantle revealed that IM-1 fiber angle and IM-2 fiber angle differ both along the length and around the circumference of the mantle in an individual squid. In the ventral portion of the mantle, there were no significant differences in IM-1 fiber angle or in IM-2 fiber angle between 1/4 and 3/4 DML. However, IM-1 fiber angle was about 10° higher at 1/10 DML and about 10° lower between 3/4 DML and the posterior tip of the mantle. Similar differences in IM-1 fiber angle along the length of the mantle were also noted in the lateral and dorsal regions. There was no correlation between mantle thickness at either 1/10 or 3/4 DML and the fiber angle at that location.
Between 1/4 and 3/4 DML, both IM-1 fiber angle and IM-2 fiber angle were about 10° lower in the dorsal region of the mantle than in either the lateral or ventral portions. Within an individual squid, there were no significant differences between the average IM-1 fiber angles or IM-2 fiber angles in the lateral or ventral portion of the mantle between 1/4 and 3/4 DML. Again, there was no apparent correlation between mantle thickness and fiber angle at a particular location around the circumference of the mantle.
The implications of these differences in collagen fiber arrangement are unclear. It is interesting, however, that MacGillivray et al. (1999) did not report significant differences in mantle mechanical properties either along the length or around the circumference of the mantle in Loligo pealei. It is possible that the differences in IM-1 and IM-2 fiber angle reported here for S. lessoniana are not present in L. pealei. Alternatively, such differences, if present, may not translate into significant differences in mantle mechanical properties.
IM-1 fiber ontogeny
IM-1 collagen fibers were scarce in newly hatched squid relative to older, larger animals (Fig. 2). Dozens of sagittal tissue sections from a hatchling squid could be searched without encountering a single IM-1 fiber. As the squid grew during ontogeny, IM-1 collagen fibers became increasingly numerous and robust (Fig. 2). The diameter of IM-1 fibers increased during ontogeny from 0.58 µm ± 0.060 µm standard deviation (SD; n = 24 from four individuals) in newly hatched squid to 0.68 µm ± 0.052 µm SD (n = 37 from three animals) in the young 2 stage squid.
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IM-2 fiber ontogeny
IM-2 collagen fibers were scarce in newly hatched animals when compared to the older, larger squid in the study (Fig. 4). As with IM-1 fibers, many mantle tissue sections could be observed without locating a single IM-2 collagen fiber. However, IM-2 fibers increased in abundance and diameter as the squid grew during ontogeny (Fig. 4). The diameter of IM-2 collagen fibers increased from an average of 0.54 µm ± 0.080 µm SD (n = 28 from four animals) in newly hatched squid to an average of 0.71 µm ± 0.087 µm SD (n = 31 from three specimens) in the young 2 stage animals.
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Outer tunic fiber ontogeny
Regardless of size, all the squid possessed a robust outer tunic (Fig. 5). The collagen fibers constituting the outer tunic changed in orientation during ontogeny. The outer tunic fiber angle was highest in newly hatched animals (between 27° and 36°) and declined during ontogeny (Fig. 3D). In squid larger than about 15 mm DML, outer tunic fiber angle decreased slightly with size from about 26° to 16° (Fig. 3D). A one-way ANOVA on ranks showed that the outer tunic fiber angle was higher in hatchling stage animals than in all older, larger squid (P < 0.05, Table 2). In addition, outer tunic fiber angle was slightly higher in juvenile 2 stage animals than in either juvenile 1 or young 2 stage animals (P = 0.05, Table 2). There were no significant differences in outer tunic fiber angle between juvenile 1 and young 2 stage squid.
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Discussion |
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TOPAbstractIntroductionMaterials and MethodsResultsDiscussionAppendixLiterature Cited |
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The outer tunic
The tunics of squid are hypothesized to restrict mantle lengthening during jet locomotion (Ward and Wainwright, 1972). This important function ensures that the mechanical work performed by the circumferential musculature is used to decrease mantle cavity volume, thereby forcing water out of the funnel and producing thrust, instead of lengthening the mantle. The average outer tunic fiber angle of 17.7° from young 2 stage Sepioteuthis lessoniana was substantially lower than the 27° average outer tunic fiber angle reported for Lolliguncula brevis and Loligo pealei by Ward and Wainwright (1972). Indeed, the outer tunic fiber angle measured for mature L. brevis and L. pealei by Ward and Wainwright (1972) is much closer to the hatchling stage outer tunic fiber angle of 33.5° in S. lessoniana.
The outer tunic fibers of all the S. lessoniana studied are oriented appropriately to resist lengthening of the mantle during jet locomotion (see Chapman, 1958, and Clark and Cowey, 1958). Both the mechanical properties and fiber angle of outer tunic collagen fibers affect mantle lengthening during jet locomotion. If the mechanical properties of the outer tunic collagen fibers do not change during ontogeny, the ability of the outer tunic to resist increases in mantle length during jet locomotion will depend on fiber angle. For example, if the maximum extensibility of an outer tunic collagen fiber is 0.13, a realistic assumption based on mechanical tests of squid mantle collagen (Gosline and Shadwick, 1983b), the mantle length of a hatchling stage squid may increase up to 23% during a jet whereas the mantle length of a young 2 stage animal may increase up to 17%. Thus, the ontogenetic variation in outer tunic fiber angle may allow greater mantle length increases during jet locomotion in newly hatched squid than in older, larger squid.
The possible increases in mantle length calculated above for S. lessoniana probably represent maximal values. The force balance between the outer tunic collagen fibers, other networks of connective tissue fibers, the chitinous gladius, and perhaps, the collagen-rich skin may all serve to limit changes in mantle length. The purpose of the calculation is simply to highlight the influence of outer tunic fiber angle on the potential for increases in mantle length during jet locomotion. Indeed, Ward (1972) did not observe increases in mantle length during jet locomotion in L. brevis. Packard and Trueman (1974), however, did notice small increases (
5%) in the ventral mantle length of subadult Loligo vulgaris and adult Sepia officinalis. As the next section illustrates, small increases in mantle length during the jet may facilitate elastic energy storage in the IM-1 collagen fibers of newly hatched S. lessoniana.
IM-1
Previous reports of IM-1SAG fiber angle from Lolliguncula brevis and Loligo pealei are about 15° lower than the fiber angle reported here for the young 2 stage S. lessoniana (Ward and Wainwright, 1972). The discrepancy may be due to species differences or to the histological methods selected for the analysis. It is also possible that age or size differences may account for the disparity because mature squid were analyzed in the previous study. It is not possible to compare the IM-1SAG hatchling fiber angle because, to our knowledge, there are no published values for newly hatched squid.
Bone et al. (1981) reported IM-1TAN fiber angle data for Alloteuthis subulata and Loligo forbesi. In both species, the IM-1TAN fiber angle was 15° to 20° lower than the angle measured here for young 2 stage S. lessoniana. The fiber angle reported by Bone et al., however, was measured in partially contracted specimens. Contraction of the mantle results in a decrease of the IM-1TAN fiber angle. Histological methodology, species differences, or age/size differences may also account for the disparity between the published fiber angle data and this study.
The significant ontogenetic change in IM-1SAG and IM-1TAN fiber angle may affect the kinematics of mantle movement during jet locomotion. To explore this idea, we developed a three-dimensional geometric model to evaluate the influence of changes in fiber angle on mantle kinematics. The model consists of a right rectangular polygon of mantle tissue (inset in Fig. 1). A single IM-1 collagen fiber extends from the front lower right corner to the rear upper left corner of the polygon (the gray dashed line in Fig. 1). The long axis of the polygon is parallel to the long axis of the mantle, and the short axis (side C) is parallel to the circumferential muscle fibers. The height of the polygon (side T) represents the thickness of a portion of the mantle wall. The dimensions of the polygon are in arbitrary units.
The polygon is assumed to have constant volume, and the IM-1 fiber is free to reorient as the polygon changes in dimensions. The short axis (side C, Fig. 1) of the polygon was decreased to simulate circumferential muscle contraction during jet locomotion. IM-1SAG and IM-1TAN average fiber angles from hatchling and young 2 stage S. lessoniana (see Table 2) were used as the initial condition (i.e., "resting" mantle circumference) in which strain in the IM-1 fiber was assumed to be zero. Initially, the mantle length was held constant during the simulations. The strain on the IM-1 fiber and the IM-1SAG and IM-1TAN fiber angles were then calculated for a range of mantle circumference changes (see Appendix for a sample calculation).
The model predicts the effects of changes in IM-1 fiber angle on mantle kinematics. If mantle length is held constant during the jet cycle and if an IM-1 collagen fiber extensibility of 0.13 is assumed (Gosline and Shadwick, 1983b), the range of possible mantle movements changes substantially during ontogeny. In the model of the hatchling stage S. lessoniana, mantle circumference may decrease about 45% (Fig. 7A) during jet locomotion, whereas the mantle circumference of a young 2 stage animal may decrease only about 30% (Fig. 7A). In both hatchling and young 2 stage squid, the models show that IM-1SAG fiber angle increases during the jet, while IM-1TAN fiber angle decreases (Fig. 7B, 7C). It is also interesting to note that the low initial IM-1SAG fiber angle and the high initial IM-1TAN fiber angle in hatchling stage squid result in IM-1 fiber compression during the initial -17% mantle circumference change (Fig. 7A). If mantle length is constant during the jet, low-amplitude movements (i.e., less than a 17% decrease in mantle circumference) of the mantle will not store strain energy in IM-1 collagen fibers in newly hatched squid.
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Incorporating mantle length increase during jet locomotion into the model results in several interesting predictions. In hatchling stage S. lessoniana, modest increases in mantle length during the jet did not substantially affect the maximum possible amplitude of mantle contraction, but they did result in an increase in IM-1 collagen fiber strain during low-amplitude mantle movements (Fig. 8A). The potentially important consequence of small increases in mantle length during jetting for newly hatched squid is that strain energy storage in IM-1 collagen fibers is possible during low-amplitude movements of the mantle (e.g., respiration and slow jet locomotion). In the young 2 stage squid, only the 15% increase in mantle length during jet locomotion had any noticeable effect on IM-1 collagen fiber strain (Fig. 8B). The maximum possible mantle circumference change during the jet, however, increased slightly with modest increases in mantle length (Fig. 8B). Thus, the model predicts that small increases in mantle length during low-amplitude mantle movements (e.g., slow jetting or respiration) in newly hatched S. lessoniana may result in increased energy storage in IM-1 collagen fibers; small increases in mantle length in older, larger squid do not. The predicted increase in elastic energy storage comes at the expense of a decrease in thrust. For slow jetting or respiration, this cost may not outweigh the benefits of elastic energy storage.
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The significant change in IM-2 fiber angle during ontogeny may contribute to substantial ontogenetic changes in mantle kinematics during jet locomotion. We examined the implications of a fiber angle change on mantle kinematics using a model similar to the one used to predict the effect of IM-1 collagen fiber angle on mantle kinematics. The IM-2 model consists of the same polygon mentioned above, except there is a single IM-2 fiber running from the lower right corner to the upper left corner of plane CT (solid gray fiber in plane CT, Fig. 1). The assumptions are the same for both the IM-1 and IM-2 models.
The model predicts the potential effects of an ontogenetic change in IM-2 fiber angle on mantle kinematics. If the extensibility of the IM-2 collagen fiber in the model is limited to 0.13 (Gosline and Shadwick, 1983b), a mantle circumference change of about -45% is possible in hatchling stage S. lessoniana during jet locomotion (Fig. 7D). During mantle contraction, the hatchling IM-2 fiber angle will increase from about 35° to about 67° (Fig. 7F). Due to the low initial fiber angle, the IM-2 collagen fiber is compressed during the first -32% change in mantle circumference (Fig. 7D). The model predicts that strain energy storage in the IM-2 collagen fibers will occur only during vigorous jet locomotion that results in large decreases (>32%) in mantle circumference. Interestingly, this suggests that if hatchling stage S. lessoniana use elastic mechanisms to restore mantle shape during respiratory movements of the mantle, as hypothesized for mature Loligo opalescens by Gosline et al. (1983), strain energy storage can only take place in the IM-1 collagen fibers.
The model predicts substantially different mantle kinematics for young 2 stage S. lessoniana. Again, if IM-2 collagen fiber extensibility is assumed to be 0.13, mantle circumference changes during jet locomotion of up to about -25% are possible (Fig. 7D). The fiber angle will increase from the initial value of 53° to about 65° at the end of the jet (Fig. 7E). Given the high initial fiber angle, the strain experienced by the IM-2 collagen fibers will increase rapidly during the jet (Fig. 7D).
Because the mantle tissue is probably constant in volume over the brief period of a single mantle contraction (Ward, 1972), increases in mantle length during jet locomotion will influence the strain experienced by the IM-2 collagen fibers. Therefore, we also examined the effect of mantle length increase during jet locomotion on mantle kinematics. Mantle length in both the hatchling and young 2 stage models was allowed to increase 5%, 10%, and 15% during the jet cycle. In the hatchling stage model, mantle length was increased gradually until a mantle circumference change of -45% was reached (i.e., the point in the previous hatchling IM-2 model where strain on the IM-2 collagen fiber was 0.13). In the young 2 stage model, mantle length was increased progressively until a mantle circumference change of -25% was reached (i.e., the point in the previous young 2 IM-2 model where strain on the IM-2 collagen fiber was 0.13). Mantle length was held constant after mantle circumference changes of -45% and -25%, for the hatchling and young 2 stage models respectively, were reached. The strain on the IM-2 fiber was calculated for a range of changes in mantle circumference.
The models predict substantial effects on both mantle kinematics and elastic energy storage when mantle length increases during jet locomotion. The hatchling stage model predicts that modest 5% or 10% increases in mantle length during jetting increase proportionately the range of possible mantle circumference changes (Fig. 8C). Increases in the maximum amplitude of mantle movements during jet locomotion, however, result in the compression of IM-2 collagen fibers for a longer portion of the jet cycle (Fig. 8C). Thus, if the mantle of a hatchling stage squid lengthens even a small amount, the IM-2 collagen fibers will store elastic energy only during vigorous jet locomotion.
The young 2 model predicts similar increases in the range of possible changes in mantle circumference with increases in mantle length during jetting (Fig. 8D). In contrast to the hatchling stage model, the young 2 stage model predicts that only increases in mantle length greater than 10% will result in compression of the IM-2 collagen fiber during jet locomotion (Fig. 8D). Thus, modest increases in mantle length will permit elastic energy storage in IM-2 collagen fibers during low-amplitude movements of the mantle.
Can IM-1 and IM-2 fiber angles predict mantle kinematics?
The models for IM-1 and IM-2 described above both suggest that a much greater range of mantle circumference change is possible during jet locomotion in newly hatched S. lessoniana than in older, larger squid. The models predict that mantle circumference changes up to -45% are possible in hatchling stage squid compared with -25% and -30% in young 2 stage squid. The few published accounts of mantle kinematics support these predictions. In Loligo opalescens the range of circumference change during vigorous jet locomotion is at least 10% greater in hatchling animals than in older, larger squid (Gilly et al., 1991). Maximum mantle circumference changes are about -40% to -42% in hatchlings and about -30% in mature animals (Gilly et al., 1991). In Loligo vulgaris, the maximum mantle circumference changes are about -45% and -30% in hatchling and adult animals, respectively, during escape-jet locomotion (calculated from Packard, 1969). During escape-jet locomotion in S. lessoniana, mantle circumference changes -45% and -33% in hatchling stage and young 2 stage squid, respectively (Thompson, 2000; Thompson and Kier, 2001). Even during less vigorous jet locomotion and respiratory mantle movements, the range of mantle circumference change is considerably greater in newly hatched L. opalescens (Preuss et al., 1997). Given the assumptions of the geometric models, the measurement errors inherent in the histological methods, the cross-species comparisons, and the lack of consideration for the role of circumferential muscle mechanics in mantle contraction, it is striking that the models accurately predict the maximum amplitude of actual mantle kinematics. Thus, we hypothesize that the arrangement of intramuscular collagen fibers likely plays a crucial role in determining the mechanical properties of squid mantle.
Predictions of elastic energy storage from the IM collagen fiber models
The mathematical models of IM-1 and IM-2 predict ontogenetic changes in the potential of the intramuscular collagen fibers to store elastic energy. During low-amplitude mantle contraction in hatchling stage S. lessoniana, the models predict that IM-1 and IM-2 collagen fibers are compressed and, thus, are unable to store elastic energy. This prediction holds if mantle length remains constant during the simulated jet or if mantle length increases (only up to 10% for IM-1 fibers) during the jet. Only during large-amplitude mantle movements (e.g., during vigorous jet locomotion) do the hatchling stage models predict that IM-1 and IM-2 collagen fibers are stretched and, thus, able to store elastic energy. Conversely, the models predict that IM-1 and IM-2 collagen fibers in young 2 stage S. lessoniana are stretched as the mantle contracts and, thus, can store elastic energy during jet locomotion.
The hatchling stage models also predict a difference in the relative elongation of IM-1 and IM-2 collagen fibers during jet locomotion. If mantle length remains constant during the jet, a mantle circumference decrease of 18% is required to elongate an IM-1 collagen fiber, whereas a mantle circumference decrease of 33% is necessary to extend an IM-2 collagen fiber. Thus, the hatchling stage models predict that IM-2 collagen fibers may not contribute to elastic energy storage in the mantle except during vigorous jet locomotion.
Volume fraction of collagen
Isolated portions of squid and cuttlefish mantle store elastic energy in experiments that simulate mantle movement during the exhalant phase of jet locomotion (Gosline and Shadwick, 1983a, b; MacGillivray et al., 1999; Curtin et al., 2000). The amount of elastic energy stored in the mantle depends on the volume of collagen in the tissue, the strain experienced by the collagen fibers, and the mechanical properties of the mantle collagen fibers. The volume fraction of collagen in IM-1 and IM-2 increased 68 times and 36 times, respectively, during ontogeny. If IM-1 and IM-2 collagen fibers are strained comparably during locomotion in squid of all ages, and if the mechanical properties of collagen do not change with growth, the elastic energy storage capacity of the mantle is likely to increase dramatically during ontogeny.
Future directions
We have described ontogenetic changes in IM-1 and IM-2 fiber angle and in mantle collagen volume fraction. To analyze these changes further, and to begin testing the predictions of the models, accurate measurement of mantle length during jet locomotion is needed. In addition, the predictions of the models assume that the mechanical properties of squid mantle collagen do not change during ontogeny. This important assumption needs to be tested, particularly because the mechanical properties of collagen change during the growth of many animals (e.g., Parry and Craig, 1988). Therefore, mechanical tests of intact portions of squid mantle, in combination with data on mantle length during jet locomotion, are necessary to test the predictions of the models and to understand better the ecological and evolutionary implications of ontogenetic changes in the morphology of mantle connective tissue.
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, outer tunic fiber angle; 
SAG, sagittal component of the IM-1 fiber angle; 
