Support and movement relies on the fact that the muscle and other tissues do not undergo significant change in volume in response to changes in pressure Kier, ; Kier and Smith, ; Smith and Kier, The basic principle of function is straightforward. Since the volume of the tentacles is essentially constant, a decrease in one dimension must result in an increase in another dimension.
Thus, the rapid elongation of the tentacles during the prey strike is caused by contraction of the transverse and associated circular muscle fibers; their shortening decreases the cross-sectional area and since there is insignificant decrease in volume, the length must increase. Shortening of the tentacles is caused by contraction of the longitudinal muscle, which increases the cross-section and thereby re-extends the transverse musculature. The transverse and longitudinal muscles thus serve as antagonists in a manner analogous to muscles on opposite sides of the joint of a vertebrate Kier, The displacement and velocity of contraction of the transverse and circular muscle fibers is amplified.
Because the transverse muscle is arranged in an orthogonal pattern, its contraction decreases both the width and the height of the tentacle. This decrease in cross-section represents a decrease in area length squared that results in tentacle elongation length to the first power and thus the shortening of the transverse and circular muscle is amplified.
This amplification of displacement is analogous to leverage in skeletons with rigid skeletal elements that have relatively shorter input than output arms. Mechanical amplification is in part responsible for the rapidity of the tentacle strike van Leeuwen and Kier, and, in addition, the transverse and circular muscle fibers show specializations for high shortening velocity see Section Mechanisms Responsible for Differences in Contractile Properties of Arm and Tentacle Transverse Muscle below.
Relationship between longitudinal and radial strain in the tentacle. From van Leeuwen and Kier During the elongation phase of the tentacle strike, the tentacles often twist and are observed to be capable of twisting in either direction, depending on prey orientation. This torsion appears to be important in orienting the tentacle club so that the side equipped with suckers strikes the prey.
A biomechanical analysis shows that the helical muscle layers cause torsion; the direction of torsion depends on the handedness of the helical muscle layer contracting Kier, The helical muscle layers must accommodate changes in the helical path length as the tentacle elongates and shortens. As the tentacles elongate beyond this point and the fiber angle decreases further, the helical muscles are elongated. The peripheral location of the helical muscle layers provides a larger moment through which torque can be applied than more central location Kier and Smith, Schematic diagram illustrating the effect of contraction of helical muscle.
A single left-hand helical muscle band is illustrated with a longitudinal black line for reference. Upon shortening of the muscle the cylinder twists. The direction of torsion depends on the handedness of the helical muscle band. The arms of squid and cuttlefish serve important roles in prey handling, manipulation of objects, swimming, and reproduction.
Unlike the specialized prey capture tentacles, the arms do not undergo significant length change. Instead, many of the tasks performed require bending movements, both with generalized bends over the entire length of the arm and also more localized bending movements. Torsion or twisting around the longitudinal axis is also common Kier, Muscle fibers in the transverse muscle mass are arranged in planes perpendicular to the longitudinal axis of the arm.
Bundles of these fibers extend between bundles of longitudinal muscle as sheets of fibers called trabeculae by Graziadei The muscle fiber bundles that extend laterally insert on the connective tissue surrounding the oblique muscles of the arm Kier, Schematic diagram of left arm of a loliginid squid. The oblique muscles located on each side of the arm have their origin and insertion on the oral and aboral fibrous connective tissue sheets. The fibers in the connective tissue sheets are arranged in a crossed fiber array with half of the fibers arranged as a right-hand helix and the other half of the fibers arranged as a left-hand helix.
The muscle fibers of the oblique muscle pair are oriented with the same fiber angle as the connective tissue fibers to which they are connected. The oblique muscles and associated connective tissue layers thus form a composite right- and left-handed helix of muscle fibers and connective tissue fibers Kier, Surrounding the oblique muscles and associated connective tissue sheets are three bundles of longitudinal muscle, one located orally and the others laterally.
The aboral surface of the arms also includes longitudinal fin-like projections called swimming keels. The cores of the swimming keels consist of non-fibrous connective tissue with scattered muscle bundles that extend transversely across the keel and longitudinal muscle fibers that extend as a sheet over the core. Projecting from the oral surface of the arm are the rows of suckers, which are enclosed on each side by protective membranes.
Girod, ; Niemiec, ; Nixon and Dilly, ; Kier, The arm is covered by a loose connective tissue dermis that contains chromatophores, iridophores, blood vessels and nerves. A simple cuboidal-to-columnar epithelium covers the dermis. One of the most important arm movements, bending, requires selective contraction of the longitudinal muscle on the side of the arm representing the inside radius of the bend.
Since longitudinal muscle bundles are present around the entire periphery of the cross-section, bending in any plane is possible, although especially large longitudinal muscle bundles are present on the oral side of the cross section and forceful bending in the oral direction is particularly important in prey handling. Longitudinal muscle contraction creates a longitudinal compressional force that would tend to simply shorten the arm, rather than bend it, without some mechanism to resist this force Kier, ; Kier and Smith, The resistance to volume change of the tissue of the arm is crucial for providing this resistance to longitudinal compression.
The transverse muscle is oriented so that it can control the diameter of the arm and thus can provide the resistance to longitudinal compression that is required for bending. Active arm bending therefore requires simultaneous contractile activity in both the longitudinal and the transverse muscle fibers of the arm. In the situation described above, the transverse muscle maintains the diameter, resisting longitudinal compression while the longitudinal fibers shorten one side of the arm.
The relative contribution of shortening of the transverse or longitudinal muscle to bending probably varies and the two situations described above represent endpoints on a continuum. The longitudinal muscle bundles are situated peripherally in the arm, which increases the bending moment compared with a more central location close to the neutral plane the neutral plane of a bending beam is where all bending stresses are zero and is usually in the center; Kier and Smith, Diagram illustrating the requirements for active bending.
Unilateral length decrease is caused by contraction of longitudinal muscle on one side. In case A, constant diameter is maintained thereby providing resistance to longitudinal compression and causing bending. Constant diameter can be maintained by contractile activity of the transverse muscle.
In case B, constant diameter is not maintained and without resistance to longitudinal compression the structure is shortened but not bent. From Kier and Smith Diameter decrease is caused by contraction of the transverse muscle. In case A, unilateral constant length is maintained by contractile activity of the longitudinal muscle on one side and thereby causes bending. In case B, unilateral constant length is not maintained and diameter decrease simply causes elongation. The torsional force that is required to twist the arms is provided by the oblique muscles and the associated crossed-fiber connective tissue sheets Kier, Both right- and left-handed muscle and connective tissue fiber layers are present.
The fibers of a given handedness can be considered as a composite of connective tissue fibers alternating with muscle fibers that wrap the arm helically along the length. Contraction of one of the composite systems will twist the arm, with the direction of twist depending on the handedness of the helical fiber system. The torsional stiffness of the arm can be increased with contractile activity of both the right- and left-handed oblique muscle systems.
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Active control of torsional stiffness is particularly important while handling struggling prey. The placement of the oblique muscle in a peripheral location provides a larger moment through which the torque can be applied than a more central location close to the neutral axis the neutral axis is located at the center of a beam in torsion and does not experience shear stress Kier and Smith, The eight arms of octopuses serve a variety of functions including prey capture, locomotion, manipulation of objects, grooming, burying, copulation, defense, chemosensing, and tactile sensing.
- The Musculature of Coleoid Cephalopod Arms and Tentacles;
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They incorporate all of the movements exhibited by both the arms and the tentacles of decapod cephalopods; they undergo significant elongation and shortening, are capable of complex and diverse bending and curling movements, and also create torsional movements in either direction. The arms are, in addition, capable of active control of stiffness. Indeed, their capabilities have attracted the attention of robotics engineers as inspiration for the design and construction of a new class of robotic arms McMahan et al. Three divisions of the musculature of the arms of octopuses were recognized by Graziadei , including 1 the intrinsic musculature of the suckers Kier and Smith, , ; Tramacere et al.
Bundles of muscle fibers of the transverse muscle mass are arranged approximately orthogonally, either extending from the oral to aboral surface or at right angles to this and thus from side to side. The transverse muscle fiber bundles that extend from the oral to the aboral surface originate on thick crossed-fiber connective tissue sheets on the oral and aboral sides of the arm. The fiber bundles project toward the central axis of the arm in longitudinal sheets termed trabeculae that extend between bundles of longitudinal muscle fibers. Many insert on a fibrous connective tissue layer surrounding the axial nerve cord or extend to insert on the fibrous connective tissue sheet on the opposite side of the arm.
The transverse muscle fiber bundles that extend from side to side in the arm originate on connective tissue surrounding the external oblique muscles located on each side on the arm and pass through the longitudinal and oblique muscles in the form of trabeculae between the longitudinal muscle bundles or as individual bundles through the oblique muscle. Many insert on the connective tissue surrounding the axial nerve cord.
Some of the transverse muscle fiber bundles that run from side to side pass oral, and especially aboral, to the axial nerve cord and extend to the opposite side to insert on the connective tissue surrounding the external oblique muscle Kier and Stella, The orientation of transverse muscle fibers perpendicular to the long axis of the arm may not, however, be universal for octopuses; Feinstein et al.
Schematic diagram of the arm of Octopus showing the three-dimensional arrangement of muscle fibers and connective tissue fibers. Longitudinal muscle fiber bundles extend the length of the arm between the trabeculae of the transverse muscle. The bundles are present on all sides of the transverse muscle mass so the entire periphery of the cross-section includes longitudinal muscle bundles, although the cross-sectional area of the aboral quadrant is larger than the other quadrants. A crescentic shaped layer of longitudinal muscle is present between the median and external oblique muscles Kier and Stella, Three sets of oblique muscle fibers are present on each side of the arm.
The external oblique muscles enclose the intrinsic muscle of the arm and are the most superficial. The median oblique muscles are more central and are separated from the external oblique muscles by longitudinal muscle fibers as described above. The internal oblique muscles are the most central and are located on each side of the core of transverse muscle. The handedness of a given oblique muscle is opposite to that of the other member of the pair on the opposite side of the arm.
In addition, on a given side, the handedness of the external and internal oblique muscles is the same and is opposite to that of the median oblique muscle. The external and the median oblique muscles have their origin and insertion on the oral and aboral connective tissue sheets. The fiber angles of the median and external oblique muscles are similar to the fibrous connective tissue layers to which they attach mean angles for O. The fibers of the inner oblique muscles do not show a distinct origin and insertion and instead appear to interdigitate with the longitudinal and transverse musculature.
Surrounding the intrinsic muscle of the arm is a thin layer of circular muscle with fibers arranged circumferentially around the arm. The layer is thickest on the aboral side of the arm, covers the aboral connective tissue sheet and extends toward the oral side of the arm, wrapping the external oblique muscles and inserting on the oral connective tissue sheet Kier and Stella, Support and movement in octopus arms is achieved in a similar manner to that described above for the arms and tentacles of decapods and relies on the resistance to volume change of the musculature of the arms.
The arms are capable of a remarkable diversity and complexity of movements Gutfreund et al. Octopus arms are notable because these deformations may be quite localized or they may occur over the entire length of the arm. In addition, they may occur at one location or at multiple locations on an individual arm. Bending movements can occur in any plane and torsional movements are observed in either direction. The stiffness in tension, compression, bending and torsion is also under active control by the animal Kier and Stella, Since the arm tissue resists volume change, a decrease in cross section must result in an increase in length.
This decrease in cross-section is likely created by contraction of the muscle fibers of the transverse muscle mass. The elongation created can either be localized, involving only a portion of the transverse muscle, or it can occur over the entire length of the arm. The thin circular muscle layer is also oriented so that its contraction will elongate the arm, but its physiological cross-sectional area is quite small and thus the force it could produce for elongation is small. One possible role for the circular muscle layer is in providing arm tonus for maintaining posture Kier and Stella, Shortening likely involves contraction of the longitudinal muscle bundles that extend the entire length of the arm.
Since the arm resists volume change, shortening of the arm results in an increase in cross-section and thus causes elongation of the transverse and circular muscle fibers. The transverse and longitudinal muscle fibers thus function as antagonists and produce the force required for re-elongation of one another Kier and Stella, The muscle activation required for bending movements is similar to that described above for bending of decapod arms. Active bending requires selective contraction of the longitudinal muscle bundles along the side of the arm that represents the inside radius of the bend.
The support required to resist the longitudinal compressional force that would otherwise simply shorten the arm is provided by the transverse muscle mass. Active bending movements thus require simultaneous contraction of the transverse and longitudinal muscle. Bending may also occur if the transverse muscle decreases the cross-section while the longitudinal muscle on one side of the arm again, the inside radius of the bend maintains a constant length. As described above for decapod arms, the two examples provided here probably represent endpoints on a continuum of relative shortening of the transverse and longitudinal muscle.
Abrupt bends, as have been observed in some behaviors Sumbre et al. The arms of octopus provide an interesting contrast to both the tentacles and arms of decapods. As described above, the tentacles function primarily in elongation and shortening while the arms of decapods exhibit little length change and instead produce bending movements.
The arms of octopuses incorporate both bending and length change Hanassy et al.
This can be achieved using the same musculature, the transverse and longitudinal muscle fibers, by simply altering their pattern of activity; sequential activity during elongation and shortening and simultaneous activity during bending Kier and Stella, Based on simple engineering considerations, the force generated by the arm during bending movements is greater if the longitudinal muscle fibers are located as far as possible from the neutral plane of the arm.
The longitudinal muscle is indeed located away from the central axis of the arm. In addition, longitudinal muscle bundles are located around the entire periphery of the cross-section of the intrinsic muscle which allows bending stresses to be exerted in any plane. The transverse muscle is most robust in the aboral portion of the arm, which is consistent with its role in supporting and producing oral bending the most common mode of forceful bending in conjunction with the longitudinal muscle bundles on the oral side Kier and Smith, ; Kier and Stella, In addition of active bending movements, co-contraction of the transverse and longitudinal muscle increases the flexural stiffness of the arm.
Such a pattern of activation is a component of the reaching behavior that has been described by Hochner, Flash and coworkers Gutfreund et al. As in the arms of decapods, torsional movements are generated by contraction of the oblique muscles. The crossed fiber helical connective tissue arrays are a key component of the helical system of muscle and connective tissue as they transmit the force generated by the oblique muscles.
The external and median oblique muscle pairs on each side of the arm and the associated cross-fiber connective tissue array represent both a left- and a right-handed helical system and thereby allow torsional forces to be generated in either direction, consistent with observations of twisting of the arms in either direction. Co-contraction of the external and median oblique muscle systems likely increases the torsional stiffness of the arm.
The torsional moment is greater if the oblique muscles are located as far from the neutral axis as possible. The external and median oblique muscles are indeed located away from the neutral axis. The functional role of the internal oblique muscles is unclear since they are more central so would be less effective in generating a torsional moment and they have the same handedness as the external oblique. Future work involving electromyography of the internal oblique muscles during arm movement and force production would be of interest in order to determine their biomechanical role Kier and Stella, Octopus arms provide an example of the highly localized movements and deformations that are possible in appendages that rely on muscular hydrostatic mechanisms.
In comparison with a conventional hydrostatic skeleton, localized activation of muscle fibers has a localized effect, rather than the more generalized effect of increasing the hydrostatic pressure of a large fluid filled cavity. Deformations can occur in many directions at any location or at multiple locations and the arms must therefore have the neuromuscular control required to activate selectively small groups of muscle fibers and to precisely modulate their force production.
Indeed, the motor units of the transverse and longitudinal muscle are small and there does not appear to be electrical coupling between the fibers Matzner et al. In addition, muscle fiber activation can be controlled directly by neural activity, thereby providing precise modulation of muscle force production Matzner et al. The difficulty with such a system, however, is the potential complexity of motor control that is required. Recent studies are providing important insights into motor pathways and mechanosensory mechanisms Gutfreund et al.
Day of the Tentacle Remastered
The majority of the musculature of the arms and tentacles of coleoid cephalopods, and indeed that of the entire animal, is obliquely striated Hanson and Lowy, ; Hoyle, , ; Amsellem and Nicaise, ; Chantler, ; Nicaise and Amsellem, ; Budelmann et al. This striation pattern is common in the invertebrates, occurring in at least 14 phyla Thompson et al. In obliquely striated muscle fibers, the thick and thin myofilaments are arranged in a staggered array, forming a helical or oblique pattern of A-bands containing thick filaments , I-bands containing thin filaments and Z material or dense bodies anchor the thin myofilaments.
Thus, the fibers lack the transverse banding pattern observed in longitudinal section that characterizes cross-striated muscle fibers. In transverse sections, however, the fibers show a similar sequence of banding to that observed in longitudinal sections of cross-striated muscle; the staggered arrangement of myofilaments means that a single transverse section passes through I-bands, A-bands, and Z material in a single fiber.
The myofilaments surround a central core containing mitochondria and the single cell nucleus. The size of the mitochondrial core varies. In the mantle and in the fins of squids there are distinct zones that include either mitochondria-rich fibers with large cores or fibers with fewer mitochondria and smaller cores.
The mitochondria rich fibers are analogs of the red muscle of vertebrates, operating primarily aerobically and used in repetitive movements, while the mitochondria-poor fibers are anaerobic, white muscle analogs that are recruited for short term maximal efforts Bone et al. The fibers of the arms and tentacles of coleoids that have been studied are predominantly the mitochondria-poor fibers, but additional work is needed to examine this issue.
The striation angle increases as the fiber shortens and decreases as the fiber is elongated. Schematic diagram of a cephalopod obliquely striated muscle fiber. Note that a cross-section of an obliquely striated muscle cell shows an analogous sequence of bands to those seen in a longitudinal section of a cross-striated fiber. It is likely that in bilaterians, striated muscle evolved independently multiple times Oota and Saitou, ; Schmidt-Rhaesa, ; Burton, ; Chiodin et al.
There are examples both of derivation of cross-striation from oblique striation and derivation of oblique striation from cross-striation Schmidt-Rhaesa, Thus, ultrastructural similarity does not necessarily indicate common evolutionary origin and the evolutionary relationships of eumetazoan striated muscle remain unclear Steinmetz et al. The fibers of the transverse muscle mass of the arms of the loliginid squid Doryteuthis pealeii and the ommastrephid squid Illex illecebrosus are obliquely striated Kier, These fibers have been examined in the most detail so the description that follows will focus on their ultrastructure.
Recent preliminary investigations of the ultrastructure of the fibers of the transverse muscle mass of the arms of the cuttlefish Sepia officinalis and of Octopus bimaculoides Shaffer and Kier, have shown similar ultrastructure to that of the arms of squid but additional work is needed. The fibers are surrounded by an amorphous, electron-dense extracellular material Kier, ; Feinstein et al. Electron micrograph of transverse section of obliquely striated muscle fibers of the transverse muscle of the arm of Doryteuthis pealeii.
Regularly spaced junctional feet are visible in the peripheral coupling labeled PC. The terminal cisternae occur where the Z elements and associated sarcoplasmic reticulum SR approach the sarcolemma. Electron micrograph of longitudinal section of obliquely striated muscle fibers of the transverse musculature of the arm of Illex illecebrosus.
The long axis of the muscle fiber is oriented horizontally on the page. The intramyoplasmic zones of sarcoplasmic reticulum SR and dense bodies arrows are oriented at a small angle with respect to the horizontally oriented thick filaments. The sarcoplasmic reticulum is present in three zones. A peripheral zone of sarcoplasmic reticulum is present in the sarcoplasm adjacent to the sarcolemma. Specialized peripheral couplings are present between the sarcolemma and the outer portion of the membrane of the terminal cisternae of the sarcoplasmic reticulum in this zone and are common where the Z elements are adjacent to the sarcolemma.
Regularly spaced junctional feet are present in the space between the sarcolemma and the membrane of the sarcoplasmic reticulum. A second zone of sarcoplasmic reticulum is present in the plane of the Z elements and consists of a network of units that are elongated parallel to the longitudinal axis of the fiber. This intramyoplasmic zone of sarcoplasmic reticulum is interspersed between the dense bodies that form the Z material in these cells. A third zone of sarcoplasmic reticulum is present surrounding the mitochondrial core.
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The fibers lack a transverse tubular system so the peripheral couplings described above likely function in excitation contraction coupling in a manner similar to that of the triad of a vertebrate skeletal muscle fibers Kier, It is challenging to obtain accurate measurements of thick filament length in these cells due to the difficulty of obtaining exactly longitudinal sections. In a study where special care was taken during sectioning, the thick filaments of the transverse muscle mass of the arms of D. The muscle fibers of the transverse muscle mass of the tentacles of D.
Recent preliminary investigation of the transverse muscle mass of the tentacles of the cuttlefish S. Unlike the obliquely striated cells of the arms, the mitochondria are not in the core and instead are located peripherally in the cell, immediately beneath the sarcolemma. The tubules of the sarcoplasmic reticulum are restricted to the same area as the mitochondria, immediately beneath the sarcolemma. The cells thus lack transverse tubules invaginated tubules and the fibers are not subdivided into myofibrils. The sarcoplasmic reticulum forms specialized couplings with the sarcolemma in a manner similar to that described above for the obliquely striated fibers of the arms.
The coupling includes regularly spaced electron dense junctional feet in the space between the outer membrane of the sarcoplasmic reticulum and the sarcolemma. The peripheral couplings of one fiber are often aligned with those of adjacent fibers Kier, Electron micrograph of transverse section of the cross-striated muscle fibers of the transverse muscle mass of the tentacle of Doryteuthis pealeii. Mitochondria M are located immediately beneath the sarcolemma.
The outer membrane of the sarcoplasmic reticulum SR makes specialized contacts or peripheral couplings PC with the sarcolemma. Note that the A band thick filaments in cross-section passes in and out of the section plane in a single fiber. Electron micrograph of longitudinal section of cross-striated muscle fibers of the transverse musculature of the tentacle of Doryteuthis pealeii. The outer membrane of the sarcoplasmic reticulum SR forms peripheral couplings PC with the sarcolemma. The inset shows a higher magnification view of a peripheral coupling in which junctional feet arrows are visible.
Note that the Z-disc Z is diffuse and sometime follows an angled course across the fiber. The thick filaments have an electron-lucent core when observed in transverse section, in contrast to the core of the thick filaments in the obliquely striated muscle fibers of the arms, which are electron dense. This may be related to the greater paramyosin content of the thick filaments of the obliquely striated muscle fibers since paramyosin occupies the core Kier and Schachat, The thick filament length of the transverse muscle fibers of D.
The fibers lack an M band, a structure present in vertebrate and arthropod cross striated muscle which is located in the center of the A band where thick filaments are bound together by cross-links. The sarcomeres of the tentacle fibers are often observed to be sheared so that the Z disc, A bands, and I bands are not perpendicular to the long axis and instead follow an angled or curved course across the diameter Kier, The Z disc of the transverse muscle fibers of the tentacles is not as regularly arranged as it is in vertebrate and arthropod muscle fibers and instead appears to be a loose grouping of electron-dense material rather than the organized network observed in the Z discs of vertebrates and arthropods Kier, The ultrastructural differentiation of the transverse muscle of the arms and tentacles of squid is especially relevant for consideration of arm and tentacle regeneration Kier, Transverse striation of the tentacle muscle cells appears at approximately 3 weeks and the adult ultrastructure is present 4—5 weeks after hatching.
High speed video recordings of prey capture show correlated behavioral changes. During the first 2—3 weeks after hatching, Sepioteuthis lessoniana hatchlings exhibit a different prey capture behavior from the adults that involves a rapid jet forward and capture of the prey with splayed arms. It is not until 4—5 weeks after hatching that the rapid tentacular strike is employed Kier, It is unknown if a similar sequence of differentiation occurs during regeneration of the tentacles.
Transverse A and longitudinal B sections of fibers from the transverse muscle of the arm arm III , and transverse C , and longitudinal D sections of muscle fibers from the transverse muscle of the tentacle. The cells at this stage in both the arm and the tentacle are obliquely striated.
The tentacle cells at this stage C,D show mitochondria M in the core and rows of tubules of the sarcoplasmic reticulum S extending into the center of the cells. The longitudinal muscle fibers of the arms and tentacles have not been studied in detail with electron microscopy. In previous work on the transverse muscle, the longitudinal muscle bundles are often included in sections so basic observations of their structure have been made.
In the arms and in the tentacles they appear to be obliquely striated muscle fibers with ultrastructural characteristics that are similar to those of the transverse muscle of the arms described above Kier, As described above, the muscle fibers of the transverse muscle of the arms provide support for the relatively slow bending movements while those of the tentacle are responsible for extremely rapid elongation during the prey strike. In order to characterize their contractile properties, Kier and Curtin dissected small bundles of fibers from the transverse muscle mass of the arms and the tentacles of D.
The length-force relationship, force-velocity relationship and stimulus frequency-force relationship were determined for both the tentacle and the arms fibers. The force-velocity relationship of the two fibers was dramatically different. A significant difference in the response to electrical stimulation was also observed. A significant difference in peak tetanic tension was also observed: The length-force relationship of the arm and the tentacle fibers was found to be similar and no difference was observed in the relationship during twitch vs.
High levels of resting tension were observed in both fiber types when they were extended beyond optimal length. The high resting tension appeared to damage the preparations so it was not possible to characterize the descending limb of the length tension curve Kier and Curtin, The high resting tension is consistent with a recent study of the mantle muscle of D.
Force is expressed relative to the isometric force of the preparation mean of repeat twitches for the tentacle and repeat ms, 50 Hz tetani for the arm, Doryteuthis pealeii.
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The lines were fitted to the data using Hill's single hyperbolic function. From Kier and Curtin The differences in contractile properties between the arm and the tentacle transverse muscle of squid are dramatic, especially with respect to the shortening velocity of the transverse tentacle muscle described above.
Next, check your email. The link to your Adventures in Middle-earth Bundle download page may take a few minutes to arrive. If you don't get a link in an hour or two, contact us: After Smaug's defeat and the Battle of Five Armies, much danger still remains. From the Orc-holds of the mountains to the dark and corrupt depths of Mirkwood a darkness waits, recovering its strength. In Dale, King Bard sends out a call for brave adventurers to journey to Laketown and assist in restoring the glory of the North.
Adventurers from across Wilderland prepare to explore Middle-earth and to battle the rising Shadow. The Quest begins with this lavishly illustrated Player's Guide, with the Middle-earth setting-specific rules and guidance to create characters and adventure in the world of The Hobbit and The Lord of the Rings using the OGL 5e ruleset.
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