1. Mechanical properties of the abdominal ventral superficial muscle of the hermit crab, Pagurus pollicarus, were examined under isometric and iso-velocity conditions. The muscle was activated by stimulating its motor nerve at different frequencies.

  2. Length-isometric tension relations were measured. Peak tension, P0, was 0·16–0·2 MN m−2 and the sarcomere length of the muscle at the optimum length, L0, was 10·8 + 1·0 μm. Passive tension was high at L0. Correlated measurements of the operating length of the muscle and L0 indicate that the operating length is at a point on the ascending limb of the length-tension curve approximately 0·77 L0.

  3. The relationship between activation level of the muscle and the length-tension relation indicates that the curve is not substantially displaced along the length axis by increasing activation level; increased force is primarily due to an increase in the slope of the ascending limb of the curve.

  4. The force-velocity relation was obtained by measuring the force at a reference length during iso-velocity shortening of an active muscle. Hill constants of a/P0 = 0·11 + 0·02 and b = 1·07 + 0·24 mm s−1 were obtained. The maximum velocity of shortening per half sarcomere was approximately 4·2μms−1,

  5. Stretch of an active muscle did not produce an abrupt short range yield but a gradual transition between short range and terminal stiffness. This behaviour is shown to be due not to differences in cross bridge stiffness between VSM and other muscle but to a non cross bridge stiffness with a value that is one-fifth that of vertebrate muscle.

  6. Such a low stiffness may provide an intrinsic mechanism for simplifying load compensation in the absence of rapid proprioceptive reflexes for the control of muscle stiffness.

It is widely recognized (Rack & Westbury, 1969; Partridge, 1979) that the mechanical properties of muscles and their regulation by the central nervous system represent important elements in the generation of movement and control of posture. To execute an appropriate movement or maintain a stable position in spite of environmental perturbations, the nervous system must contend with the dependence of muscle tension on length and velocity, as well as with a number of time-dependent factors such as fatigue, facilitation and ‘catch’ phenomena. Moreover, it has become in creasingly evident that muscles are quite diverse and may be employed and controlled by the central nervous system in different ways. Thus, it is important to understand the mechanical properties of different types of muscle fibres in order to understand their functions in movement, and how appropriate movements are generated.

Despite much interest in the mechanisms of arthropod movement (Kennedy & Davis, 1977) there is little information about the mechanical properties of arthropod muscles likely to be important in these movements. Numerous reviews (Hoyle, 1969; Atwood, 1972; Pringle, 1972; Franzini-Armstrong, 1972; Chapple, 1982a) have stressed the morphological and physiological diversity of arthropod muscle but mechanical correlates of this diversity have generally been restricted to measurements of twitch contraction times and peak forces. The few studies involving dynamic measurements of arthropod muscle properties have been primarily directed towards an understanding of contractile mechanisms (Pringle, 1972; Kawai, Brandt & Orentlicher, 1977). Moreover, the graded nature of activation of arthropod slow muscle means that tension is determined by factors such as frequency and the synaptic characteristics of the neuromuscular junction as well as length and velocity. Such information is important if we are to understand, for example, how deviations from a desired position are corrected or movement trajectories are generated. Recent studies in vertebrates (Grillner & Udo, 1971; Bizzi, Dev, Morasso & Polit, 1978) have shown that muscle properties play a greater role in the dynamics of movement than has been generally assumed.

In the present study, to provide information on the dynamic properties of an arthropod slow muscle, a crustacean muscle has been subjected to iso-velocity length changes at different levels of activation. The abdominal ventral superficial muscle (VSM) of the hermit crab, Pagurus pollicarus, is composed of muscle fibres that do not support an action potential, have long sarcomeres, and are innervated by a small number of excitor motoneurones as well as an inhibitor. Although it is part of the hydrostatic skeletal system of the hermit crab abdomen, it is a typical striated muscle and is thus similar to many other crustacean slow muscles. A preliminary report of some of this material has been presented in abstract form (Chapple, 1982b).

Pagurus pollicarus, ranging in weight from 5–50 g, were obtained at all times of the year from sublittoral protected sandy areas in Fishers Island Sound off the coast of Connecticut. Animals were maintained at 13 °C in an artificial sea water aquarium. A physiological saline for these experiments was composed of 460mm-NaCl, 15·7 mm-KCl, 25·9mm-CaC12, 8-3 y-MgCl2-6H2O, 8·4y-NazSO4 and 5·0mm-Hepes buffer. The pH was adjusted to 7·6, and 1 mg ml−1 of glucose was added to the saline before use.

The right fourth segment of the VSM was isolated by opening the abdomen with a longitudinal incision along the medial dorsal surface and removing the hepato-pancreas. The fast flexor muscles were dissected from the ventral nerve cord and body wall, and two 1/16 inch Plexiglass plates with stainless steel wire rings inserted in them were glued to the external ventral surface of the third and fifth segments with k cyanoacrylate adhesive (Eastman 910). The cuticle was dissected from the fourth segment and the muscle mounted in an oxygenated bath mounted on a thermoelectric cooler which maintained the preparation at 12·5 °C. Stimulation was indirect; the right connective of the fourth abdominal segment rostral to the exit of the third ganglionic root which innervates the VSM was drawn into a suction electrode and stimulated with 0·2-ms pulses at 1·5–8 V. The stimulus threshold was set below the threshold for the inhibitor at a level at which all three of the excitors to the muscle were active. Control experiments with 2× 10−5M picrotoxin added to the saline (to suppress inhibition) demonstrated that higher stimulus intensities did not result in any added increments in tension.

Sarcomere lengths of the ventral superficial abdominal muscles (Chapple, 1969a) were measured by fixing the muscle at the optimum length, Lo. Maximum isometric tension was measured at increasing muscle lengths and Lo was defined as the point between the ascending limb of the length-tension curve and its plateau. After such an experiment, the length of the right fourth segmental VSM was measured with an ocular micrometer. Muscles were then relaxed in a saline in which magnesium chloride was substituted for calcium chloride and then fixed overnight in 10% buffered formaldehyde in saline. Individual muscle fibres were teased out, split longitudinally, and mounted in gelatin-glycerol for examination under a polarizing microscope. The length of ten successive sarcomeres was measured in each muscle fibre and divided by ten to give an average sarcomere length. Ten muscle fibres were examined from each muscle. Myofibrillar ATPase and NADH diaphorase activity were determined according to the method of Ogonowski & Lang (1979). Muscles were examined under the electron microscope after fixing them according to the method of Jahromi & Charlton (1979).

Instrumentation

The force transducer was a cantilever spring steel beam to which four semiconductor strain gauges (Celescoe Transducer Products) were bonded. This transducer had a compliance of 2μmg−1 and a resonant frequency of 900 Hz.

Length in the isometric tension experiments was determined by a micrometer. In experiments in which stretches or releases of the muscle were desired, one end of the muscle was attached to a rod mounted on the cone of a 60 W ‘woofer’ loudspeaker (Lafayette). The position of an infrared LED mounted on the rod was recorded with a United Detector Technology Position Sensing Detector (PIN-LSC/30D). Resolution of length was better than 10 pm. Both position and its derivative were used to obtain an error signal for a servo-amplifier that supplied power to the loudspeaker. The compliance of the servo was 0 · 8 μm g−1. The maximum velocity of linear stretch with this device was 50 mm s−1.

Force and length signals were connected to separate channels of an A-D converter interfaced to an LSI-11/23 computer. At the beginning of an experiment calibration weights and displacements were recorded. The computer generated ramps of different velocities with a D-A converter connected to the servo-amplifier, as well as triggering the stimulator, and timing 5-min intervals between trials in a run. For most of these experiments force and length were sampled at 100Hz; for ramp velocities above 8 mm s−1, however, the sampling rate was 1 kHz during the ramp and for a brief period after it.

Experimental procedure

Measurements of the length-tension relation were performed by setting the muscle to slack length and stimulating at 80 Hz, a stimulus frequency determined to produce maximum tension. The muscle was then lengthened in millimetre increments with a 5-min period between each trial to minimize fatigue and the decay in passive tension at the new length due to the viscoelastic properties of the muscle. Passive force was considered to be the muscle force just before the onset of stimulation and active force the difference between this value and that of the force just before the end of stimulation. Except at lengths above the optimum length, the plateau of isometric tension was flat.

Force-velocity relationships were obtained by generating a series of iso-velocity releases of an isometrically contracting muscle. By examining the force at the same length for different constant velocity releases, a force-velocity curve is obtained (Hill, 1970). Each trial was composed of a 6-s stimulus train; the iso-velocity ramp release was started 3·95 s after the onset of stimulation. An experimental series consisted of trials of different velocities separated by 5-min intervals. At the beginning and end of a series, an isometric tetanus without muscle shortening was used to control for muscle fatigue during the series. Each release was initiated at the control length plus 0·5, 1·0 or 1·5 mm and terminated at a length 0·5, 1·0 or 1·5 mm less than the control length. Thus, the distance through which the muscle was allowed to shorten before the force was recorded was approximately 4%, 8% and 12% of the total muscle length. The force-velocity relation was then obtained by plotting the ratio of the sampled force, Ps, and the peak isometric tension, Po, at that length as a function of velocity, V. Plots of (1–Ps/P0)/V as a function of Ps/P0 provided a linear transformation of the Hill equation (Katz, 1939); a regression line was fitted to this transformation to obtain the Hill constants a and b. Velocities varying from 0·5·25 mm s−1 were presented in a pseudo-random order.

The response of the muscle to active stretch was performed by stretching the muscle at the optimum length with an iso-velocity ramp at 25 mm s−1 or by using the same procedure described for the force-velocity determination, but reversing the direction of the ramp. A linear least squares fit to the initial eight samples of force and length after the onset of the ramp was used to calculate the short-range stiffness; the stiffness after the short-range yield point, the ‘terminal’ stiffness, was calculated in the same way at the end of the ramp. By plotting the ratio of force to short-range stiffness as a function of force, an alpha plot (Morgan, 1977) was used to separate cross bridge from non cross bridge stiffness.

Previous work has established that the longitudinal muscles of the VSM are typical slow postural muscles (Chapple, 1969a,b). Although there is a small bundle of muscle fibres on the lateral margins of the VSM that is intermediate in character, the majority of longitudinal VSM are innervated by tonically active motoneurones that produce a hraded depolarization to increased frequency of stimulation, and have time constants m the order of 50–80 ms. Histochemically as well, these muscles are slow. The distribution of myofibrillar ATPase was assayed in both fast and slow abdominal muscles. The fast muscles (Fig. 1A) are uniformly dark; the VSM (Fig. IB) in contrast are lightly coloured or colourless within much of the VSM. The layer of muscle fibres facing the coelom are intermediate in colour, whereas the outer layer of longitudinal fibres is colourless. A histochemical assay for NADH reductase produces an opposite reaction, with the fast muscles (Fig. 1C) appearing colourless whereas the VSM (Fig. ID) exhibits prominent staining throughout the muscle fibres. Sodium azide, a mitochondrial ATPase inhibitor (Hajek, Chari, Bass & Gutmann, 1973) did not alter the reaction of the VSM to the stain.

Fig. 1.

Histochemical and morphological criteria by which the abdominal ventral superficial muscle (VSM) is identified as a slow crustacean muscle. Myosin ATPase staining of abdominal fast flexors (A) and VSM (B). NADH reductase staining of abdominal fast flexors (C) and VSM (D). (E) Longitudinal electron micrograph of VSM fixed at Lo = 3 mm. Scale bars: A-D, 100μm; E, 1 pm.

Fig. 1.

Histochemical and morphological criteria by which the abdominal ventral superficial muscle (VSM) is identified as a slow crustacean muscle. Myosin ATPase staining of abdominal fast flexors (A) and VSM (B). NADH reductase staining of abdominal fast flexors (C) and VSM (D). (E) Longitudinal electron micrograph of VSM fixed at Lo = 3 mm. Scale bars: A-D, 100μm; E, 1 pm.

The ultrastructural profile of the VSM (Fig. IE) is also consistent with its role as a slow muscle. The A band is irregular, and averages 5·6 μm. No M line is present and the Z band is irregular along its length with a width of 0·1 μm. Sarcoplasmic reticulum is sparse; mitochondria are particularly common at the surface of the fibres. Thus, by a number of criteria the majority of longitudinal VSM fibres are slow.

Length-tension relationship

The length dependence of isometric tension in VSM at a stimulus frequency of 80 Hz is shown for five animals in Fig. 2. The optimum length, L0, was at a sarcomere length of 10·8+l·0μm (N = 13). Maximum isometric force (0·3–0·5N) ranged between 0·16 and 0·2 MN m−2 but this normalized value is likely to be low because of the error in estimating the cross-sectional area of active muscle. At short lengths (not illustrated), tension increased gradually with length, but at approximately 0·5 L0 the slope of the length-tension curve increased sharply and remained constant with increasing muscle length until the optimum length was reached. At the highest activation levels, the plateau was quite narrow. At muscle lengths greater than the plateau, the active force declined rapidly, but no attempt was made to determine the intersection of the curve with the length axis.

Fig. 2.

Length-tension measurements from five experiments. Open symbols: active tension at the end of the isometric tetanus. Closed symbols: corresponding passive tension just prior to the tetanus. Dotted line represents the resting length of the muscle during shell support on the length-tension curve.

Fig. 2.

Length-tension measurements from five experiments. Open symbols: active tension at the end of the isometric tetanus. Closed symbols: corresponding passive tension just prior to the tetanus. Dotted line represents the resting length of the muscle during shell support on the length-tension curve.

The operating point of the VSM was estimated by photographing three animals in shells and then determining the length-tension relationship of their muscles. Mean length of the ventral medial surface of the fourth abdominal segment was 9 mm and the optimum length was 11·7mm. The operating length was thus 2·7+ 0·3mm shorter than L0 or 0·77 L0. At this point, indicated by the dashed line in Fig. 2 the isometric tension is approximately three-quarters that of the isometric tension at the optimum length. In contrast to the usual assumption that the operating point of a muscle is at the peak of the length-tension curve where force is constant, in the VSM it is on the ascending limb of the length-tension curve.

The shape of the length-tension relation is controlled, as in other muscles, by the level of activation of the muscle. The VSM was stimulated at frequencies of 5, 10, 20,40 and 80 Hz and isometric tension was recorded at a number of muscle lengths. Fig. 3 shows one such determination; results from six other experiments were qualitatively similar. As the stimulus frequency was increased, the slope of the ascending limb of the length-tension relation as well as the peak tension at L0 increased.

Fig. 3.

Length-tension relationship as a function of activation. Regression lines fitted to the ascending portion of the length-tension curve. 5 Hz: P(force) = 0·2517 — 0·0148 (length,x). 10 Hz:P = 0·2844 — 0·0162x, 20 Hz: P = 0·4145 - 0·225×. 40 Hz: P = 0·596 - 0·031 l×.. 80Hz: P = 1·0557 - 0·0551×.

Fig. 3.

Length-tension relationship as a function of activation. Regression lines fitted to the ascending portion of the length-tension curve. 5 Hz: P(force) = 0·2517 — 0·0148 (length,x). 10 Hz:P = 0·2844 — 0·0162x, 20 Hz: P = 0·4145 - 0·225×. 40 Hz: P = 0·596 - 0·031 l×.. 80Hz: P = 1·0557 - 0·0551×.

A point of some interest to motor physiologists is whether activation of a muscle by the central nervous system results in a shift of the length-tension relationship along the length-axis to shorter lengths (Rack & Westbury, 1969) or whether muscle activation primarily affects the slope of the length-tension relationship. To estimate the relative contributions of these two effects to the force at a particular length, the relation between isometric tension, P, of the muscle at Lo and tension F, at a particular length, x, was calculated by fitting a linear regression line to the ascending limb of the length-tension curve. The equation was F = K(x—x0), in which K is the slope of the regression line, and xo is the intercept of the regression line with the length axis. Only those points that could be reasonably fitted to a line were included, as the purpose was to estimate the relative contributions of the change in slope and shift along the length axis to total force, and not to imply that the ascending limb of the length-tension relation was linear. Both the slope, K, and the intercept, xo, were found to vary with the activation level of the muscle. K increased with activation level (K = 0·11 P + 0·004N mm−1) and xo decreased (xo = –5·5P–6·1 mm). As the level of activation increased, the consequent change in slope accounted for 75% of the increase in force and only 13% of the change in the intercept. Thus, under this regime of muscle activation, the slope is almost six times more effective than a shift in the zero force length in increasing muscle force.

Passive tension at the optimum length was not negligible as in many other muscles. It averaged 20% of peak isometric tension; (0·065 + 0·033 N, N = 11). The external cuticle contributed a substantial portion of the passive tension (in one experiment 60% of passive force) and was removed in those experiments involving dynamic length changes. Moreover, as occurs in other arthropod muscle (Hoyle, 1969, 1978; Yox, diCaprio & Fourtner, 1982), the passive tension includes an ‘active’ component. Placing the muscle in a saline in which magnesium had been substituted for calcium reduced its passive tension by 50%.

Stretch of an inactive muscle produced a prominent stress relaxation after the completion of the length change. The time constant of the relaxation increased with muscle length, and appeared to be composed of two components, a fast one with a time constant of less than 1 s at the optimum length, and a slower component with a time constant of the order of 20 s. Passive tension was, therefore, measured 5 min after a length change. In addition, a more complex change in passive tension occurred during the first few stretches of a muscle, as has been reported for other tissues (Fung, 1972).

Force-velocity measurements

The force-velocity relationship was determined by an iso-velocity method; force was sampled in most cases at the optimum length. Over the range of velocities tested (0·5–20·0mms−1), the VSM behaved much like a vertebrate slow muscle. Force at the sampled length was a function of muscle length, level of activation and velocity. Since the response to active shortening and lengthening is quite different they will be discussed separately.

Active shortening

At maximum activation of the muscle, the force was inversely related to shortening velocity (Fig. 4). This relationship was only observed when the distance through which the muscle was allowed to shorten was greater than the range of the short-range stiffness for all shortening velocities (0·08 muscle lengths). Beyond this point, the force-velocity relationship conformed to the Hill equation with a/P0 = 0·11 +0·02 and b= 1·07 + 0·24 mm s−1(N = 5). The intrinsic speed of shortening (0·82 lengths s−1) was calculated for a half-sarcomere to be 4·2 μm s−1. Several factors affected these measurements. In some preparations, initial values of P0 and Vmax declined over a period of four or five trials before reaching a value that remained stable for over 1 h of successive trials. Moreover, creep in the initial period of the experiment shifted the muscle to a slightly shorter length on the length-tension curve, as could be observed by a decline in passive tension during this period. Fatigue, identified by a progressive decline in the isometric tension prior to the onset of active shortening over the course of a series of trials, became a problem in most preparations after about 90 min. In order to minimize these effects, force-velocity measurements were made after an initial sequence of trials to insure that the muscle exhibited stable behaviour and before a decrease in isometric tension greater than 10% of the initial value was observed. At low shortening velocities (Fig. 4), the sampled force was often less than that predicted from the Hill equation. Although this effect has been observed in single muscle fibres in vertebrates (Edman, Elzinga & Noble, 1978; Lannergren, 1978), it typically at much lower shortening velocities.

Fig. 4.

Force-velocity relationships from six animals. ▫ ◊ ○ ▪, 3mm release at Lo + l·5mm. ▴ 3 mm release at Lo — 0·5 mm (the same preparation as the filled square). ●▾1mm release at Lo + 0·-5 mm. Solid line is the rectangular hyperbola calculated from the Hill equation with a = 0-1 and b " 1-1. Inset, relative force, P./Pso at the sampled length during active shortening at +mms−1 as a function of relative activation level (ratio of isometric tension, Pso to peak isometric tension, P0). Ps/Pso = — 0·28 + 0·49 Pso/Po. Data from three experiments. N = 21, r= 0·8536.

Fig. 4.

Force-velocity relationships from six animals. ▫ ◊ ○ ▪, 3mm release at Lo + l·5mm. ▴ 3 mm release at Lo — 0·5 mm (the same preparation as the filled square). ●▾1mm release at Lo + 0·-5 mm. Solid line is the rectangular hyperbola calculated from the Hill equation with a = 0-1 and b " 1-1. Inset, relative force, P./Pso at the sampled length during active shortening at +mms−1 as a function of relative activation level (ratio of isometric tension, Pso to peak isometric tension, P0). Ps/Pso = — 0·28 + 0·49 Pso/Po. Data from three experiments. N = 21, r= 0·8536.

For smaller shortening distances (Fig. 4), the force declined from peak isometric tension at low velocities according to the Hill equation, but at velocities greater than about 1 mm s−1 (at a shortening distance of 0·04 muscle lengths) the force did not decrease as expected but remained high (20% of Po at a shortening velocity of two muscle lengths s−1). This behaviour was observed in all preparations. It was only observed at short distances of shortening and is consistent with the interpretation that the muscle was acting as a linear elastic element within the range of the short-range stiffness.

The intrinsic speed of shortening of the VSM, like that of other muscle (Abbott & Wilkie, 1953) is relatively independent of muscle length (Fig. 4). In contrast, the intrinsic speed of shortening decreases rapidly with decreases in activation level. At the same shortening velocity, the ratio of force at the sampled length is a linear function of activation level (Fig. 4, inset), as would be expected if the Hill constant b showed a linear decrease with activation level.

Active lengthening

Stretch of the VSM during activation (Fig. 5) produces an increase in force that can be separated into two periods, an early period of high stiffness, referred to as the short-range stiffness (Rack & Westbury, 1969) and a later period of decreased ‘terminal’ stiffness. In contrast to frog (Fig. 5D; Flitney & Hirst, 1978; Edman et al. 1978) and mammalian muscle (Rack & Westbury, 1969; Nichols & Houk, 1976), the transition between the two portions of the force record in the VSM is less abrupt (Fig. 5B, C, Fig. 6) and the stiffness of the muscle during the later portion of the stretch is quite high. Both the short-range stiffness and the terminal stiffness are functions of activation level and muscle length (Fig. 6A, B). Neither short-range nor terminal stiffness vary much with velocity of stretch (Fig. 6C). Terminal stiffness varies relatively little with stretch amplitude (Fig. 6D). The lack of a discrete yield point and the presence of a considerable stiffness in the terminal portions of the ramp was observed at all stimulus intensities and at different lengths. The increase in length necessary to exceed the short-range stiffness increases with the velocity of stretch. At 12·5 mms−1 it was about 400μm; at 25 mms−1 about 700μm.

Fig. 5.

Force as a function of activation level during active lengthening of VSM and frog sartorius. Stretch velocity for A, B, C (VSM) 12·5 mms’1, for D (frog aartorius) 10 mm s−1. Upper trace of each panel is force, lower trace is length. The bar beneath the length trace indicates the portion of the record in which the sampling frequency was increased ten times. Ramp in D is twice as long as A, B and C because the sartorius was over twice as long as the VSM.

Fig. 5.

Force as a function of activation level during active lengthening of VSM and frog sartorius. Stretch velocity for A, B, C (VSM) 12·5 mms’1, for D (frog aartorius) 10 mm s−1. Upper trace of each panel is force, lower trace is length. The bar beneath the length trace indicates the portion of the record in which the sampling frequency was increased ten times. Ramp in D is twice as long as A, B and C because the sartorius was over twice as long as the VSM.

Fig. 6.

Force-length plots of VSM response to trapezoidal length changes. (A) Stimulus frequencies of 80, 40, 20 and 0 Hz at L0 to a velocity of 12·5 mm s−1. (B) Asin (A) but at L0 — 2 mm. (C) Velocities of 6·25, 12·5 and 25 mms−1 at Lo. Stimulus frequency of 40 Hz. (D) Length changes of 0·5, 1·0, 2·0 and 3·0 mm at L0. Stimulus frequency of 40 Hz.

Fig. 6.

Force-length plots of VSM response to trapezoidal length changes. (A) Stimulus frequencies of 80, 40, 20 and 0 Hz at L0 to a velocity of 12·5 mm s−1. (B) Asin (A) but at L0 — 2 mm. (C) Velocities of 6·25, 12·5 and 25 mms−1 at Lo. Stimulus frequency of 40 Hz. (D) Length changes of 0·5, 1·0, 2·0 and 3·0 mm at L0. Stimulus frequency of 40 Hz.

A possible explanation for this difference from other muscles might be the presence of a high series elastic compliance that would reduce the length changes at the level of the cross bridges. Alternatively the cross bridges themselves might be more com pliant, allowing a certain portion of them to make new bonds during the yield. One way of distinguishing between these alternatives is to utilize the method introduced by Morgan (1977) for separating cross bridge and non cross bridge compliance. Cross bridge compliance should be a function of the number of activated cross bridges whereas non cross bridge compliance is considered to be constant over the range of the stretch. By plotting a short-range stiffness normalized to the isometric force as a function of a range of isometric forces, the cross bridge contribution to the compliance appears as the intercept of the linear relationship and the non cross bridge compliance its slope. Fig. 7 shows such plots of VSM at a stretch velocity of 12·5mms−1. The intercept of this line, αo, (muscle shortening required to reduce force to zero), is approximately 0·04mm and the non cross bridge compliance, Ct, is 0·64mmN−1. In five experiments αo was 0·035 + 0·004 mm and Ct was 0·646 + 0·095 mm N−1. At Lo the number of sarcomeres in series in the VSM was 1214 + 146 (N = 6) so that αo per half sarcomere was 14·7 + 2·5 nm, similar to that observed in frog (Huxley & Simmons, 1971; Gregory, Luff, Morgan & Proske, 1978). Thus, cross bridge compliance of the VSM is not significantly different from that of vertebrate muscle.

Fig. 7.

a plots of VSM. a (isometric tension just prior to stretch/muscle stiffness in initial 8 ms of ramp) is plotted as a function of isometric tension. (A) ○, initial series at L0 ▵, series at L0 — 2 mm; ▫, final series at Lo. Note that the lines at the two lengths have the same intercept at Oo. (B) ●, control a plot below the threshold of the inhibitor. ▴, Stimulus intensity increased to recruit the inhibitor. The slopes of the two lines are the same, indicating that the non cross bridge compliance has not changed, but the cross bridge compliance has increased.

Fig. 7.

a plots of VSM. a (isometric tension just prior to stretch/muscle stiffness in initial 8 ms of ramp) is plotted as a function of isometric tension. (A) ○, initial series at L0 ▵, series at L0 — 2 mm; ▫, final series at Lo. Note that the lines at the two lengths have the same intercept at Oo. (B) ●, control a plot below the threshold of the inhibitor. ▴, Stimulus intensity increased to recruit the inhibitor. The slopes of the two lines are the same, indicating that the non cross bridge compliance has not changed, but the cross bridge compliance has increased.

Cross bridge and non cross bridge stiffness can be independently varied. If the measurements are made at a shorter length, the cross bridge stiffness should be the same, but the non cross bridge stiffness, due to the lower passive stiffness, should be less, as is seen in Fig. 7A. Alterations in the level of activation of different series elements while the length remains constant should result in a shift in the value of α0 but no change in the non cross bridge compliance. This experiment was performed by increasing the stimulus intensity above the threshold for the inhibitor. The α plot (Fig. 7B) shows an increase in the value for α0 while the non cross bridge stiffness remains the same.

A complicating factor in comparing the non cross bridge compliance of VSM with that of vertebrate muscle is that the compliance of the passive elastic elements is not negligible at the operating lengths of the muscle. By subjecting the inactive muscle to ramp stretches at the same length as the active muscle measurements, the mag nitude of this element can be estimated. If the response of the muscle to a ramp stretch is modelled as an elastic element with a stiffness, Kt, composed of a passive stiffness, Kt, in parallel with two springs in series (representing the cross bridge, Kb, and non cross bridge, Kn, stiffnesses), an expression for the value of the non cross bridge stiffness Kn can be derived:
formula
Since α= P/Kt = α0 + CtP and Kb = P/α0, Kb and Kt can be obtained from the α plot and Kp determined by stretching the passive muscle. Using values from four animals, Kb (at P = 0 · 2 N) was 5 · 76 + 0 · 68 N mm−1, Kt was T31 + 0 · 02N mm−1, and Kp was 0 · 4 + 0 · 08 N mm−1. Kn was calculated to be 1 · 03 + 0 · 24N mm−1.
The portion of the force record after the yield represents a steady state in which cross bridges are cyclically attached and broken by the movement of thick and thin filaments. To estimate how great a change in the contribution of the cross bridges to the total stiffness has occurred, an expression similar to equation (1) was derived:
formula
Kp during this part of the stretch was 0·19 + 0·04 N mm−1, Kt was 0·37 + 0·05 N mm−1, and Kn was assumed to be unchanged. Kb was calculated to be 0·24 +0·08 N mm−1, having decreased to about 4% of its pre-yield stiffness. In contrast, the total stiffness of the muscle had only decreased to about 30% of its pre-yield value.

The results of this study indicate that this crustacean slow muscle is similar in many of its mechanical properties to other slow muscles. Only in the high compliance of its series elastic element is it remarkable, a feature, incidentally, shared with other crustacean slow muscles (Hoyle & Abbott, 1967; Tameyasu & Sugi, 1979). This high compliance may provide certain advantages in the conditions under which the muscle operates. Although abdominal stretch in the intact animal elicits reflex activation of the VSM muscle (Chapple, 1973), the abdomen does not possess the muscle receptor organs found in many other decapods. The other decapod muscle receptors are under efferent control by the central nervous system (Fields, 1976) and are thus analogous to muscle spindles. A recent hypothesis of muscle spindle function (Nichols & Houk, 1976; Cordo & Rymer, 1982) suggests that these receptors may compensate reflexly for the non-linear behaviour of muscle to length changes. As shown in the Results, the isolated VSM does not exhibit these non-linearities, and behaves in a number of ways as a spring, the stiffness of which is controlled directly by the central nervous system. The length of the muscle during shell support is at 77% of the optimum length. Since the abdomen does not appear to vary its length while supporting the shell, it is likely that the operating range of the muscle is no more than 10% of the optimum length on either side of the operating point of the muscle. Under some conditions, the abdomen will shorten or lengthen much more than this (as the animal enters its shell) but these are during movements in which adjustments for external perturbations are not likely to be of importance. Thus, the tonic activity of excitor motoneurones and the relatively high compliance of the series elastic element will ensure that small perturbations are within the short range stiffness of the muscle. Moreover, even beyond this point, the muscle behaves as a spring both because it is operating on the ascending limb of the length-tension curve and because the terminal stiffness during a stretch is high. Even at the optimum length and beyond, the high level of passive tension will ensure the elastic behaviour of the muscle.

The behaviour of the length-tension relationship as the level of activation is varied is also consistent with this view. As the activation of the muscle increases, the slope of the length-tension curve increases much more than the decrease in the zero force length to shorter lengths. Due to the high compliance of the series elastic element, it is likely that this shift of the zero force length is due primarily to internal shortening within the muscle. In cat soleus muscle (Rack & Westbury, 1969) increases in th^ stimulus frequency alter the slope of the length-tension curve less than the zero force length. Recruitment of additional motor units, however, does increase the slope (Cordo & Rymer, 1982). In the VSM in which recruitment may play a much smaller role in controlling muscle force, it is the slope that is altered by rate modulation by the motoneurones. The disadvantages of a system in which an appreciable length of time must elapse before a desired stiffness is achieved is presumably offset by the advantages of simplicity of control.

Also consistent with this view of the VSM as being adapted for a postural role as a linear spring is the behaviour of the muscle during active lengthening. It is quite different from frog Sartorius (Flitney & Hirst, 1978), frog semitendinosus (Edman et al. 1978) and cat soleus (Joyce, Rack & Westbury, 1969; Nichols & Houk, 1976). The initial short-range stiffness is not terminated by a discrete yield followed by a negative stiffness, but instead there is a gradual transition to a stiffness about one-third of that in the initial portion of the record. Such a graded response has been observed in mammalian muscles such as the kangaroo (Morgan, Proske & Warren, 1978) and in frog sartorius at low stretch velocities (Flitney & Hirst, 1978). Since no accentuation of the short-range yield was observed as the velocity of stretch increased to 50 mm s−1 (4 muscle lengths s— 1), it is probable that the explanation for the absence of a sharply defined yield is the same as in kangaroo soleus. In this muscle a long compliant tendon is in series with the muscle itself. As shown in the Results, the non cross bridge compliance for hermit crab VSM is about 1 mm N−1. Published values for the tendon compliance for cat soleus (Walmsley & Proske, 1981) are 0·05 mm N−1; peak isometric tension is 15 N, fifty times that of the VSM. Since the greater force is produced by many more fibres in parallel, the compliance, scaled to that of the VSM, would be 2·5 mm N−1. However, there are approximately twelve times the number of sarcomeres in series in cat soleus as in VSM so that, disregarding the soleus tendon as a source of compliance, cat soleus per sarcomere has a non cross bridge compliance of about 0·2 mm N−1, about one-fifth that of the VSM.

The effect of this greater compliance would be to reduce the velocity of stretch of the cross bridges and to increase the length required to stretch the sarcomere before the short-range stiffness is exceeded. Fig. 8 shows the results of calculating the expected force record produced by VSM cross bridges at the same level of activation for VSM (heavy solid line) and cat (light solid line) non cross bridge compliances. The dotted line is the force record from the VSM in the absence of the parallel elastic element. The high compliance of the non cross bridge elastic element results in a more gradual transition between the two portions of the force record and a higher terminal stiffness of the muscle.

Fig. 8.

Model of the effects of active lengthening under three different conditions at an activation level of 0·2N. Heavy line: VSM response calculated from the values for total stiffness with Kb = 5·26 N mm−1, K” = 1 Nmm−1 and Kp = 0·3 N mm:−1 in the early portion of the stretch and Kb = 0·16 N mm−1, K” = 1 N mm−1 and Kp = 0·2 N mm−1 in the terminal portion of the stretch. Dotted line: Kp 0·2, but other values as in the first case. Thin line: Kp = 0, Ks =5 N mm−1 (as in cat soleus) and Kb is the same as in the two other cases.

Fig. 8.

Model of the effects of active lengthening under three different conditions at an activation level of 0·2N. Heavy line: VSM response calculated from the values for total stiffness with Kb = 5·26 N mm−1, K” = 1 Nmm−1 and Kp = 0·3 N mm:−1 in the early portion of the stretch and Kb = 0·16 N mm−1, K” = 1 N mm−1 and Kp = 0·2 N mm−1 in the terminal portion of the stretch. Dotted line: Kp 0·2, but other values as in the first case. Thin line: Kp = 0, Ks =5 N mm−1 (as in cat soleus) and Kb is the same as in the two other cases.

The greater non cross bridge compliance of VSM could be due either to its attach ments to the apparatus, the connections between sarcomeres and supporting tissue, or to a greater compliance of individual sarcomeres. Each of these factors is likely to play a role. The high bonding strength of the cyanoacrylate adhesive and the low compliance of the apparatus suggest that the high non cross bridge compliance must be either in the intervening tissues or in the muscle itself. Under isometric conditions the ends of the muscle shorten to a greater extent than the centre of the muscle. I attempted to measure length changes in the middle of the muscle as it was stretched at different levels of activation. The method selected (movements of flags fixed on the muscle across the fields of two photo-transistors) did not give reliable results; it appeared that the length changes decreased as the level of activation increased, consistent with a substantial end compliance independent of the parallel elastic element. However, Tameyasu & Sugi (1979) have reported a high non cross bridge compliance in individual sarcomeres of crayfish slow abdominal extensor muscles. Thus, it is possible that part of the greater compliance of the VSM resides within the sarcomeres themselves.

Fatigue and the heterogeneity of the VSM have contributed to making the force-velocity properties difficult to determine accurately under the present experimental conditions. The high frequencies of stimulation necessary to activate the muscle maximally produce substantial fatigue so that there is an initial decline in peak isometric tension. Because this decline is followed by a period during which the peak isometric tension and force-velocity properties remain stable it may be that there is a group of faster fatiguable fibres. During the portion of the experiment in which isometric tension was stable, muscle fibres had a Vmax of 4·2 μm s−1 per half sarcomere and a/P0 of 0·1. This is greater than the Vmax and a/P0 of tortoise muscle (Katz, 1939; Woledge, 1968) and Mytilus ABRM (Gilbert, 1978) and comparable to slow muscle fibres in Xenopus (Lannergren, 1978). In all of these cases the curvature of the force-velocity relationship is great and Woledge (1968) has suggested that such muscles are more efficient than fast muscle in converting free energy into work.

At low shortening velocities the force produced by the muscle at the sampled length is often lower than that predicted from the Hill equation; such deviations have often been observed in frog (Edman, Mulieri & Scubon-Mulieri, 1976), Xenopus (Lannergren, 1978) and cardiac muscle (van Heuningen, Rijnsburger & ter Keurs, 1982). However, the deviations from the Hill equation in VSM occur at lower force levels than in other preparations.

Force-velocity properties of the VSM for small movements are primarily determined by the properties of the short range stiffness. Within its range, the force is not inversely related to shortening velocity but is almost constant. Although this behaviour is qualitatively similar to mammalian muscles (Joyce et al. 1969) it governs the behaviour of the muscle over a distance of 5% of total muscle length.

Thus, the different mechanical features of this muscle seem to accentuate its resemblance to an elastic element the stiffness of which can be controlled by the central nervous system. The cellular basis for this behaviour is still unclear. But, whatever the cellular basis of the high non cross bridge compliance, the VSM is much more linear in its response to external stretch than are vertebrate muscles. It is, therefore, possible that the linear properties of the VSM may obviate the necessity for the proprioceptive control of muscle properties postulated for vertebrates (Nichols & Houk, 1976; Houk & Rymer, 1981) and thus be of adaptive significance.

I would like to thank Patricia Marsan for technical assistance, Robert Degoursey for collecting animals, Sean True for providing me with some of the software used in this work, and the Electron Microscopy Laboratory of the University of Connecticut for aid in preparing the electron micrographs. This work was supported by N.I.H. Grant NS15210.

Abbott
,
B. C.
&
Wilkie
,
D. R.
(
1953
).
The relation between velocity of shortening and the tension-length curve of skeletal muscle
.
J. Physiol., Land
.
120
,
214
223
.
Atwood
,
H. L.
(
1972
).
Crustacean muscle
.
In The Structure and Function of Muscle
, Vol.
1
, (ed.
G. H.
Bourne
), pp.
421
489
.
New York
:
Academic Press
.
Bizzi
,
E.
,
Dev
,
P.
,
Morasso
,
P.
&
Polt
,
A.
(
1978
).
Effect of load disturbances during centrally initiated movements
.
J. Neurophysiol
.
41
,
542
556
.
Chapple
,
W. D.
(
1969a
).
Postural control of shell position by the abdomen of the hermit crab, Pagarus pollicarus. I. Morphology of the superficial muscles and their nerves
.
J. exp. Zool
.
171
,
397
408
.
Chapple
,
W. D.
(
1969b
).
Postural control of shell position by the abdomen of the hermit crab, Pagarus pollicarus. II. Reflex control of the ventral superficial muscles
.
J. exp. Zool
.
171
,
409
416
.
Chapple
,
W. D.
(
1973
).
Changes in abdominal motoneuron frequency correlated with changes of shell position in the hermit crab, Pagarus pollicarus
.
J. comp. Physiol
.
87
,
49
64
.
Chapple
,
W. D.
(
1982a
).
Muscle
.
In The Biology of Crustacea
, Vol.
3
, (eds
H. L.
Atwood
&
D. C.
Sandeman
), pp.
151
184
.
New York
:
Academic Press
.
Chapple
,
W. D.
(
1982b
).
Mechanical properties of a slow crustacean muscle
.
Society for Neurosciences
8
,
331
.
Cordo
,
P. J.
&
Rymer
,
W. Z.
(
1982
).
Contributions of motor-unit recruitment and rate modulation to compen sate for muscle yielding
.
J. Neurophysiol
.
47
,
797
809
.
Edman
,
K. A. P.
,
Elzinca
,
G.
&
Noble
,
M. I. M.
(
1978
).
Enhancement of mechanical performance by stretch during tetanic contractions of vertebrate skeletal muscle fibres
.
J. Physiol., Lond
.
281
,
139
155
.
Edman
,
K. A. P.
,
Muueri
,
L. A.
&
Scubon-Muueri
,
B.
(
1976
).
Non-hyperbolic force-velocity relationship in single muscle fibers
.
Acta physiol, scand
.
98
,
143
156
.
Fields
,
H. L.
(
1976
).
Crustacean abdominal and thoracic muscle receptor organs
.
In Structure and Function of Proprioceptors in the Invertebrates
, (ed.
P. J.
Mill
).
London
:
Chapman and Hall
.
Futney
,
F. W.
&
Hirst
,
D. G.
(
1978
).
Cross bridge detachment and sarcomere ‘give’ during stretch of active frog’s muscle
.
J. Physiol., Lond
.
276
,
449
465
.
Franzini-Armstrong
,
C.
(
1973
).
Membranous systems in muscle fiber
.
In The Structure and Function of Muscle
, Vol.
1
, (ed.
G. H.
Bourne
), pp.
532
619
.
New York
:
Academic Press
.
Fung
,
Y. B.
(
1972
).
Stress-strain-history relations of soft tissues in simple elongation
.
In Biomechamcs: Its Foundations and Objectivity
, (eds
Y. C.
Fung
,
N.
Perrone
&
M.
Anliker
), pp.
181
208
.
Englewood Cliffs, New Jersey
:
Prentice-Hall
.
Gilbert
,
S. H.
(
1978
).
Tension and heat production during isometric contractions and shortening in the k anterior byssus retractor muscle of Mytilus edulis
.
J. Physiol., Lond
.
282
,
7
20
.
Grillner
,
J. E.
,
Luff
,
A. R.
,
Morgan
,
D. L.
&
Prosee
,
U.
(
1978
).
The stiffness of amphibian slow and twitch muscle during high speed stretches
.
Pflügers Arch. ges. Physiol
.
375
,
207
211
.
Grillner
,
S.
&
Udo
,
M.
(
1971
).
Motor unit activity and stiffness of the contracting muscle fibers in the tonic stretch reflex
.
Acta physiol, scand
.
81
,
422
424
.
Hajek
,
I.
,
Chari
,
N.
,
Bass
,
A.
&
Gutmann
,
G.
(
1973
).
Differences in contractile and some biochemical properties between fast and slow abdominal muscles of the crayfish (Astacus leptodactylus)
.
Physiologia bohemoslov
.
22
,
603
612
.
Hill
,
A. V.
(
1970
).
First and last Experiments in Muscle Mechanics
.
Cambridge, EngLond
:
Cambridge University Press
.
Houk
,
J. C.
&
Rymer
,
W. Z.
(
1981
).
Neural control of muscle length and tension
.
Handbook of Physiology Sect. 1
, Vol.
II
, Part 1, pp.
257
324
.
American Physiological Society, Bethesda, MaryLond
.
Hoyle
,
G.
(
1969
).
Comparative aspects of muscle
.
Ann. Rev. Physiol
31
,
43
84
.
Hoyle
,
G.
(
1978
).
Intrinsic rhythm and basic tonus in insect skeletal muscle
.
J. exp. Biol
.
73
,
173
203
.
Hoyle
,
G.
&
Abbott
,
B. C.
(
1967
).
Dynamic properties of giant muscle fibers of the barnacle
.
Am. Zool
.
7
,
611
614
.
Huxley
,
A. F.
&
Simmons
,
R. M.
(
1971
).
Mechanical properties of the cross-bridges of frog striated muscle
.
J. Physiol., Lond
.
218
,
59
60P
.
Jahromi
,
S. S.
&
Charlton
,
M. P.
(
1979
).
Transverse sarcomere splitting: a possible means of longitudinal growth in crab muscles
.
J. Cell. Biol
.
80
,
736
742
.
Joyce
,
G. C.
,
Rack
,
P. M. H.
&
Westbury
,
D. R.
(
1969
).
The mechanical properties of cat soleus muscle during controlled lengthening and shortening movements
,
J. Physiol., Lond
.
204
,
461
474
.
Katz
,
B.
(
1939
).
The relation between force and speed in muscular contraction
.
J. Physiol., Lond
.
96
,
45
64
.
Kawai
,
M.
,
Brandt
,
P. W.
&
Orentlicher
,
M.
(
1977
).
Dependence of energy transduction in intact skeletal muscles on the time in tension
.
Biophys. J
.
18
,
161
171
.
Kennedy
,
D.
&
Davis
,
W. J.
(
1977
).
Organization of invertebrate motor systems
.
InHandbook of Physiology
, Vol.
1
, Part. 2, pp.
1023
1087
.
American Physiological Society
,
Bethesda, MaryLond
.
Lannergren
,
J.
(
1978
).
The force-velocity relation of isolated twitch and slow muscle fibers of Xenopus laevis
.
J. Physiol., Lond
.
283
,
501
521
.
Morgan
,
D. L.
(
1977
).
Separation of active and passive components of short-range stiffness of muscle
.
Am. J. Physiol
.
232
(
1
),
C45
C49
.
Morgan
,
D. L.
,
Proske
,
U.
&
Warren
,
D.
(
1978
).
Measurements of muscle stiffness and the mechanism of elastic storage of energy in hopping kangaroos
.
J. Physiol., Lond
.
282
,
253
261
.
Nichols
,
T. R.
&
Houk
,
J. C.
(
1976
).
Improvement in linearity and regulation of stiffness that results from actions of stretch reflex
.
J. Neurophysiol
.
39
,
119
142
.
Ogonowski
,
M. M.
&
Lang
,
F.
(
1979
).
Histochemical evidence for enzyme differences in crustacean fast and slow muscle
.
J. exp. Zool
.
207
,
143
151
.
Partridge
,
L. D.
(
1979
).
Muscle properties: a problem for the motor physiologist
.
In Posture and Movement
, (eds
R. E.
Talbott
&
D. R.
Humphrey
).
New York
:
Raven Press
.
Pringle
,
J. W. S.
(
1972
).
Arthropod muscle
.
In The Structure and Function of Muscle
, Vol.
1
, (ed.
G. H.
Bourne
), pp.
491
541
.
New York
:
Academic Press
.
Rack
,
P. M. H.
&
Westbury
,
D. R.
(
1969
).
The effects of length and stimulus rate on tension in the isometric cat soleus muscle
.
J. Physiol., Lond
.
204
,
443
560
.
Tameyasu
,
T.
&
Sugi
,
H.
(
1979
).
The origin of the series elastic component in single crayfish muscle fibers
.
Experientia
35
,
210
211
.
Van Heunincen
,
R.
,
Rijnsburger
,
W.
&
Ter Keurs
,
E. D. J.
(
1982
).
Sarcomere length control in striated muscle
.
Am. J. Physiol
.
242
,
H411
420
.
Walmsley
,
B.
&
Proske
,
U.
(
1981
).
Comparison of stiffness of soleus and medial gastrocnemius muscles in cats
.
J. Neurophysiol
.
46
,
250
259
.
Woledge
,
R. C.
(
1968
).
The energetics of tortoise muscle
.
J. Physiol., Lond
.
197
,
685
707
.
Yox
,
D. P.
,
Dicaprio
,
R. A.
&
Fourtner
,
C. R.
(
1982
).
Resting tension and posture in arthropods
.
J. exp. Biol
.
96
,
421
425
.