1. Isometric contraction kinetics and force-velocity relations were examined in wing muscles of two tettigoniid insects, Neoconocephalus robustus and N. triops. The muscles were first tergocoxal muscles of the mesothoracic and metathoracic segments. The metathoracic muscle is a flight muscle. The mesothoracic muscle is used in flight and in stridulation.

  2. In the field, the wing stroke frequency during stridulation by N. triops is about 100 Hz ; the thoracic temperature during singing is about 30 C ; and the temperature gradient between the thorax and surround is about 15 C. Published data for N. robustus give the wing-stroke frequency during stridulation as about 200 Hz at a thoracic temperature of 35–40 C. The wing-stroke frequency during flight by both species is approximately 20 Hz at 25 C.

  3. The twitch time course is similar in equivalent muscles of the two species. At 35 C the twitch duration (onset to 50 % relaxation) is 5·5–6·5 ms for mesothoracic muscles and 11–13 ms for metathoracic ones. Twitch and tetanic tension per unit area are about twice as great in the metathoracic muscles as in the faster, mesothoracic ones.

  4. Despite the differences in isometric contraction kinetics, the maximum shortening velocity (Vmax) is similar in mesothoracic and metathoracic wing muscles. Vmax values (lengths per second, 35 C), determined by extrapolation of force-velocity curves, were 10·1 (mesothoracic) and 11·1 (metathoracic) for N. robustus; 12·2 (mesothoracic) and 16·1 (metathoracic) for N. triops. With N. triops, Vmax was also determined from the time taken to re-develop tension following quick release. The values obtained were somewhat higher than from extrapolation of force-velocity curves, but again similar for mesothoracic and metathoracic muscles.

  5. Twitch time course becomes more rapid and Vmax increases with increasing temperature. Neither twitch nor tetanic tension is greatly affected by temperature change in the range 25 – 35 C.

  6. As for many other fast muscles, force-velocity plots for these muscles have little curvature. It is suggested that the relative straightness of these plots is a consequence of internal viscosity.

The shortening velocity of a muscle increases with decreasing load, reaching its maximum value at zero load. There is often an inverse relationship between the maximum shortening velocity of a muscle and the twitch rise time (Close, 1965). This inverse relationship may reflect co-evolution of the processes which control shortening velocity and those which regulate muscle activation time -tasks which require brief contractions are also likely to require rapid shortening during the period of activity. However, it has been suggested that muscle shortening velocity and the duration of muscle activation following a stimulus are linked in some unspecified, causal way (Close, 1965, 1972). The inferior rectus (IR) muscles of the rat and mouse are exceptions to the usual inverse relation between twitch rise time and maximum shortening velocity (Close & Luff, 1974; Luff, 1981). The twitch rise times of these eye muscles are about one-half those of the extensor digitorum longus (EDL) muscles of the same species, but in each species the IR and EDL muscles have essentially identical force-velocity curves. The IR and the EDL are both unusually fast mammalian muscles and it is possible that the intrinsic shortening velocity in each is approaching a natural limit and is no longer subject to the usual controls.

In this paper, the relationship between maximum shortening velocity and twitch time course is compared in wing muscles with different functions in tettigoniid insects. The forewings of male tettigoniids are used in stridulation and flight, the hind wings for flight alone. In some species the wing-stroke frequency during stridulation is extraordinarily high; often much higher than the wing-stroke frequency during flight. For example, in Neoconocephalus robustus the wing-stroke frequency of the forewings during stridulation is about 200 Hz (Josephson & Halverson, 1971), while the wing-stroke frequency during flight is about 20 Hz (Ready, 1983). Thus in this species there is an order of magnitude difference in maximum operating frequency between the wing muscles of the mesothoracic segment which drive the forewings and those of the adjacent metathoracic segment which drive the hindwings. The isometric contraction kinetics of mesothoracic and metathoracic wing muscles are quite different in N. robustus, corresponding to the different maximum operating frequencies of these muscles. Both twitch rise time and decay time in mesothoracic muscles are about one-half as long as in metathoracic homologues (Josephson & Stokes, 1982; Table 2A). The twitch durations recorded from mesothoracic wing muscles are 5 – 8 ms (onset to 50 % relaxation, 35 ° C) which makes these muscles among the fastest known in terms of twitch time course. On the basis of the usual relationship between twitch rise time and maximum shortening velocity, the maximum shortening velocities of mesothoracic wing muscles in N. robustus and similar species should be considerably greater than those of metathoracic wing muscles, and should be among the highest shortening velocities to be found in any muscle. It is shown below that neither of these predictions is fulfilled.

Animals

The animals used were adult, male, cone-headed katydids (Orthoptera: Tettigoniidae) : Neoconocephalus robustus collected from salt marshes in the vicinity of Woods Hole, Massachusetts; and a species identified tentatively as N. triops collected from fields and urban areas in Irvine, California. They were captured while singing in the early evening in August and September for N. robustus, and from late February to May for N. triops. Animals were kept in screened cages, fed freshly collected grass, and used within a day of capture.

Wing-stroke frequency and muscle operating temperature

Tape recordings were made of singing N. triops which were then caught and a thermocouple probe (0·3 mm o.d.) was quickly inserted into the mesothoracic muscles. Temperature readings were then recorded vocally on the tape recorder. The recording for each animal thus provided information on: (1) the sound pulse frequency during singing (= wing-stroke frequency, see Josephson & Halverson, 1971), (2) the delay between the cessation of song and the first temperature measurement, and (3) a series of temperature measurements as a function of time after capture from which a cooling curve could be constructed. Upon completion of each set of readings the temperature at the site of capture was measured. As was earlier found in post-singing cooling of another tettigoniid (Josephson, 1973), cooling at the cessation of stridulation in N. triops is approximately exponential, but to an asymptotic temperature which is distinctly higher than the measured ambient temperature. A computer programme was used to provide the best exponential fit to the measured temperature points from N. triops (Josephson, 1973; see Fig. 1). The programme systematically varied the estimated asymptote of the cooling curve in order to determine the value of asymptote which gave the largest linear regression coefficient between the logarithm of the temperature excess and elapsed time; temperature excess being the difference between the measured temperature and the estimated asymptotic temperature. Only those instances were analysed in which the first temperature value was obtained within 15 s of the cessation of singing.

Fig. 1.

Thoracic cooling at the cessation of singing in Neoconocephalus triops. An exponential curve has been fitted to the individual data points. The ambient temperature during singing for this animal was 14·7 ° C.

Fig. 1.

Thoracic cooling at the cessation of singing in Neoconocephalus triops. An exponential curve has been fitted to the individual data points. The ambient temperature during singing for this animal was 14·7 ° C.

The wing-stroke frequency of N. triops was determined by attaching the animal by its prothorax to the needle of a phonograph cartridge and monitoring the up and down thrust generated by wing movements. Flight was initiated by lifting the animal from the substrate and blowing air posteriorly across the animal’s head.

Muscle preparations

The muscles used were first tergocoxal muscles of the mesothoracic and metathoracic segments. This muscle is a bundle of parallel fibres which runs from the tergum to an apodeme attached to the anterior coxa. Fast insect muscles such as the tergocoxal muscles are quite sensitive to oxygen lack and perform poorly if the tracheal system to the muscle, which is responsible for gas exchange, is disturbed (e.g. WeisFogh, 1956). In order to minimize damage to a muscle and its tracheal system, an in vivo preparation was used (Josephson, 1973) in which the muscle was de-innervated by removal of the ganglion that supplies its motor axons but in which the muscle was otherwise intact, with a complete tracheal supply and bathed by normal haemolymph. The muscle was stimulated with 0·5-ms shocks applied through thin (50 μm) silver wire electrodes that were inserted through small holes in the exoskeleton into the dorsal origin of the muscle and waxed in place. This mode of stimulation activates the muscle by exciting its motoneurones, branches of which course throughout the muscle (Josephson, 1973; Fig. 2). After removal of the insect’s legs, wings and the appropriate thoracic ganglion, and placement of the stimulating electrodes, the insect was fixed, dorsal side down, to a Leucite platform with fast-setting epoxy cement. The limb of the muscle in which the stimulating electrodes were placed was cut off distal to the coxa. The coxa, to which the tergocoxal muscle inserts, was freed from all connections to the animal except for the apodeme of the muscle. The resuting coxal ring of cuticle was used as an attachment point for an ergometer. A light hook (approximately 15 mg), made from an insect pin, attached the ergometer to the coxa and hence to the tergocoxal muscle. The ergometer, Cambridge Technology 300 H (Cambridge Technology, Cambridge, Mass. U.S.A.), incorporated a galvanometer motor with capacitance sensors for position control and force measurement. The nominal response time for a step change in force was 1·5 ms and the maximal excursion rate with the recommended lever was about 4 ms− 1 which, for the muscles used, was several hundred muscle lengths per second. The Leucite platform to which the insect was attached was mounted on a manipulator so that muscle length could be varied. Tension measurements were made with the muscle under slight tension and at about the length of the muscle in an intact animal. This length was the starting length of the muscle in experiments involving shortening. The exposed ventral end of the muscle was moistened occasionally with saline (Usherwood, 1968; pH adjusted to 7 with NaOH before use). Muscle temperature was monitored with a thermocouple probe (0·3 mm o.d.) inserted into the contralateral tergocoxal muscle through the base of the contralateral leg stump. Muscle temperature was controlled by adjusting the intensity of a microscope lamp whose beam shone equally on both sides of the thorax.

Fig. 2.

Isometric twitches from mesothoracic and metathoracic wing muscles of Neoconocephalus triops, 25 ° C. The muscles were stimulated with shocks of gradually increased intensity. Each tension level represents a number of superimposed sweeps over a range of stimulus intensities. The presence of three tension increments indicates that each of the muscles is innervated by three excitatory axons. Note that the time to peak tension does not change appreciably as new motor units are recruited, indicating that the time course of tension is similar in each of the motor units of a muscle. The mesothoracic and metathoracic muscles shown are the preparations whose twitch durations (onset-50 % relaxation) lay closest to the mean values in Table 2.

Fig. 2.

Isometric twitches from mesothoracic and metathoracic wing muscles of Neoconocephalus triops, 25 ° C. The muscles were stimulated with shocks of gradually increased intensity. Each tension level represents a number of superimposed sweeps over a range of stimulus intensities. The presence of three tension increments indicates that each of the muscles is innervated by three excitatory axons. Note that the time to peak tension does not change appreciably as new motor units are recruited, indicating that the time course of tension is similar in each of the motor units of a muscle. The mesothoracic and metathoracic muscles shown are the preparations whose twitch durations (onset-50 % relaxation) lay closest to the mean values in Table 2.

In the experiments done with N. robustus the animal was removed from the apparatus at the end of the series of measurements and hemi-sected in the sagittal plane. The experimental muscle was stretched to approximately the same length as during the experiment, as judged by the relative positions of the coxa and surrounding cuticular structures, and the muscle length was measured with an ocular micrometer. The preparation was then preserved in 70% ethanol. After several weeks in alcohol the muscle was dissected free from its attachments, rehydrated in saline and weighed. Muscle weight was corrected for a 12% weight loss associated with alcohol fixation and rehydration (Ready, 1983). The average cross-sectional area was determined as the ratio of muscle weight to length. Since fibres of the muscle were parallel, running from end to end, no correction for angle of pinnation was required in determining the effective cross-sectional area. In the series with N. triops, which was done later than that with N. robustus, the muscle was superfused with 70 % ethanol and ethanol was injected into the thorax for 10 – 20 min before disconnecting the muscle from the ergometer, the goal being to fix the muscle at the length at which it had been studied. The preparation was then preserved in 70% ethanol until it was later dissected, the muscle length measured, and its cross-sectional area determined as with the N. robustus muscle (Table 1). In N. triops the length of the contralateral control muscle, fixed in situ attached to its coxa but with the remaining leg amputated, was measured in addition to that of the experimental muscle. This was done to determine the length of the experimental muscle during the measurements in relation to its length in an undisturbed insect, which was assumed to be that of the control muscle. The ratio of the length of the experimental muscle to that of the control averaged 0·99 (S.D. = 0·09, N = 16).

Table 1.

Dimensions of first tergocoxal muscles in adult, male animals, mean (S.D.)

Dimensions of first tergocoxal muscles in adult, male animals, mean (S.D.)
Dimensions of first tergocoxal muscles in adult, male animals, mean (S.D.)

Additional methods are described where appropriate.

Operating frequency and temperature of wing muscles

The sound pulse frequency (= wing-stroke frequency) of the 14 N. triops providing the thoracic temperature data below averaged 99·9Hz (S.D. = 9·1 Hz). Sound recordings from 44 animals singing in the field had pulse frequencies of 52– 115 Hz at ambient temperatures ranging from 11·5 – 18·2 ° C. A few animals from which recordings were obtained while they were singing in the laboratory had pulse frequencies of 140 – 160 Hz at an ambient temprature of 25 ° C. There was much scatter in the plot of singing frequency against ambient temperature for the field data, but the linear correlation coefficient was statistically significant (r = 0·52) and positive. Walker, Whitesell & Alexander (1973) have reported a similar low correlation between pulse frequency and ambient temperature for singing in N. robustus.

The predicted thoracic temperature during singing in N. triops, obtained by extra-polation of the cooling curves to zero time, i.e. to the immediate cessation of stridulation, was 32·2 ° C (S.E. =0·7 ° C, N =14). This is probably an overestimate since it assumes that heat production by the animals ceased immediately upon capture, whereas they did struggle and therefore probably generated heat. The first temperature values actually measured in these animals averaged 30·1 ° C (S.E. = 0·6 ° C). This value is certainly an underestimate, since some cooling undoubtedly occurred before the first measurement. With some confidence, then, one can fix the average thoracic temperature at the cessation of singing in these animals as between 30 and 32 ° C. The average ambient temperature for this set of animals was 15·4 ° C (S.D. = 1·7 ° C), so the usual temperature gradient between the thorax and its surround was about 15 ° C. In N. robustus the contraction frequency of the forewings during stridulation is 150 – 212 Hz (Josephson & Halverson, 1971), and the thoracic temperature during singing is approximately 35 ° C which is 5 – 15 ° C higher than the ambient temperature (Heath & Josephson, 1970).

The usual singing frequency in N. triops (100 Hz) was about one-half that of N robustus but the ambient temperature and the thoracic temperature at which N. triops operates is considerably lower than is characteristic of N. robustus. N. robustus in Massachusetts rarely sings if the ambient temperature is less than about 18 ° C while N. triops in California sings in early evening temperatures which are almost always well below 18 ° C.

The wing-stroke frequency during flight by N. triops averaged 22·9 HZ (S.D. =0·9 Hz, N = 7, ambient temperature = 25 ° C). The wing-stroke frequency during flight by N. robustus, determined in a similar way, is about 20 Hz (Ready, 1983).

Isometric twitch contractions

Stimulating either a mesothoracic or a metathoracic first tergocoxal muscle of N. robustus or of N. triops with shocks of gradually increasing intensity initiated muscle twitches in three discrete tension increments, indicating that the tergocoxal muscle was innervated by three excitatory axons which each evoke significant twitch tension (Fig. 2). The time course of each of the three tension increments was similar, showing that the three motor units of a muscle are temporally homogeneous.

The contractile properties of equivalent muscles in N. robustus and N. triops were quite similar (Table 2). The twitch time course in mesothoracic and metathoracic muscles of the two species was like that reported earlier for dorsal longitudinal flight muscles of N. robustus (Josephson & Stokes, 1982) and a bit faster than that found for first tergocoxal muscles of the tettigoniid Euconocephalus nasutus (Josephson, 1973). In all these examples the twitch rise rime and relaxation time was about half as long in mesothoracic as in metathoracic wing muscles. In the first tergocoxal muscles of N. triops, N. robustus and E. nasutus the twitch tension of the metathoracic muscle was considerably greater than of the mesothoracic homologue as was also the twitch to tetanic tension ratio. The relaxation time changed less and the twitch tension changed more with increasing temperature in N. robustus than in N. triops (Table 2). why this might be is not clear. The apparent difference in temperature sensitivity may be at least partially due to differences in experimental protocol with the two species The data on twitch characteristics come from the same set of experiments used to obtain force-velocity curves (see below). In N. robustus twitches were obtained at three, ascending temperature steps with no intervening tetanic stimulation while in N. triops periods of tetanic stimulation were interposed between the twitch measurements. Further, in N. triops deterioration of the preparation was systematically monitored and preparations with declining performance were discarded; this was not done with N. robustus.

Table 2.

Isometric twitch characteristics of first tergocoxal muscles, mean ± S.E.

Isometric twitch characteristics of first tergocoxal muscles, mean ± S.E.
Isometric twitch characteristics of first tergocoxal muscles, mean ± S.E.

Force-velocity relations

The relationship between muscle load and shortening velocity was determined with afterloaded, isotonic, tetanic contractions; i.e. with tetanic contractions in which the muscle developed tension isometrically against a fixed load until the force developed equalled that of the load, after which the muscle shortened isotonically against the load (Fig. 3). The stimulating frequency was 400 Hz for metathoracic muscles, and 500 Hz for mesothoracic muscles. The experimental protocols were different with the two species. With N. robustus a number of twitches were evoked at 25, 30 and 35 °C following which sets of isotonic, tetanic contractions for force-velocity data were given at 35, 30 and finally 25 °C. A different approach was used with N. triops so that the condition of the preparation could be monitored. With N. triops sets of isotonic tetanic contractions were obtained successively at 25, 30, 25, 35 and 25 °C. Single shocks for evaluation of twitch properties were given at the first exposure to each temperature. The continuing condition of the preparation was assessed from the repeated measurements made at 25 °C, and preparations were discarded whose maximum isometric tension (Po) during the second or third set at 25 °C fell below 80 % of that during the first set. Final muscle sample sizes of six meeting this criterion were obtained with a starting group of 10 metathoracic preparations and 12 mesothoracic ones.

Fig. 3.

Shortening (upper set of traces) and muscle tension (lower traces) during after-loaded, tetanic contractions, mesothoracic muscle, 30 °C. The dots are stimulus markers. The muscle contracted isometrically until its tension reached the pre-set load, after which it shortened under constant load. The upper shortening trace corresponds to the lowest force trace and the lowest shortening trace (the straight line) corresponds to the upper force trace which is an isometric contraction. Shortening velocity was measured as the initial slope of the shortening curves. The small oscillations in some of the force traces are a consequence of under-damping of the ergometer. A force-velocity curve for this preparation is shown in Fig. 4.

Fig. 3.

Shortening (upper set of traces) and muscle tension (lower traces) during after-loaded, tetanic contractions, mesothoracic muscle, 30 °C. The dots are stimulus markers. The muscle contracted isometrically until its tension reached the pre-set load, after which it shortened under constant load. The upper shortening trace corresponds to the lowest force trace and the lowest shortening trace (the straight line) corresponds to the upper force trace which is an isometric contraction. Shortening velocity was measured as the initial slope of the shortening curves. The small oscillations in some of the force traces are a consequence of under-damping of the ergometer. A force-velocity curve for this preparation is shown in Fig. 4.

A number of mathematical models have been proposed as being appropriate representations of the force velocity relations of contracting muscle (e.g. Pringle, 1960; Close & Luff, 1974). The data from the tettigoniid wing muscle was analysed using Hill’s (1938) hyperbolic equation, not because it is necessarily the best model of the basic contractile process but because it is the model most often used and its selection facilitates comparison to the performance of other muscles. Further, the Hill equation does give an objective way to get seemingly reasonable values for Vmax which was the principal goal of this study.

The curve-fitting procedure used was that of Edman, Mulieri & Scubon-Mulieri (1976). The basic equation to be fitted was
formula
where V = shortening velocity (lengthss−1), P = force on muscle (Ncm−2), Po = maximum isometric tension (N cm−2) and a and b are constants. This equation was solved for V and linearized as :
formula
where C = b (P0 + a) and Z = (P + a)−1. A computer programme divided a supplied search range for a into 10 equal steps. Each of these values was used to create a set of values of Z from the supplied experimental data (V, P), and linear regression analysis was used to determine the values of C and of b given the best least squares fit for the selected value of a. The value of a giving the smallest sum of squares error between predicted and measured values of V was used as the centre of a new search range for a which was one-tenth the size of the original range. This procedure was repeated until the desired resolution in the estimate of a was reached.

A hyperbola can be fitted to the force-velocity values over the full range of forces against which a muscle can shorten but, as has been noted earlier by Edman et al. (1976) for frog muscle fibres, there are systematic errors between predicted and experimental values for shortening velocity throughout the force range. These systematic errors include a tendency to underestimate shortening velocities at the very lowest forces and to overestimate them at the highest forces. Shortening velocities at forces approaching Po clearly do not lie on the hyperbolic curve defined by shortening velocities in the lower portion of the force range (Fig. 4). The fit of a hyperbolic curve to the experimental data is improved (i.e. the mean squared error is reduced) in the tettigoniid data, as in that from frog muscle fibres (Edman et al. 1976), if values from the upper end of the force range are excluded. Consequently, in fitting the tettigoniid data to a hyperbola, and in using the hyperbola to predict Vmax data for forces greater than 0·78 Po were excluded. The cut-off limit, 0·78 Po, was chosen because it is proximately the force at which there is often a change in the curvature of the line defined by the data points, and because this is the truncation level giving a good hyperbolic fit to data for frog muscle fibres (Edman et al. 1976).

Fig. 4.

Shortening velocity as a function of load in first tergocoxal muscles of Neoconocephalus trops, 30°C. Hyperbolic curves are fitted to data points with force values less than 0·78 Po (truncation levels marked by arrows). The preparations shown are the ‘median’ muscles. Each of these muscles had the fourth highest maximum shortening velocity out of the six muscles of that type.

Fig. 4.

Shortening velocity as a function of load in first tergocoxal muscles of Neoconocephalus trops, 30°C. Hyperbolic curves are fitted to data points with force values less than 0·78 Po (truncation levels marked by arrows). The preparations shown are the ‘median’ muscles. Each of these muscles had the fourth highest maximum shortening velocity out of the six muscles of that type.

The twitch rise time was shorter in mesothoracic than in metathoracic wing muscles by a factor of about two in both N robustus and N. triops (Table 2). Nevertheless, the maximum shortening velocities of mesothoracic and metathoracic muscles were similar (Table 3). If anything, the metathoracic muscles, which had the slower rise time, had the faster maximum shortening velocity. The differences between Vmax in mesothoracic and metathoracic muscles listed in Table 3 were statistically significant in only two cases (N. triops, 30 °C and the third set at 25 °C, P< 0·05) but the mean Vmax for metathoracic muscles was consistently greater than for mesothoracic ones. There was a striking difference in the maximum isometric tension (Po) of mesothoracic and metathoracic muscles. At each temperature the average values of Po in mesothoracic muscles were half or less of those from metathoracic homologues. There was a consistent tendency for the values of Vmax and Po to be greater in N. triops than in equivalent muscles of N. robustus (Table 3). This may be a consequence of the selection procedure used with N. triops. Eliminating preparations in which responses deteriorated during the course of the investigation, as was done with N. triops, may have selectively pruned preparations which were slower and weaker and thus raised average values. Because deteriorating preparations were eliminated, the data from N. triops is probably more representative of conditions in intact insects than is that from N. robustus.

Table 3.

Maximum shortening velocity (Vmax, muscle lengths per second) and maximum tetanic tension (Po, Ncm2) for wing muscles, mean (S.E)

Maximum shortening velocity (Vmax, muscle lengths per second) and maximum tetanic tension (Po, Ncm−2) for wing muscles, mean (S.E)
Maximum shortening velocity (Vmax, muscle lengths per second) and maximum tetanic tension (Po, Ncm−2) for wing muscles, mean (S.E)

Sarcomere length in tergocoxal muscles from N. robustus was determined from material fixed and embedded as for electron microscopy (Elder, 1971). Semi-thin, longitudinal sections were stained and examined with light microscopy. The total length of 20 adjacent sarcomeres was measured with an ocular micrometer; five replicate measurements from different fields were made for each muscle. The average sarcomere length in mesothoracic muscles was 3·3μm (S.E. = 0·3μm, N=3 muscles); and 3·1μm (S.E. = 0·3μm, N = 3) in metathoracic muscles. From these values, the maximum shortening velocities of muscles from N. robustus were 30– 35 μm s−1 per sarcomere at 35 °C. Assuming sarcomere lengths are similar in N. triops, the maximum shortening velocities of mesothoracic and metathoracic muscles in this species were 40 and 50 μm s−1 per sarcomere at 35 °C.

Determination of Vmax by quick release

The maximum shortening velocity of wing muscles from N. triops was also determined from the time course of tension redevelopment following quick release of the muscle. The measurements were done with some of the preparations used to obtain force-velocity data, usually after completion of the force-velocity measurements. Only those preparations which gave stable responses, as evidenced by maintenance of the maximum isometric tension during the successive testing periods at 25 C, were analysed in detail.

The technique used was a variation of that of Edman (1979) which, in turn, is a modification of methods used by Millman (1963) and by Hill (1970). In Edman’s approach a stimulated muscle is suddenly released by a distance long enough so that tension drops to zero. The released muscle then shortens against zero load and the time from release to the first appearance of re-developed tension is measured. This is repeated for a series of release distances. The slope of the line relating release distance (ordinate) and time to tension re-development (abcissa) is the shortening velocity under zero load; the ordinal intercept is the distance by which series compliance elements were stretched at the time of release.

In the tettigoniid muscles at normal operating temperatures, the onset of tension re-development following a quick-release was quite rapid, taking only a few ms for release distances up to 10% of the initial muscle length (Figs 5, 6). There was some bounce in the ergometer lever immediately following release which, at the brief time intervals of interest, obscured measurement of the onset of tension re-development. Therefore the time to tension re-development was measured not to the first detectable tension but rather to a selected criterion tension level which was usually about 0 ·2 Po. The time from the onset of release to the attainment of the criterion tension included three components: (1) the time from the onset of release until tension reached zero ; (2) shortening time under zero load until the slack was taken up and tension re-development began; and (3) contraction time from the onset of tension to the achievement of the criterion tension. Of these, with the ergometer and muscles used, only the shortening time under zero load was a significant function of release distance (Fig. 5). At each of the new muscle lengths following release, the redevelopment of tension followed an approximately parallel time course ; therefore the time from the onset of tension to attainment of the tension criterion should be nearly constant. Consequently the slope of the line relating shortening distance to the time taken for tension re-development (Fig. 6) was the shortening velocity under zero load even when the time was measured to a finite tension rather than to the onset of measurable tension. The intercept, however, was a function of both muscle compliance and the tension criterion level selected, and not of compliance alone.

Fig. 5.

Position (upper traces) and muscle tension (lower traces) during quick release from an isometric contraction, mesothoracic muscle of Neoconocephalus triops, 30 °C. The lower dots are stimulus markers. Muscle shortening is shown as an upward deflection of the position trace. The arrow marks the criterion tension level used in measuring the time taken for tension re-development after release. This muscle is the same mesothoracic muscle as that of Fig. 4.

Fig. 5.

Position (upper traces) and muscle tension (lower traces) during quick release from an isometric contraction, mesothoracic muscle of Neoconocephalus triops, 30 °C. The lower dots are stimulus markers. Muscle shortening is shown as an upward deflection of the position trace. The arrow marks the criterion tension level used in measuring the time taken for tension re-development after release. This muscle is the same mesothoracic muscle as that of Fig. 4.

Fig. 6.

The time taken to re-develop tension following quick release, mesothoracic muscle, 30°C. The data points are from the experiment shown in part in Fig. 4. The slope of the line (= unloaded shortening velocity) is 16·2 muscle lengths per second.

Fig. 6.

The time taken to re-develop tension following quick release, mesothoracic muscle, 30°C. The data points are from the experiment shown in part in Fig. 4. The slope of the line (= unloaded shortening velocity) is 16·2 muscle lengths per second.

The maximum shortening velocity determined from quick-release was similar in mesothoracic and metathoracic muscles (Table 4), confirming the conclusion derived from force-velocity curves. The values for maximum shortening velocity with the quick-release method were consistently greater than those obtained from the same muscles by extrapolation of force-velocity curves to the velocity axis. For the 21 determinations represented in Table 4 (seven animals, three testing temperatures per animal) the ratio of Vmax from the quick-release method to that from force-velocity curves averaged 1·32 (S.D. = 0·20). In frog muscle fibres the quickrelease method has been found to give Vmaxvalues which were about 7 % greater than those from force-velocity curves (Edman, 1979). Why the two methods should give different values, and why the difference is so much greater in tettigoniid muscles than in those from a frog, is not obvious.

Table 4.

Vmax(muscle lengths per second) in Neoconocephalus triops determined from quick-release measurements, mean (S.E.)

Vmax(muscle lengths per second) in Neoconocephalus triops determined from quick-release measurements, mean (S.E.)
Vmax(muscle lengths per second) in Neoconocephalus triops determined from quick-release measurements, mean (S.E.)

The ability of the muscle to develop tension was consistently reduced following quick-release, and the reduction was greater for greater release distances (Fig. 5). The reason for the depression of tension following release was not investigated. It was probably due at least partially to actual shortening so that the muscle was operating on a different part of its length-tension curve, and there may also have been some deactivation upon shortening as has been reported for frog muscle (Edman, 1981).

Shortening velocity of ‘fast’ insect muscles

On the basis of twitch time course, the metathoracic, tergocoxal muscles of N. triops and of N. robustus are quite fast. Their twitch rise times of 6–7 ms at 35 °C are comparable to those of such fast muscles as the extensor digitorum longus (EDL) of the mouse (6·9 ms, Luff, 1981), extraocular muscles of the cat (5–7 ms at 37 °C, Bachy-Rita & Ito, 1966) or of the rabbit (6·4ms, Asmussen & Gaunitz, 1981), or hummingbird flight muscle (8 ms at 40°C, Hagiwara, Chichibu & Simpson, 1968). Twitches from mesothoracic muscles are even briefer. At 35 °C the twitch rise time (3·3-3·5ms) and twitch duration (5·5–6·5ms, onset to 50% relaxation) of the mesothoracic wing muscles are similar to those of the fastest mammalian muscles measured, the extraocular muscles of the mouse and rat (rise times 3·7 and 4·4ms; 50% relaxation times 4-0 and 4-8ms; Luff, 1981; Close & Luff, 1974). The twitch brevity of the tettigoniid mesothoracic wing muscles is exceeded among the striated muscles which have been examined only by that of the singing muscle of the cicada Psaltoda claripennis (onset to 50% relaxation 6·6 ms at 30 °C, Young & Josephson, 1983) and that of the lobster sound-producing muscle (rise time 2·5–3 ms, total relaxation time 6·5–7ms, 16–17°C, Mendelson, 1969), especially if allowance is made for the lower temperature used in studies of the lobster muscle.

Tettigoniid wing muscles do not have unusually high shortening velocities. The average values for maximum shortening velocity, determined from force-velocity curves, range from 10–16 muscle lengths per second (30–50μm s−1 per sarcomere) at 35 °C in the different muscles examined. The maximum shortening velocities of the tettigoniid muscles are somewhat less than those of rat and mouse extraocular muscles, also determined from force-velocity curves (50–60 μm s−1 per sarcomere at 35°C; Luff, 1981 ; Close & Luff, 1974), and similar to those of several mouse, rat and cat limb muscles, some of which have isometric twitches which are much longer than those of the insect muscles (30–50μm s−1 per sarcomere; Luff, 1975, 1981; Close, 1964; Kean, Lewis & McGarrick, 1974; Spector et al. 1980). The maximum shortening velocities recorded from tettigoniid muscles at 25 °C are less than or insignificantly greater than those reported for fast frog muscle fibres and fast chicken muscles at 20–21 °C (Cecchi, Colomo & Lombardi, 1978, 1981; Rall & Schottelius, 1973) even though the latter muscles have much longer twitches. Thus insect muscles which are extraordinarily ‘fast’ for twitch duration need not be unusually fast in terms of shorterning velocity. Further, comparison of mesothoracic and metathoracic wing muscles indicates that there need be no correlation between twitch time course and maximum shortening velocity in insect muscles.

Buchthal, Weis-Fogh & Rosenfalck (1957) determined force-velocity relations for an isolated locust flight muscle, the metathoracic dorsal longitudinal muscle, during isotonic twitch contractions. This is the only previous study of which I am aware of force-velocity relations for synchronous insect muscle. The maximum shortening velocity of the locust muscle was about 10mms−1 at 11 °C. Since the length of this muscle is about 7 mm (Buchthal & Weis-Fogh, 1956), the shortening velocity of the locust muscle is about 1·4 muscle lengths per second. Buchthal et al. do not give direct values for the maximum shortening velocity at higher temperatures, but they do indicate that b, the velocity constant in the Hill equation, increases from 1·5–1·8 Ls−1 at 11 °C to 6–9Ls−1 at 30°C. The maximum shortening velocity from the Hill equation is given by b (P0/a). The value of Po/a (usually expressed as the reciprocal a/Po) is not very temperature dependent (Lannergren, 1978; Cecchi et al. 1978) ; so, as an approximation, maximum shortening velocity might be taken as being proportional to b. From this assumption, the expected Vmax for the locust muscle at 30 °C would be about 5–8 Ls−1 which is slightly less than values for tettigoniid muscles at this temperature (Table 3).

Buchthal et al. (1957) report that their isolated locust muscles were difficult to keep excitable at temperatures of 20 °C and above, especially during tetanic stimulation. Weis-Fogh (1956), working also with isolated locust wing muscles, found that tetanic contraction against very light loads or isometric tetanic contraction irreversibly damaged the muscle, especially at temperatures greater than about 20 °C. In contrast, the tettigoniid wing muscle preparations of the present study were often stable for hours. In the series with N. triops the isometric tetanic tension and maximum shortening velocity were usually similar at the onset of the first set of measurements at 25 °C and at the end of the third set of measurements at 25 °C, even though the muscle had been subject to dozens of twitch contractions, of the order of 100 or more tetanic contractions at loads ranging from isometric to nearly zero, and temperatures up to 35 °C during the intervening period. The remarkable stability of the tettigoniid muscles is almost certainly a consequence of using an in vivo preparation rather than an isolated muscle as in the locust studies. With the in vivo approach the muscle’s tracheation is largely intact and the saline bathing the muscle is, for the most part, the animal’s own haemolymph.

Twitch duration and muscle strength

The force-velocity curves of mesothoracic and metathoracic wing muscles differ in shape and force intercept; plots of mesothoracic data have less curvature and a considerably lower value for Po, the maximum isometric tension, than do metathoracic counterparts. The shapes of the force-velocity curves are considered further below. Part of the difference in isometric tension between mesothoracic and metathoracic muscles is due to differences in the relative volume of myofibrils in the two muscles types. In mesothoracic first tergocoxal muscles of N. robustus, 44% of the fibre cross-sectional area is myofibril; in metathoracic muscles 57 % of the fibre area is fibril (Ready, 1983; the remaining volume in each muscle is principally composed of mitochondria, sarcoplasmic reticulum and tracheoles). Ignoring the fraction of a muscle which is extracellular space, the maximum isometric tension of N. robustus wing muscles at 35 °C is 10·9 N cm−2 myofibril for mesothoracic muscles and 24 N cm−2 myofibril for metathoracic muscles. Thus correcting for myofibril area diminishes, but does not eliminate, the differences in tetanic tension between mesothoracic and metathoracic muscles; mesothoracic myofibrils are apparently much weaker than their metathoracic counterparts.

The area-specific tension of the metathoracic wing muscles is similar to that reported for most striated muscles (range = 15–30 N cm−2, e.g. Close, 1972); the tension of the mesothoracic muscle is seemingly quite low. A low capacity for tension generation may be a general feature of muscles with extraordinarily brief twitches. The maximum isometric tension of mammalian extraocular muscles is considerably less than that of limb muscles (about 10 N cm−2 in rat and mouse inferior rectus; Close & Luff, 1974; Luff, 1981 ; 6·4 N cm−2 in rabbit inferior oblique, Asmussen & Gaunitz, 1981). The maximum isometric tension of the extraordinarily fast, lobster sound producing muscle is only 0·25 N cm−2 (Mendelson, 1969); since myofibrils make up about one-fourth of the volume of the muscle (Rosenbluth, 1969) this force is equivalent to 1 N cm−2 myofibril. Why there should be an inverse relation between twitch rapidity and maximum tension per unit area of myofibril in very fast muscles is unclear.

Curvature of the force-velocity relation

The force-velocity plots for tettigoniid wing muscles are less curved than are the force-velocity curves which have been obtained from other striated muscles (e.g. Fig. 7A). The curvature of a force-velocity plot is typically measured by the ratio a/Po (a = the force constant in the Hill equation, Po the maximum tetanic tension) ; the larger the value of this ratio, the closer the plot approximates a straight line. For plots with little curvature, as in those from tettigoniid wing muscles, a small change in apparent curvature leads to a large change in the value of a/P0. Since a/Po is probably not a normally distributed variable, it seemed inappropriate to use the average value of the ratio determined from a number of preparations as a measure of the curvature of the force-velocity relation for a particular muscle type. Instead, the data from a preparation were normalized by dividing velocity and force values by Vmax and Po for that preparation and temperature. The normalized data from all preparations of a muscle type at a given temperature were merged and fitted with a single hyperbola. The determined values of a/P0 at 35 °C were 1·75 and 1·02 for mesothoracic and metathoraic muscles of N. robustus ; 2·06 and 0·90 for mesothoracic and metathoracic muscles of N. triops.

Fig. 7.
(A) Comparison of force-velocity relations for tettigoniid, frog and tortoise muscles. The tettigoniid curves were obtained by normalizing all data points.collected at 30 ° C and fitting a hyperbola to all values. The data were normalized by dividing each force and velocity value by Po Vmax and determined for that animal and temperature. The mesothoracic curve is fitted to 143 points, the metathoracic curve to 163 points. The ratio a/Po was 0·73 for the metathoracic muscle and 2·60 for the mesothoracic muscle. The frog and tortoise curves are from values provided by Hill (1938) and Woledge (1968). (B) The effect of adding a viscosity term to the Hill equation for force-velocity relations. The equation used to generate the curves was:
formula
The product KV is the force due to internal viscosity. The magnitude of the viscous force was varied by changing K. The values of a/Po and b are the same as those of the tortoise muscle in (A).
Fig. 7.
(A) Comparison of force-velocity relations for tettigoniid, frog and tortoise muscles. The tettigoniid curves were obtained by normalizing all data points.collected at 30 ° C and fitting a hyperbola to all values. The data were normalized by dividing each force and velocity value by Po Vmax and determined for that animal and temperature. The mesothoracic curve is fitted to 143 points, the metathoracic curve to 163 points. The ratio a/Po was 0·73 for the metathoracic muscle and 2·60 for the mesothoracic muscle. The frog and tortoise curves are from values provided by Hill (1938) and Woledge (1968). (B) The effect of adding a viscosity term to the Hill equation for force-velocity relations. The equation used to generate the curves was:
formula
The product KV is the force due to internal viscosity. The magnitude of the viscous force was varied by changing K. The values of a/Po and b are the same as those of the tortoise muscle in (A).

The low curvature of the force-velocity curves from tettigoniid wing muscles is an exaggeration of a tendency noted by other investigators for ‘fast’ muscles to have less curved force-velocity plots than do ‘slow’ muscles. This tendency is seen in comparing frog and tortoise muscles (Woledge, 1968) and in intraspecific comparisons of fast and slow muscles from Xenopus, chickens and rats (Lannergren, 1978; Rail & Schottelius, 1973; Wells, 1965; Close, 1972; Ranatunga, 1982). Woledge (1968) has hypothesized that with greater curvature of a muscle’s force-velocity plot, there is greater mechanical efficiency; efficiency being defined as the ratio between the work liberated and the sum of the work and heat liberated. If Woledge’s proposal is correct, tettigoniid wing muscles, with their nearly straight force-velocity relations, are rather inefficient and the fast mesothoracic muscles are even less efficient than the slower metathoracic wing muscles.

Internal viscosity is a potential contributor to the shape of a force-velocity plot. Simple viscosity would add a force against which the myofibrils shorten ; a force which would be proportional to the shortening velocity. A viscous contribution to the total force should depress shortening velocities preferentially in the higher velocity range of a force-velocity plot and in this way reduce the curvature of the plot. The effects of internal viscosity are explored in Fig. 7B, in which it is assumed that the contractile elements themselves have force-velocity relations as described by the Hill equation but that the force on the contractile element is the sum of the external force, P, and an internal viscous force which is proportional to the shortening velocity, V. The equation used to generate the curves was:
formula
The values of a/P0 (= 0·07) and of b (= 0·02 Ls− 1) used in Fig. 7B were selected as being those given by Woledge (1968) for tortoise muscle at 0 ° C. The tortoise muscle has a deeply-curved force-velocity relation (Fig. 7A) and so provides a good background for examining the effects of adding internal viscosity. As expected, increasing the value of K reduces the curvature of force-velocity plots. Since the viscous force depends on both velocity and the value of K, increasing the inherent shortening velocity, for example by increasing the velocity constant b, also results in flatter curves. Introducing a viscous component in the Hill equation does not result in a distinct change in slope at the high force end of the curve as is observed in frog muscle fibres (Edman et al. 1976) and in tettigoniid wing muscle (Fig. 4) ; this deviation from a hyperbolic force—velocity relation is not due to simple internal viscosity.

The relative flatness of force-velocity curves for muscles with high shortening velocities may be due in part to internal viscosity since the viscous component of the force is greater the greater the velocity. A difference in shortening velocity, however, cannot account for the differences in curvature of the force-velocity data from tettigoniid mesothoracic and metathoracic wing muscles since the faster metathoracic muscle has the more curved force-velocity relation (Fig. 4). If the difference in the mesothoracic and metathoracic tettigoniid muscles is due to differences in viscous forces, the mesothoracic muscle must have greater internal viscosity. Mesothoracic muscles fibres do have more abundant sarcoplasmic reticulum than do metathoracic fibres (Elder, 1971; Ready, 1983). Perhaps the sarcoplasmic reticulum acts as a viscous drag on the myofibrils which it surrounds, and the magnitude of this drag is related to the development of the reticulum.

A viscous component added to the Hill equation improves the fit to force-velocity data from frog ventricular muscle at short muscle lengths but not at long muscle lengths (Mashima, 1979). Internal viscosity seems not to be an important factor in frog skeletal muscle as judged by the low resistance to rapid stretch in unstimulated muscle (Edman & Hwang, 1977) and the independence of the maximum shortening velocity from muscle length or degree of muscle activation (Gordon, Huxley & Julian, 1966; Edman & Hwang, 1977; Edman, 1979). The constancy of shortening velocity under these conditions indicates that the velocity under zero external load is independent of the number of active cross bridges between thick and thin filaments. This in turn suggests that there is not a significant internal viscous load which would be apportioned among the cross bridges in relation to their number and whose effect on cross bridge kinetics, therefore, should vary with the number of active bridges. Frog muscle has a moderately curved force-velocity relation and on this basis would be expected to have low internal viscosity (Fig. 7A). It would be of interest to know if the maximum shortening velocity of tettigoniid muscles, like that in frog muscles, is independent of muscle length or degree of muscle activation. If so, the hypothesis that the lack of curvature in force-velocity curves of tettigoniid muscles is a consequence of internal viscosity should be discarded.

This work was supported by PHS Grant NS 14564 and NSF Grant PCM-8201559. I want to thank Dr A. Kammer for helpful suggestions on the manuscript.

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