Force-velocity Data Research Articles

2,3-Butanedione monoxime increases speed of relaxation in single muscle fibres of frog.

The effects of 2,3-butanedione monoxime (BDM) on intracellular Ca2+ transient and cross-bridge function were studied in frog single fibres from the anterior tibialis muscle of Rana temporaria (sarcomere length, 2.2 microm; temperature, 2-4 degrees C). The fluorescent dye fluo-3 was used to monitor the intracellular free calcium concentration ([Ca2+]i) during isometric contractions. BDM (1-5 mM) reduced the amplitude of the Ca2+ transient during twitches, but this effect was too small to explain the marked inhibition of BDM on twitch force. [Ca2+]i reached at the end of 1-s tetanic stimulation was not significantly affected by BDM (1.0 and 1.8 mM) while the maximum tetanic tension was substantially reduced. The rate of relaxation during isometric tetanus was increased by BDM whereas the rate of decay of the Ca2+ transient was reduced in the presence of BDM. The results strongly suggest that BDM, under the experimental conditions used, mainly affects the contractile machinery resulting in altered performance of the cross-bridges. These effects of BDM were evaluated in terms of the cross-bridge model of Huxley (1957) which was fitted to the experimental force-velocity data in the presence and absence of BDM.

Crossbridge kinetics in single frog muscle fibres in presence of ethylene glycol.

Single fibres isolated from frog muscle were tetanically stimulated at 14 degrees C to produce isometric tetani at a sarcomere length of about 2.16 microm, using a striation follower device to measure the sarcomere length of a selected segment of fibre. Force-velocity data were obtained by applying ramp releases at pre-set velocity at the tetanus plateau. Sarcomere stiffness was measured at isometric plateau and during isotonic shortening by using sinusoidal length changes at 2 kHz frequency and about 1 nm per half sarcomere (hs) peak to peak amplitude. A correction method was used to compensate for the force truncation due to the quick recovery. After data collection, the bathing solution was substituted with Ringer plus ethylene glycol (EG) at 2 M (11.2% v/v). When the fibre was fully equilibrated with the new solution, the measurements were repeated. Ethylene glycol reduced the speed of the tetanus rise and tetanus relaxation without altering the isometric tension, and reduced the maximum shortening velocity by about 20%. During isotonic contraction tension and stiffness at each given shortening velocity were reduced by about the same amount, so that the stiffness/tension ratio remained almost unaltered. Force-velocity and stiffness data in both standard and EG Ringer were analysed in terms of a two state model (Huxley, 1957). The analysis showed that our results can be accounted for by assuming that EG at 2 M concentration reduces all the rate constants for crossbridges interaction by about the same amount.

A weakly coupled version of the Huxley crossbridge model can simulate energetics of amphibian and mammalian skeletal muscle.

This study aimed to establish whether quantitatively accurate predictions of the rate of crossbridge-dependent energy output from shortening muscle could be made on the basis of a 2-state model of crossbridge kinetics incorporating weak coupling between mechanical cycles and ATP hydrolysis. The model was based on Huxley's (1957) model but included rapid detachment, without ATP hydrolysis, of crossbridges when their strain energy increased sufficiently that crossbridge free energy exceeded that of the unbound state (Cooke et al., 1994). An expression was derived relating force to steady-state velocity in terms of the model's rate constants. The values of the rate constants that both provided the best fit through force-velocity data and correctly predicted crossbridge-dependent rate of energy output during an isometric contraction were found and used to predict the variation in rate of energy liberation with shortening velocity. The model predictions closely matched the estimated crossbridge energetics of frog sartorius muscle, including the decline in rate of enthalpy output at high shortening velocities. Data from fast- and slow-twitch muscles of the mouse were also simulated. The velocity-dependence of rate of energy liberation from fast-twitch EDL muscle was well described by the model. The model overestimated crossbridge-dependent energy output from slow-twitch soleus at low shortening velocities but provided accurate predictions of energy output at high velocities. In terms of this model, the distinctive energetics of fast and slow muscles cannot be explained exclusively by differences in cross-bridge detachment rate; differences in the relative rates of crossbridge attachment must also be considered to explain the different relations between energy output and shortening velocity.

Temperature dependence of mechanical power output in mammalian (rat) skeletal muscle.

Force-velocity data at different temperatures (range, 10-35 degrees C) from intact fibre bundles are analysed to determine the temperature dependence of the maximal mechanical power output of fast and slow rat muscles. At 35 degrees C, the maximal mechanical power was approximately 250 kW m(-3) (=250 microW mm(-3)) in fast (probably an underestimate) and approximately 100 kW m(-3) in slow muscle. Within the more physiological temperature range (25-35 degrees C), the temperature coefficient (Q10) of maximum power was 2-2.5. In both muscles, the maximal power at 10 degrees C was only about 3-5% of that at 35 degrees C, the decrease being particularly pronounced at temperatures below 20 degrees C (Q10 of 5-7).

A re-examination of calcium activation in the Huxley cross-bridge model.

This paper investigates mathematical relations between models of calcium activation kinetics and Huxley-type models of cross-bridge dynamics in muscle. It is found that different calcium-activation schemes lead to the same form of generalized Huxley rate equation with calcium activation. [formula: see text] if it is assumed that calcium-troponin interaction rates are fast compared to the rates of transition associated with force-generating cross-bridge states. Calcium affects cross-bridge dynamics by modifying the bonding rate f, but does not affect the number of interacting cross bridges a or the unbonding rate g; this occurs through the appearance in the equation of an activation factor, r, which is a pure function of sarcoplasmic free calcium concentration. In particular, it is shown that both the "tight-coupling" and "loose-coupling" calcium-activation schemes introduced by Zahalak and Ma [1] lead to the same rate equation with the same activation factor; the difference between them appears in the calcium mass-balance equation. While both of these activation models can be made to fit simple twitch and force-velocity data equally well, experimentally observed load-dependent shifts in the free calcium concentration are compatible with the right-coupling scheme, but not with loose coupling.

Nitric oxide effects on shortening velocity and power production in the rat diaphragm.

The present experiments tested nitric oxide (NO) effects on shortening velocity and power production in maximally activated rat diaphragm. Diaphragm fiber bundles (n = 10/group) were incubated at 37 degrees C in Krebs-Ringer solution containing no added drug (control), the NO synthase inhibitor N omega-nitro-L-arginine (L-NNA; 10 mM), the NO donor sodium nitroprusside (SNP; 1 mM), or a combination (L-NNA + SNP) Loaded shortening velocity was measured via the load-clamp technique over a range of afterloads. Force-velocity data were fitted to the Hill equation to determine maximum velocity of shortening (Vmax). Unloaded shortening velocity was measured in control and L-NNA-treated bundles (n = 12/group) by using the slack test. Maximal isometric force and unloaded shortening velocity were not altered by L-NNA. In contrast, L-NNA decreased maximum velocity of shortening (P < 0.05), loaded shortening velocity (P < 0.0001), and power production (P < 0.0001). All L-NNA effects were prevented by coincubating fiber bundles with L-NNA + SNP. SNP alone had no effect on any variable. These data indicate that endogenous NO is essential for optimal myofilament function during active shortening.

Rectangular hyperbola fitted to muscle force-velocity data using three-dimensional regression analysis.

A simple method is described for fitting a rectangular hyperbola to force-velocity data derived from active muscle. The approach is based on three-dimensional regression analysis of the variables force, velocity and (force x velocity). The usage of the method is illustrated by practical applications. A pocket calculator is sufficient for the mathematical treatment.

The high-force region of the force-velocity relation in frog skinned muscle fibres.

The force-velocity relation has been studied during calcium-induced contracture of chemically skinned fibres from the semitendinosus muscle of Rana temporaria with special interest focused on the high-load region. The force-velocity curve was hyperbolic at low and intermediate loads but departed below the hyperbola as the load exceeded about 80% of the isometric force (P0). The force intercept (P*0) of the hyperbola derived from force-velocity data truncated at 0.78 P0 was higher than P0 (P*0/P0 = 1.14 +/- 0.04). At submaximum Ca2+ concentration, where the isometric force of the fibre was 65-75% of the maximum value, the force-velocity data still departed below the hyperbola at high loads (P*0/P0 = 1.09 +/- 0.04). The departure of the force-velocity data from the hyperbola at high force was also found at high ionic strength (250 mM), but not at low ionic strength (150 mM) (P*0/P0 = 1.09 +/- 0.03 and 0.98 +/- 0.03, respectively). The force-velocity relations derived under different experimental conditions could be fitted well by a modified version of Hill's (1938) hyperbolic equation (Edman 1988) using similar numerical values of k1 and k2 in the latter equation. The results indicate that the force-velocity relation in skinned muscle fibres is biphasic, and that the two curvatures, as in intact muscle fibres, are closely related to one another. Furthermore the evidence supports the hypothesis that the altered shape of the force-velocity relation at high loads is not related to the force level per se but rather to the speed of shortening of the contractile system (Edman 1992).

Effects of 2,3-butanedione monoxime on the crossbridge kinetics in frog single muscle fibres.

The effects of 2,3-butanedione monoxime (BDM) on contraction characteristics were studied at 5 degrees C in single intact fibres isolated from the tibialis anterior muscle of the frog. The force-velocity relation was determined using the controlled-velocity method in either whole fibres or short fibre segments in which sarcomere shortening was measured by a laser light diffraction method. It is shown that 3 mM BDM decreases the speed of rise and the amount of tetanus tension, reduces the maximum velocity of shortening and increases the curvature of the force-velocity relation, as well as the value for the stiffness to tension ratio. BDM also slowed down the redevelopment of tetanus tension after a period of unloaded shortening both in fixed-end and in length-clamp conditions. In normal and in BDM-treated fibres length-clamping increased the speed of the initial rise of tetanus tension but not that of the recovery after shortening. The observed force-velocity data points were fitted by the Huxley (1957) equation. It was found that BDM produces a conspicuous decrease of the rate constant for crossbridge attachment. This effect, and also a reduction of the force per crossbridge, are responsible for the depression of the contractile characteristics produced by BDM.

Response of slow and fast muscle to hypothyroidism: maximal shortening velocity and myosin isoforms

This study examined both the shortening velocity and myosin isoform distribution of slow- (soleus) and fast-twitch (plantaris) skeletal muscles under hypothyroid conditions. Adult female Sprague-Dawley rats were randomly assigned to one of two groups: control (n = 7) or hypothyroid (n = 7). In both muscles, the relative contents of native slow myosin (SM) and type I myosin heavy chain (MHC) increased in response to the hypothyroid treatment. The effects were such that the hypothyroid soleus muscle expressed only the native SM and type I MHC isoforms while repressing native intermediate myosin and type IIA MHC. In the plantaris, the relative content of native SM and type I MHC isoforms increased from 5 to 13% and from 4 to 10% of the total myosin pool, respectively. Maximal shortening velocity of the soleus and plantaris as measured by the slack test decreased by 32 and 19%, respectively, in response to hypothyroidism. In contrast, maximal shortening velocity as estimated by force-velocity data decreased only in the soleus (-19%). No significant change was observed for the plantaris.

Influence of hyperthyroidism on maximal shortening velocity and myosin isoform distribution in skeletal muscles

The objectives of this study were 1) to examine the effects of hyperthyroidism on the myosin isoform distribution in slow and fast skeletal muscle, 2) to explore how these effects were manifested with respect to the force-velocity relationship and maximal shortening velocity, and 3) to contrast two different techniques of measuring maximal shortening velocity under normal and hyperthyroid conditions. Adult female Sprague-Dawley rats were randomly assigned to one of two groups: control (n = 8) or hyperthyroid (n = 8). Hyperthyroidism was induced by injections of 3,3',5-triiodo-L-thyronine every other day for 20 wk. We found that hyperthyroidism produced a significant shift in the myosin isoform distribution of the soleus but not the plantaris. The relative amount of the slow myosin isoform was reduced from a control value of 93 to 69% in the hyperthyroid condition. In contrast, both the intermediate and fast myosin-3 isoform pools were substantially increased (P less than 0.001) by approximately fourfold. Hyperthyroidism produced an increase in the maximal shortening velocity of the soleus as measured either by the slack test (+57%; P less than 0.001) or by extrapolation of force-velocity data (+33%; P less than 0.001). The hyperthyroid condition did not, however, affect the mechanical properties of the plantaris.

Force-Velocity Relationship of Human Elbow Flexors in Voluntary Isotonic Contraction under Heavy Loads

The force-velocity relationships of the human elbow flexors as one muscle in maximal voluntary contraction were determined using isotonic lever systems for seven men (19-38 yrs). The external loads used for the contraction weighed 0%, 20%, 40% 60%, 80% and 90% of maximum voluntary isometric force (Fo). The force and velocity were determined at an elbow angle of 90 degrees. The effect of the inertia of the forearm on the force was corrected using the angular acceleration of the forearm during an elbow flexion. The effect of muscular fatigue on the velocity during an elbow flexion was minimized by adjusting the initial elbow angle at the onset of the elbow flexion to the size of the load and reducing the time duration of the elbow flexion with a heavy load. Hill equation fitted fairly well to the force-velocity data observed in the experiments up to 90% Fo. The maximum isometric force predicted using Hill equation was larger by 6% (mean) than that observed in the experiments.

Force and velocity of sarcomere shortening in trabeculae from rat heart. Effects of temperature.

The effect of temperature on the force-sarcomere velocity relation (20 degrees, 25 degrees, and 30 degrees C) and maximum velocity of sarcomere shortening (Vo; range 15 degrees-35 degrees C) was studied in trabeculae from rat heart. Sarcomere length and Vo were measured by laser diffraction techniques. Sarcomere length and sarcomere velocity, determined from each of the first-order diffraction lines, differed by less than 4%. Slack sarcomere length in the trabeculae appeared to be 1.9 microns. Isovelocity release techniques were used to obtain sarcomere velocity and Vo directly. Sarcomere velocity was measured at SL = 1.9-2.0 microns for elimination of contributions of parallel elastic force and restoring force to the external load of the sarcomeres. Peak twitch force development (Fo) was maximal (Fo-max) at 25 degrees C at [Ca2+]o = 1.5 mM. Lowering of the temperature below 25 degrees C led to development of spontaneous sarcomere activity and depression of Fo; both responses could be prevented by the addition of 0.5 mM procaine. Increase of temperature above 25 degrees C reduced twitch duration and Fo. Hill's rectangular hyperbola fitted the force-velocity data if the load during shortening was less than 70% of Fo. Vo appeared to be independent of the level of activation at all temperatures when Fo was maintained above 90% of Fo-max, either by an increase of [Ca2+]o (to 3.0 mM) or by paired pulse stimulation. Vo increased with increasing temperature; the parameter a, calculated from force-velocity relations measured at 20 degrees, 25 degrees, and 30 degrees C, decreased with increasing temperature. The Arrhenius plot of Vo was studied in detail over a wider temperature range (15 degrees-35 degrees C) and in smaller temperature increments. The relation was linear between 18 degrees and 33 degrees C; the observed Q10, defined as the ratio of Vo measured at temperature (T) over Vo at T-10 degrees C, was 4.6 A Q10 of 4.6 for Vo is consistent with the reported temperature dependence of rat cardiac actin-activated myosin ATPase, which suggests that the same reaction step may limit the activity of the enzyme in vitro and during shortening of the cardiac sarcomeres at zero external load.

Cross-bridge cycling theories cannot explain high-speed lengthening behavior in frog muscle

The Huxley 1957 model of cross-bridge cycling accounts for the shortening force-velocity curve of striated muscle with great precision. For forced lengthening, however, the model diverges from experimental results. This paper examines whether it is possible to bring the model into better agreement with experiments, and if so what must be assumed about the mechanical capabilities of cross-bridges. Of particular interest is how introduction of a maximum allowable cross-bridge strain, as has been suggested by some experiments, affects the predictions of the model. Because some differences in the models are apparent only at high stretch velocities, we acquired new force-velocity data to permit a comparison with experiment. Using whole, isolated frog sartorius muscles at 2 degrees C, we stretched active muscle at speeds up to and exceeding 2 Vmax. Force during stretch was always greater than the peak isometric level, even during the fastest stretches, and was approximately independent of velocity for stretches faster than 0.5 Vmax. Although certain modifications to the model brought it into closer correspondence with the experiments, the accompanying requirements on cross-bridge extensibility were unreasonable. We suggest (both in this paper and the one that follows) that sarcomere inhomogeneities, which have been implicated in such phenomena as "tension creep" and "permanent extra tension," may also play an important role in determining the basic force-velocity characteristics of muscle.

A biomechanical comparison between two shotputting techniques

The pattern of the activatory inputs that control the spontaneous in vitrocontraction of the rat uterine horn is investigated. A mathematical model is used in this study. The model gives the time course of intraluminal pressure, longitudinal force, and wall morphology, when the mechanical parameters and the activatory inputs of the two muscular layers of the wall are assigned. The mechanical parameters of the smooth muscle tissue are deduced from the mecasured force-length and the force-velocity data of the myometrial tissue. The possibility of determining uniquely, from the experimental data of pressure and force, the parameters that characterize the model input is investigated. The results of the estimation of these parameters from a set of experimental data is presented.

The mechanical properties of polyneuronally innervated, myotomal muscle fibres isolated from a teleost fish (Myoxocephalus scorpius).

Single or small bundles of fibres were isolated from the abdominal myotomes of the sculpin Myoxocephalus scorpius, a teleost with a polyneuronal pattern of fast muscle innervation. Fibres responded to a supra-threshold stimulus with an all-or-none twitch. Tetanic fusion frequency at 3 degrees C was 40-60 Hz, and the twitch tetanus ratio 0.70. Maximum isometric tension was 281 kN m-2. Similar isometric contractile properties were obtained from the focally innervated fast muscle fibres of another teleost, the eel, Anguilla anguilla. The response of sculpin fibres to stretch during tetanus was similar to that reported for frog twitch fibres. A 5% stretch of 25-50 ms duration increased force to 1.4 Po which decayed to a steady level 5-10% above that of a control tetanus. The force-velocity relationship was also studied. Maximum contraction velocity was 4.75 Ls-1. Force-velocity data were not adequately described by a simple hyperbola. Alternative methods of curve fitting have been explored and discussed.

Motility of the Rat Uterine Horn: Analysis of Activatory Inputs

The pattern of the activatory inputs that control the spontaneous in vitrocontraction of the rat uterine horn is investigated. A mathematical model is used in this study. The model gives the time course of intraluminal pressure, longitudinal force, and wall morphology, when the mechanical parameters and the activatory inputs of the two muscular layers of the wall are assigned. The mechanical parameters of the smooth muscle tissue are deduced from the mecasured force-length and the force-velocity data of the myometrial tissue. The possibility of determining uniquely, from the experimental data of pressure and force, the parameters that characterize the model input is investigated. The results of the estimation of these parameters from a set of experimental data is presented.

The consequences of fibre heterogeneity on the force-velocity relation of skeletal muscle.

The consequences of fibre heterogeneity on the collective force-velocity properties of bundles of parallel fibres were examined in a simulation model. The model was tested by comparing the actual force-velocity curve of a bundle of three fibres, each of which had been individually characterized, with the force-velocity curve predicted by the model for the bundle based on the individual fibre properties. The predicted and measured force-velocity curves were in excellent agreement. The curvature of the force-velocity relation for a muscle, as indicated by a/P0 in Hill's (1938) hyperbolic equation, increases with increasing heterogeneity in the maximum shortening velocities (Vmax(i] of the individual fibres in the muscle. In a muscle that is heterogeneous with respect to Vmax(i), the maximum shortening velocity determined by the slack test method (V0) can be expected to represent the fastest fibre(s) in the muscle. The maximum velocity of shortening (Vm), determined by extrapolation from a hyperbola that is fitted to force-velocity data at finite loads, is substantially lower than V0. The difference in estimates of V0 and Vm is a function of: (i) the degree of heterogeneity of the muscle with respect to Vmax(i) and the curvature of the force-velocity relationship of the individual fibres, and (ii) the force range used to establish the hyperbola from which Vm is derived. The ratio of Vm to V0 can be used as an index to estimate the degree of variability in the maximum velocity of shortening among individual fibres in a muscle.

A multipurpose muscle ergometer

A fast (0.1 mm steps within 2 ms), strong (40 N continuously) and accurate (resolution 0.002 N and 1.0 μm) muscle ergometer was developed to test dynamic and static properties of mammalian muscle. Both for twitches and for tetani isometric, isokinetic and isotonic contractions can be measured accurately. Force-velocity data and time to peak-force data of four EDL muscles, as well as force-extension data of their serial tendinous structures are shown to demonstrate the machine.

The force-velocity relation of the rabbit digastric muscle

In 30 animals, the digastric was made to pull actively against a slide loaded by a servo-controlled linear motor. Force and velocity were recorded at the end of active shortening to the in-situ (jaw-closed) muscle length. Passive and active force-length relations were also determined in 17 of the rabbits. The empirical force-velocity data were fitted to a hyperbolic equation. The average speed of muscle shortening at zero load was 14.67 cm/s. Mean maximum isometric force at in-situ length ( P 0) was 1267 g, and the mean ratio a P 0 was 0.18. The average time-to-peak twitch tension was 31.8 ms under isometric conditions. In-situ muscle-belly length was about 3 per cent less than optimum length for isometric force. Maximum muscle force was positively correlated with animal size, but maximum velocity showed no relation to force or length. The estimated maximum speed of sarcomere shortening was 26 μm/s, which is slightly slower than in fast limb muscles of the cat, and may indicate the presence of both histochemical type I and II fibres. The isometric force after shortening had ceased was less than P 0, and was correlated with the velocity during shortening. This depression of isometric force may result from an alteration of the excitation-coupling system during activation. These observations suggest a role for the digastric in the rapid acceleration and deceleration of the mandible near the jaw-closed position during opening and closing.