Force-velocity Curve Research Articles

GASTROCNEMIUS AND SOLEUS MUSCLE LENGTH AND EMG RESPONSES TO CHANGES IN PEDALING CADENCE

1806 Previous research has shown that gastrocnemius (GAST) activation increases systematically with increases in pedaling cadence, whereas soleus (SOL) shows little activation change (Marsh and Martin, MSSE, 1995). The purpose of this study was to examine GAST and SOL length and velocity changes as a function of pedaling cadence to consider mechanisms underlying GAST and SOL activation differences. Nine male and one female cyclists rode at 6 randomly assigned cadences (50, 65, 80, 95, 110 rpm and a preferred cadence) at a 200 W power output while EMG of the GAST and SOL and sagittal plane video was recorded. Joint coordinate data for the knee and ankle were used with equations of Grieve et al. (Biomechanics VI-A, 1978) to compute GAST and SOL lengths and velocity. Consistent with Marsh and Martin, the GAST displayed a significant (p<.05) increase in iEMG with increasing cadence, whereas cadence had no significant effect on iEMG of the SOL. The ankle became significantly (p<.05) more plantar flexed and reflected a reduced range of motion with increasing cadence while the knee became significantly (p<.05) less extended. Contrasting the SOL and GAST length changes showed that from 50 to 110 rpm SOL decreased its ROM (max-min) by 46% whereas GAST decreased its ROM by 8%. In contrast, SOL increased its velocity range (max-min) by 42% and GAST increased by 64%. These data show that with increased cadence GAST operates over a narrower range of operating lengths but at a higher range of shortening velocity than SOL. The higher range of velocity may have resulted in the need for a relatively higher activation, as indicated by the iEMG, as the muscle was working at a different range on its force-velocity curve.

Molecular model of muscle contraction.

A quantitative stochastic model of the mechanochemical cycle of myosin, the protein that drives muscle contraction, is proposed. It is based on three premises: (i) the myosin head incorporates a lever arm, whose equilibrium position adjusts as each of the products of ATP hydrolysis dissociates from the nucleotide pocket; (ii) the chemical reaction rates are modified according to the work done in moving the arm; and (iii) the compliance of myosin's elastic element is designed to permit many molecules to work together efficiently. The model has a minimal number of parameters and provides an explanation, at the molecular level, of many of the mechanical and thermodynamic properties of steadily shortening muscle. In particular, the inflexion in the force-velocity curve at a force approaching the isometric load is reproduced. Moreover, the model indicates that when large numbers of myosin molecules act collectively, their chemical cycles can be synchronized, and that this leads to stepwise motion of the thin filament. The oscillatory transient response of muscle to abrupt changes of load is interpreted in this light.

The force-velocity properties of a crustacean muscle during lengthening

Muscle force during active lengthening was characterized for scaphognathite levator muscle L2B from the crab Carcinus maenas. The muscle was tetanically stimulated and, during the peak of the contraction, stretched at constant velocity. The total strain was approximately 4 %, the strain rates ranged from 0.03 to 1.6 muscle lengths s-1 (L s-1), and the temperature was 15 degreesC. Force increased throughout stretch. During low-velocity stretch, up to approximately 0.3 L s-1, force rose during isovelocity stretch along an approximately exponential trajectory. The asymptotic force approached during the stretch increased and the time constant of the response decreased with increasing strain rate. With stretch at 0.6 L s-1 and greater, the force increased to a distinct yield point, reached after a strain of approximately 1 %, after which force continued to increase but with a slope approximately one-quarter as great as that before yield. Because force changes continuously during constant-velocity lengthening, the adequate descriptor for the force-velocity relationship in a lengthening crab muscle is not a two-dimensional force-velocity curve, but rather a three-dimensional force-velocity-time or force-velocity-strain surface. Stimulating muscle L2B at 20 Hz or 50 Hz gives a smoothly fused tetanic contraction in which muscle activation is only partial and the plateau force reached is less than that at the optimum stimulus frequency of approximately 100 Hz. The force-velocity relationships of a partially activated muscle are not simply those of a fully activated one scaled down in proportion to the reduction in the maximum isometric force. At low stretch velocities, the asymptotic force approached is larger in proportion to the pre-stretch isometric tension, and the time constant of the force increase is greater, in partially activated than in fully activated muscles. At high stretch velocities, the force at yield relative to the pre-stretch force, and the relative values of the slopes of the force increase before and after yield, are all greater in partially activated than in fully activated muscles, while the strain at yield is smaller.

Computer simulation of flagellar movement: VII. Conventional but functionally different cross-bridge models for inner and outer arm dyneins can explain the effects of outer arm dynein removal.

Outer arm dynein removal from flagella by genetic or chemical methods causes decreased frequency and power, but little change in bending pattern. These results suggest that outer arm dynein operates within bends to increase the speed of bend propagation, but does not produce forces that alter the bending pattern established by inner arm dyneins. A flagellar model incorporating different cross-bridge models for inner and outer arm dyneins has been examined. The inner arm dynein model has a hyperbolic force-velocity curve, with a maximum average force at 0 sliding velocity of about 14 pN for each 96 nm group of inner arm dyneins. The outer arm dynein model has a very different force-velocity curve, with a maximum force at about 10-15% of V(max). The outer arm dynein model is adjusted so that the unloaded sliding velocity for a realistic mixture of inner and outer arm dyneins is twice the unloaded sliding velocity for the inner arm dynein model alone. With these cross-bridge models, a flagellar model can be obtained that reduces its sliding velocity and frequency by approximately 50% when outer arm dyneins are removed, with little change in bending pattern. The addition of outer arm dyneins, therefore, gives an approximately 4-fold increase in power output against viscous resistances, and outer arm dyneins may generate 90% or more of the power output. Cell Motil.

Force and velocity measured for single molecules of RNA polymerase.

RNA polymerase (RNAP) moves along DNA while carrying out transcription, acting as a molecular motor. Transcriptional velocities for single molecules of Escherichia coli RNAP were measured as progressively larger forces were applied by a feedback-controlled optical trap. The shapes of RNAP force-velocity curves are distinct from those of the motor enzymes myosin or kinesin, and indicate that biochemical steps limiting transcription rates at low loads do not generate movement. Modeling the data suggests that high loads may halt RNAP by promoting a structural change which moves all or part of the enzyme backwards through a comparatively large distance, corresponding to 5 to 10 base pairs. This contrasts with previous models that assumed force acts directly upon a single-base translocation step.

Simulating the Role of Microtubules in Depolymerization-Driven Transport: A Monte Carlo Approach

In this paper we present a model that simulates the role of microtubules in depolymerization-driven transport. The model simulates a system that consists of a 13-protofilament microtubule with “five-start” helical structure and a motor protein-coated bead that moves along one of the protofilaments of the microtubule, as in in vitro experiments. The microtubule is simulated using the lateral cap model, with substantial generalizations. For the new terminal configurations in the presence of the bead, rate constants for association and dissociation events of tubulin molecules are calculated by exploring the geometric similarities between different patterns of terminal configurations and by decomposing complex patterns into simpler patterns whose corresponding rate constants are known. In comparison with a previous model, in which simplifications are made about the structure of the microtubule and in which the microtubule can only depolymerize, the detailed structure of the microtubule is taken into account in the present model. Furthermore, the microtubule can be either polymerizing or depolymerizing. Force-velocity curves are obtained for both zero and non-zero tubulin guanosine 5′-triphosphate (GTP) concentrations. By analyzing the trajectory of the bead under different parameters, the condition for “run and pause” is analyzed, and the time scale of “run” and “pause” is found to be different for different motor proteins. We also suggest experiments that can be used to examine the results predicted by the model.

Force-velocity and power-load curves in rat skinned cardiac myocytes.

1. This study utilized a skinned myocyte preparation with low end compliance to examine force-velocity and power-load curves at 12 C in myocytes from rat hearts. 2. In maximally activated myocyte preparations, shortening velocities appeared to remain constant during load clamps in which shortening took place over a sarcomere length range of approximately 2.30-2.00 micro m. These results suggest that previously reported curvilinear length traces during load clamps of multicellular preparations were due in part to extracellular viscoelastic structures that give rise to restoring forces during myocardial shortening. 3. During submaximal Ca2+ activations, the velocity of shortening at low loads slowed and the time course of shortening became curvilinear, i.e. velocity progressively slowed as shortening continued. This result implies that cross-bridge cycling kinetics are slower at low levels of activation and that an internal load arises during shortening of submaximally activated myocytes, perhaps due to slowly detaching cross-bridges. 4. Reduced levels of activator Ca2+ also reduced maximal power output and increased the relative load at which power output was optimal. For a given absolute load, the shift has the effect of maintaining power output near the optimum level despite reductions in cross-bridge number and force generating capability at lower levels of Ca2+.

Muscle contraction as a Markov process I: energetics of the process

Force generation during muscle contraction can be understood in terms of cyclical length changes in segments of actin thin filaments moving through the three-dimensional lattice of myosin thick filaments. Recent anomalies discovered in connection with analysis of myosin step sizes in in vitro motility assays and with skinned fibres can be rationalized by assuming that ATP hydrolysis on actin accompanies these length changes. The paradoxically rapid regeneration of tension in quick release experiments, as well as classical energetic relationships, such as Hill's force–velocity curve, the Fenn effect, and the unexplained enthalpy of shortening, can be given mutually self-consistent explanations with this model. When muscle is viewed as a Markov process, the vectorial process of chemomechanical transduction can be understood in terms of lattice dependent transitions, wherein the phosphate release steps of the myosin and actin ATPases depend only on occurrence of allosteric changes in neighbouring molecules. Tropomyosin has a central role in coordinating the steady progression of these cooperative transitions along actin filaments and in gearing up the system in response to higher imposed loads.

Muscle contraction as a Markov process. I: Energetics of the process.

Force generation during muscle contraction can be understood in terms of cyclical length changes in segments of actin thin filaments moving through the three-dimensional lattice of myosin thick filaments. Recent anomalies discovered in connection with analysis of myosin step sizes in in vitro motility assays and with skinned fibres can be rationalized by assuming that ATP hydrolysis on actin accompanies these length changes. The paradoxically rapid regeneration of tension in quick release experiments, as well as classical energetic relationships, such as Hill's force-velocity curve, the Fenn effect, and the unexplained enthalpy of shortening, can be given mutually self-consistent explanations with this model. When muscle is viewed as a Markov process, the vectorial process of chemomechanical transduction can be understood in terms of lattice dependent transitions, wherein the phosphate release steps of the myosin and actin ATPases depend only on occurrence of allosteric changes in neighbouring molecules. Tropomyosin has a central role in coordinating the steady progression of these cooperative transitions along actin filaments and in gearing up the system in response to higher imposed loads.

Optimal shortening velocity (V/Vmax) of skeletal muscle during cyclical contractions: length-force effects and velocity-dependent activation and deactivation.

The force-velocity relationship has frequently been used to predict the shortening velocity that muscles should use to generate maximal net power output. Such predictions ignore other well-characterized intrinsic properties of the muscle, such as the length-force relationship and the kinetics of activation and deactivation (relaxation). We examined the effects of relative shortening velocity on the maximum net power output (over the entire cycle) of mouse soleus muscle, using sawtooth strain trajectories over a range of cycle frequencies. The strain trajectory was varied such that the proportion of the cycle spent shortening was 25, 50 or 75 % of the total cycle duration. A peak isotonic power output of 167 W kg-1 was obtained at a relative shortening velocity (V/Vmax) of 0.22. Over the range of cyclical contractions studied, the optimal V/Vmax for power production ranged almost fourfold from 0.075 to 0.30, with a maximum net power output of 94 W kg-1. The net power output increased as the proportion of the cycle spent shortening increased. Under conditions where the strain amplitude was high (i.e. low cycle frequencies and strain trajectories where the proportion of time spent shortening was greater than that spent lengthening), the effects of the length-force relationship reduced the optimal V/Vmax below that predicted from the force-velocity curve. At high cycle frequencies and also for strain trajectories with brief shortening periods, higher rates of activation and deactivation with increased strain rate shifted the optimal V/Vmax above that predicted from the force-velocity relationship. Thus, the force-velocity relationship alone does not accurately predict the optimal V/Vmax for maximum power production in muscles that operate over a wide range of conditions (e.g. red muscle of fish). The change in the rates of activation and deactivation with increasing velocity of stretch and shortening, respectively, made it difficult to model force accurately on the basis of the force-velocity and length-force relationships and isometric activation and deactivation kinetics. The discrepancies between the modelled and measured forces were largest at high cycle frequencies.

Relation between muscle contraction speed and hydraulic performance in skeletal muscle ventricles.

The fatigue resistance and power-to-weight ratio of skeletal muscle that has been conditioned by electrical stimulation makes cardiac assistance from a graft of such muscle a realistic prospect. A skeletal muscle must be surgically reconfigured to act on the circulating blood, but little is known about the power losses that accompany such interventions. We investigated in acute experiments the hydraulic performance of approximately cylindrical pumps made from sheep latissimus dorsi (LD) muscles, having first characterized the performance of each muscle in situ. Force-length and force-velocity relations were measured in situ for LD that had received either 8 weeks of stimulation at 2 Hz or no chronic stimulation. Two sizes of skeletal muscle ventricle (SMV) were formed from the same muscles, and their hydraulic performance was measured. The hydraulic performance was also calculated from the linear data, models of the force-length and force-velocity curves, and a description of the stress distribution within the SMV wall. The model predicted well the isovolumetric function of the ventricles and the optimum afterload but overestimated the flow and therefore the power. In conditioned ventricles the performance was particularly poor because of the slow contractile properties of the muscles. If SMVs are to pump effectively against the arterial impedance, the pressure drop caused by flow (or the internal resistance) should be lower than that of the ventricles we constructed. Progress can be made through refinement of surgical technique and stimulation protocols that generate faster fatigue-resistant muscles.

Mechanics of single kinesin molecules measured by optical trapping nanometry

We have analyzed the mechanics of individual kinesin molecules by optical trapping nanometry. A kinesin molecule was adsorbed onto a latex bead, which was captured by an optical trap and brought into contact with an axoneme that was bound to a glass surface. The displacement of kinesin during force generation was determined by measuring the position of the beads with nanometer accuracy. As the displacement of kinesin was attenuated because of the compliance of the kinesin-to-bead and kinesin-to-microtubule linkages, the compliance was monitored during force generation and was used to correct the displacement of kinesin. Thus the velocity and the unitary steps could be obtained accurately over a wide force range. The force-velocity curves were linear from 0 to a maximum force at 10 microM and 1 mM ATP, and the maximum force was approximately 7 pN, which is larger by approximately 30% than values previously reported. Kinesin exhibited forward and occasionally backward stepwise displacements with a size of approximately 8 nm. The histograms of step dwell time show a monotonic decrease with time. Model calculations indicate that each kinesin head steps by 16-nm, whereas kinesin molecule steps by 8-nm.

Velocity-spectrum testing using a closed kinetic chain

Two force and two power variables were monitored during standardized multiple-joint, closed-chain, velocity-spectrum tests to ascertain if contiguous velocities produced discrete or redundant output. Measurements were obtained from 52 men and 50 women during squats performed at six velocities ranging from 0.51 to 2.04 m· S-l. Main effects as well as the sex-by-main-effects interaction were significant (P < 0.001) for all four variables. Therefore, post hoc tests were performed separately for men and women. Maximal squatting forces over the velocity spectrum produced force-velocity curves resembling classical single-joint ones. The highest force output occurred at the slowest test velocity as expected and signifcantly decreased (P < 0.05) for each increment in velocity for both men and women. Concurrently, maximal squatting power over the velocity spectrum produced power-velocity curves resembling classical single-joint ones. The highest power output (x = 1.26 m . S-l) occurred as part of a plateau at intermediate velocities as expected and was signifcantly less at faster and slower velocities. However, maximal power output generally materialized at faster velocities for men (x = 1.54 m·s- 1 ) than for women (x = 0.97 m·s- 1 ). It appears the six squatting velocities used in this investigation elicit discrete force data for both men and women, and results for force and power resemble what would be expected for isolated single-joint testing protocols. However, it remains unclear why an apparent gender difference exists in the velocity at which the highest peak power is produced.

The load dependence of kinesin's mechanical cycle.

Kinesin is a dimeric motor protein that transports organelles in a stepwise manner toward the plus-end of microtubules by converting the energy of ATP hydrolysis into mechanical work. External forces can influence the behavior of kinesin, and force-velocity curves have shown that the motor will slow down and eventually stall under opposing loads of approximately 5 pN. Using an in vitro motility assay in conjunction with a high-resolution optical trapping microscope, we have examined the behavior of individual kinesin molecules under two previously unexplored loading regimes: super-stall loads (>5 pN) and forward (plus-end directed) loads. Whereas some theories of kinesin function predict a reversal of directionality under high loads, we found that kinesin does not walk backwards under loads of up to 13 pN, probably because of an irreversible transition in the mechanical cycle. We also found that this cycle can be significantly accelerated by forward loads under a wide range of ATP concentrations. Finally, we noted an increase in kinesin's rate of dissociation from the microtubule with increasing load, which is consistent with a load dependent partitioning between two recently described kinetic pathways: a coordinated-head pathway (which leads to stepping) and an independent-head pathway (which is static).

Dynamic force responses of muscle involving eccentric contraction

Normal movements commonly involve dynamic conditions where active muscles operate against other muscle forces, or against forces arising from decelerating limb inertia. In these situations, some active muscles spanning the joint are lengthened. Presently, our understanding of the muscle mechanics which operate in lengthening contractions, or during large muscle length changes is incomplete. Consequently, existing mathematical descriptions of muscle action are usually constrained to small operating ranges (requiring very restricted inputs), or do not apply to conditions involving lengthening contractions. Although Hill's hyperbolic relation between muscle force and shortening velocity is well established, the force-velocity relation during lengthening is poorly defined. Experiments were performed to measure the steadystate force-velocity curve for both concentric and eccentric (lengthening) contractions in isolated muscle, and to document muscle response to complex length inputs that combine concentric and eccentric phases as might occur in natural movements. A Hill-type muscle model applicable to these motions was synthesized to determine how well a description based on steady-state parameters captures dynamic muscle behavior. The simulated model responses were compared to experimental records exhibiting complex, dynamic force responses involving both eccentric and concentric contractions, and reproduced these forces with average errors ranging from 2.3 to 13.4%.

Mechanical efficiency and fatigue of fast and slow muscles of the mouse.

1. In this study, the efficiency of energy conversion in skeletal muscles from the mouse was determined before and after a series of contractions that produced a moderate level of fatigue. 2. Initial mechanical efficiency was defined as the ratio of mechanical power output to the rate of initial enthalpy output. The rate of initial enthalpy output was the sum of the power output and rate of initial heat output. Heat output was measured using a thermopile with high temporal resolution. 3. Experiments were performed in vitro (25 degrees C) using bundles of fibres from fast-twitch extensor digitorum longus (EDL) and slow-twitch soleus muscles from mice. Muscles were fatigued using a series of thirty isometric tetani. Initial mechanical efficiency was determined before and again immediately after the fatigue protocol using a series of isovelocity contractions at shortening velocities between 0 and the maximum shortening velocity (Vmax). Efficiency was determined over the second half of the shortening at each velocity. 4. The fatigue protocol significantly reduced maximum isometric force Vmax, maximum power output and flattened the force-velocity curve. The magnitude of these effects was greater in EDL muscle than soleus muscle. In unfatigued muscle, the maximum mechanical efficiency was 0.333 for EDL muscles and 0.425 for soleus muscles. In both muscle types, the fatiguing contractions caused maximum efficiency to decrease. The magnitude of the decrease was 15% of the pre-fatigue value in EDL and 9% in soleus. 5. In a separate series of experiments, the effect of the fatigue protocol on the partitioning of energy expenditure between crossbridge and non-crossbridge sources was determined. Data from these experiments enabled the efficiency of energy conversion by the crossbridges to be estimated. It was concluded that the decrease in initial mechanical efficiency reflected a decrease in the efficiency of energy conversion by the crossbridges.

Force-velocity properties of human skeletal muscle fibres: myosin heavy chain isoform and temperature dependence.

1. A large population (n = 151) of human skinned skeletal muscle fibres has been studied. Force-velocity curves of sixty-seven fibres were obtained by load-clamp manoeuvres at 12 degrees C. In each fibre maximum shortening velocity (Vmax), maximum power output (Wmax), optimal velocity (velocity at which Wmax is developed, Vopt), optimal force (force at which Wmax is developed, Popt), specific tension (Po/CSA, isometric tension/cross-sectional area) were assessed. Unloaded shortening velocity (Vo) was also determined at 12 degrees C in a different group (n = 57) of fibres by slack-test procedure. 2. All fibres used for mechanical experiments were characterized on the basis of the myosin heavy chain (MHC) isoform composition by sodium dodecyl sulphate (SDS)-polyacrylamide gel electrophoresis and divided into five types: type I (or slow), types IIA and IIB (or fast), and types I-IIA and IIA-IIB (or mixed types). 3. Vmax, Wmax, Vopt, Popt, Vopt/Vmax ratio, Po/CSA and Vo were found to depend on MHC isoform composition. All parameters were significantly lower in type I than in the fast (type IIA and IIB) fibres. Among fast fibres, Vmax, Wmax, Vopt and Vo were significantly lower in type IIA and than in IIB fibres, whereas Popt, Po/CSA and Vopt/Vmax were similar. 4. The temperature dependence of Vo and Po/CSA was assessed in a group of twenty-one fibres in the range 12-22 degrees C. In a set of six fibres temperature dependence of Vmax was also studied. The Q10 (5.88) and activation energy E (125 kJ mol-1) values for maximum shortening velocity calculated from Arrhenius plots pointed to a very high temperature sensitivity. Po/CSA was very temperature dependent in the 12-17 degrees C range, but less dependent between 17 and 22 degrees C.

Force production by depolymerizing microtubules: load-velocity curves and run-pause statistics

Experiments indicate that depolymerization of microtubules generates sufficient force to produce the minus-end-directed transport of chromosomes during mitosis (Koshland et al., 1988). In vitro, analogous transport of kinesin-coated microspheres exhibits a paradoxical effect. Minus-end-directed transport of the microspheres driven by depolymerization is enhanced by the presence of ATP, which fuels the motor action of kinesin driving the microspheres in the opposite direction, toward the plus end of the microtubule. Here we present a mathematical model to explain this behavior. We postulate that a microsphere at the plus end of the microtubule facilitates depolymerization and hence enhances minus-end-directed transport. The force-velocity curve of the model is derived; it has the peculiar feature that velocity is maximal at some positive load (opposing the motion) rather than at zero load. The model is used to simulate the stochastic process of microsphere-facilitated depolymerization-driven transport. Simulated trajectories at low load show distinctive runs and pauses, the statistics of which are calculated from the model. The statistics of the process provide sufficient information to determine all of the model's parameters.

Maximum speed of shortening and ATPase activity in atrial and ventricular myocardia of hyperthyroid rats

The kinetic properties of the myofibrillar system of atrial and ventricular myocardia of hyperthyroid rats were analyzed by determining ATPase activity and maximum shortening velocity. Hyperthyroidism was induced by daily subcutaneous injections of triiodothyronine (0.2 mg/kg body wt) for 2 wk. The treatment induced a marked atrial and ventricular hypertrophy and, in ventricular myocardium, an isomyosin shift toward a homogeneous V1 composition. Skinned trabeculae and purified myofibrils were prepared from atrial and ventricular myocardia. Enzymatic assays on the myofibrils showed that both Ca-stimulated ATPase activity and Ca-Mg-dependent ATPase activity had equal values in atrial and ventricular myocardia. In skinned trabeculae during maximal Ca activations, force-velocity curves were determined by load-clamp maneuvers, and unloaded shortening velocity (Vo) was obtained with the slack-test method. Both maximum shortening velocities extrapolated from the force-velocity curves (Vmax) and Vo were significantly higher (+68 and +52%, respectively) in atrial than in ventricular preparations. Developed tension was significantly greater in ventricular preparations. Maximum power output was not significantly different. Previous findings (V. Cappelli, R. Bottinelli, C. Poggesi, R. Moggio, and C. Reggiani. Circ. Res. 65: 446-457, 1989) had led to the conclusion that variations in ATPase activity and shortening velocity of ventricular myocardium can be accounted for by changes in isomyosin composition. In this light, the present results suggest that 1) ATPase activity is equal in atrial and ventricular myocardia as the two tissues contain the same myosin heavy chain isoform, 2) the difference in maximum speed of shortening between atrium and ventricle might be due to the presence of tissue-specific isoforms of myosin light chains.

The force-velocity curve in passive whole muscle is asymmetric about zero velocity

The force-velocity property of passive muscle was investigated to determine if a discontinuity of slope occurred at zero velocity. Isolated, unstimulated whole frog sartorius muscles were subjected to constant-velocity stretches and releases using a servo-controlled lever. The force due to damping (Δ T) was calculated by subtracting the tension measured at a very low speed (1.0 mm s −1) from the tension measured at the same length while the muscle was shortening or lengthening at a particular test speed. The experiments were performed over a range of speeds at each of several lengths and at two temperatures. For comparison, the same experiments were performed using a strip of pure latex rubber and a steel spring. Curves showing the magnitude of Δ T vs velocity were nearly symmetric about the zero-velocity axis for the steel spring and the rubber strip, but were markedly asymmetric for passive muscle, showing a positive Δ T for lengthening at all speeds that was between four and 11 times the negative Δ T for shortening at the same speed, depending on the temperature and initial stretch length. The force due to damping at a given speed increased with extension above the rest length in passive muscle but decreased with increasing length in experiments using the latex strip. Predictions obtained from a mathematical model based on a damping element in series with a lightly damped spring were fitted to the experimental measurements of Δ T vs velocity. The damping parameter provisionally representing interfilamentary sliding was between six and 12 times larger for lengthening than for shortening. We conclude that the force-velocity curve in passive whole muscle, as in activated muscle, is asymmetric about zero velocity. Furthermore, the slope of the force-velocity curve is discontinuous at zero velocity.