Contractile properties of the axolotl ventricle at 17 and 21 °C

Mammalian cardiac muscle exhibits a number of intrinsic response systems which adjust function to changing conditions. These include the Frank–Starling response and the slow force response which are activated upon myocardial stretch, and the force–frequency response, which is evident upon changes in cardiac frequency. In this study we have examined the effect of myocardial stretch and changes in pacing frequency on isolated ventricular muscle preparations from the ectothermic amphibian, the axolotl (Ambystoma mexicanum). We preformed these studies at two physiologically relevant temperatures 17 °C and 21 °C. We found that increasing the length of the muscle increased active force via the Frank–Starling response at both temperatures, which is consistent with cardiac muscle preparations in other vertebrates. We found no evidence for the slow force response at either temperature suggesting that in axolotl, unlike mammals but similar to fish, the slow force response is not associated with the Frank–Starling response. Increasing contraction frequency caused a decrease in active force across all frequencies tested (0.5−2.0 Hz)—a monophasic negative force–frequency response, independent of temperature.     

Contribution of muscle short-range stiffness to initial changes in joint kinetics and kinematics during perturbations to standing balance: A simulation study

Simulating realistic musculoskeletal dynamics is critical to understanding neural control of muscle activity evoked in sensorimotor feedback responses that have inherent neural transmission delays. Thus, the initial mechanical response of muscles to perturbations in the absence of any change in muscle activity determines which corrective neural responses are required to stabilize body posture. Muscle short-range stiffness, a history-dependent property of muscle that causes a rapid and transient rise in muscle force upon stretch, likely affects musculoskeletal dynamics in the initial mechanical response to perturbations. Here we identified the contributions of short-range stiffness to joint torques and angles in the initial mechanical response to support surface translations using dynamic simulation. We developed a dynamic model of muscle short-range stiffness to augment a Hill-type muscle model. Our simulations show that short-range stiffness can provide stability against external perturbations during the neuromechanical response delay. Assuming constant muscle activation during the initial mechanical response, including muscle short-range stiffness was necessary to account for the rapid rise in experimental sagittal plane knee and hip joint torques that occurs simultaneously with very small changes in joint angles and reduced root mean square errors between simulated and experimental torques by 56% and 47%, respectively. Moreover, forward simulations lacking short-range stiffness produced unreasonably large joint angle changes during the initial response. Using muscle models accounting for short-range stiffness along with other aspects of history-dependent muscle dynamics may be important to advance our ability to simulate inherently unstable human movements based on principles of neural control and biomechanics.     

Activation in a Skeletal Muscle Contraction Model with a Modification for Insect Fibrillar Muscle

A sliding filament model for muscle contraction is extended by including an activation mechanism based on the hypothesis that the binding of calcium by a regulating protein in the myofibrils must occur before the rate constant governing the making of interactions between cross-bridges and thin filament sites can take on nonzero values. The magnitude of the rate constant is proportional to the amount of bound calcium. The model's isometric twitch and rise of force in an isometric tetanus are similar to the curves produced by real muscles. It redevelops force after a quick release in an isometric tetanus faster than the initial rise. Quick release experiments on the model during an isometric twitch show that the “active state” curve produced is different from the postulated calcium binding curve. The force developed by the model can be increased by a small quick stretch delivered soon after activation to values near the maximum generated in an isometric tetanus. Following the quick stretch, the force remains near the tetanic maximum for a long time even though the calcium binding curve rises to a peak and subsequently decays by about 50%. The model satisfies the constraint of shortening with a constant velocity under a constant load. Modifications can be made in the model so that it produces the delayed force changes following step length changes characteristic of insect fibrillar muscle.     

The role of passive structures in force enhancement of skeletal muscles following active stretch

We recently found that force enhancement following active stretch in skeletal muscles is accompanied by an increase in passive force following deactivation (J. Exp. Biol. 205 (2002) 1275). However, it is not known if this increase in passive force contributes to the force enhancement observed in the active muscle, and if it is observed at all muscle lengths. The purposes of this study were to quantify the amount of passive force increase as a function of muscle lengths, and to determine if this passive force contributes to the force enhancement observed in the active muscle. Experiments were performed on cat soleus (n = 24) using techniques published previously (J. Biomech. 30(9) (1997) 865). Conceptually, tests involved comparisons of force enhancement and passive force increase for a variety of stretch tests in soleus. Furthermore, in one test, activation of the soleus was interrupted for 1s in the force-enhanced state, and soleus was then re-activated. We found that total force enhancement and passive force increase were positively correlated for all test conditions, that passive force increase following stretch of the active soleus only occurred at muscle lengths corresponding to the descending limb of the force-length relationship, that increases in passive force for a given stretch magnitude became greater at long muscle lengths, and that upon reactivation, there was a remnant passive force enhancement. We conclude from these results that the passive force enhancement following stretch of an active muscle contributes to the total force enhancement, that this passive contribution increases with increasing muscle length, and that there must be at least one other factor than passive force increase that contributes to the total force enhancement, as the passive force increase was always smaller than the total force enhancement. A by-product of this investigation was that we observed a shift in the passive force-length relationship that was dependent on muscle activation, stretch magnitude and muscle length. Therefore, the passive force-length relationship is not a constant property of skeletal muscle, but depends critically on the muscle's contractile history.     

Considerations on the history dependence of muscle contraction.

When a skeletal muscle that is actively producing force is shortened or stretched, the resulting steady-state isometric force after the dynamic phase is smaller or greater, respectively, than the purely isometric force obtained at the corresponding final length. The cross-bridge model of muscle contraction does not readily explain this history dependence of force production. The most accepted proposal to explain both, force depression after shortening and force enhancement after stretch, is a nonuniform behavior of sarcomeres that develops during and after length changes. This hypothesis is based on the idea of instability of sarcomere lengths on the descending limb of the force-length relationship. However, recent evidence suggests that skeletal muscles may be stable over the entire range of active force production, including the descending limb of the force-length relationship. The purpose of this review was to critically evaluate hypotheses aimed at explaining the history dependence of force production and to provide some novel insight into the possible mechanisms underlying these phenomena. It is concluded that the sarcomere nonuniformity hypothesis cannot always explain the total force enhancement observed after stretch and likely does not cause all of the force depression after shortening. There is evidence that force depression after shortening is associated with a reduction in the proportion of attached cross bridges, which, in turn, might be related to a stress-induced inhibition of cross-bridge attachment in the myofilament overlap zone. Furthermore, we suggest that force enhancement is not associated with instability of sarcomeres on the descending limb of the force-length relationship and that force enhancement has an active and a passive component. Force depression after shortening and force enhancement after stretch are likely to have different origins.     

Phase transition in force during ramp stretches of skeletal muscle.

Active glycerinated rabbit psoas fibers were stretched at constant velocity (0.1-3.0 lengths/s) under sarcomere length control. As observed by previous investigators, force rose in two phases: an initial rapid increase over a small stretch (phase I), and a slower, more modest rise over the remainder of the stretch (phase II). The transition between the two phases occurred at a critical stretch (LC) of 7.7 +/- 0.1 nm/half-sarcomere that is independent of velocity. The force at critical stretch (PC) increased with velocity up to 1 length/s, then was constant at 3.26 +/- 0.06 times isometric force. The decay of the force response to a small step stretch was much faster during stretch than in isometric fibers. The addition of 3 mM vanadate reduced isometric tension to 0.08 +/- 0.01 times control isometric tension (P0), but only reduced PC to 0.82 +/- 0.06 times P0, demonstrating that prepowerstroke states contribute to force rise during stretch. The data can be explained by a model in which actin-attached cross-bridges in a prepowerstroke state are stretched into regions of high force and detach very rapidly when stretched beyond this region. The prepowerstroke state acts as a mechanical rectifier, producing large forces during stretch but small forces during shortening.     

Stretch of active muscle during the declining phase of the calcium transient produces biphasic changes in calcium binding to the activating sites

In voltage-clamped barnacle single muscle fibers, muscle shortening during the declining phase of the calcium transient increases myoplasmic calcium. This extra calcium is probably released from the activating sites by a change in affinity when cross-bridges break (Gordon, A. M., and E. B. Ridgway, 1987. J. Gen. Physiol. 90:321-340). Stretching the muscle at similar times causes a more complex response, a rapid increase in intracellular calcium followed by a transient decrease. The amplitudes of both phases increase with the rate and amplitude of stretch. The rapid increase, however, appears only when the muscle is stretched more than approximately 0.4%. This is above the length change that produces the breakpoint in the force record during a ramp stretch. This positive phase in response to large stretches is similar to that seen on equivalent shortening at the same point in the contraction. For stretches at different times during the calcium transient, the peak amplitude of the positive phase has a time course that is delayed relative to the calcium transient, while the peak decrease during the negative phase has an earlier time course that is more similar to the calcium transient. The amplitudes of both phases increase with increasing strength of stimulation and consequent force. When the initial muscle the active force. A large decrease in length (which drops the active force to zero) decreases the extra calcium seen on a subsequent restretch. After such a shortening step, the extra calcium on stretch recovers (50 ms half time) toward the control level with the same time course as the redeveloped force. Conversely, stretching an active fiber decreases the extra calcium on a subsequent shortening step that is imposed shortly afterward. Enhanced calcium binding due to increased length alone cannot explain our data. We hypothesize that the calcium affinity of the activating sites increases with cross-bridge attachment and further with cross-bridge strain. This accounts for the biphasic response to stretch as follows: cross-bridges detached by stretch first decrease calcium affinity, then upon reattachment increase calcium affinity due to the strained configuration brought on by the stretch. The experiments suggest that cross-bridge attachment and strain can modify calcium binding to the activating sites in intact muscle.     

Motor unit recruitment patterns during reflex compensation of muscle yield investigated by computer simulations

 An important function of the stretch reflex in the soleus muscle in the decerebrate cat preparation is to compensate for the tendency of muscle suddenly to yield during ramp increases in length. As the level of background (i.e. pre-stretch) force increases, there is a systematic change in the curvature of the force trajectory during this reflex compensation, from concave to convex with respect to increasing force. The hypothesis that this change in curvature was due to background force-dependent changes in the recruitment pattern of motor units was investigated with a combined computer simulation/ experimental technique. The simulation consisted of 20 model motor units for the soleus muscle, each based on a distributed moment muscle model. The timing of recruitment of the motor units was optimized to allow the simulation outputs to fit a set of experimental data records on the reflex response to stretch initiated at five different levels of pre-stretch force. The resulting recruitment patterns showed that a tendency for recruitment to be concentrated progressively in the early portion of the stretch as pre-stretch force increased could account for the changes in reflex force curvature. These results are consistent with the skewed distribution of intrinsic electrical thresholds of motoneurons, in which low-threshold units are much more frequent than high-threshold ones. Therefore the changes in recruitment pattern and reflex force curvature may be due primarily to the intrinsic properties of motoneurons. Received: 18 September 1995/Accepted in revised form: 21 May 1996     

Activation dependence of stretch activation in mouse skinned myocardium: implications for ventricular function

Recent evidence suggests that ventricular ejection is partly powered by a delayed development of force, i.e., stretch activation, in regions of the ventricular wall due to stretch resulting from torsional twist of the ventricle around the apex-to-base axis. Given the potential importance of stretch activation in cardiac function, we characterized the stretch activation response and its Ca2+ dependence in murine skinned myocardium at 22 degrees C in solutions of varying Ca2+ concentrations. Stretch activation was induced by suddenly imposing a stretch of 0.5-2.5% of initial length to the isometrically contracting muscle and then holding the muscle at the new length. The force response to stretch was multiphasic: force initially increased in proportion to the amount of stretch, reached a peak, and then declined to a minimum before redeveloping to a new steady level. This last phase of the response is the delayed force characteristic of myocardial stretch activation and is presumably due to increased attachment of cross-bridges as a consequence of stretch. The amplitude and rate of stretch activation varied with Ca2+ concentration and more specifically with the level of isometric force prior to the stretch. Since myocardial force is regulated both by Ca2+ binding to troponin-C and cross-bridge binding to thin filaments, we explored the role of cross-bridge binding in the stretch activation response using NEM-S1, a strong-binding, non-force-generating derivative of myosin subfragment 1. NEM-S1 treatment at submaximal Ca2+-activated isometric forces significantly accelerated the rate of the stretch activation response and reduced its amplitude. These data show that the rate and amplitude of myocardial stretch activation vary with the level of activation and that stretch activation involves cooperative binding of cross-bridges to the thin filament. Such a mechanism would contribute to increased systolic ejection in response to increased delivery of activator Ca2+ during excitation-contraction coupling.     

A mathematical model of the sarcomere mechanics of cross-striated muscle with consideration of the stretch and twist of actin filaments

A mathematical model of sarcomere mechanics, which takes into account the elongation of actin and myosin filaments and also twisting of the actin filaments in the sarcomere of striated muscle during contraction is presented. The model accounts for the experimentally observed phenomena of the stretch and twist of the actin filaments due to strong binding of myosin heads and the pulling force. Some model parameters were estimated from published experimental data. The results of modeling show that the twist of actin filaments can play a substantial role in the mechanical responses of contracting muscle fibers to step changes of their length.     

A mathematical model for sarcomere mechanics in cross-striated muscles taking into account the stretch and twist of actin filaments

A model of sarcomere mechanics, which takes into account the elongation of the actin and myosin filaments and twisting of the actin filaments during muscle contraction is suggested. The model accounts for the experimentally observed phenomena of the stretch and twist of actin filaments due to strong binding of myosin heads and pulling force. Some model parameters were estimated from published experimental data. The results of modelling suggest that the twist of actin filaments may play an essential role in mechanical responses of contracting muscle fibres to stepwise changes in their length.     

The mechanical response of active human muscle during and after stretch

Five subjects contracted forearm supinator muscles which were stretched after development of maximal isometric torque. The ratio of torque at the end of stretch over isometric torque at that position was calculated as excess torque. Excess torque increased with stretch velocity and decreased with stretch amplitude, and it was not dependent upon final muscle length. The rate of decay of torque following stretch could not be shown to depend upon stretch variables. The absence of significant changes in myoelectric activity suggested that with high initial forces, reflex activity did not account for the observed changes. Time-constants of decay (0.15 s to 1.8 s) were much greater than time-constants of rise (approx. 0.07 s) of isometric torque at the same muscle length. This indicates that interaction of series elastic and contractile elements is not the sole cause of prolonged torque following stretch. It is concluded that stretch temporarily enhances the intrinsic contractile properties of a group of human muscles in a manner similar to, but quantitatively different from that seen in isolated muscle preparations.     

A mathematical model of muscle containing heterogeneous half-sarcomeres exhibits residual force enhancement

A skeletal muscle fiber that is stimulated to contract and then stretched from L₁ to L₂ produces more force after the initial transient decays than if it is stimulated at L₂. This behavior has been well studied experimentally, and is known as residual force enhancement. The underlying mechanism remains controversial. We hypothesized that residual force enhancement could reflect mechanical interactions between heterogeneous half-sarcomeres. To test this hypothesis, we subjected a computational model of interacting heterogeneous half-sarcomeres to the same activation and stretch protocols that produce residual force enhancement in real preparations. Following a transient period of elevated force associated with active stretching, the model predicted a slowly decaying force enhancement lasting >30 seconds after stretch. Enhancement was on the order of 13% above isometric tension at the post-stretch muscle length, which agrees well with experimental measurements. Force enhancement in the model was proportional to stretch magnitude but did not depend strongly on the velocity of stretch, also in agreement with experiments. Even small variability in the strength of half-sarcomeres (2.1% standard deviation, normally distributed) was sufficient to produce a 5% force enhancement over isometric tension. Analysis of the model suggests that heterogeneity in half-sarcomeres leads to residual force enhancement by storing strain energy introduced during active stretch in distributions of bound cross-bridges. Complex interactions between the heterogeneous half-sarcomeres then dissipate this stored energy at a rate much slower than isolated cross-bridges would cycle. Given the variations in half-sarcomere length that have been observed in real muscle preparations and the stochastic variability inherent in all biological systems, half-sarcomere heterogeneity cannot be excluded as a contributing source of residual force enhancement.     

Evidence for increased low force cross-bridge population in shortening skinned skeletal muscle fibers: implications for actomyosin kinetics.

The dynamic characteristics of the low force myosin cross-bridges were determined in fully calcium-activated skinned rabbit psoas muscle fibers shortening under constant loads (0.04-0.7 x full isometric tension Po). The shortening was interrupted at various times by a ramp stretch (duration, 10 ms; amplitude, up to 1.8% fiber length) and the resulting tension response was recorded. Except for the earlier period of velocity transients, the tension response showed nonlinear dependence on stretch amplitude; i.e., the magnitude of the tension response started to rise disproportionately as the stretch exceeded a critical amplitude, as in the presence of inorganic phosphate (Pi). This result, as well as the result of stiffness measurement, suggests that the low force cross-bridges similar to those observed in the presence of Pi (presumably A.M.ADP.Pi) are significantly populated during shortening. The critical amplitude of the shortening fibers was greater than that of isometrically contracting fibers, suggesting that the low force cross-bridges are more negatively strained during shortening. As the load was reduced from 0.3 to 0.04 P0, the shortening velocity increased more than twofold, but the amount of the negative strain stayed remarkably constant (approximately 3 nm). This This insensitiveness of the negative strain to velocity is best explained if the dissociation of the low force cross-bridges is accelerated approximately in proportion to velocity. Along with previous reports, the results suggest that the actomyosin ATPase cycle in muscle fibers has at least two key reaction steps in which rate constants are sensitively regulated by shortening velocity and that one of them is the dissociation of the low force A.M.ADP.Pi cross-bridges. This step may virtually limit the rate of actomyosin ATPase turnover and help increase efficiency in fibers shortening at high velocities.     

Stretch-activated channels in the heart: contributions to length-dependence and to cardiomyopathy

The stretch-induced increase in force production of ventricular muscle is biphasic. An abrupt increase in force coincides with the stretch, which is then followed by a slower response that develops over minutes (the slow force response or SFR). The SFR is accompanied by a slow increase in the magnitude of the intracellular Ca2+ transient, but the stretch-dependent mechanisms that give rise to this remain controversial. We characterized the SFR using right ventricular trabeculae from mouse hearts. Application of three different blockers of stretch-activated non-selective cation channels (SAC NSC) reduced the magnitude of the SFR 60s after stretch (400 microM streptomycin: from 86+/-25% to 38+/-14%, P<0.01, n=9; 10 microM GdCl3: from 65+/-21%, to 12+/-7%, P<0.01, n=7; 10 microM GsMTx-4 from 122+/-40% to 15+/-8%, P<0.05, n=6). Streptomycin also decreased the increase in Ca2+ transient amplitude 60s after the stretch from 43.5+/-12.7% to 5.7+/-3.5% (P<0.05, n=4), and reduced the stretch-dependent increase in intracellular Ca2+ in quiescent muscles when stretched. The transient receptor potential, canonical channels TRPC1 and TRPC6 are mechano-sensitive, non-selective cation channels. They are expressed in mouse ventricular muscle, and could therefore be responsible for stretch-dependent influx of Na+ and/or Ca2+ during the SFR. Expression of TRPC1 was investigated in the mdx heart, a mouse model of Duchenne's muscular dystrophy. Resting Ca2+ was raised in isolated myocytes from old mdx animals, which was blocked by application of SAC blockers. Expression of TRPC1 was increased in the older mdx animals, which have developed a dilated cardiomyopathy, and might therefore contribute to the dilated cardiomyopathy.     

A model of muscle contraction based on the Langevin equation with actomyosin potentials

We propose a muscle contraction model that is essentially a model of the motion of myosin motors as described by a Langevin equation. This model involves one-dimensional numerical calculations wherein the total force is the sum of a viscous force proportional to the myosin head velocity, a white Gaussian noise produced by random forces and other potential forces originating from the actomyosin structure and intra-molecular charges. We calculate the velocity of a single myosin on an actin filament to be 4.9–49 μm/s, depending on the viscosity between the actomyosin molecules. A myosin filament with a hundred myosin heads is used to simulate the contractions of a half-sarcomere within the skeletal muscle. The force response due to a quick release in the isometric contraction is simulated using a process wherein crossbridges are changed forcibly from one state to another. In contrast, the force response to a quick stretch is simulated using purely mechanical characteristics. We simulate the force–velocity relation and energy efficiency in the isotonic contraction and adenosine triphosphate consumption. The simulation results are in good agreement with the experimental results. We show that the Langevin equation for the actomyosin potentials can be modified statistically to become an existing muscle model that uses Maxwell elements.     

The effects of muscle stretching and shortening on isometric forces on the descending limb of the force-length relationship

The purpose of this study was to examine the effects of stretching and shortening on the isometric forces at different lengths on the descending limb of the force-length relationship. Cat soleus (N = 10) was stretched and shortened by various amounts on the descending limb of the force-length relationship, and the steady-state forces following these dynamic contractions were compared to the isometric forces at the corresponding muscle lengths. We found a shift of the force-length relationship to greater force values following muscle stretching, and to smaller force values following muscle shortening. Shifts in both directions critically depended on the magnitude of stretching/shortening and the final muscle length. We confirm recent findings that the steady-state isometric force following some stretch conditions clearly exceeded the maximal isometric forces at optimum muscle length, and that force enhancement was associated with an increase in the passive force, i.e., a passive force enhancement. When the passive force enhancement was subtracted from the total force enhancement, forces following stretch were always equal to or smaller than the isometric force at optimum muscle length. Together, these findings led to the conclusions: (a). that force enhancement is composed of an "active and a "passive" component; (b). that the "passive" component of force enhancement allows for forces greater than the maximal isometric forces at the muscle's optimum length; and (c). that force enhancement and force depression are critically affected by muscle length and stretch/shortening amplitude.     

Modeling the oscillation dynamics of activated airway smooth muscle strips

When strips of activated airway smooth muscle are stretched cyclically, they exhibit force-length loops that vary substantially in both position and shape with the amplitude and frequency of the stretch. This behavior has recently been ascribed to a dynamic interaction between the imposed stretch and the number of actin-myosin interactions in the muscle. However, it is well known that the passive rheological properties of smooth muscle have a major influence on its mechanical properties. We therefore hypothesized that these rheological properties play a significant role in the force-length dynamics of activated smooth muscle. To test the plausibility of this hypothesis, we developed a model of the smooth muscle strip consisting of a force generator in series with an elastic component. Realistic steady-state force-length loops are predicted by the model when the force generator obeys a hyperbolic force-velocity relationship, the series elastic component is highly nonlinear, and both elastic stiffness and force generation are adjusted so that peak loop force equals isometric force. We conclude that the dynamic behavior of airway smooth muscle can be ascribed in large part to an interaction between connective tissue rheology and the force-velocity behavior of contractile proteins.     

Spasticity and spastic dystonia: the two faces of velocity-dependent hypertonia

BackgroundSpasticity and spastic dystonia are two separate phenomena of the upper motor neuron syndrome. Spasticity is clinically defined by velocity-dependent hypertonia and tendon jerk hyperreflexia due to the hyper-excitability of the stretch reflex. Spastic dystonia is the inability to relax a muscle leading to a spontaneous tonic contraction. Both spasticity and spastic dystonia are present in patients who are at rest; however, only patients with spasticity are actually able to kept their muscles relaxed prior to muscle stretch. The idea that has inspired the present work is that also in patients with spastic dystonia the stretch reflex is likely to be hyper-excitable. Therefore, velocity-dependent hypertonia could be mediated not only by spasticity, but also by spastic dystonia.MethodsTonic stretch reflexes in the rectus femoris muscle were evoked in 30 patients with multiple sclerosis showing velocity-dependent hypertonia of leg extensors and the habituation of the reflex was studied. Moreover, the capability of relax the muscle prior to muscle stretch (spastic dystonia) was also investigated.ResultsA tonic stretch reflex was evoked in all the enrolled patients. 73% of the patients were able to relax their rectus femoris muscle prior to stretch (spasticity). In the overwhelming majority of these patients, the tonic stretch reflex decreased during repeated stretches. In the remaining 27% of the subjects, the muscle was tonically activated prior to muscle stretch (spastic dystonia). In the patients in whom spastic dystonia progressively increased over the subsequent stretches (50% of the subjects with spastic dystonia), the habituation of the reflex was replaced by a progressive reflex facilitation.DiscussionThis study shows for the first time that velocity-dependent hypertonia can be caused by two distinct phenomena: spasticity and spastic dystonia. The habituation of the tonic stretch reflex, which is a typical feature of spasticity, is replaced by a reflex facilitation in the half of the subject with spastic dystonia. These preliminary findings suggest that differentiating the two types of velocity-dependent muscle hypertonia (spasticity and spastic dystonia) could be clinically relevant.