Effects of Hydrostatic-Pressure on Muscle Contraction: A Look Back on Some Experimental Findings.

Findings from experiments that used hydrostatic pressure changes to analyse the process of skeletal muscle contraction are re-examined. The force in resting muscle is insensitive to an increase in hydrostatic pressure from 0.1 MPa (atmospheric) to 10 MPa, as also found for force in rubber-like elastic filaments. The force in rigour muscle rises with increased pressure, as shown experimentally for normal elastic fibres (e.g., glass, collagen, keratin, etc.). In submaximal active contractions, high pressure leads to tension potentiation. The force in maximally activated muscle decreases with increased pressure: the extent of this force decrease in maximal active muscle is sensitive to the concentration of products of ATP hydrolysis (Pi-inorganic phosphate and ADP-adenosine diphosphate) in the medium. When the increased hydrostatic pressure is rapidly decreased, the force recovered to the atmospheric level in all cases. Thus, the resting muscle force remained the same: the force in the rigour muscle decreased in one phase and that in active muscle increased in two phases. The rate of rise of active force on rapid pressure release increased with the concentration of Pi in the medium, indicating that it is coupled to the Pi release step in the ATPase-driven crossbridge cycle in muscle. Pressure experiments on intact muscle illustrate possible underlying mechanisms of tension potentiation and causes of muscle fatigue.

The Location and Rate of the Phosphate Release Step in the Muscle Cross-Bridge Cycle.

It is controversial whether the phosphate (Pi) release step in the cross-bridge cycle occurs before or after the first tension-generating step and whether it is fast or slow. We have therefore modified our previous model of the frog cross-bridge cycle by including a Pi release step either before (model A) or after (model B) the first tension-generating step and refined the two models by downhill simplex runs against experimental data for the force-velocity relation and the tension transients after length steps. Pi release step was initially made slow (70 s-1), but after refinement, it became fast (∼500 s-1 for model A and ∼6000 s-1 for model B). The two models gave similar fits to the experimental tension transients after length steps, but model A gave a better fit to the lengthening limb of the force-velocity relation than model B. 50 mM Pi inhibited the isometric tension of model A by ∼50% but that of model B by only ∼25%. The half-inhibition was at 6.0 mM Pi for model A and at 1.6 mM Pi for model B. The values for model A were consistent with experimental data. We also simulated the effect Pi jump as in caged Pi experiments. For model A, a Pi jump induced a tension fall at a rate similar to the experimental phase II. There was then a small rise in tension to the steady state mimicking the experimental phase III. The initial tension fall was caused by detachment of M⋅ADP⋅Pi myosin heads from actin and reversal of the first tension-generating step. For model B, the fall in tension was more rapid and due to reversal of the first tension-generating step, and phase III was not observed. We conclude that, as in model A, the Pi release step is before the first tension-generating step and is moderately fast.

Temperature Effects on Force and Actin⁻Myosin Interaction in Muscle: A Look Back on Some Experimental Findings.

Observations made in temperature studies on mammalian muscle during force development, shortening, and lengthening, are re-examined. The isometric force in active muscle goes up substantially on warming from less than 10 °C to temperatures closer to physiological (>30 °C), and the sigmoidal temperature dependence of this force has a half-maximum at ~10 °C. During steady shortening, when force is decreased to a steady level, the sigmoidal curve is more pronounced and shifted to higher temperatures, whereas, in lengthening muscle, the curve is shifted to lower temperatures, and there is a less marked increase with temperature. Even with a small rapid temperature-jump (T-jump), force in active muscle rises in a definitive way. The rate of tension rise is slower with adenosine diphosphate (ADP) and faster with increased phosphate. Analysis showed that a T-jump enhances an early, pre-phosphate release step in the acto-myosin (crossbridge) ATPase cycle, thus inducing a force-rise. The sigmoidal dependence of steady force on temperature is due to this endothermic nature of crossbridge force generation. During shortening, the force-generating step and the ATPase cycle are accelerated, whereas during lengthening, they are inhibited. The endothermic force generation is seen in different muscle types (fast, slow, and cardiac). The underlying mechanism may involve a structural change in attached myosin heads and/or their attachments on heat absorption.

The force-generation process in active muscle is strain sensitive and endothermic: a temperature-perturbation study.

In experiments on active muscle, we examined the tension decline and its temperature sensitivity at the onset of ramp shortening and at a range of velocities. A segment (∼1.5 mm long) of a skinned muscle fibre isolated from rabbit psoas muscle was held isometrically (sarcomere length ∼2.5 µm) at 8-9°C, maximally Ca2+-activated and a ramp shortening applied. The tension decline with a ramp shortening showed an early decrease of slope (the P1 transition) followed by a slower decrease in slope (the P2 transition) to the steady (isotonic) force. The tension level at the initial P1 transition and the time to that transition decreased as the velocity was increased; the length change to this transition increased with shortening velocity to a steady value of ∼8 nm half-sarcomere-1 A small, rapid, temperature jump (T-jump) (3-4°C, <0.2 ms) applied coincident with the onset of ramp shortening showed force enhancement by T-jump and changed the tension decline markedly. Analyses showed that the rate of T-jump-induced force rise increased linearly with increase of shortening velocity. These results provide crucial evidence that the strain-sensitive cross-bridge force generation, or a step closely coupled to it, is endothermic.

Reinterpretation of the Tension Response of Muscle to Stretches and Releases.

We have reexamined the experimental time courses of tension in frog muscle after rapid length steps. The early tension recoveries are biexponential. After 3 nm/hs stretches and releases, the rates of the immediate rapid tension changes are similar but the subsequent tension fall after a stretch is much slower than the rise after a release. After 1.5 nm/hs length steps, the entire tension responses are more nearly mirror images. To identify the underlying processes, we used a model of the muscle cross-bridge cycle with two tension-generating (tensing) steps. Analysis of the time course of the tension, the rates of the steps in the cycle, and their contributions to tension provided insights into previously puzzling features of the experimental response. After a stretch, the initial rapid tension fall in the model is caused principally by the reversal of the first tensing step, but after a few milliseconds the tensing step resumes its forward direction. We conclude that the remaining response should not be included in phase 2, the period of early tension recovery. With this exclusion, T2, the tension at the end of this period, rises with an increase of stretch. The rate of early tension recovery also increases with stretch size, showing that the reversal of the first tensing step is strain sensitive. After small length steps, the fast and slow components of the early tension recovery are both caused mainly by the first tensing step. The fast component is triggered by the initial sliding of the filaments, and the slow component is due to further sliding that occurs as the tension recovers. With small length steps (<0.5 nm/hs), the time course of the response to a stretch is the reverse of that to a release.

The endothermic ATP hydrolysis and crossbridge attachment steps drive the increase of force with temperature in isometric and shortening muscle.

The isometric tetanic tension of skeletal muscle increases with temperature because attached crossbridge states bearing a relatively low force convert to those bearing a higher force. It was previously proposed that the tension-generating step(s) in the crossbridge cycle was highly endothermic and was therefore itself directly targeted by changes in temperature. However, this did not explain why a rapid rise in temperature (a temperature jump) caused a much slower rate of rise of tension than a rapid length step. This led to suggestions that the step targeted by a temperature rise is not the tension-generating step but is an extra step in the attached pathway of the crossbridge cycle, perhaps located on a parallel pathway. This enigma has been a major obstacle to a full understanding of the operation of the crossbridge cycle. We have now used a previously developed mechano-kinetic model of the crossbridge cycle in frog muscle to simulate the temperature dependence of isometric tension and shortening velocity. We allowed all five steps in the cycle to be temperature-sensitive. Models with different starting combinations of enthalpy changes and activation enthalpies for the five steps were refined by downhill simplex runs and scored by their ability to fit experimental data on the temperature dependence of isometric tension and the relationship between force and shortening velocity in frog muscle. We conclude that the first tension-generating step may be weakly endothermic and that the rise of tension with temperature is largely driven by the preceding two strongly endothermic steps of ATP hydrolysis and attachment of M.ADP.Pi to actin. The refined model gave a reasonable fit to the available experimental data and after a temperature jump the overall rate of tension rise was much slower than after a length step as observed experimentally. The findings aid our understanding of the crossbridge cycle by showing that it may not be necessary to include an additional temperature-sensitive step.

A cross-bridge cycle with two tension-generating steps simulates skeletal muscle mechanics.

We examined whether cross-bridge cycle models with one or two tension-generating steps can account for the force-velocity relation of and tension response to length steps of frog skeletal muscle. Transition-state theory defined the strain dependence of the rate constants. The filament stiffness was non-Hookean. Models were refined against experimental data by simulated annealing and downhill simplex runs. Models with one tension-generating step were rejected, as they had a low efficiency and fitted the experimental data relatively poorly. The best model with two tension-generating steps (stroke distances 5.6 and 4.6 nm) and a cross-bridge stiffness of 1.7 pN/nm gave a good account of the experimental data. The two tensing steps allow an efficiency of up to 38% during shortening. In an isometric contraction, 54.7% of the attached heads were in a pre-tension-generating state, 44.5% of the attached heads had undergone the first tension-generating step, and only 0.8% had undergone both tension-generating steps; they bore 34%, 64%, and 2%, respectively, of the isometric tension. During slow shortening, the second tensing step made a greater contribution. During lengthening, up to 93% of the attached heads were in a pre-tension-generating state yet bore elevated tension by being dragged to high strains before detaching.

Mechanism of force enhancement during and after lengthening of active muscle: a temperature dependence study.

The aim of the present study was to examine the temperature dependence of active force in lengthening and shortening muscle. Experiments were done, in vitro, on bundles of intact fibres (fibre length L(0) ~2 mm; sarcomere length ~2.5 µm) isolated from a rat fast muscle (flexor hallucis brevis) and a ramp length change of 5-7% L(0) was applied on the plateau of an isometric tetanic contraction. Ramp lengthening increased and ramp shortening decreased the muscle tension to new approximately steady levels in a velocity-dependent way. The isometric tension and the lower steady tension reached at a given shortening velocity, increased with warming from 10 to 35 °C and the relation between tension and reciprocal absolute temperature was sigmoidal. However, the tension-temperature curve of shortening muscle was sharper and shifted to higher temperature with increased velocity. In contrast, the enhanced steady tension during lengthening at a given velocity was largely temperature-insensitive within the same temperature range; we hypothesize that the tension-temperature curve may be shifted to lower temperatures in lengthening muscle. Consequently, when normalised to the isometric tension at each temperature, the tension during lengthening at a given velocity decreased exponentially with increase of temperature. The residual force enhancement that remains after ramp lengthening showed a similar behaviour and was markedly reduced in warming from 10 to 35 °C. The findings are consistent with the thesis that active force generation in muscle is endothermic and strain-sensitive; during shortening with a faster crossbridge cycle it becomes more pronounced, but during lengthening it becomes depressed as the cycle slows in a velocity-dependent way. The residual force enhancement may be caused by the same process in addition to non-crossbridge mechanism(s).

Force and power generating mechanism(s) in active muscle as revealed from temperature perturbation studies.

The basic characteristics of the process of force and power generation in active muscle that have emerged from temperature studies are examined. This is done by reviewing complementary findings from temperature-dependence studies and rapid temperature-jump (T-jump) experiments and from intact and skinned fast mammalian muscle fibres. In isometric muscle, a small T-jump leads to a characteristic rise in force showing that crossbridge force generation is endothermic (heat absorbed) and associated with increased entropy (disorder). The sensitivity of the T-jump force generation to added inorganic phosphate (Pi) indicates that a T-jump enhances an early step in the actomyosin (crossbridge) ATPase cycle before Pi-release. During muscle lengthening when steady force is increased, the T-jump force generation is inhibited. Conversely, during shortening when steady force is decreased, the T-jump force generation is enhanced in a velocity-dependent manner, showing that T-jump force generation is strain sensitive. Within the temperature range of ∼5­35◦C, the temperature dependence of steady active force is sigmoidal both in isometric and in shortening muscle. However, in shortening muscle, the endothermic character of force generation becomes more pronounced with increased velocity and this can, at least partly, account for the marked increase with warming of the mechanical power output of active muscle.

Temperature jump induced force generation in rabbit muscle fibres gets faster with shortening and shows a biphasic dependence on velocity.

We examined the tension responses to ramp shortening and rapid temperature jump (<0.2 ms, 3-4 degrees C T-jump) in maximally Ca(2+)-activated rabbit psoas muscle fibres at 8-9 degrees C (the fibre length (L(0)) was approximately 1.5 mm and sarcomere length 2.5 microm). The aim was to investigate the strain sensitivity of crossbridge force generation in muscle. The T-jump induced tension rise was examined during steady shortening over a wide range of velocities (V) approaching the V(max) (V range approximately 0.01 to approximately 1.5 L(0) s(1)). In the isometric state, a T-jump induced a biphasic tension rise consisting of a fast (approximately 50 s(1), phase 2b) and a slow (approximately 10 s(1), phase 3) component, but if treated as monophasic the rate was approximately 20 s(1). During steady shortening the T-jump tension rise was monophasic; the rate of tension rise increased linearly with shortening velocity, and near V(max) it was approximately 200 s(1), approximately 10x faster than in the isometric state. Relative to the tension reached after the T-jump, the amplitude increased with shortening velocity, and near V(max) it was 4x larger than in the isometric state. Thus, the temperature sensitivity of muscle force is markedly increased with velocity during steady shortening, as found in steady state experiments. The rate of tension decline during ramp shortening also increased markedly with increase of velocity. The absolute amplitude of T-jump tension rise was larger than that in the isometric state at the low velocities (<0.5 L(0) s(1)) but decreased to below that of the isometric state at the higher velocities. Such a biphasic velocity dependence of the absolute amplitude of T-jump tension rise implies interplay between, at least, two processes that have opposing effects on the tension output as the shortening velocity is increased, probably enhancement of crossbridge force generation and faster (post-stroke) crossbridge detachment by negative strain. Overall, our results show that T-jump force generation is strain sensitive and becomes considerably faster when exposed to negative strain. Thus the crossbridge force generation step in muscle is both temperature sensitive (endothermic) and strain sensitive.

Crossbridge and filament compliance in muscle: implications for tension generation and lever arm swing.

The stiffness of myosin heads attached to actin is a crucial parameter in determining the kinetics and mechanics of the crossbridge cycle. It has been claimed that the stiffness of myosin heads in the anterior tibialis muscle of the common frog (Rana temporaria) is as high as 3.3 pN/nm, substantially higher than its value in rabbit muscle (~1.7 pN/nm). However, the crossbridge stiffness measurement has a large error since the contribution of crossbridges to half-sarcomere compliance is obtained by subtracting from the half-sarcomere compliance the contributions of the thick and thin filaments, each with a substantial error. Calculation of its value for isometric contraction also depends on the fraction of heads that are attached, for which there is no consensus. Surprisingly, the stiffness of the myosin head from the edible frog, Rana esculenta, determined in the same manner, is only 60% of that in Rana temporaria. In our view it is unlikely that the value of such a crucial parameter could differ so substantially between two frog species. Since the means of the myosin head stiffness in these two species are not significantly different, we suggest that the best estimate of the stiffness of the myosin heads for frog muscle is the average of these data, a value similar to that for rabbit muscle. This would allow both frog and rabbit muscles to operate the same low-cooperativity mechanism for the crossbridge cycle with only one or two tension-generating steps. We review evidence that much of the compliance of the myosin head is located in the pliant region where the lever arm emerges from the converter and propose that tension generation ("tensing") caused by the rotation and movement of the converter is a separate event from the passive swinging of the lever arm in its working stroke in which the strain energy stored in the pliant region is used to do work.

Crossbridge mechanism(s) examined by temperature perturbation studies on muscle.

An overall view of the contractile process that has emerged from -temperature-studies on active muscle is outlined. In isometric muscle, a small rapid temperature-jump (T-jump) enhances an early, pre-phosphate release, step in the acto-myosin (crossbridge) ATPase cycle and induces a characteristic rise in force indicating that crossbridge force generation is endothermic (force rises when heat is absorbed). Sigmoidal temperature dependence of steady force is largely due to the endothermic nature of force generation. During shortening, when muscle force is decreased, the T-jump force generation is enhanced; conversely, when a muscle is lengthening and its force increased, the T-jump force generation is inhibited. Taking T-jump force generation as a signature of the crossbridge - ATPase cycle, the results suggest that during lengthening the ATPase cycle is truncated before endothermic force generation, whereas during shortening this step and the ATPase cycle, are accelerated; this readily provides a molecular basis for the Fenn effect.

Crossbridge and non-crossbridge contributions to force in shortening and lengthening muscle.

Analysis of tension responses to ramp length changes in muscle can provide important information about the crossbridge cycle. During a ramp length change, the force response of an active muscle shows an early change in slope (the P1 transition) followed by a later, gradual change in slope (the P2 transition). Modeling shows that the first transition reflects the tension change associated with the crossbridge power stroke in shortening and with its reversal in lengthening; the reduction in slope at the second transition occurs when most of the crossbridges (myosin heads) that were attached at the start of the ramp become detached; the steady tension during shortening is borne mainly by post-stroke heads whereas tension during lengthening is borne mostly by pre-stroke heads. After the P2 transition, the tension reaches a steady level in the model whereas in the experiments the tension continues to increase during lengthening or to decrease during shortening; this tension change is seen at a wide range of sarcomere lengths and even when active force is reduced by a myosin inhibitor. It appears that some non-crossbridge components in muscle fibers stiffen upon activation and contribute to the continued tension rise during lengthening; release of such tension leads to tension decline during shortening. Thus, non-crossbridge visco-elasticity in sarcomeres may also contribute to energy storage and release during in situ muscle function.

Muscle fatigue examined at different temperatures in experiments on intact mammalian (rat) muscle fibers.

In experiments on small bundles of intact fibers from a rat fast muscle, in vitro, we examined the decline in force in repeated tetanic contractions; the aim was to characterize the effect of shortening and of temperature on the initial phase of muscle fatigue. Short tetanic contractions were elicited at a control repetition rate of 1/60 s, and fatigue was induced by raising the rate to 1/5 s for 2-3 min, both in isometric mode (no shortening) and in shortening mode, in which each tetanic contraction included a ramp shortening at a standard velocity. In experiments at 20 degrees C (n = 12), the force decline during a fatigue run was 25% in the isometric mode but was significantly higher (35%) in the shortening mode. In experiments at different temperatures (10-30 degrees C, n = 11), the tetanic frequency and duration were adjusted as appropriate, and for shortening mode, the velocity was adjusted for maximum power output. In isometric mode, fatigue of force was significantly less at 30 degrees C ( approximately 20%) than at 10 degrees C ( approximately 30%); the power output (force x velocity) was >10x higher at 30 degrees C than at 10 degrees C, and power decline during a fatigue run was less at 30 degrees C ( approximately 20-30%) than at 10 degrees C ( approximately 50%). The finding that the extent of fatigue is increased with shortening contractions and is lower at higher temperatures is consistent with the view that force depression by inorganic phosphate, which accumulates within fibers during activity, may be a primary cause of initial muscle fatigue.

Effects of inorganic phosphate on endothermic force generation in muscle.

Using a rapid (ca. 0.2 ms) laser temperature jump technique, the rate of endothermic force generation was examined in single-skinned (rabbit psoas) muscle fibres when they were exposed to different levels of inorganic phosphate (a product released during ATP hydrolysis in active muscle). The steady force is reduced by increased phosphate but the apparent rate constant of force generation induced by a standard temperature jump (from ca. 9 degrees C to ca. 12 degrees C) increases two- to threefold when the phosphate added is increased from zero to ca. 25 mM. The increase in the apparent rate constant also exhibits saturation at higher phosphate levels and the relation is hyperbolic. Detailed examination of the data, particularly in relation to our pressure release experiments, leads to a scheme for the molecular steps involved in phosphate release and force generation in active muscle fibres, where phosphate release from attached cross-bridges involves three reversible and sequentially faster molecular steps. Step one is a moderately slow, pre-force generation step that probably represents a transition of cross-bridges from non-specific to stereospecific attached states. Step two is moderately fast and represents endothermic cross-bridge force generation (temperature sensitive) and step three is a very rapid phosphate release. Such a scheme accommodates findings from a variety of different studies, including pressure perturbation experiments and other studies where the effect of phosphate on muscle force was studied.

Resting tension characteristics in differentiating intact rat fast- and slow-twitch muscle fibers.

The postnatal changes in resting muscle tension were investigated at 20 degrees C by using small muscle fiber bundles isolated from either the extensor digitorum longus or the soleus of both neonatal (7-21 days old) and adult rats. The results show that the tension-extension characteristics of the bundles depended on the age of the rats. For example, both the extensor digitorum longus and soleus bundles of rats older than 14 days showed characteristic differences that were absent in bundles from younger rats. Furthermore, the tension-extension relation of the adult slow muscle fiber bundles were similar to those of the two neonatal muscles and were shifted to longer sarcomere lengths relative to those of the adult fast-fiber bundles. Thus, at the extended sarcomere length of 2.9 microm, the adult fast muscle fiber bundles developed higher resting tensions (5.6 +/- 0.5 kN/m2) than either the two neonatal ( approximately 3 kN/m2) or the adult slow (3.1 +/- 0.4 kN/m2) muscle fiber bundles. At all ages examined, the resting tension responses to a ramp stretch were qualitatively similar and consisted of three components: a viscous, a viscoelastic, and an elastic tension. However, in rats older than 14 days, all three tension components showed clear fast- and slow-fiber type differences that were absent in younger rats. Bundles from 7-day-old rats also developed significantly lower resting tensions than the corresponding adult ones. Additionally, the resting tension characteristics of the adult muscles were not affected by chemical skinning. From these results, we conclude that in rats resting muscle tension, like active tension, differentiates within the first 3 wk after birth.