Effects of sarcomere length and temperature on the rate of ATP utilisation by rabbit psoas muscle fibres

More than energy cost: multiple benefits of the long Achilles tendon in human walking and running

Elastic strain energy that is stored and released from long, distal tendons such as the Achilles during locomotion allows for muscle power amplification as well as for reduction of the locomotor energy cost: as distal tendons perform mechanical work during recoil, plantar flexor muscle fibres can work over smaller length ranges, at slower shortening speeds, and at lower activation levels. Scant evidence exists that long distal tendons evolved in humans (or were retained from our more distant Hominoidea ancestors) primarily to allow high muscle-tendon power outputs, and indeed we remain relatively powerless compared to many other species. Instead, the majority of evidence suggests that such tendons evolved to reduce total locomotor energy cost. However, numerous additional, often unrecognised, advantages of long tendons may speculatively be of greater evolutionary advantage, including the reduced limb inertia afforded by shorter and lighter muscles (reducing proximal muscle force requirement), reduced energy dissipation during the foot-ground collisions, capacity to store and reuse the muscle work done to dampen the vibrations triggered by foot-ground collisions, reduced muscle heat production (and thus core temperature), and attenuation of work-induced muscle damage. Cumulatively, these effects should reduce both neuromotor fatigue and sense of locomotor effort, allowing humans to choose to move at faster speeds for longer. As these benefits are greater at faster locomotor speeds, they are consistent with the hypothesis that running gaits used by our ancestors may have exerted substantial evolutionary pressure on Achilles tendon length. The long Achilles tendon may therefore be a singular adaptation that provided numerous physiological, biomechanical, and psychological benefits and thus influenced behaviour across multiple tasks, both including and additional to locomotion. While energy cost may be a variable of interest in locomotor studies, future research should consider the broader range of factors influencing our movement capacity, including our decision to move over given distances at specific speeds, in order to understand more fully the effects of Achilles tendon function as well as changes in this function in response to physical activity, inactivity, disuse and disease, on movement performance.

American Society of Biomechanics Journal of Biomechanics Award 2021: Exploring the Functional Boundaries and Metabolic Consequences of Triceps Surae Force-Length Relations during Walking

The relationship between individual muscle dynamics and whole-body metabolic cost is not well established. Here we use biofeedback to modulate triceps surae (TS) activity during walking to test the following hypotheses based on basic principles of muscle physiology: (1) increased TS activity would increase metabolic cost via shorter muscle fascicle lengths and thus reduced force capacity and (2) decreased TS activity would decrease metabolic cost via longer muscle fascicle lengths and thus increased force capacity. 23 young adults walked on an instrumented treadmill at 1.25 m/s using electromyographic (EMG) biofeedback to match targets corresponding to ±20 and ±40% TS activity during push-off (late stance). B-mode ultrasound imaged the medial gastrocnemius (MG). Participants increased net metabolic power up to 85% and 21% when targeting increased and decreased TS activity, respectively (p < 0.001). At the instant of peak gastrocnemius force, MG fascicle length was 7% shorter (p < 0.001) and gastrocnemius force was 6% larger (p < 0.001) when targeting + 40% TS activity. Fascicle length was 3% shorter (p = 0.004) and force was 7% lower (p = 0.010) when targeting -40% TS activity; participants were unable to achieve decreased activation targets. MG fascicle length and activity mediated 11.7% (p = 0.036) and 57.2% (p = 0.006) of the changes in net metabolic power, respectively. MG force did not mediate changes in net metabolic power (p = 0.948). These findings suggest that changes in the functional operating length of muscle, induced here by volitional changes in TS activity, mediated changes in the metabolic cost of walking, relatively independently of force. Thus, shifts to shorter fascicle lengths (e.g., aging) may mediate activity-induced increases in metabolic cost.

Faster triceps surae muscle cyclic contractions alter muscle activity and whole body metabolic rate

Hundred years ago, Fenn demonstrated that when a muscle shortens faster, its energy liberation increases. Fenn's results were the first of many that led to the general understanding that isometric muscle contractions are energetically cheaper than concentric contractions. However, this evidence is still primarily based on single fiber or isolated (ex vivo) muscle studies and it remains unknown whether this translates to whole body metabolic rate. In this study, we specifically changed the contraction velocity of the ankle plantar flexors and quantified the effects on triceps surae muscle activity and whole body metabolic rate during cyclic plantar flexion (PF) contractions. Fifteen participants performed submaximal ankle plantar flexions (∼1/3 s activation and ∼2/3 s relaxation) on a dynamometer at three different ankle angular velocities: isometric (10° PF), isokinetic at 30°/s (5-15° PF), and isokinetic at 60°/s (0-20° PF) while target torque (25% MVC) and cycle frequency were kept constant. In addition, to directly determine the effect of ankle angular velocity on muscle kinematics we collected gastrocnemius medialis muscle fascicle ultrasound data. As expected, increasing ankle angular velocity increased gastrocnemius medialis muscle fascicle contraction velocity and positive mechanical work (P < 0.01), increased mean and peak triceps surae muscle activity (P < 0.01), and considerably increased net whole body metabolic rate (P < 0.01). Interestingly, the increase in triceps surae muscle activity with fast ankle angular velocities was most pronounced in the gastrocnemius lateralis (P < 0.05). Overall, our results support the original findings from Fenn in 1923 and we demonstrated that greater triceps surae muscle contraction velocities translate to increased whole body metabolic rate.NEW & NOTEWORTHY Single muscle fiber studies or research on isolated (ex vivo) muscles demonstrated that faster concentric muscle contractions yield increased energy consumption. Here we translated this knowledge to muscle activation and whole body metabolic rate. Increasing ankle angular velocity increased triceps surae contraction velocity and mechanical work, increasing triceps surae muscle activity and substantially elevating whole body metabolic rate. Additionally, we demonstrated that triceps surae muscle activation strategy depends on the mechanical demands of the task.

Shorter muscle fascicle operating lengths increase the metabolic cost of cyclic force production

During locomotion, force-producing limb muscles are predominantly responsible for an animal's whole body metabolic energy expenditure. Animals can change the length of their force-producing muscle fascicles by altering body posture (e.g., joint angles), the structural properties of their biological tissues over time (e.g., tendon stiffness), or the body's kinetics (e.g., body weight). Currently, it is uncertain whether relative muscle fascicle operating lengths have a measurable effect on the metabolic energy expended during cyclic locomotion-like contractions. To address this uncertainty, we quantified the metabolic energy expenditure of human participants, as they cyclically produced two distinct ankle moments at three ankle angles (90°, 105°, and 120°) on a fixed-position dynamometer using their soleus. Overall, increasing participant ankle angle from 90° to 120° (more plantar flexion) reduced minimum soleus fascicle length by 17% (both moment levels, P < 0.001) and increased metabolic energy expenditure by an average of 208% across both moment levels (both P < 0.001). For both moment levels, the increased metabolic energy expenditure was not related to greater fascicle positive mechanical work (higher moment level, P = 0.591), fascicle force rate (both P ≥ 0.235), or model-estimated active muscle volume (both P ≥ 0.122). Alternatively, metabolic energy expenditure correlated with average relative soleus fascicle length (r = -0.72, P = 0.002) and activation (r = 0.51, P < 0.001). Therefore, increasing active muscle fascicle operating lengths may reduce metabolic energy expended during locomotion.NEW & NOTEWORTHY During locomotion, active muscles undergo cyclic length-changing contractions. In this study, we isolated confounding variables and revealed that cyclically producing force at relatively shorter fascicle lengths increases metabolic energy expenditure. Therefore, muscle fascicle operating lengths likely have a measurable effect on the metabolic energy expenditure during locomotion.

Adding carbon fiber to shoe soles may not improve running economy: a muscle-level explanation

In an attempt to improve their distance-running performance, many athletes race with carbon fiber plates embedded in their shoe soles. Accordingly, we sought to establish whether, and if so how, adding carbon fiber plates to shoes soles reduces athlete aerobic energy expenditure during running (improves running economy). We tested 15 athletes as they ran at 3.5 m/s in four footwear conditions that varied in shoe sole bending stiffness, modified by carbon fiber plates. For each condition, we quantified athlete aerobic energy expenditure and performed biomechanical analyses, which included the use of ultrasonography to examine soleus muscle dynamics in vivo. Overall, increased footwear bending stiffness lengthened ground contact time (p = 0.048), but did not affect ankle (p ≥ 0.060), knee (p ≥ 0.128), or hip (p ≥ 0.076) joint angles or moments. Additionally, increased footwear bending stiffness did not affect muscle activity (all seven measured leg muscles (p ≥ 0.146)), soleus active muscle volume (p = 0.538; d = 0.241), or aerobic power (p = 0.458; d = 0.04) during running. Hence, footwear bending stiffness does not appear to alter the volume of aerobic energy consuming muscle in the soleus, or any other leg muscle, during running. Therefore, adding carbon fiber plates to shoe soles slightly alters whole-body and calf muscle biomechanics but may not improve running economy.

Exhaustion of Skeletal Muscle Fibers Within Seconds: Incorporating Phosphate Kinetics Into a Hill-Type Model

Initiated by neural impulses and subsequent calcium release, skeletal muscle fibers contract (actively generate force) as a result of repetitive power strokes of acto-myosin cross-bridges. The energy required for performing these cross-bridge cycles is provided by the hydrolysis of adenosine triphosphate (ATP). The reaction products, adenosine diphosphate (ADP) and inorganic phosphate (P i ), are then used-among other reactants, such as creatine phosphate-to refuel the ATP energy storage. However, similar to yeasts that perish at the hands of their own waste, the hydrolysis reaction products diminish the chemical potential of ATP and thus inhibit the muscle's force generation as their concentration rises. We suggest to use the term "exhaustion" for force reduction (fatigue) that is caused by combined P i and ADP accumulation along with a possible reduction in ATP concentration. On the basis of bio-chemical kinetics, we present a model of muscle fiber exhaustion based on hydrolytic ATP-ADP-P i dynamics, which are assumed to be length- and calcium activity-dependent. Written in terms of differential-algebraic equations, the new sub-model allows to enhance existing Hill-type excitation-contraction models in a straightforward way. Measured time courses of force decay during isometric contractions of rabbit M. gastrocnemius and M. plantaris were employed for model verification, with the finding that our suggested model enhancement proved eminently promising. We discuss implications of our model approach for enhancing muscle models in general, as well as a few aspects regarding the significance of phosphate kinetics as one contributor to muscle fatigue.

Ultrasound imaging links soleus muscle neuromechanics and energetics during human walking with elastic ankle exoskeletons

Unpowered exoskeletons with springs in parallel to human plantar flexor muscle-tendons can reduce the metabolic cost of walking. We used ultrasound imaging to look 'under the skin' and measure how exoskeleton stiffness alters soleus muscle contractile dynamics and shapes the user's metabolic rate during walking. Eleven participants (4F, 7M; age: 27.7 ± 3.3 years) walked on a treadmill at 1.25 m s-1 and 0% grade with elastic ankle exoskeletons (rotational stiffness: 0-250 Nm rad-1) in one training and two testing days. Metabolic savings were maximized (4.2%) at a stiffness of 50 Nm rad-1. As exoskeleton stiffness increased, the soleus muscle operated at longer lengths and improved economy (force/activation) during early stance, but this benefit was offset by faster shortening velocity and poorer economy in late stance. Changes in soleus activation rate correlated with changes in users' metabolic rate (p = 0.038, R2 = 0.44), highlighting a crucial link between muscle neuromechanics and exoskeleton performance; perhaps informing future 'muscle-in-the loop' exoskeleton controllers designed to steer contractile dynamics toward more economical force production.

Modular footwear that partially offsets downhill or uphill grades minimizes the metabolic cost of human walking

Walking on different grades becomes challenging on energetic and muscular levels compared to level walking. While it is not possible to eliminate the cost of raising or lowering the centre of mass (COM), it could be possible to minimize the cost of distal joints with shoes that offset downhill or uphill grades. We investigated the effects of shoe outsole geometry in 10 participants walking at 1 m s^-1 on downhill, level and uphill grades. Level shoes minimized metabolic rate during level walking (P _{second-order effect} < 0.001). However, shoes that entirely offset the (overall) treadmill grade did not minimize the metabolic rate of walking on grades: shoes with a +3° (upward) inclination minimized metabolic rate during downhill walking on a -6° grade, and shoes with a -3° (downward) inclination minimized metabolic rate during uphill walking on a +6° grade (P _{interaction effect} = 0.023). Shoe inclination influenced (distal) ankle joint parameters, including soleus muscle activity, ankle moment and work rate, whereas treadmill grade influenced (whole-body) ground reaction force and COM work rate as well as (distal) ankle joint parameters including tibialis anterior and plantarflexor muscle activity, ankle moment and work rate. Similar modular footwear could be used to minimize joint loads or assist with walking on rolling terrain.

The force-length-velocity potential of the human soleus muscle is related to the energetic cost of running

According to the force-length-velocity relationships, the muscle force potential is determined by the operating length and velocity, which affects the energetic cost of contraction. During running, the human soleus muscle produces mechanical work through active shortening and provides the majority of propulsion. The trade-off between work production and alterations of the force-length and force-velocity potentials (i.e. fraction of maximum force according to the force-length-velocity curves) might mediate the energetic cost of running. By mapping the operating length and velocity of the soleus fascicles onto the experimentally assessed force-length and force-velocity curves, we investigated the association between the energetic cost and the force-length-velocity potentials during running. The fascicles operated close to optimal length (0.90 ± 0.10 L₀) with moderate velocity (0.118 ± 0.039 V_max [maximum shortening velocity]) and, thus, with a force-length potential of 0.92 ± 0.07 and a force-velocity potential of 0.63 ± 0.09. The overall force-length-velocity potential was inversely related (r = -0.52, p = 0.02) to the energetic cost, mainly determined by a reduced shortening velocity. Lower shortening velocity was largely explained (p < 0.001, R² = 0.928) by greater tendon gearing, shorter Achilles tendon lever arm, greater muscle belly gearing and smaller ankle angle velocity. Here, we provide the first experimental evidence that lower shortening velocities of the soleus muscle improve running economy.

Enhanced Development of Skeletal Myotubes from Porcine Induced Pluripotent Stem Cells

The pig is recognized as a valuable model in biomedical research in addition to its agricultural importance. Here we describe a means for generating skeletal muscle efficiently from porcine induced pluripotent stem cells (piPSC) in vitro thereby providing a versatile platform for applications ranging from regenerative biology to the ex vivo cultivation of meat. The GSK3B inhibitor, CHIR99021 was employed to suppress apoptosis, elicit WNT signaling events and drive naïve-type piPSC along the mesoderm lineage, and, in combination with the DNA methylation inhibitor 5-aza-cytidine, to activate an early skeletal muscle transcription program. Terminal differentiation was then induced by activation of an ectopically expressed MYOD1. Myotubes, characterized by myofibril development and both spontaneous and stimuli-elicited excitation-contraction coupling cycles appeared within 11 days. Efficient lineage-specific differentiation was confirmed by uniform NCAM1 and myosin heavy chain expression. These results provide an approach for generating skeletal muscle that is potentially applicable to other pluripotent cell lines and to generating other forms of muscle.

Energetics of contraction

Muscles convert energy from ATP into useful work, which can be used to move limbs and to transport ions across membranes. The energy not converted into work appears as heat. At the start of contraction heat is also produced when Ca(2+) binds to troponin-C and to parvalbumin. Muscles use ATP throughout an isometric contraction at a rate that depends on duration of stimulation, muscle type, temperature and muscle length. Between 30% and 40% of the ATP used during isometric contraction fuels the pumping Ca(2+) and Na(+) out of the myoplasm. When shortening, muscles produce less force than in an isometric contraction but use ATP at a higher rate and when lengthening force output is higher than the isometric force but rate of ATP splitting is lower. Efficiency quantifies the fraction of the energy provided by ATP that is converted into external work. Each ATP molecule provides 100 zJ of energy that can potentially be converted into work. The mechanics of the myosin cross-bridge are such that at most 50 zJ of work can be done in one ATP consuming cycle; that is, the maximum efficiency of a cross-bridge is ∼50%. Cross-bridges in tortoise muscle approach this limit, producing over 90% of the possible work per cycle. Other muscles are less efficient but contract more rapidly and produce more power.

Single molecule detection approach to muscle study: kinetics of a single cross-bridge during contraction of muscle

D166V point mutation in the ventricular myosin regulatory light chain (RLC) is one of the causes of familial hypertrophic cardiomyopathy (FHC). We show here that the rates of cross-bridge attachment and dissociation are significantly different in isometrically contracting cardiac myofibrils from right ventricle of WT and Tg-D166V mice. To avoid averaging over ensembles of molecules composing muscle fibers, the data was collected from a single molecule. Kinetics were derived by tracking the orientation of a single actin molecule by fluorescence anisotropy. Orientation oscillated between two states, corresponding to the actin-bound and actin-free states of the myosin cross-bridge. The cross-bridge in a wild-type (healthy) heart stayed attached and detached from thin filament on average for 0.7 and 2.7 s, respectively. In FHC heart, these numbers increased to 2.5 and 5.8 s, respectively. These findings suggest that alterations in myosin cross-bridge kinetics associated with D166V mutation of RLC ultimately affect the ability of a heart to efficiently pump the blood.

Cross-bridge kinetics in myofibrils containing familial hypertrophic cardiomyopathy R58Q mutation in the regulatory light chain of myosin

Familial hypertrophic cardiomyopathy (FHC) is a heritable form of cardiac hypertrophy caused by single-point mutations in genes encoding sarcomeric proteins including ventricular myosin regulatory light chain (RLC). FHC often leads to malignant outcomes and sudden cardiac death. The FHC mutations are believed to alter the kinetics of the interaction between actin and myosin resulting in inefficient energy utilization and compromised function of the heart. We studied the effect of the FHC-linked R58Q-RLC mutation on the kinetics of transgenic (Tg)-R58Q cardiac myofibrils. Kinetics was determined from the rate of change of orientation of actin monomers during muscle contraction. Actin monomers change orientation because myosin cross-bridges deliver periodic force impulses to it. An individual impulse (but not time average of impulses) carries the information about the kinetics of actomyosin interaction. To observe individual impulses it was necessary to scale down the experiments to the level of a few molecules. A small population (∼4 molecules) was selected by using (deliberately) inefficient fluorescence labeling and observing fluorescent molecules by a confocal microscope. We show that the kinetic rates are significantly smaller in the contracting cardiac myofibrils from Tg-R58Q mice then in control Tg-wild type (WT). We also demonstrate a lower force per cross-section of muscle fiber in Tg-R58Q versus Tg-WT mice. We conclude that the R58Q mutation-induced decrease in cross-bridge kinetics underlines the mechanism by which Tg-R58Q fibers develop low force and thus compromise the ability of the mutated heart to efficiently pump blood.

Observing cycling of a few cross-bridges during isometric contraction of skeletal muscle

During muscle contraction a myosin cross-bridge imparts periodic force impulses to actin. It is possible to visualize those impulses by observing a few molecules of actin or myosin. We have followed the time course of orientation change of a few actin molecules during isometric contraction by measuring parallel polarized intensity of its fluorescence. The orientation of actin reflects local bending of a thin filament and is different when a cross-bridge binds to, or is detached from, F-actin. The changes in orientation were characterized by periods of activity during which myosin cross-bridges interacted normally with actin, interspersed with periods of inactivity during which actin and myosin were unable to interact. The periods of activity lasted on average 1.2 +/- 0.4 s and were separated on average by 2.3 +/- 1.0 s. During active period, actin orientation oscillated between the two extreme values with the ON and OFF times of 0.4 +/- 0.2 and 0.7 +/- 0.4 s, respectively. When the contraction was induced by a low concentration of ATP both active and inactive times were longer and approximately equal. These results imply that cross-bridges interact with actin in bursts and suggest that during active period, on average 36% of cross-bridges are involved in force generation.

Effect of phosphate and temperature on force exerted by white muscle fibres from dogfish

Effects of Pi (inorganic phosphate) are relevant to the in vivo function of muscle because Pi is one of the products of ATP hydrolysis by actomyosin and by the sarcoplasmic reticulum Ca²⁺ pump. We have measured the Pi sensitivity of force produced by permeabilized muscle fibres from dogfish (Scyliorhinus canicula) and rabbit. The activation conditions for dogfish fibres were crucial: fibres activated from the relaxed state at 5, 12, and 20°C were sensitive to Pi, whereas fibres activated from rigor at 12°C were insensitive to Pi in the range 5–25 mmol l⁻¹. Rabbit fibres activated from rigor were sensitive to Pi. Pi sensitivity of force produced by dogfish fibres activated from the relaxed state was greater below normal body temperature (12°C for dogfish) in agreement with what is known for other species. The force-temperature relationship for dogfish fibres (intact and permeabilized fibres activated from relaxed) showed that at 12°C, normal body temperature, the force was near to its maximum value.

Synchronous in situ ATPase activity, mechanics, and Ca2+ sensitivity of human and porcine myocardium

Flash-frozen myocardium samples provide a valuable means of correlating clinical cardiomyopathies with abnormalities in sarcomeric contractile and biochemical parameters. We examined flash-frozen left-ventricle human cardiomyocyte bundles from healthy donors to determine control parameters for isometric tension (P(o)) development and Ca(2+) sensitivity, while simultaneously measuring actomyosin ATPase activity in situ by a fluorimetric technique. P(o) was 17 kN m(-2) and pCa(50%) was 5.99 (28 degrees C, I = 130 mM). ATPase activity increased linearly with tension to 132 muM s(-1). To determine the influence of flash-freezing, we compared the same parameters in both glycerinated and flash-frozen porcine left-ventricle trabeculae. P(o) in glycerinated porcine myocardium was 25 kN m(-2), and maximum ATPase activity was 183 microM s(-1). In flash-frozen porcine myocardium, P(o) was 16 kN m(-2) and maximum ATPase activity was 207 microM s(-1). pCa(50%) was 5.77 in the glycerinated and 5.83 in the flash-frozen sample. Both passive and active stiffness of flash-frozen porcine myocardium were lower than for glycerinated tissue and similar to the human samples. Although lower stiffness and isometric tension development may indicate flash-freezing impairment of axial force transmission, we cannot exclude variability between samples as the cause. ATPase activity and pCa(50%) were unaffected by flash-freezing. The lower ATPase activity measured in human tissue suggests a slower actomyosin turnover by the contractile proteins.

Time course and strain dependence of ADP release during contraction of permeabilized skeletal muscle fibers

A phosphorylated, single cysteine mutant of nucleoside diphosphate kinase, labeled with N-[2-(iodoacetamido)ethyl]-7-diethylaminocoumarin-3-carboxamide (P approximately NDPK-IDCC), was used as a fluorescence probe for time-resolved measurement of changes in [MgADP] during contraction of single permeabilized rabbit psoas fibers. The dephosphorylation of the phosphorylated protein by MgADP occurs within the lattice environment of permeabilized fibers with a second-order rate constant at 12 degrees C of 10(5) M(-1) s(-1). This dephosphorylation is accompanied by a change in coumarin fluorescence. We report the time course of P approximately NDPK-IDCC dephosphorylation during the period of active isometric force redevelopment after quick release of fiber strain at pCa(2+) of 4.5. After a rapid length decrease of 0.5% was applied to the fiber, the extra NDPK-IDCC produced during force recovery, above the value during the approximately steady state of isometric contraction, was 2.7 +/- 0.6 microM and 4.7 +/- 1.5 microM at 12 and 20 degrees C, respectively. The rates of P approximately NDPK-IDCC dephosphorylation during force recovery were 28 and 50 s(-1) at 12 and 20 degrees C, respectively. The time courses of isometric force and P approximately NDPK-IDCC dephosphorylation were simulated using a seven-state reaction scheme. Relative isometric force was modeled by changes in the occupancy of strongly bound A.M.ADP.P(i) and A.M.ADP states. A strain-sensitive A.M.ADP isomerization step was rate-limiting (3-6 s(-1)) in the cross-bridge turnover during isometric contraction. At 12 degrees C, the A.M.ADP.P(i) and the pre- and postisomerization A.M.ADP states comprised 56%, 38%, and 7% of the isometric force-bearing AM states, respectively. At 20 degrees C, the force-bearing A.M.ADP.P(i) state was a lower proportion of the total force-bearing states (37%), whereas the proportion of postisomerization A.M.ADP states was higher (19%). The simulations suggested that release of cross-bridge strain caused rapid depopulation of the preisomerization A.M.ADP state and transient accumulation of MgADP in the postisomerization A.M.ADP state. Hence, the strain-sensitive isomerization of A.M.ADP seems to explain the rate of change of P approximately NDPK-IDCC dephosphorylation during force recovery. The temperature-dependent isometric distribution of myosin states is consistent with the previous observation of a small decrease in amplitude of the P(i) transient during force recovery at 20 degrees C and the current observation of an increase in amplitude of the ADP-sensitive NDPK-IDCC transient.

Two-state model of acto-myosin attachment-detachment predicts C-process of sinusoidal analysis

The force response of activated striated muscle to length perturbations includes the so-called C-process, which has been considered the frequency domain representation of the fast single-exponential force decay after a length step (phases 1 and 2). The underlying molecular mechanisms of this phenomenon, however, are still the subject of various hypotheses. In this study, we derived analytical expressions and created a corresponding computer model to describe the consequences of independent acto-myosin cross-bridges characterized solely by 1), intermittent periods of attachment (t(att)) and detachment (t(det)), whose values are stochastically governed by independent probability density functions; and 2), a finite Hookian stiffness (k(stiff)) effective only during periods of attachment. The computer-simulated force response of 20,000 (N) cross-bridges making up a half-sarcomere (F(hs)(t)) to sinusoidal length perturbations (L(hs)(t)) was predicted by the analytical expression in the frequency domain, (F(hs)(omega)/L(hs)(omega))=(t(att)/t(cycle))Nk(stiff)(iomega/(t(att)(-1)+iomega)), where t(att) = mean value of t(att), t(cycle) = mean value of t(att) + t(det), k(stiff) = mean stiffness, and omega = 2pi x frequency of perturbation. The simulated force response due to a length step (L(hs)) was furthermore predicted by the analytical expression in the time domain, F(hs)(t)=(t(att)/t(cycle))Nk(stiff)L(hs)e(-t/t(att)). The forms of these analytically derived expressions are consistent with expressions historically used to describe these specific characteristics of a force response and suggest that the cycling of acto-myosin cross-bridges and their associated stiffnesses are responsible for the C-process and for phases 1 and 2. The rate constant 2pic, i.e., the frequency parameter of the historically defined C-process, is shown here to be equal to t(att)(-1). Experimental results from activated cardiac muscle examined at different temperatures and containing predominately alpha- or beta-myosin heavy chain isoforms were found to be consistent with the above interpretation.

Hibernating bears conserve muscle strength and maintain fatigue resistance

Black bears spend several months each winter confined to a small space within their den without food or water. In nonhibernating mammals, these conditions typically result in severe muscle atrophy, causing a loss of strength and endurance. However, an initial study indicated that bears appeared to conserve strength while denning. We conducted an in vivo, nonsubjective measurement of strength, resistance to fatigue, and contractile properties on the tibialis anterior muscle of six hibernating bears during both early and late winter using a rigid leg brace and foot force plate. After 110 d of anorexia and confinement, skeletal muscle strength loss in hibernating bears was about one-half that in humans confined to bed rest. Bears lost 29% of muscle strength over 110 d of denning without food, while humans on a balanced diet but confined to bed for 90 d have been reported to lose 54% of their strength. Additionally, muscle contractile properties, including contraction time, half-relaxation time, half-maximum value time, peak rate of development and decay, time to peak force development, and time to peak force decay did not change, indicating that no small-scale alterations in whole-muscle function occurred over the winter. This study further supports our previous findings that black bears have a high resistance to atrophy despite being subjected to long-term anorexia and limited mobility.

Effect of strain on actomyosin kinetics in isometric muscle fibers

Investigations were conducted into the biochemical and mechanical states of cross-bridges during isometric muscle contraction. Rapid length steps (3 or 6 nm hs(-1)) were applied to rabbit psoas fibers, permeabilized and isometric, at either 12 degrees C or 20 degrees C. Fibers were activated by photolysis of P(3)-1-(2-nitrophenyl)-ethyl ester of ATP infused into rigor fibers at saturating Ca(2+). Sarcomere length, tension, and phosphate release were recorded-the latter using the MDCC-PBP fluorescent probe. A reduction in strain, induced by a rapid release step, produced a short-lived acceleration of phosphate release. Rates of the phosphate transient and that of phases 3 and 4 of tension recovery were unaffected by step size but were elevated at higher temperatures. In contrast the amplitude of the phosphate transient was smaller at 20 degrees C than 12 degrees C. The presence of 0.5 or 1.0 mM added ADP during a release step reduced both the rate of tension recovery and the poststep isometric tension. A kinetic scheme is presented to simulate the observed data and to precisely determine the rate constants for the elementary steps of the ATPase cycle.

The effects of the myosin-II inhibitor N-benzyl-p-toluene sulphonamide on fatigue in mouse single intact toe muscle fibres

AIM

This study determined whether fatigue in skeletal muscle is primarily due to the repeated elevations of myoplasmic free calcium concentration ([Ca(2+)](i)) or to metabolite accumulation.

METHODS

We examined the effects of N-benzyl-p-toluene sulphonamide (BTS) which is a potent and specific inhibitor of fast muscle myosin-II on the development of fatigue in mouse flexor digitorum brevis (FDB) muscle fibres. Single intact FDB fibres were micro-injected with indo-1 to monitor changes in [Ca(2+)](i) and stimulated repeatedly for a maximum of 150 tetani or until force declined to 40%.

RESULTS

BTS markedly reduced tetanic force but had no effect on the tetanic [Ca(2+)](i) transients. When fatigue was induced in the presence of BTS, the reduction in [Ca(2+)](i) and force transients occurred much more slowly than in the absence of BTS. The extent of force depression was similar after induction of fatigue in fibres exposed to Tyrode only or to BTS and force recovered to the same extent.

CONCLUSION

The results suggest that the decrease in tetanic [Ca(2+)](i) and force caused during fatigue are due mainly to accumulated metabolic changes.

The depressive effect of Pi on the force-pCa relationship in skinned single muscle fibers is temperature dependent

Increases in P(i) combined with decreases in myoplasmic Ca(2+) are believed to cause a significant portion of the decrease in muscular force during fatigue. To investigate this further, we determined the effect of 30 mM P(i) on the force-Ca(2+) relationship of chemically skinned single muscle fibers at near-physiological temperature (30 degrees C). Fibers isolated from rat soleus (slow) and gastrocnemius (fast) muscle were subjected to a series of solutions with an increasing free Ca(2+) concentration in the presence and absence of 30 mM P(i) at both low (15 degrees C) and high (30 degrees C) temperature. In slow fibers, 30 mM P(i) significantly increased the Ca(2+) required to elicit measurable force, referred to as the activation threshold at both low and high temperatures; however, the effect was twofold greater at the higher temperature. In fast fibers, the activation threshold was unaffected by elevating P(i) at 15 degrees C but was significantly increased at 30 degrees C. At both low and high temperatures, 30 mM P(i) increased the Ca(2+) required to elicit half-maximal force (pCa(50)) in both slow and fast fibers, with the effect of P(i) twofold greater at the higher temperature. These data suggest that during fatigue, reductions in the myoplasmic Ca(2+) and increases in P(i) act synergistically to reduce muscular force. Consequently, the combined changes in these ions likely account for a greater portion of fatigue than previously predicted based on studies at lower temperatures or high temperatures at saturating Ca(2+) levels.

Using optical tweezers to relate the chemical and mechanical cross-bridge cycles

In most current models of muscle contraction there are two translational steps, the working stroke, whereby an attached myosin cross-bridge moves relative to the actin filament, and the repriming step, in which the cross-bridge returns to its original orientation. The development of single molecule methods has allowed a more detailed investigation of the relationship of these mechanical steps to the underlying biochemistry. In the normal adenosine triphosphate cycle, myosin.adenosine diphosphate.phosphate (M.ADP.Pi) binds to actin and moves it by ca. 5 nm on average before the formation of the end product, the rigor actomyosin state. All the other product-like intermediate states tested were found to give no net movement indicating that M.ADP.Pi alone binds in a pre-force state. Myosin states with bound, unhydrolysed nucleoside triphosphates also give no net movement, indicating that these must also bind in a post-force conformation and that the repriming, post- to pre-transition during the forward cycle must take place while the myosin is dissociated from actin. These observations fit in well with the structural model in which the working stroke is aligned to the opening of the switch 2 element of the ATPase site.

Mechanokinetics of rapid tension recovery in muscle: the Myosin working stroke is followed by a slower release of phosphate

Crystallographic and biochemical evidence suggests that the myosin working stroke that generates force in muscle is accompanied by the release of inorganic phosphate (Pi), but the order and relative speed of these transitions is not firmly established. To address this problem, the theory of A. F. Huxley and R. M. Simmons for the length-step response is averaged over elastic strains imposed by filament structure and extended to include a Pi-release transition. Models of this kind are applied to existing tension-recovery data from length steps at different phosphate concentrations, and from phosphate jumps upon release of caged phosphate. This body of data is simulated by the model in which the force-generating event is followed by Pi release. A version in which the Pi-release transition is slow provides a better fit than a version with rapid Pi release and a slow transition preceding force generation. If Pi is released before force generation, the predicted rate of slow recovery increases with the size of the step, which is not observed. Some implications for theories of muscle contraction are discussed.

The ATP hydrolysis and phosphate release steps control the time course of force development in rabbit skeletal muscle

The time course of isometric force development following photolytic release of ATP in the presence of Ca(2+) was characterized in single skinned fibres from rabbit psoas muscle. Pre-photolysis force was minimized using apyrase to remove contaminating ATP and ADP. After the initial force rise induced by ATP release, a rapid shortening ramp terminated by a step stretch to the original length was imposed, and the time course of the subsequent force redevelopment was again characterized. Force development after ATP release was accurately described by a lag phase followed by one or two exponential components. At 20 degrees C, the lag was 5.6 +/- 0.4 ms (s.e.m., n = 11), and the force rise was well fitted by a single exponential with rate constant 71 +/- 4 s(-1). Force redevelopment after shortening-restretch began from about half the plateau force level, and its single-exponential rate constant was 68 +/- 3 s(-1), very similar to that following ATP release. When fibres were activated by the addition of Ca(2+) in ATP-containing solution, force developed more slowly, and the rate constant for force redevelopment following shortening-restretch reached a maximum value of 38 +/- 4 s(-1) (n = 6) after about 6 s of activation. This lower value may be associated with progressive sarcomere disorder at elevated temperature. Force development following ATP release was much slower at 5 degrees C than at 20 degrees C. The rate constant of a single-exponential fit to the force rise was 4.3 +/- 0.4 s(-1) (n = 22), and this was again similar to that after shortening-restretch in the same activation at this temperature, 3.8 +/- 0.2 s(-1). We conclude that force development after ATP release and shortening-restretch are controlled by the same steps in the actin-myosin ATPase cycle. The present results and much previous work on mechanical-chemical coupling in muscle can be explained by a kinetic scheme in which force is generated by a rapid conformational change bracketed by two biochemical steps with similar rate constants -- ATP hydrolysis and the release of inorganic phosphate -- both of which combine to control the rate of force development.

Interplay of troponin- and Myosin-based pathways of calcium activation in skeletal and cardiac muscle: the use of W7 as an inhibitor of thin filament activation

To investigate the interplay between the thin and thick filaments during calcium activation in striated muscle, we employed n-(6-aminohexyl) 5-chloro-1-napthalenesulfonamide (W7) as an inhibitor of troponin C and compared its effects with that of the myosin-specific inhibitor, 2,3-butanedione 2-monoxime (BDM). In both skeletal and cardiac fibers, W7 reversibly inhibited ATPase and tension over the full range of calcium activation between pCa 8.0 and 4.5, resulting in reduced calcium sensitivity and cooperativity of ATPase and tension activations. At maximal activation in skeletal fibers, the W7 concentrations for half-maximal inhibition (KI) were 70-80 micro M for ATPase and 20-30 micro M for tension, nearly >200-fold lower than BDM (20 mM and 5-8 mM, respectively). When W7 (50 microM) and BDM (20 mM) were combined in skeletal fibers, the ATPase and tension-pCa curves exhibited lower apparent cooperativity and maxima and higher calcium sensitivity than expected from two independent activation pathways, suggesting that the interplay between the thin and thick filaments varies with the level of activation. Significantly, the inhibition of W7 increased the ATPase/tension ratio during activation in both muscle types. W7 holds much promise as a potent and reversible inhibitor of thin filament-mediated calcium activation of skeletal and cardiac muscle contraction.

Actomyosin energy turnover declines while force remains constant during isometric muscle contraction

Energy turnover was measured during isometric contractions of intact and Triton-permeabilized white fibres from dogfish (Scyliorhinus canicula) at 12 degrees C. Heat + work from actomyosin in intact fibres was determined from the dependence of heat + work output on filament overlap. Inorganic phosphate (Pi) release by permeabilized fibres was recorded using the fluorescent protein MDCC-PBP, N-(2-[1-maleimidyl]ethyl)-7-diethylamino-coumarin-3 carboxamide phosphate binding protein. The steady-state ADP release rate was measured using a linked enzyme assay. The rates decreased five-fold during contraction in both intact and permeabilized fibres. In intact fibres the rate of heat + work output by actomyosin decreased from 134 +/-s.e.m. 28 microW mg(-1) (n = 17) at 0.055 s to 42% of this value at 0.25 s, and to 20% at 3.5 s. The force remained constant between 0.25 and 3.5 s. Similarly in permeabilized fibres the Pi release rate decreased from 5.00 +/- 0.39 mmol l(-1) s(-1) at 0.055 s to 39% of this value at 0.25 s and to 19% at 0.5 s. The steady-state ADP release rate at 15 s was 21% of the Pi rate at 0.055 s. Using a single set of rate constants, the time courses of force, heat + work and Pi release were described by an actomyosin model that took account of the transition from the initial state (rest or rigor) to the contracting state, shortening and the consequent work against series elasticity, and reaction heats. The model suggests that increasing Pi concentration slows the cycle in intact fibres, and that changes in ATP and ADP slow the cycle in permeabilized fibres.

Relationship between isometric force and myofibrillar MgATPase at short sarcomere length in skeletal and cardiac muscle and its relevance to the concept of activation heat

1. This paper has been written in recognition of the seminal contributions to cardiac and skeletal muscle energetics made by Professor Colin Gibbs during his distinguished academic career. 2. The paper focuses on what is now known about the relationship between Ca2+-activated isometric force production and myofibrillar MgATPase in intact and skinned (surface membrane rendered permeable) skeletal and cardiac muscle preparations at short sarcomere lengths. 3. The relevance of this relationship to understanding the interactions between the actin and myosin filaments at the cross-bridge level in the region of double actin filament overlap and the cellular basis of 'activation heat' measurements in intact striated muscles is discussed.

Effect of active shortening on the rate of ATP utilisation by rabbit psoas muscle fibres

1. The rate of ATP utilisation during active shortening of single skinned fibres from rabbit psoas muscle at 10 degrees C was measured using an NADH-linked assay. Fibres were immersed in silicone oil and illuminated with 365 nm light. The amounts of NADH and carboxytetramethylrhodamine (CTMR) in the illuminated region of the fibre were measured simultaneously from fluorescence emission at 425-475 and 570-650 nm, respectively. The ratio of these two signals was used to determine the intracellular concentration of NADH, and thus the ATP utilisation, without interference from movements of the fibre with respect to the measuring light beam. 2. The total extra ATP utilisation due to shortening (ATP) was determined by extrapolation of the steady isometric rates before and after shortening to the mid-point of the shortening period. ATP had a roughly linear dependence on the extent of shortening in the range 1-15 % fibre length (L0) at a shortening velocity of 0.4 L0 s-1 from initial sarcomere length 2.7 microm. For shortening of 1 % L0, ATP was 21 +/- 1 M (mean +/- S.E.M., n = 3). 3. The mean rate of ATP utilisation during ramp shortening of 10 % L0 had a roughly linear dependence on shortening velocity in the range 0.05-1.2 L0 s-1. During unloaded shortening at 1.2 L0 s-1 the mean rate of ATP utilisation was 1.7 mM s-1, about 9 times the isometric rate. ATP was roughly independent of shortening velocity, and was 84 +/- 9 microM (mean +/- S.E.M., n = 6) for shortening of 10 % L0. 4. The implications of these results for mechanical-chemical coupling in muscle are discussed. The total ATP utilisation associated with shortening of 1 % L0 is only about 17 % of the concentration of the myosin heads in the fibre, suggesting that during isometric contraction either less than 17 % of the myosin heads are attached to actin, or that heads can detach without commitment to ATP splitting. The fraction of myosin heads attached to actin during unloaded shortening is estimated from the rate of ATP utilisation to be less than 7 %.