Revisiting specific force loss in human permeabilized single skeletal muscle fibers obtained from older individuals.

Specific force (SF) has been shown to be reduced in some but not all studies of human aging using chemically skinned single muscle fibers. This may be due, in part, not only to the health status/physical activity levels of different older cohorts, but also from methodological differences in studying skinned fibers. The aim of the present study was to compare SF in fibers from older hip fracture patients (HFP), healthy master cyclists (MC), and healthy nontrained young adults (YA) using two different activating solutions. Quadriceps muscle samples and 316 fibers were obtained from HFPs (74.6 ± 4 years, n = 5), MCs (74.8 ± 1, n = 5), and YA (25.5 ± 2, n = 6). Fibers were activated (pCa 4.5, 15°C) in solutions containing either 60 mM N-tris(hydroxymethyl)methyl-2-aminoethanesulfonic acid pH buffer (TES) or 20 mM imidazole. SF was determined by normalizing force to fiber cross-sectional area (CSA) assuming either an elliptical or circular shape and to fiber myosin heavy chain content. Activation in TES resulted in significantly higher MHC-I SF in all groups and YA MHC-IIA fibers, irrespective of normalization method. Although there were no differences in SF between the participant groups, the ratio of SF between the TES and imidazole solutions was lower in HFPs compared with YAs (MHC-I P < 0.05; MHC-IIA P = 0.055). Activating solution composition, as opposed to donor characteristics, had a more notable effect on single fiber SF. However, this two-solution approach revealed an age-related difference in sensitivity in HFPs, which was not shown in MCs. This suggests further novel approaches may be required to probe age/activity-related differences in muscle contractile quality.NEW & NOTEWORTHY Whether specific force (SF) decreases with advancing age in human single skeletal muscle fibers is uncertain. Equivocal published findings may be due to the different physical activity levels of the elderly cohorts studied and/or different chemical solutions used to measure force. We compared single fiber SF between young adults, elderly cyclists, and hip fracture patients (HFP) using two solutions. The solution used significantly affected force and revealed a difference in sensitivity of HFP muscle fibers.

The predominant stride-frequency for routine swimming in catsharks (Scyliorhinus canicula) generates high power at high efficiency in the red musculature.

Videos of free swimming of catsharks (Scyliorhinus canicula) were analysed to give values of swimming speed (units: FL (fish lengths) s-1), stride-length (forward movement in the direction of travel per cycle of body undulation (units: FL) and stride-frequency (units: s-1). Most of the swims (139 of 163, 85%) were at speeds less than 0.545 FL s-1 and were categorized as slow. The rest (24/163, 15%) were categorized as fast. Stride-lengths and stride-frequencies could be evaluated for 115 of the slow swims and 16 of the fast swims. We discuss the fast swim results, but there were so few fast swims that no firm conclusions could be made. As swim speed increased during slow swims, there was a strong increase stride-length [slope 0.965, P < 0.0001)] and a small increase in stride-frequency. Most stride-frequencies (70/115, 61%) were in the range 0.68-0.88 s-1. Previous experiments on red muscle isolated of catshark showed that in this range of frequencies of sinusoidal movement, high power was produced at high efficiency (Curtin and Woledge b). Lower frequencies gave less power and at higher frequencies the efficiency of energy conversion was lower. Thus, we conclude that during routine swimming catsharks choose a swimming speed that optimizes red muscle performance in terms of power and efficiency.

Methodological considerations in measuring specific force in human single skinned muscle fibres.

Chemically skinned fibres allow the study of human muscle contractile function in vitro. A particularly important parameter is specific force (SF), that is, maximal isometric force divided by cross-sectional area, representing contractile quality. Although SF varies substantially between studies, the magnitude and cause of this variability remains puzzling. Here, we aimed to summarize and explore the cause of variability in SF between studies. A systematic search was conducted in Medline, Embase and Web of Science databases in June 2020, yielding 137 data sets from 61 publications which studied healthy, young adults. Five-fold differences in mean SF data were observed. Adjustments to the reported data for key methodological differences allowed between-study comparisons to be made. However, adjustment for fibre shape, swelling and sarcomere length failed to significantly reduce SF variance (I2 = 96%). Interestingly, grouping papers based on shared authorship did reveal consistency within research groups. In addition, lower SF was found to be associated with higher phosphocreatine concentrations in the fibre activating solution and with Triton X-100 being used as a skinning agent. Although the analysis showed variance across the literature, the ratio of SF in single fibres containing myosin heavy chain isoforms IIA or I was found to be consistent across research groups. In conclusion, whilst the skinned fibre technique is reliable for studying in vitro force generation of single fibres, the composition of the solution used to activate fibres, which differs between research groups, is likely to heavily influence SF values.

Energy turnover in mammalian skeletal muscle in contractions mimicking locomotion: effects of stimulus pattern on work, impulse and energetic cost and efficiency.

Active muscle performs various mechanical functions during locomotion: work output during shortening, work absorption when resisting (but not preventing) lengthening, and impulse (force-time integral) whenever there is active force. The energetic costs of these functions are important components in the energy budget during locomotion. We investigated how the pattern of stimulation and movement affects the mechanics and energetics of muscle fibre bundles isolated from wild rabbits (Oryctolagus cuniculus). The fibres were from muscles consisting of mainly fast-twitch, type 2 fibres. Fibre length was held constant (isometric) or a sinusoidal pattern of movement was imposed at a frequency similar to the stride frequency of running wild rabbits. Duty cycle (stimulation duration×movement frequency) and phase (timing of stimulation relative to movement) were varied. Work and impulse were measured as well as energy produced as heat. The sum of net work (work output-work input) and heat was taken as a measure of energetic cost. Maximum work output was produced with a long duty cycle and stimulation starting slightly before shortening, and was produced quite efficiently. However, efficiency was even higher with other stimulation patterns that produced less work. The highest impulse (considerably higher than isometric impulse) was produced when stimulation started while the muscle fibres were being lengthened. High impulse was produced very economically because of the low cost of producing force during lengthening. Thus, locomotion demanding high work, high impulse or economical work output or impulse requires a distinct pattern of stimulation and movement.

Biomechanics of predator-prey arms race in lion, zebra, cheetah and impala.

The fastest and most manoeuvrable terrestrial animals are found in savannah habitats, where predators chase and capture running prey. Hunt outcome and success rate are critical to survival, so both predator and prey should evolve to be faster and/or more manoeuvrable. Here we compare locomotor characteristics in two pursuit predator-prey pairs, lion-zebra and cheetah-impala, in their natural savannah habitat in Botswana. We show that although cheetahs and impalas were universally more athletic than lions and zebras in terms of speed, acceleration and turning, within each predator-prey pair, the predators had 20% higher muscle fibre power than prey, 37% greater acceleration and 72% greater deceleration capacity than their prey. We simulated hunt dynamics with these data and showed that hunts at lower speeds enable prey to use their maximum manoeuvring capacity and favour prey survival, and that the predator needs to be more athletic than its prey to sustain a viable success rate.

Does 'Kinesio tape' alter thoracolumbar fascia movement during lumbar flexion? An observational laboratory study.

BACKGROUND: Changes in thoracolumbar fascial thickness, structure and shear strain are associated with lower back pain (LBP). Therapeutic taping techniques such as Kinesio-Taping (KT) are increasingly used to treat LBP, albeit with variable effects and unclear mechanisms. However, evidence for quantifying how treatment effects in vivo fascia properties is inadequate. We therefore aimed to explore taping mechanisms using an in vivo ultrasound measurement. METHODS: Thoracolumbar ultrasound videos of known orientations and positions were taken from 12 asymptomatic participants (8 males and 4 females, aged 22.9 ± 3.59) while performing velocity-guided lumbar flexion with and without KT applied. An automated algorithm using cross-correlation to track contiguous tissue layers across sequential frames in the sagittal plane, was developed and applied to two movements of each subject in each taping condition. Differences of inter-tissue movements and paracutaneous translation at tissue boundaries were compared. RESULTS: Significant reduction in the mean movement of subcutaneous tissue during lumbar flexion before and after taping was found. There was no difference in other observed tissue layers. Tissue paracutaneous translations at three boundaries were significantly reduced during lumbar flexion when KT was applied (skin-subcutaneous: 0.25 mm, p < 0.01; subcutaneous-perimuscular tissue: 0.5 mm, p = 0.02; and perimuscular-muscle: 0.46, p = 0.05). No overall reduction in lumbar flexion was found (p = 0.10). CONCLUSIONS: KT reduced subcutaneous inter-tissue movement and paracutaneous translation in the superficial thoracolumbar fascia during lumbar flexion, and the relationship of such difference to symptomatic change merits exploration. Combining ultrasound data with muscle activation information may be useful to reveal potential mechanisms of therapeutic taping in patients with LBP.

Skinned fibres produce the same power and force as intact fibre bundles from muscle of wild rabbits.

Skinned fibres have advantages for comparing the muscle properties of different animal species because they can be prepared from a needle biopsy taken under field conditions. However, it is not clear how well the contractile properties of skinned fibres reflect the properties of the muscle fibres in vivo. Here, we compare the mechanical performance of intact fibre bundles and skinned fibres from muscle of the same animals. This is the first such direct comparison. Maximum power and isometric force were measured at 25 °C using peroneus longus (PL) and extensor digiti-V (ED-V) muscles from wild rabbits (Oryctolagus cuniculus). More than 90% of the fibres in these muscles are fast-twitch, type 2 fibres. Maximum power was measured in force-clamp experiments. We show that maximum power per volume was the same in intact (121.3 ± 16.1 W l(-1), mean ± s.e.m.; N=16) and skinned (122.6 ± 4.6 W l(-1); N=141) fibres. Maximum relative power (power/F(IM) Lo, where F(IM) is maximum isometric force and Lo is standard fibre length) was also similar in intact (0.645 ± 0.037; N=16) and skinned (0.589 ± 0.019; N=141) fibres. Relative power is independent of volume and thus not subject to errors in measurement of volume. Finally, maximum isometric force per cross-sectional area was also found to be the same for intact and skinned fibres (181.9 kPa ± 19.1; N=16; 207.8 kPa ± 4.8; N=141, respectively). These results contrast with previous measurements of performance at lower temperatures where skinned fibres produce much less power than intact fibres from both mammals and non-mammalian species.

Eccentric and concentric loading of the triceps surae: an in vivo study of dynamic muscle and tendon biomechanical parameters.

Triceps surae eccentric exercise is more effective than concentric exercise for treating Achilles tendinopathy, however the mechanisms underpinning these effects are unclear. This study compared the biomechanical characteristics of eccentric and concentric exercises to identify differences in the tendon load response. Eleven healthy volunteers performed eccentric and concentric exercises on a force plate, with ultrasonography, motion tracking, and EMG applied to measure Achilles tendon force, lower limb movement, and leg muscle activation. Tendon length was ultrasonographically tracked and quantified using a novel algorithm. The Fourier transform of the ground reaction force was also calculated to investigate for tremor, or perturbations. Tendon stiffness and extension did not vary between exercise types (P = .43). However, tendon perturbations were significantly higher during eccentric than concentric exercises (25%-40% higher, P = .02). Furthermore, perturbations during eccentric exercises were found to be negatively correlated with the tendon stiffness (R2 = .59). The particular efficacy of eccentric exercise does not appear to result from variation in tendon stiffness or extension within a given session. However, varied perturbation magnitude may have a role in mediating the observed clinical effects. This property is subject-specific, with the source and clinical time-course of such perturbations requiring further research.

Mechanical and energetic properties of papillary muscle from ACTC E99K transgenic mouse models of hypertrophic cardiomyopathy.

We compared the contractile performance of papillary muscle from a mouse model of hypertrophic cardiomyopathy [α-cardiac actin (ACTC) E99K mutation] with nontransgenic (non-TG) littermates. In isometric twitches, ACTC E99K papillary muscle produced three to four times greater force than non-TG muscle under the same conditions independent of stimulation frequency and temperature, whereas maximum isometric force in myofibrils from these muscles was not significantly different. ACTC E99K muscle relaxed slower than non-TG muscle in both papillary muscle (1.4×) and myofibrils (1.7×), whereas the rate of force development after stimulation was the same as non-TG muscle for both electrical stimulation in intact muscle and after a Ca²âº jump in myofibrils. The EC50 for Ca²âº activation of force in myofibrils was 0.39 ± 0.33 µmol/l in ACTC E99K myofibrils and 0.80 ± 0.11 µmol/l in non-TG myofibrils. There were no significant differences in the amplitude and time course of the Ca²âº transient in myocytes from ACTC E99K and non-TG mice. We conclude that hypercontractility is caused by higher myofibrillar Ca²âº sensitivity in ACTC E99K muscles. Measurement of the energy (work + heat) released in actively cycling heart muscle showed that for both genotypes, the amount of energy turnover increased with work done but with decreasing efficiency as energy turnover increased. Thus, ACTC E99K mouse heart muscle produced on average 3.3-fold more work than non-TG muscle, and the cost in terms of energy turnover was disproportionately higher than in non-TG muscles. Efficiency for ACTC E99K muscle was in the range of 11-16% and for non-TG muscle was 15-18%.

Power output of skinned skeletal muscle fibres from the cheetah (Acinonyx jubatus).

Muscle samples were taken from the gluteus, semitendinosus and longissimus muscles of a captive cheetah immediately after euthanasia. Fibres were 'skinned' to remove all membranes, leaving the contractile filament array intact and functional. Segments of skinned fibres from these cheetah muscles and from rabbit psoas muscle were activated at 20°C by a temperature-jump protocol. Step and ramp length changes were imposed after active stress had developed. The stiffness of the non-contractile ends of the fibres (series elastic component) was measured at two different stress values in each fibre; stiffness was strongly dependent on stress. Using these stiffness values, the speed of shortening of the contractile component was evaluated, and hence the power it was producing. Fibres were analysed for myosin heavy chain content using gel electrophoresis, and identified as either slow (type I) or fast (type II). The power output of cheetah type II fibre segments was 92.5±4.3 W kg(-1) (mean ± s.e., 14 fibres) during shortening at relative stress 0.15 (the stress during shortening/isometric stress). For rabbit psoas fibre segments (presumably type IIX) the corresponding value was significantly higher (P<0.001), 119.7±6.2 W kg(-1) (mean ± s.e., 7 fibres). These values are our best estimates of the maximum power output under the conditions used here. Thus, the contractile filament power from cheetah was less than that of rabbit when maximally activated at 20°C, and does not account for the superior locomotor performance of the cheetah.

Effects of whole body vibration on motor unit recruitment and threshold.

Whole body vibration (WBV) has been suggested to elicit reflex muscle contractions but this has never been verified. We recorded from 32 single motor units (MU) in the vastus lateralis of 7 healthy subjects (34 ± 15.4 yr) during five 1-min bouts of WBV (30 Hz, 3 mm peak to peak), and the vibration waveform was also recorded. Recruitment thresholds were recorded from 38 MUs before and after WBV. The phase angle distribution of all MUs during WBV was nonuniform (P < 0.001) and displayed a prominent peak phase angle of firing. There was a strong linear relationship (r = -0.68, P < 0.001) between the change in recruitment threshold after WBV and average recruitment threshold; the lowest threshold MUs increased recruitment threshold (P = 0.008) while reductions were observed in the higher threshold units (P = 0.031). We investigated one possible cause of changed thresholds. Presynaptic inhibition in the soleus was measured in 8 healthy subjects (29 ± 4.6 yr). A total of 30 H-reflexes (stimulation intensity 30% Mmax) were recorded before and after WBV: 15 conditioned by prior stimulation (60 ms) of the antagonist and 15 unconditioned. There were no significant changes in the relationship between the conditioned and unconditioned responses. The consistent phase angle at which each MU fired during WBV indicates the presence of reflex muscle activity similar to the tonic vibration reflex. The varying response in high- and low-threshold MUs may be due to the different contributions of the mono- and polysynaptic pathways but not presynaptic inhibition.

Millisecond-scale biochemical response to change in strain.

Muscle fiber contraction involves the cyclical interaction of myosin cross-bridges with actin filaments, linked to hydrolysis of ATP that provides the required energy. We show here the relationship between cross-bridge states, force generation, and Pi release during ramp stretches of active mammalian skeletal muscle fibers at 20°C. The results show that force and Pi release respond quickly to the application of stretch: force rises rapidly, whereas the rate of Pi release decreases abruptly and remains low for the duration of the stretch. These measurements show that biochemical change on the millisecond timescale accompanies the mechanical and structural responses in active muscle fibers. A cross-bridge model is used to simulate the effect of stretch on the distribution of actomyosin cross-bridges, force, and Pi release, with explicit inclusion of ATP, ADP, and Pi in the biochemical states and length-dependence of transitions. In the simulation, stretch causes rapid detachment and reattachment of cross-bridges without release of Pi or ATP hydrolysis.

Muscle activity and acceleration during whole body vibration: effect of frequency and amplitude.

BACKGROUND: Whole body vibration may improve muscle and bone strength, power and balance although contradictory findings have been reported. Prolonged exposure may result in adverse effects. We investigated the effects of high (5.5 mm) and low (2.5mm) amplitude whole body vibration at various frequencies (5-30 Hz) on muscle activity and acceleration throughout the body. METHODS: Surface electromyographic activity was recorded from 6 leg muscles in 12 healthy adults (aged 31.3 (SD 12.4) years). The average rectified acceleration of the toe, ankle, knee, hip and head was recorded from 15 healthy adults (36 (SD 12.1) years) using 3D motion analysis. FINDINGS: Whole body vibration increased muscle activity 5-50% of maximal voluntary contraction with the greatest increase in the lower leg. Activity was greater with high amplitude at all frequencies, however this was not always significant (P<0.05-0.001). Activation tended to increase linearly with frequency in all muscles except gluteus maximus and biceps femoris. Accelerations throughout the body ranged from approximately 0.2 to 9 g and decreased with distance from the platform. Acceleration at the head was always < 0.33 g. The greatest acceleration of the knee and hip occurred at approximately 15 Hz and thereafter decreased with increasing frequency. INTERPRETATION: Above the knee at frequencies > 15 Hz acceleration decreased with distance from the platform. This was associated with increased muscle activity, presumably due to postural control and muscle tuning mechanisms. The minimal acceleration at the head reduces the likelihood of adverse reactions. The levels of activation are unlikely to cause hypertrophy in young healthy individuals but may be sufficient in weak and frail people.

Motion analysis study of a scapular orientation exercise and subjects' ability to learn the exercise.

Exercises to retrain the orientation of the scapula are often used by physiotherapists to optimise shoulder girdle function. The movements and muscle activity required to assume this position have not yet been quantified. Further, patients often find this a difficult exercise to learn accurately, with no data being available on the accuracy of repeated performance. The primary objective of this study was to quantify the movements occurring during a commonly used scapular orientation exercise. The secondary objective was to describe the ability of subjects to learn this position after a brief period of instruction. A group of normal subjects (13 subjects; mean age 32, SD=9) were taught the scapular orientation exercise. Measurement of the position and muscle actions were made with a motion analysis system and surface electromyography. Further comparison was made of the accuracy of repeated trials. The most consistent movements were upward (mean=4 degrees, SEM=0.9 degrees) and posterior rotation (mean=4 degrees, SEM=1.6 degrees). All parts of the trapezius muscle demonstrated significant activity in maintaining the position while latissimus dorsi did not. Repeated trials showed that subjects were able to accurately repeat the movement without guidance. The key movements of, and immediate efficacy of a teaching approach for, scapular orientation have been established.

The variable component of lateral body sway during walking in young and older humans.

INTRODUCTION: Because sideways falls are common in elderly persons, we devised a method to measure variable lateral movements of the thorax with respect to foot position during normal walking. METHODS: Movements of the ankles and shoulders were measured during walking a distance of 9 m. Two age groups were studied: young (n = 17, 6 male, mean age 27.3 years) and older (n = 21, 13 male, mean age 72.7 years) people. During walking, the path followed in the horizontal plane by the midpoint between the two shoulders was compared to the line connecting successive positions of the ankles during stance. Lateral deviations between these two paths were divided into a regular component (average of about 30 strides) and a variable component (the difference between the deviation during each stride and the average). Lateral sway was also observed while standing with eyes open for 1 minute. RESULTS: The older group had more lateral movement during walking in the variable component (p =.006) and a nonsignificant trend (p =.054) in the same direction in the regular component. Eight of the older participants had a value for the variable component greater than the 95% confidence limit for the young participants. Only two of the older participants had a standing sway outside the confidence limit for the young participants. The variable component was associated with variability in stride width. DISCUSSION: The variable component of lateral sway during walking provides good discrimination between age groups, as does variability in step width. It remains to be seen whether these variables are different in fallers and nonfallers.

Influence of ionic strength on the time course of force development and phosphate release by dogfish muscle fibres.

We measured the effects of ionic strength (IS), 200 (standard) and 400 mmol l(-1) (high), on force and ATP hydrolysis during isometric contractions of permeabilized white fibres from dogfish myotomal muscle at their physiological temperature, 12 degrees C. One goal was to test the validity of our kinetic scheme that accounts for energy release, work production and ATP hydrolysis. Fibres were activated by flash photolysis of the P(3)-1-(2 nitrophenyl) ethyl ester of ATP (NPE-caged ATP), and time-resolved phosphate (P(i)) release was detected with the fluorescent protein MDCC-PBP, N-(2[1-maleimidyl]ethyl)-7-diethylamino-coumarin-3-carboxamide phosphate binding protein. High IS slowed the transition from rest to contraction, but as the fibres approached the isometric force plateau they showed little IS sensitivity. By 0.5 s of contraction, the force and the rate of P(i) release at standard and high IS values were not significantly different. A five-step reaction mechanism was used to account for the observed time courses of force and P(i) release in all conditions explored here. Only the rate constants for reactions of ATP, ADP and P(i) with the contractile proteins varied with IS, thus suggesting that the actin-myosin interactions are largely non-ionic. Our reaction scheme also fits previous results for intact fibres.

Muscle directly meets the vast power demands in agile lizards.

Level locomotion in small, agile lizards is characterized by intermittent bursts of fast running. These require very large accelerations, often reaching several times g. The power input required to increase kinetic energy is calculated to be as high as 214 W kg(-1) muscle (+/-20 W kg(-1) s.e.; averaged over the complete locomotor cycle) and 952 W kg(-1) muscle (+/-89 W kg(-1) s.e.; instantaneous peak power). In vitro muscle experiments prove that these exceptional power requirements can be met directly by the lizard's muscle fibres alone; there is no need for mechanical power amplifying mechanisms.

Effects of voluntary activation level on force exerted by human adductor pollicis muscle during rapid stretches.

We have observed the force resulting from sudden stretches (3-10 mm in 10-20 ms) of human adductor pollicis muscle during voluntary contractions maintaining different proportions of the maximum voluntary force from 20% to 100%. The ratio of the peak force during stretch (S) to the voluntary force (I) just before the start of the stretch was calculated. The S/ I ratio was dependent both on the level of activation and the speed of the stretch. At all levels of activation S/ I increased exponentially with velocity towards a plateau value with an exponential constant of about 150 mm/s. The plateau values reached were dependent on activation level (P<0.02, linear regression, n=24). At 96% activation the plateau value of the S/ I ratio was 1.82+/-0.13 (mean+/-95% confidence limits); at 32% activation the value was 2.72+/-0.23.

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.

The theoretical limits to the power output of a muscle-tendon complex with inertial and gravitational loads.

When a muscle delivers power to an inertial load through a spring, the peak power can exceed the maximum that the muscle alone could produce. Using normalized differential equations relating dimensionless quantities we show, by solving the equations either analytically or numerically, that one dimensionless constant (Xi), representing the inertial load, is sufficient to specify the behaviour during shortening of a muscle-tendon complex with linear force-velocity and force-extension properties. In the presence of gravity, an additional constant (Gamma), representing the gravitational acceleration, is required. Nonlinear force-velocity and force-extension relationships each introduce an additional constant, representing their curvature. In the absence of gravity the power output delivered to an inertial load is limited to approximately 1.4 times the maximum power of the muscle alone, and when gravity is present the power delivered is limited to approximately twice the power of muscle alone. These limits are found for the purely inertial load at Xi ca. 1 and with gravity acting at XiGamma = 0.5 with Xi arbitrarily small. The effects of nonlinear muscle and tendon properties tend to cancel each other out and do not produce large deviations from these optima. A lever system of constant ratio between muscle and load does not alter these limits. Cams and catches are required to exceed these limits and attain the high power outputs sometimes observed during explosive animal movement.