Length dependence of changes in sarcoplasmic calcium concentration and myofibrillar calcium sensitivity in striated muscle fibres

Assessment and modelling of the activation-dependent shift in optimal length of the human soleus muscle in vivo

Previous in vitro and in situ studies have reported a shift in optimal muscle fibre length for force generation (L0) towards longer length at decreasing activation levels (also referred to as length-dependent activation), yet the relevance for in vivo human muscle contractions with a variable activation pattern remains largely unclear. By a combination of dynamometry, ultrasound and electromyography (EMG), we experimentally obtained muscle force-fascicle length curves of the human soleus at 100%, 60% and 30% EMGmax levels from 15 participants aiming to investigate activation-dependent shifts in L0 in vivo. The results showed a significant increase in L0 of 6.5 ± 6.0% from 100% to 60% EMGmax and of 9.1 ± 7.2% from 100% to 30% EMGmax (both P < 0.001), respectively, providing evidence of a moderate in vivo activation dependence of the soleus force-length relationship. Based on the experimental results, an approximation model of an activation-dependent force-length relationship was defined for each individual separately and for the collective data of all participants, both with sufficiently high accuracy (R2 of 0.899 ± 0.056 and R2 = 0.858). This individual approximation approach and the general approximation model outcome are freely accessible and may be used to integrate activation-dependent shifts in L0 in experimental and musculoskeletal modelling studies to improve muscle force predictions. KEY POINTS: The phenomenon of the activation-dependent shift in optimal muscle fibre length for force generation (length-dependent activation) is poorly understood for human muscle in vivo dynamic contractions. We experimentally observed a moderate shift in optimal fascicle length towards longer length at decreasing electromyographic activity levels for the human soleus muscle in vivo. Based on the experimental results, we developed a freely accessible approximation model that allows the consideration of activation-dependent shifts in optimal length in future experimental and musculoskeletal modelling studies to improve muscle force predictions.

Behavioral Motor Performance

The human sensorimotor control system has exceptional abilities to perform skillful actions. We easily switch between strenuous tasks that involve brute force, such as lifting a heavy sewing machine, and delicate movements such as threading a needle in the same machine. Using a structure with different control architectures, the motor system is capable of updating its ability to perform through our daily interaction with the fluctuating environment. However, there are issues that make this a difficult computational problem for the brain to solve. The brain needs to control a nonlinear, nonstationary neuromuscular system, with redundant and occasionally undesired degrees of freedom, in an uncertain environment using a body in which information transmission is subject to delays and noise. To gain insight into the mechanisms of motor control, here we survey movement laws and invariances that shape our everyday motion. We then examine the major solutions to each of these problems in the three parts of the sensorimotor control system, sensing, planning, and acting. We focus on how the sensory system, the control architectures, and the structure and operation of the muscles serve as complementary mechanisms to overcome deviations and disturbances to motor behavior and give rise to skillful motor performance. We conclude with possible future research directions based on suggested links between the operation of the sensorimotor system across the movement stages. © 2024 American Physiological Society. Compr Physiol 14:5179-5224, 2024.

Late-life Rapamycin Treatment Enhances Cardiomyocyte Relaxation Kinetics and Reduces Myocardial Stiffness

Diastolic dysfunction is a key feature of the aging heart. We have shown that late-life treatment with mTOR inhibitor, rapamycin, reverses age-related diastolic dysfunction in mice but the molecular mechanisms of the reversal remain unclear. To dissect the mechanisms by which rapamycin improves diastolic function in old mice, we examined the effects of rapamycin treatment at the levels of single cardiomyocyte, myofibril and multicellular cardiac muscle. Compared to young cardiomyocytes, isolated cardiomyocytes from old control mice exhibited prolonged time to 90% relaxation (RT 90 ) and time to 90% Ca 2+ transient decay (DT 90 ), indicating slower relaxation kinetics and calcium reuptake with age. Late-life rapamycin treatment for 10 weeks completely normalized RT 90 and partially normalized DT 90 , suggesting improved Ca 2+ handling contributes partially to the rapamycin-induced improved cardiomyocyte relaxation. In addition, rapamycin treatment in old mice enhanced the kinetics of sarcomere shortening and Ca 2+ transient increase in old control cardiomyocytes. Myofibrils from old rapamycin-treated mice displayed increased rate of the fast, exponential decay phase of relaxation compared to old controls. The improved myofibrillar kinetics were accompanied by an increase in MyBP-C phosphorylation at S282 following rapamycin treatment. We also showed that late-life rapamycin treatment normalized the age-related increase in passive stiffness of demembranated cardiac trabeculae through a mechanism independent of titin isoform shift. In summary, our results showed that rapamycin treatment normalizes the age-related impairments in cardiomyocyte relaxation, which works conjointly with reduced myocardial stiffness to reverse age-related diastolic dysfunction.

Changes in Muscle Shear Modulus and Urinary Titin N-Terminal Fragment after Eccentric Exercise

This study aimed to investigate the relationship between the muscle shear modulus of the biceps brachii, urinary titin N-terminal fragment (UTF), and other damage markers after eccentric exercise. Seventeen healthy males performed five sets of ten eccentric exercises with dumbbells weighing 50% of the maximum voluntary contraction (MVC) at the elbow joint. Muscle shear modulus with range of interest set to only biceps brachii muscle measured by ultrasound shear wave elastography, UTF, MVC, range of motion (ROM), and soreness (SOR) were recorded before, immediately after, and 1, 24, 48, 72, 96, and 168 h after eccentric exercise. Each marker changed in a time course pattern, as found in previous studies. The peak shear modulus showed a moderate negative correlation with peak MVC (r = -0.531, P < 0.05) and a strong positive correlation with peak UTF (r = 0.707, P < 0.01). Our study results revealed a significant relationship between muscle strength, shear modulus measured by ultrasound SWE, and titin measured by UTF, as a non-invasive damage marker after eccentric exercise to track changes in EIMD.

Muscle active force-length curve explained by an electrophysical model of interfilament spacing

The active isometric force-length relation (FLR) of striated muscle sarcomeres is central to understanding and modeling muscle function. The mechanistic basis of the descending arm of the FLR is well explained by the decreasing thin:thick filament overlap that occurs at long sarcomere lengths. The mechanistic basis of the ascending arm of the FLR (the decrease in force that occurs at short sarcomere lengths), alternatively, has never been well explained. Because muscle is a constant-volume system, interfilament lattice distances must increase as sarcomere length shortens. This increase would decrease thin and thick-filament electrostatic interactions independently of thin:thick filament overlap. To examine this effect, we present here a fundamental, physics-based model of the sarcomere that includes filament molecular properties, calcium binding, sarcomere geometry including both thin:thick filament overlap and interfilament radial distance, and electrostatics. The model gives extremely good fits to existing FLR data from a large number of different muscles across their entire range of measured activity levels, with the optimized parameter values in all cases lying within anatomically and physically reasonable ranges. A local first-order sensitivity analysis (varying individual parameters while holding the values of all others constant) shows that model output is most sensitive to a subset of model parameters, most of which are related to sarcomere geometry, with model output being most sensitive to interfilament radial distance. This conclusion is supported by re-running the fits with only this parameter subset being allowed to vary, which increases fit errors only moderately. These results show that the model well reproduces existing experimental data, and indicate that changes in interfilament spacing play as central a role as changes in filament overlap in determining the FLR, particularly on its ascending arm.

Functional and structural differences between skinned and intact muscle preparations

Myofilaments and their associated proteins, which together constitute the sarcomeres, provide the molecular-level basis for contractile function in all muscle types. In intact muscle, sarcomere-level contraction is strongly coupled to other cellular subsystems, in particular the sarcolemmal membrane. Skinned muscle preparations (where the sarcolemma has been removed or permeabilized) are an experimental system designed to probe contractile mechanisms independently of the sarcolemma. Over the last few decades, experiments performed using permeabilized preparations have been invaluable for clarifying the understanding of contractile mechanisms in both skeletal and cardiac muscle. Today, the technique is increasingly harnessed for preclinical and/or pharmacological studies that seek to understand how interventions will impact intact muscle contraction. In this context, intrinsic functional and structural differences between skinned and intact muscle pose a major interpretational challenge. This review first surveys measurements that highlight these differences in terms of the sarcomere structure, passive and active tension generation, and calcium dependence. We then highlight the main practical challenges and caveats faced by experimentalists seeking to emulate the physiological conditions of intact muscle. Gaining an awareness of these complexities is essential for putting experiments in due perspective.

Post-activation potentiation induced by concentric contractions at three speeds in humans

NEW FINDINGS

What is the central question of this study? Is the degree of in human muscle affected by different shortening velocities, or contraction type? What are the main findings and their importance? The PAP response following maximal concentric contractions was independent of velocity. Slow and moderate velocity maximal contractions produced PAP responses like those from maximal isometric contractions when matched for contraction duration. Despite contraction type differences in cross-bridge and Ca²⁺ kinetics, maximal contractions, regardless of contraction modality, likely generate sufficient Ca²⁺ to induce maximal PAP.

ABSTRACT

Post-activation potentiation (PAP) is the acute enhancement of contractile properties following a brief (<10 s) high-intensity contraction. Compared with isometric contractions, little is known about the PAP response induced by concentric conditioning contractions (CCs) and the effect of velocity. In the dorsiflexors of 11 participants, twitch responses were measured following 5 s of maximal effort concentric CCs at each of 10, 20 and 50°/s. Concentric PAP responses were compared to a maximal isometric voluntary contraction (MVC) matched for contraction time. Additionally, concentric CCs were compared to isometric CCs matched for mean torque, contraction area and time. The PAP response following maximal concentric CCs was independent of velocity and there was no difference in the PAP response between concentric CCs and an isometric MVC. During maximal contractions, regardless of contraction modality, there is likely sufficient Ca²⁺ to induce a similar full PAP response, and thus there was no difference between speeds or contraction type. Following concentric CCs there was a significantly larger peak twitch torque than following their isometric torque matches (49-58%), and faster maximal rates of torque development at the three speeds (62-77%). However, these responses are likely related to greater EMG in concentric contractions, 125-129% of isometric maximum compared to 38-54%, and not to contraction modality per se. Thus, PAP responses following maximal concentric CCs are not affected by velocity and responses are not different from an isometric MVC. This indicates maximal CCs of 5 s produce a maximal PAP response independent of contraction type (isometric vs. concentric) or shortening velocity.

Rightward shift of optimal fascicle length with decreasing voluntary activity level in the soleus and lateral gastrocnemius muscles

Much of our understanding of in vivo skeletal muscle properties is based on studies performed under maximal activation, which is problematic because muscles are rarely activated maximally during movements such as walking. Currently, force-length properties of the human triceps surae at submaximal voluntary muscle activity levels are not characterized. We therefore evaluated plantar flexor torque- and force-ankle angle, and torque- and force-fascicle length properties of the soleus and lateral gastrocnemius muscles during voluntary contractions at three activity levels: 100, 30 and 22% of maximal voluntary contraction. Soleus activity levels were controlled by participants via real-time electromyography feedback and contractions were performed at ankle angles ranging from 10 deg plantar flexion to 35 deg dorsiflexion. Using dynamometry and ultrasound imaging, torque-fascicle length curves of the soleus and lateral gastrocnemius muscles were constructed. The results indicate that small muscle activity reductions shift the torque- and force-angle, and torque- and force-fascicle length curves of these muscles to more dorsiflexed ankle angles and longer fascicle lengths (from 3 to 20% optimal fascicle length, depending on ankle angle). The shift in the torque- and force-fascicle length curves during submaximal voluntary contraction have potential implications for human locomotion (e.g. walking) as the operating range of fascicles shifts to the ascending limb, where muscle force capacity is reduced by at least 15%. These data demonstrate the need to match activity levels during construction of the torque- and force-fascicle length curves to activity levels achieved during movement to better characterize the lengths that muscles operate at relative to their optimum during a specific task.

Mechanisms underlying performance impairments following prolonged static stretching without a comprehensive warm-up

Whereas a variety of pre-exercise activities have been incorporated as part of a "warm-up" prior to work, combat, and athletic activities for millennia, the inclusion of static stretching (SS) within a warm-up has lost favor in the last 25 years. Research emphasized the possibility of SS-induced impairments in subsequent performance following prolonged stretching without proper dynamic warm-up activities. Proposed mechanisms underlying stretch-induced deficits include both neural (i.e., decreased voluntary activation, persistent inward current effects on motoneuron excitability) and morphological (i.e., changes in the force-length relationship, decreased Ca²⁺ sensitivity, alterations in parallel elastic component) factors. Psychological influences such as a mental energy deficit and nocebo effects could also adversely affect performance. However, significant practical limitations exist within published studies, e.g., long-stretching durations, stretching exercises with little task specificity, lack of warm-up before/after stretching, testing performed immediately after stretch completion, and risk of investigator and participant bias. Recent research indicates that appropriate durations of static stretching performed within a full warm-up (i.e., aerobic activities before and task-specific dynamic stretching and intense physical activities after SS) have trivial effects on subsequent performance with some evidence of improved force output at longer muscle lengths. For conditions in which muscular force production is compromised by stretching, knowledge of the underlying mechanisms would aid development of mitigation strategies. However, these mechanisms are yet to be perfectly defined. More information is needed to better understand both the warm-up components and mechanisms that contribute to performance enhancements or impairments when SS is incorporated within a pre-activity warm-up.

Parameter estimation and experimental design for Hill-type muscles: Impulses from optimization-based modeling

The benefits of optimization-based modeling for parameter estimation of Hill-type muscle models are demonstrated. Therefore, we examined the model and data of Günther et al. (2007), who analyzed isometric, concentric, and quick-release contractions of a piglet calf muscle. We found that the isometric experiments are suitable for derivative-based parameter estimation while the others did not provide any additional value. During the estimation process, certain parameters had to be fixed. We give possible reasons and provide impulses for modelers. Subsequently, unnecessarily complex or deprecated model parts were exchanged and the new model was fitted to the data. In order to be able to provide a reliable estimation of the whole parameter set, we propose two isometric and two quick-release experiments, which are real-life feasible and together allow an identification of all parameters based on a local sensitivity analysis. These experiments can be used as qualitative guidelines for practitioners to reduce the experimental effort when estimating parameters for macroscopic muscle models.

Post-activation Potentiation Versus Post-activation Performance Enhancement in Humans: Historical Perspective, Underlying Mechanisms, and Current Issues

Post-activation potentiation (PAP) is a well-described phenomenon with a short half-life (~28 s) that enhances muscle force production at submaximal levels of calcium saturation (i.e., submaximal levels of muscle activation). It has been largely explained by an increased myosin light chain phosphorylation occurring in type II muscle fibers, and its effects have been quantified in humans by measuring muscle twitch force responses to a bout of muscular activity. However, enhancements in (sometimes maximal) voluntary force production detected several minutes after high-intensity muscle contractions are also observed, which are also most prominent in muscles with a high proportion of type II fibers. This effect has been considered to reflect PAP. Nonetheless, the time course of myosin light chain phosphorylation (underpinning “classic” PAP) rarely matches that of voluntary force enhancement and, unlike PAP, changes in muscle temperature, muscle/cellular water content, and muscle activation may at least partly underpin voluntary force enhancement; this enhancement has thus recently been called post-activation performance enhancement (PAPE) to distinguish it from “classical” PAP. In fact, since PAPE is often undetectable at time points where PAP is maximal (or substantial), some researchers have questioned whether PAP contributes to PAPE under most conditions in vivo in humans. Equally, minimal evidence has been presented that PAP is of significant practical importance in cases where multiple physiological processes have already been upregulated by a preceding, comprehensive, active muscle warm-up. Given that confusion exists with respect to the mechanisms leading to acute enhancement of both electrically evoked (twitch force; PAP) and voluntary (PAPE) muscle function in humans after acute muscle activity, the first purpose of the present narrative review is to recount the history of PAP/PAPE research to locate definitions and determine whether they are the same phenomena. To further investigate the possibility of these phenomena being distinct as well as to better understand their potential functional benefits, possible mechanisms underpinning their effects will be examined in detail. Finally, research design issues will be addressed which might contribute to confusion relating to PAP/PAPE effects, before the contexts in which these phenomena may (or may not) benefit voluntary muscle function are considered.

Evaluation of linear and non-linear activation dynamics models for insect muscle

In computational modelling of sensory-motor control, the dynamics of muscle contraction is an important determinant of movement timing and joint stiffness. This is particularly so in animals with many slow muscles, as is the case in insects-many of which are important models for sensory-motor control. A muscle model is generally used to transform motoneuronal input into muscle force. Although standard models exist for vertebrate muscle innervated by many motoneurons, there is no agreement on a parametric model for single motoneuron stimulation of invertebrate muscle. Although several different models have been proposed, they have never been evaluated using a common experimental data set. We evaluate five models for isometric force production of a well-studied model system: the locust hind leg tibial extensor muscle. The response of this muscle to motoneuron spikes is best modelled as a non-linear low-pass system. Linear first-order models can approximate isometric force time courses well at high spike rates, but they cannot account for appropriate force time courses at low spike rates. A linear third-order model performs better, but only non-linear models can account for frequency-dependent change of decay time and force potentiation at intermediate stimulus frequencies. Some of the differences among published models are due to differences among experimental data sets. We developed a comprehensive toolbox for modelling muscle activation dynamics, and optimised model parameters using one data set. The "Hatze-Zakotnik model" that emphasizes an accurate single-twitch time course and uses frequency-dependent modulation of the twitch for force potentiation performs best for the slow motoneuron. Frequency-dependent modulation of a single twitch works less well for the fast motoneuron. The non-linear "Wilson" model that optimises parameters to all data set parts simultaneously performs better here. Our open-access toolbox provides powerful tools for researchers to fit appropriate models to a range of insect muscles.

Cardiac troponin-I phosphorylation underlies myocardial contractile dysfunction induced by hypothermia rewarming

Rewarming the intact heart after a period of hypothermia is associated with reduced myocardial contractility, decreased Ca²⁺ sensitivity, and increased cardiac troponin-I (cTnI) phosphorylation. We hypothesized that hypothermia/rewarming (H/R) induces left ventricular (LV) contractile dysfunction due to phosphorylation of cTnI at Ser^23/24. To test this hypothesis, the response of wild-type mice (n = 7) to H/R was compared with transgenic (TG) mice expressing slow skeletal TnI (TG-ssTnI; n = 7) that lacks the Ser^23/24 phosphorylation sites. Hypothermia was induced by surface cooling and maintained at 23-25°C for 3 h. Subsequently, the animals were rewarmed to 37°C. LV systolic and diastolic function was assessed using a 1.4 F pressure-volume Millar catheter introduced via the right carotid artery. At baseline conditions, there were no significant differences in LV systolic function between wild-type and TG-ssTnI mice, whereas measurements of diastolic function [isovolumic relaxation constant (τ) and end-diastolic pressure-volume relationship (EDPVR)] were significantly (P < 0.05) reduced in TG-ssTnI animals. Immediately after rewarming, significant differences between groups were found in cardiac output (CO; wild-type 6.6 ± 0.7 vs. TG-ssTnI 8.8 ± 0.7 mL/min), stroke work (SW; wild-type 796 ± 112 vs. TG-ssTnI 1208 ± 67 mmHg/μL), and the preload recruited stroke work (PRSW; wild-type 38.3 ± 4.9 vs. TG-ssTnI 68.8 ± 8.2 mmHg). However, EDPVR and τ returned to control levels within 1 h in both groups. We conclude that H/R-induced LV systolic dysfunction results from phosphorylation of cTnI at Ser^23/24.NEW & NOTEWORTHY Rewarming following a period of accidental hypothermia leads to a form of acute cardiac failure (rewarming shock), which is in part due to reduced sensitivity to Ca²⁺ activation of myocardial contraction. The results of the present study support the hypothesis that rewarming shock is due to phosphorylation of cardiac troponin I.

Concentric strength training at optimal or short muscle length improves strength equally but does not reduce fatigability of hamstring muscles

The purpose of this study was to compare the effect of a 6-week period of knee flexion strength training at either optimal or short muscle length, on length-specific muscle strength and fatigue. Twelve healthy volunteers performed dynamic (isokinetic concentric) training with one leg at short and the contralateral leg at optimal muscle length for 6 weeks. Knee flexor muscle strength was assessed before and after training, comprising maximal voluntary isometric and dynamic contractions at short, intermediate and near optimal muscle length and electrically evoked, contractions at near optimal length only. Fatigability was tested by performing 60 maximal concentric contractions at either short or optimal muscle length. Isometric torque at all muscle lengths improved equally by training at short and optimal muscle length, for example, tested at short 18 (17) versus 21 (17) % (CI) and at optimal 14 (8) versus 17 (16) % muscle length, respectively. Likewise, equal improvements were observed for dynamic contractions in both groups. Prior to training, fatigue induced at optimal muscle length tended to be more pronounced than at short muscle length (fatigue-indexes -41 (6) vs. -34 (7) %, respectively, P = 0.05). However, training at either length did not reduce fatigability. Training with maximal concentric contractions at either short or optimal muscle length for 6 weeks improved isometric and dynamic muscle strength in the entire range of motion without inducing any discernible length-specific adaptations. However, strength training at restricted muscle length did not reduce relative fatigue when induced at either short or optimal muscle length.

Optimal length, calcium sensitivity and twitch characteristics of skeletal muscles from mdm mice with a deletion in N2A titin

During isometric contractions, the optimal length of skeletal muscles increases with decreasing activation. The underlying mechanism for this phenomenon is thought to be linked to length dependence of Ca²⁺ sensitivity. Muscular dystrophy with myositis (mdm), a recessive titin mutation in mice, was used as a tool to study the role of titin in activation dependence of optimal length and length dependence of Ca²⁺ sensitivity. We measured the shift in optimal length between tetanic and twitch stimulation in mdm and wild-type muscles, and the length dependence of Ca²⁺ sensitivity at short and long sarcomere lengths in mdm and wild-type fiber bundles. The results indicate that the mdm mutation leads to a loss of activation dependence of optimal length without the expected change in length dependence of Ca²⁺ sensitivity, demonstrating that these properties are not linked, as previously suggested. Furthermore, mdm muscles produced maximum tetanic stress during sub-optimal filament overlap at lengths similar to twitch contractions in both genotypes, but the difference explains less than half of the observed reduction in active force of mdm muscles. Mdm muscles also exhibited increased electromechanical delay, contraction and relaxation times, and decreased rate of force development in twitch contractions. We conclude that the small deletion in titin associated with mdm in skeletal muscles alters force production, suggesting an important regulatory role for titin in active force production. The molecular mechanisms for titin's role in regulating muscle force production remain to be elucidated.

Can Strain Dependent Inhibition of Cross-Bridge Binding Explain Shifts in Optimum Muscle Length?

Skeletal muscle force is generated by cross-bridge interactions between the overlapping contractile proteins, actin and myosin. The geometry of this overlap gives us the force-length relationship in which maximum isometric force is generated at an intermediate, optimum, length. However, the force-length relationship is not constant; optimum length increases with decreasing muscle activation. This effect is not predicted from actin-myosin overlap. Here we present evidence that this activation-dependent shift in optimum length may be due to a series compliance within muscles. As muscles generate force during fixed-end contractions, fibers shorten against series compliance until forces equilibrate and they become isometric. Shortening against series-compliance is proportional to activation, and creates conditions under which shortening-induced force depression may suppress full force development. Greater shortening will result in greater force depression. Hence, optimum length may decrease as activation rises due to greater fiber shortening. We discuss explanations of such history dependence, giving a review of previously proposed processes and suggesting a novel mechanistic explanation for the most likely candidate process based on tropomyosin kinetics. We suggest this mechanism could change the relationship between actin-myosin overlap and cross-bridge binding potential, not only depressing force at any given length, but also altering the relationship between force and length. This would have major consequences for our understanding of in vivo muscle performance.

Improved Hill-type musculotendon models with activation-force-length coupling

BACKGROUND

Hill-type musculotendon models are most commonly used in biomechanical simulations for their computational efficacy and efficiency. But these models are generally built for maximally-activated muscles and linearly scale muscle properties when applied to submaximal conditions. However, the precondition of this scaling, which is muscle activation and properties are independent each other, has been proven unreal in many studies. Actually, the maximal activation condition is not ubiquitous for muscles in vivo, so it is necessary to adapt the linear scaling approach to improve the model practicability.

OBJECTIVE

This paper aimed at proposing two improved Hill-type musculotendon models that are better suited for submaximal conditions.

METHOD

These two models were built by including the activation-force-length coupling and their biological accuracy and computation speed were evaluated by a series of benchmark simulations.

RESULTS

Compared to experimental measurements, the percent root mean square errors of forces calculated by the two AFLC models were less than 13.98% and 13.81% respectively. However, the average running time of the second AFLC model was nearly 17 times that of the first one with only a little improvement in accuracy.

CONCLUSION

The two AFLC models were validated more accurate than the common Hill-type model in submaximally activated conditions and the first one was recommended in the construction of upper-layer musculoskeletal models.

The effect of muscle length on transcranial magnetic stimulation-induced relaxation rate in the plantar flexors

Transcranial magnetic stimulation (TMS) of the motor cortex during a maximal voluntary contraction (MVC) permits functionally relevant measurements of muscle group relaxation rate (i.e., when muscles are actively contracting under voluntary control). This study's purpose was twofold: (1) to explore the impact of muscle length on TMS‐induced plantar flexor relaxation rate; and (2) to incorporate ultrasonography to measure relaxation‐induced lengthening of medial gastrocnemius (MG) fascicles and displacement of the muscle–tendon junction (MTJ). Eleven males (24.8 ± 7.0 years) performed 21 brief isometric plantar flexor MVCs. Trials were block‐randomized every three MVCs among 20° dorsiflexion (DF), a neutral ankle position, and 30° plantar flexion (PF). During each MVC, TMS was delivered and ultrasound video recordings captured MG fascicles or MTJ length changes. Peak relaxation rate was calculated as the steepest slope of the TMS‐induced drop in plantar flexor torque or the rate of length change for MG fascicles and MTJ. Torque relaxation rate was slower for PF (−804 ± 162 Nm·s⁻¹) than neutral and DF (−1896 ± 298 and −2008 ± 692 Nm·s⁻¹, respectively). Similarly, MG fascicle relaxation rate was slower for PF (−2.80 ± 1.10 cm·s⁻¹) than neutral and DF (−5.35 ± 1.10 and −4.81 ± 1.87 cm·s⁻¹, respectively). MTJ displacement rate showed a similar trend (P = 0.06), with 3.89 ± 1.93 cm·s⁻¹ for PF compared to rates of 6.87 ± 1.55 and 6.36 ± 2.97 cm·s⁻¹ for neutral and DF, respectively. These findings indicate muscle length affects the torque relaxation rate recorded after TMS during an MVC. Comparable results were obtained from muscle fascicles, indicating ultrasound imaging is suitable for measuring evoked contractile properties during voluntary contraction.

The sag response in human muscle contraction

PURPOSE

We examined how muscle length and time between stimuli (inter-pulse interval, IPI) influence declines in force (sag) seen during unfused tetani in the human adductor pollicis muscle.

METHODS

A series of 16-pulse contractions were evoked with IPIs between 1 × and 5 × the twitch time to peak tension (TPT) at large (long muscle length) and small (short muscle length) thumb adduction angles. Unfused tetani were mathematically deconstructed into a series of overlapping twitch contractions to examine why sag exhibits length- and IPI-dependencies.

RESULTS

Across all IPIs tested, sag was 62% greater at short than long muscle length, and sag increased as IPI was increased at both muscle lengths. Force attributable to the second stimulus increased as IPI was decreased. Twitch force declined from maximal values across all IPI tested, with the greatest reductions seen at short muscle length and long IPI. At IPI below 2 × TPT, the twitch with highest force occurred earlier than the peak force of the corresponding unfused tetani. Contraction-induced declines in twitch duration (TPT + half relaxation time) were only observed at IPI longer than 1.75 × TPT, and were unaffected by muscle length.

CONCLUSIONS

Sag is an intrinsic feature of healthy human adductor pollicis muscle. The length-dependence of sag is related to greater diminution of twitch force at short relative to long muscle length. The dependence of sag on IPI is related to IPI-dependent changes in twitch duration and twitch force, and the timing of peak twitch force relative to the peak force of the associated unfused tetanus.

Changes in contractile and metabolic parameters of skeletal muscle as rats age from 3 to 12 months

Laboratory rats are considered mature at 3 months despite that musculoskeletal growth is still occurring. Changes in muscle physiological and biochemical characteristics during development from 3 months, however, are not well understood. Whole muscles and single skinned fibres from fast-twitch extensor digitorum longus (EDL) and predominantly slow-twitch soleus (SOL) muscles were examined from male Sprague-Dawley rats (3, 6, 9, 12 months). Ca²⁺ sensitivity of contractile apparatus decreased with age in both fast- (~ 0.04 pCa units) and slow-twitch (~ 0.07 pCa units) muscle fibres, and specific force increased (by ~ 50% and ~ 25%, respectively). Myosin heavy chain composition of EDL and SOL muscles altered to a small extent with age (decrease in MHCIIa proportion after 3 months). Glycogen content increased with age (~ 80% in EDL and 25% in SOL) and GLUT4 protein density decreased (~ 35 and 20%, respectively), whereas the glycogen-related enzymes were little changed. GAPDH protein content was relatively constant in both muscle types, but COXIV protein decreased ~ 40% in SOL muscle. Calsequestrin (CSQ) and SERCA densities remained relatively constant with age, whereas there was a progressive ~ 2-3 fold increase in CSQ-like proteins, though their role and importance remain unclear. There was also ~ 40% decrease in the density of the Na⁺, K⁺-ATPase (NKA) α1 subunit in EDL and the α2 subunit in SOL. These findings emphasise there are substantial changes in skeletal muscle function and the density of key proteins during early to mid-adulthood in rats, which need to be considered in the design and interpretation of experiments.

Hill equation and Hatze's muscle activation dynamics complement each other: enhanced pharmacological and physiological interpretability of modelled activity-pCa curves

In pharmacology, particularly receptor theory, the drug dose-effect relation of bio-active substances is frequently described by a sigmoidal function formulated by A.V. Hill. In biomechanics and muscle physiology then again, H. Hatze had elaborated a mathematical model for the stimulation- and length-dependent dynamics of the calcium-induced activation of mammalian skeletal muscle. Here, we prove that muscular activity-pCa curves described by the Hill equation and the equilibrium state predicted by Hatze's activation dynamics are equivalent. Thus, the exponent introduced by Hatze can be directly identified with its counterpart in the Hill equation, by which the former model gains further physiological interpretability. Conversely, the Hill constant can now be interpreted as a function of the fibre length, generally allowing for advanced Hill plots based on model ideas. We derive and examine the complementary relation of both model approaches, highlight the benefits of mutually viewing one approach from the perspective of the other, and address the physiology behind sigmoidal curves.

Muscle length-dependent contribution of motoneuron Cav1.3 channels to force production in model slow motor unit

Persistent inward current (PIC)-generating Ca_v1.3 channels in spinal motoneuron dendrites are thought to be actively recruited during normal behaviors. However, whether and how the activation of PIC channels influences force output of motor unit remains elusive. Here, building a physiologically realistic model of slow motor unit I demonstrated that force production induced by the PIC activation is much smaller for short than lengthened muscles during the regular firing of the motoneuron that transitions from the quiescent state by either a brief current pulse at the soma or a brief synaptic excitation at the dendrites. By contrast, the PIC-induced force potentiation was maximal for short muscles when the motoneuron switched from a stable low-frequency firing state to a stable high-frequency firing state by the current pulse at the soma. Under the synaptic excitation at the dendrites, however, the force could not be potentiated by the transitioning of the motoneuron from a low- to a high-frequency firing state due to the simultaneous onset of PIC at the dendrites and firing at the soma. The strong dependency of the input-output relationship of the motor unit on the neuromodulation and Ia afferent inputs for the PIC channels was further shown under static variations in muscle length. Taken together, these findings suggest that the PIC activation in the motoneuron dendrites may differentially affect the force production of the motor unit, depending not only on the firing state history of the motoneuron and the variation in muscle length but also on the mode of motor activity.NEW & NOTEWORTHY Ca_v1.3 channels in motoneuron dendrites are actively involved during normal motor activities. To investigate the effects of the activation of motoneuron Ca_v1.3 channels on force production, a model motor unit was built based on best-available data. The simulation results suggest that force potentiation induced by Ca_v1.3 channel activation is strongly modulated not only by firing history of the motoneuron but also by length variation of the muscle as well as neuromodulation inputs from the brainstem.

Muscle and Limb Mechanics

Understanding of the musculoskeletal system has evolved from the collection of individual phenomena in highly selected experimental preparations under highly controlled and often unphysiological conditions. At the systems level, it is now possible to construct complete and reasonably accurate models of the kinetics and energetics of realistic muscles and to combine them to understand the dynamics of complete musculoskeletal systems performing natural behaviors. At the reductionist level, it is possible to relate most of the individual phenomena to the anatomical structures and biochemical processes that account for them. Two large challenges remain. At a systems level, neuroscience must now account for how the nervous system learns to exploit the many complex features that evolution has incorporated into muscle and limb mechanics. At a reductionist level, medicine must now account for the many forms of pathology and disability that arise from the many diseases and injuries to which this highly evolved system is inevitably prone. © 2017 American Physiological Society. Compr Physiol 7:429-462, 2017.

Vastus lateralis maximum force-generating potential occurs at optimal fascicle length regardless of activation level

PURPOSE

Despite the fact that everyday movements are hardly ever performed with muscles contracting maximally, our understanding of the force-length relationship is mostly based on in vitro studies using maximal activation. In this study, the in vivo submaximal and maximal force-length relationships of vastus-lateralis were investigated. Force-length relationships were obtained based on maximal and submaximal levels of force and, also, on EMG activation.

METHODS

Nine subjects performed isometric knee extensor contractions at ten knee angles (80°-170°). Knee extensor torque, and vastus-lateralis EMG and fascicle lengths were acquired simultaneously. Fascicle lengths and knee angles at peak force occurrence were compared across maximal and submaximal conditions.

RESULTS

The submaximal force-fascicle length relationships depend crucially on the approach used: in the force-based approach, peak forces are constrained to occur at the same MTU length and, because of series elasticity, occur at longer fascicle lengths for decreasing force levels. In contrast, in the activation-based approach, peak force occurrence is not constrained to a given muscle length for submaximal contractions and occurs at similar fascicle lengths but shorter MTU lengths (more extended knee angles) as force decreases.

CONCLUSIONS

Our results support the hypothesis that vastus-lateralis fascicle length for maximal force production is about constant for maximal and submaximal levels of activation, presumably taking advantage of optimal myofilament overlap at that fascicle length. This result implies that optimal vastus-lateralis lengths occur at different knee angles for different levels of activation, which is in stark contrast to findings in the literature in which submaximal force-fascicle length relationships were based on force rather than activation.

An action potential-driven model of soleus muscle activation dynamics for locomotor-like movements

OBJECTIVE

The goal of this study was to develop a physiologically plausible, computationally robust model for muscle activation dynamics (A(t)) under physiologically relevant excitation and movement.

APPROACH

The interaction of excitation and movement on A(t) was investigated comparing the force production between a cat soleus muscle and its Hill-type model. For capturing A(t) under excitation and movement variation, a modular modeling framework was proposed comprising of three compartments: (1) spikes-to-[Ca(2+)]; (2) [Ca(2+)]-to-A; and (3) A-to-force transformation. The individual signal transformations were modeled based on physiological factors so that the parameter values could be separately determined for individual modules directly based on experimental data.

MAIN RESULTS

The strong dependency of A(t) on excitation frequency and muscle length was found during both isometric and dynamically-moving contractions. The identified dependencies of A(t) under the static and dynamic conditions could be incorporated in the modular modeling framework by modulating the model parameters as a function of movement input. The new modeling approach was also applicable to cat soleus muscles producing waveforms independent of those used to set the model parameters.

SIGNIFICANCE

This study provides a modeling framework for spike-driven muscle responses during movement, that is suitable not only for insights into molecular mechanisms underlying muscle behaviors but also for large scale simulations.

Interdependence of torque, joint angle, angular velocity and muscle action during human multi-joint leg extension

PURPOSE

Force and torque production of human muscles depends upon their lengths and contraction velocity. However, these factors are widely assumed to be independent of each other and the few studies that dealt with interactions of torque, angle and angular velocity are based on isolated single-joint movements. Thus, the purpose of this study was to determine force/torque-angle and force/torque-angular velocity properties for multi-joint leg extensions.

METHODS

Human leg extension was investigated (n = 18) on a motor-driven leg press dynamometer while measuring external reaction forces at the feet. Extensor torque in the knee joint was calculated using inverse dynamics. Isometric contractions were performed at eight joint angle configurations of the lower limb corresponding to increments of 10° at the knee from 30 to 100° of knee flexion. Concentric and eccentric contractions were performed over the same range of motion at mean angular velocities of the knee from 30 to 240° s(-1).

RESULTS

For contractions of increasing velocity, optimum knee angle shifted from 52 ± 7 to 64 ± 4° knee flexion. Furthermore, the curvature of the concentric force/torque-angular velocity relations varied with joint angles and maximum angular velocities increased from 866 ± 79 to 1,238 ± 132° s(-1) for 90-50° knee flexion. Normalised eccentric forces/torques ranged from 0.85 ± 0.12 to 1.32 ± 0.16 of their isometric reference, only showing significant increases above isometric and an effect of angular velocity for joint angles greater than optimum knee angle.

CONCLUSIONS

The findings reveal that force/torque production during multi-joint leg extension depends on the combined effects of angle and angular velocity. This finding should be accounted for in modelling and optimisation of human movement.

Time-course effect of exercise-induced muscle damage on localized muscle mechanical properties assessed using elastography

AIM

Changes in muscle stiffness after exercise-induced muscle damage have been classically inferred from passive torque-angle curves. Elastographic techniques can be used to estimate the shear modulus of a localized muscular area. This study aimed to quantify the changes in shear elastic modulus in different regions of the elbow flexors after eccentric exercise and their relation to muscle length.

METHODS

Shear elastic modulus and transverse relaxation time (T2 ) were measured in the biceps brachii and brachialis muscles of sixteen participants, before, 1 h, 48 h and 21 days after three sets of ten maximal isokinetic eccentric contractions performed at 120° s(-1) .

RESULTS

The shear elastic modulus of the elbow flexors significantly increased 1 h (+46%; P = 0.005), with no significant change at 48 h and 21D, post-exercise. In contrast, T2 was not modified at 1 h but significantly increased at 48 h (+15%; P < 0.05). The increase in shear elastic modulus was more pronounced at long muscle lengths and reached a similar extent in the different regions of the elbow flexors. The normalized hysteresis area of shear elastic modulus-length relationship for the biceps brachii increased 1 h post-exercise (31%) in comparison with the pre-exercise value (18%), but was not significantly altered after five stretching cycles (P = 0.63).

CONCLUSION

Our results show homogeneous changes in muscle shear elastic modulus within and between elbow flexors. The greater increase in shear elastic modulus observed at long muscle lengths suggests the putative involvement of both cross-bridges number and titin in the modifications of muscle shear elastic modulus after damaging exercise.

Accuracy of gastrocnemius muscles forces in walking and running goats predicted by one-element and two-element Hill-type models

Hill-type models are commonly used to estimate muscle forces during human and animal movement-yet the accuracy of the forces estimated during walking, running, and other tasks remains largely unknown. Further, most Hill-type models assume a single contractile element, despite evidence that faster and slower motor units, which have different activation-deactivation dynamics, may be independently or collectively excited. This study evaluated a novel, two-element Hill-type model with "differential" activation of fast and slow contractile elements. Model performance was assessed using a comprehensive data set (including measures of EMG intensity, fascicle length, and tendon force) collected from the gastrocnemius muscles of goats during locomotor experiments. Muscle forces predicted by the new two-element model were compared to the forces estimated using traditional one-element models and to the forces measured in vivo using tendon buckle transducers. Overall, the two-element model resulted in the best predictions of in vivo gastrocnemius force. The coefficient of determination, r(2), was up to 26.9% higher and the root mean square error, RMSE, was up to 37.4% lower for the two-element model than for the one-element models tested. All models captured salient features of the measured muscle force during walking, trotting, and galloping (r(2)=0.26-0.51), and all exhibited some errors (RMSE=9.63-32.2% of the maximum in vivo force). These comparisons provide important insight into the accuracy of Hill-type models. The results also show that incorporation of fast and slow contractile elements within muscle models can improve estimates of time-varying, whole muscle force during locomotor tasks.

The activation time-course of contractile elements estimated from in vivo fascicle behaviours during twitch contractions

To better understand the cascade from neural activation up to force production within in vivo contracting muscle-tendon units, we estimated activation of contractile elements from experimentally measured human fascicle length change and force using a Hill-type muscle model. The experiment was conducted with respect to twitch contractions of the tibialis anterior muscle at three joint angles. As muscle contractile element force is a function of its length and velocity, the activation of contractile elements was calculated using a Hill-type muscle model and measured data. The results were able to reproduce the continuous rising activation of contractile elements after termination of electromyographic activity, the earlier shift of peak activation in time compared to twitch force, and the differences in time-course activation at three different joint angles. These findings are consistent with the predicted change in the activation of contractile elements from previous reports. Also, the results suggest that the time-course of the activation of contractile elements was greatly influenced by the change in force generating capacities related to both length and velocity, even in fixed end contractions, which could result from muscle-tendon interaction.

A muscle's force depends on the recruitment patterns of its fibers

Biomechanical models of whole muscles commonly used in simulations of musculoskeletal function and movement typically assume that the muscle generates force as a scaled-up muscle fiber. However, muscles are comprised of motor units that have different intrinsic properties and that can be activated at different times. This study tested whether a muscle model comprised of motor units that could be independently activated resulted in more accurate predictions of force than traditional Hill-type models. Forces predicted by the models were evaluated by direct comparison with the muscle forces measured in situ from the gastrocnemii in goats. The muscle was stimulated tetanically at a range of frequencies, muscle fiber strains were measured using sonomicrometry, and the activation patterns of the different types of motor unit were calculated from electromyographic recordings. Activation patterns were input into five different muscle models. Four models were traditional Hill-type models with different intrinsic speeds and fiber-type properties. The fifth model incorporated differential groups of fast and slow motor units. For all goats, muscles and stimulation frequencies the differential model resulted in the best predictions of muscle force. The in situ muscle output was shown to depend on the recruitment of different motor units within the muscle.

Contribution of stretch to the change of activation properties of muscle fibers in the diaphragm at the transition from fetal to neonatal life

The transition from fetal to postnatal life involves clearance of liquid from the lung and airways, and rapid formation of a functional residual capacity. Despite the importance of the diaphragm in this process, the impact of birth on the mechanical and functional activity of its muscle fibers is not known. This study determined the contractile characteristics of individual “skinned” diaphragm fibers from 70 days (0.47) gestation to after birth in sheep. Based on differential sensitivity to the divalent ions calcium (Ca²⁺) and strontium (Sr²⁺), all fibers in the fetal diaphragm were classified as “fast,” whereas fibers from the adult sheep diaphragm exhibited a “hybrid” phenotype where both “fast” and “slow” characteristics were present within each single fiber. Transition to the hybrid phenotype occurred at birth, was evident after only 40 min of spontaneous breathing, and could be induced by simple mechanical stretch of diaphragm fibers from near-term fetuses (∼147 days gestation). Both physical stretch of isolated fibers, and mechanical ventilation of the fetal diaphragm in situ, significantly increased sensitivity to Ca²⁺ and Sr²⁺, maximum force generating capacity, and decreased passive tension in near-term and preterm fetuses; however, only fibers from near-term fetuses showed a complete transition to a “hybrid” activation profile. These findings suggest that stretch associated with the transition from a liquid to air-filled lung at birth induces physical changes of proteins determining the activation and elastic properties of the diaphragm. These changes may allow the diaphragm to meet the increased mechanical demands of breathing immediately after birth.

Methodological aspects of SEMG recordings for force estimation--a tutorial and review

Insight into the magnitude of muscle forces is important in biomechanics research, for example because muscle forces are the main determinants of joint loading. Unfortunately muscle forces cannot be calculated directly and can only be measured using invasive procedures. Therefore, estimates of muscle force based on surface EMG measurements are frequently used. This review discusses the problems associated with surface EMG in muscle force estimation and the solutions that novel methodological developments provide to this problem. First, some basic aspects of muscle activity and EMG are reviewed and related to EMG amplitude estimation. The main methodological issues in EMG amplitude estimation are precision and representativeness. Lack of precision arises directly from the stochastic nature of the EMG signal as the summation of a series of randomly occurring polyphasic motor unit potentials and the resulting random constructive and destructive (phase cancellation) superimpositions. Representativeness is an issue due the structural and functional heterogeneity of muscles. Novel methods, i.e. multi-channel monopolar EMG and high-pass filtering or whitening of conventional bipolar EMG allow substantially less variable estimates of the EMG amplitude and yield better estimates of muscle force by (1) reducing effects of phase cancellation, and (2) adequate representation of the heterogeneous activity of motor units within a muscle. With such methods, highly accurate predictions of force, even of the minute force fluctuations that occur during an isometric and isotonic contraction have been achieved. For dynamic contractions, EMG-based force estimates are confounded by the effects of muscle length and contraction velocity on force producing capacity. These contractions require EMG amplitude estimates to be combined with modeling of muscle contraction dynamics to achieve valid force predictions.

Large-scale models reveal the two-component mechanics of striated muscle

This paper provides a comprehensive explanation of striated muscle mechanics and contraction on the basis of filament rotations. Helical proteins, particularly the coiled-coils of tropomyosin, myosin and alpha-actinin, shorten their H-bonds cooperatively and produce torque and filament rotations when the Coulombic net-charge repulsion of their highly charged side-chains is diminished by interaction with ions. The classical "two-component model" of active muscle differentiated a "contractile component" which stretches the "series elastic component" during force production. The contractile components are the helically shaped thin filaments of muscle that shorten the sarcomeres by clockwise drilling into the myosin cross-bridges with torque decrease (= force-deficit). Muscle stretch means drawing out the thin filament helices off the cross-bridges under passive counterclockwise rotation with torque increase (= stretch activation). Since each thin filament is anchored by four elastic alpha-actinin Z-filaments (provided with force-regulating sites for Ca(2+) binding), the thin filament rotations change the torsional twist of the four Z-filaments as the "series elastic components". Large scale models simulate the changes of structure and force in the Z-band by the different Z-filament twisting stages A, B, C, D, E, F and G. Stage D corresponds to the isometric state. The basic phenomena of muscle physiology, i. e. latency relaxation, Fenn-effect, the force-velocity relation, the length-tension relation, unexplained energy, shortening heat, the Huxley-Simmons phases, etc. are explained and interpreted with the help of the model experiments.

The length dependency of maximum force development in rat medial gastrocnemius muscle in situ

During many movements (e.g., running, jumping, and kicking) there is little time for skeletal muscles to build up force, thus rapid force development is important. The length dependency of isometric force development was investigated in maximally activated rat medial gastrocnemius muscles in situ with intact blood flow at 35 °C. Depending on time available for muscle activation, the length dependency of force development was expected to differ from that of the maximal isometric force (Fmax) reached much later during the contraction. During isometric force development in intact muscle–tendon preparations, the contractile elements actually shortened. Therefore, similar to previous findings on shortening contractions, it was hypothesized that maximal rate of force development (MRFD) would be obtained at a length below the optimum (Lo) for maximal isometric force production. To measure the effect of the entire time history of activation, force time integrals (FTIs) for different activation times (10–50 ms) were also calculated. The highest MRFD was obtained 1.94 ± 0.42 mm below (p < 0.05) Lo. When expressed relative to Fmax obtained at each individual length, the optimum was found at Lo – 4.4 mm. For FTI 10 ms and FTI 20 ms, optimum length was obtained at ~2 and 1 mm above (p < 0.05) Lo, respectively, whereas the optima for FTI 30, 40, and 50 ms were ~1 mm below (p < 0.05) Lo. In addition, at short lengths (< Lo – 4 mm) and for all activation times FTIs were relatively more decreased than Fmax. In conclusion, length dependency of force output during rapid force development differed from that of maximal isometric force; specifically, MRFD was obtained 2 mm below Lo.

The extensor tibiae muscle of the stick insect: biomechanical properties of an insect walking leg muscle

We investigated the properties of the extensor tibiae muscle of the stick insect (Carausius morosus) middle leg. Muscle geometry of the middle leg was compared to that of the front and hind legs and to the flexor tibiae, respectively. The mean length of the extensor tibiae fibres is 1.41+/-0.23 mm and flexor fibres are 2.11+/-0.30 mm long. The change of fibre length with joint angle was measured and closely follows a cosine function. Its amplitude gives effective moment arm lengths of 0.28+/-0.02 mm for the extensor and 0.56+/-0.04 mm for the flexor. Resting extensor tibiae muscle passive tonic force increased from 2 to 5 mN in the maximum femur-tibia (FT)-joint working range when stretched by ramps. Active muscle properties were measured with simultaneous activation (up to 200 pulses s(-1)) of all three motoneurons innervating the extensor tibiae, because this reflects most closely physiological muscle activation during leg swing. The force-length relationship corresponds closely to the typical characteristic according to the sliding filament hypothesis: it has a plateau at medium fibre lengths, declines nearly linearly in force at both longer and shorter fibre lengths, and the muscle's working range lies in the short to medium fibre length range. Maximum contraction velocity showed a similar relationship. The force-velocity relationship was the traditional Hill curve hyperbola, but deviated from the hyperbolic shape in the region of maximum contraction force close to the isometric contraction. Step-like changes in muscle length induced by loaded release experiments characterised the non-linear series elasticity as a quadratic spring.

Regulation of muscle contraction by Ca2+ and ADP: focusing on the auto-oscillation (SPOC)

A molecular motor in striated muscle, myosin II, is a non-processive motor that is unable to perform physiological functions as a single molecule and acts as an assembly of molecules. It is widely accepted that a myosin II motor is an independent force generator; the force generated at a steady state is usually considered to be a simple sum of those generated by each motor. This is the case at full activation (pCa < 5 in the presence of MgATP); however, we found that the myosin II motors show cooperative functions, i.e., non-linear auto-oscillation, named SPOC (SPontaneous Oscillatory Contraction), when the activation level is intermediate between those of contraction and relaxation (that is, at the intermediate level of pCa, 5-6, for cardiac muscle, or at the coexistence of MgATP, MgADP and inorganic phosphate (Pi) at higher pCa (> 7) for both skeletal and cardiac muscles). Here, we summarize the characteristics of SPOC phenomena, especially focusing on the physiological significance of SPOC in cardiac muscle. We propose a new concept that the auto-oscillatory property, which is inherent to the contractile system of cardiac muscle, underlies the molecular mechanism of heartbeat. Additionally, we briefly describe the dynamic properties of the thin filaments, i.e., the Ca(2+)-dependent flexibility change of the thin filaments, which may be the basis for the SPOC phenomena. We also describe a newly developed experimental system named "bio-nanomuscle," in which tension is asserted on a single reconstituted thin filament by interacting with crossbridges in the A-band composed of the thick filament lattice. This newly devised hybrid system is expected to fill the gap between the single-molecule level and the muscle system.

In situ muscle power differs without varying in vitro mechanical properties in two insect leg muscles innervated by the same motor neuron

The mechanical behavior of muscle during locomotion is often predicted by its anatomy, kinematics, activation pattern and contractile properties. The neuromuscular design of the cockroach leg provides a model system to examine these assumptions, because a single motor neuron innervates two extensor muscles operating at a single joint. Comparisons of the in situ measurements under in vivo running conditions of muscle 178 to a previously examined muscle (179) demonstrate that the same inputs (e.g. neural signal and kinematics) can result in different mechanical outputs. The same neural signal and kinematics, as determined during running, can result in different mechanical functions, even when the two anatomically similar muscles possess the same contraction kinetics, force-velocity properties and tetanic force-length properties. Although active shortening greatly depressed force under in vivo-like strain and stimulation conditions, force depression was similarly proportional to strain, similarly inversely proportional to stimulation level, and similarly independent of initial length and shortening velocity between the two muscles. Lastly, passive pre-stretch enhanced force similarly between the two muscles. The forces generated by the two muscles when stimulated with their in vivo pattern at lengths equal to or shorter than rest length differed, however. Overall, differences between the two muscles in their submaximal force-length relationships can account for up to 75% of the difference between the two muscles in peak force generated at short lengths observed during oscillatory contractions. Despite the fact that these muscles act at the same joint, are stimulated by the same motor neuron with an identical pattern, and possess many of the same in vitro mechanical properties, the mechanical outputs of two leg extensor muscles can be vastly different.

The mechanoelectric feedback: a novel "calcium clamp" method, using tetanic contraction, for testing the role of the intracellular free calcium

Mechanical perturbations affect the membrane action potential, a phenomenon denoted as the mechanoelectric feedback (MEF), and may elicit cardiac arrhythmias. Two plausible mechanisms were suggested to explain this phenomenon: (i) stretch-activated channels (SACs) within the cell membrane and (ii) modulation of the action potential by the intracellular Ca(2+) (the Calcium hypothesis). The intracellular Ca(2+) varies mainly due to the effects of the mechanical perturbations on the affinity of troponin for calcium. The present study concentrates on the unique experimental methods that allow differentiating between the effects of SAC and Ca(2+) on the action potential. This is achieved by controlling the sarcomere lengths (SLs) independently of the intracellular Ca(2+) concentration, in the intact fiber. A dedicated experimental setup allowed simultaneous measurements of the membrane potential and the mechanical performance (Force and SL). The action potential was measured by voltage-sensitive dye (Di-4-ANEPPS). The SL was measured by laser diffraction technique and was controlled by a fast servomotor. The intracellular Ca(2+) was controlled (calcium clamp) by imposing stable tetanic contractions at various extracellular calcium concentrations ([Ca(2+)](0)s). Tetanus was obtained by 8 Hz stimulation in the presence of cyclopiazonic acid (CPA) (30 muM). Isolated trabeculae from a rat's right ventricle were studied at different SLs and [Ca(2+)](0)s. The experimental data strongly support the calcium hypothesis. Although the action potential duration (APD) decreases at longer SL, the [Ca(2+)](0) has a significantly larger effect on the APD. The APD decreases as the [Ca(2+)](0) increases. Understanding the underlying mechanism opens new research avenues for the development of therapeutic modalities for cardiac arrhythmias.

Myofascial force transmission is increasingly important at lower forces: firing frequency-related length-force characteristics of rat extensor digitorum longus

AIM

Effects of submaximal stimulation frequencies on myofascial force transmission were investigated for rat anterior crural muscles with all motor units activated.

METHODS

Tibialis anterior and extensor hallucis longus (TAEHL) muscles were kept at constant muscle-tendon complex length, but extensor digitorum longus muscle (EDL) was lengthened distally. All muscles were activated simultaneously at 10, 20, 30 and 100 Hz within an intact anterior crural compartment.

RESULTS

At lower frequencies, significant proximo-distal EDL force differences exist. Absolute EDL proximo-distal active force differences were highest at 100 Hz (deltaF(dist-prox) = 0.4 N). However, the normalized difference was highest at 10 Hz (deltaF(dist-prox) = 30%F(dist)). Firing-frequency dependent shifts of the ascending limb of the EDL length-force curve to higher lengths were confirmed for a muscle within an intact compartment, although effects of firing frequency assessed at proximal and distal EDL tendons differed quantitatively. As EDL was lengthened distally, TAEHL distal isometric active force decreased progressively. The absolute decrease was highest for 100 Hz (deltaF(from initial) = -0.25 N). However, the highest normalized decrease was found for 10 Hz stimulation (deltaF(from initial) = -40%).

CONCLUSIONS

At submaximal stimulation frequencies, myofascial force transmission is present and the fraction of force transmitted myofascially increases with progressively lower firing frequencies. Evidently, the stiffness of epimuscular myofascial paths of force transmission decreases less than the stiffness of serial sarcomeres and myotendinous pathways. It is concluded that low firing frequencies as encountered in vivo enhance the relative importance of epimuscular myofascial force transmission with respect to myotendinous force transmission.

Muscle activation assessment: Effects of method, stimulus number, and joint angle

Activation capacity has traditionally been assessed using the interpolated twitch technique (ITT) and central activation ratio (CAR). However, the quantitative agreement of the two methods and the physiological mechanisms underpinning any possible differences have not been fully elucidated. The aim of this study was to compare and assess the sensitivity of the ITT and CAR to potential errors introduced by (1) evoking inadequate force, by manipulating the number of stimuli, and (2) neglecting differences in series elasticity between conditions, by manipulating joint angle. Ten subjects performed knee extension contractions at 30 degrees and 90 degrees knee-joint angles during which the ITT and CAR methods were applied using 1, 2, 4, and 8 electrical stimuli. Joint angle influenced the ITT outcome with higher values taken at 90 degrees (P < 0.05), while the number of stimuli influenced the CAR outcome with a higher number of stimuli yielding lower values (P < 0.05). For any given joint angle and stimulus number, the CAR method produced higher activation values than the ITT method by 8%-16%. Therefore, in the quantification of voluntary drive with the ITT and CAR methods consideration should be given not only to the number of stimuli applied but also to the effect of series elasticity due to joint-angle differences, since these factors may differently affect the outcome of the calculation, depending on the approach followed.

Length-dependent [Ca2+] sensitivity adds stiffness to muscle

It is well documented that muscle fibers become more sensitive for [Ca2+] with increasing sarcomere length. In mechanical terms this length-dependent [Ca2+] sensitivity (LDCS) adds to the stiffness of muscle fibers, because muscle force, normalized for the force-length relationship at maximal stimulation, increases with contractile element (CE) length. Although LDCS is well-documented in the physiological literature, it is ignored in most motor control studies. The aim of the present study was to investigate the importance of LDCS as a contributor to the stiffness of a muscle. Comparison of experimental data with predictions derived from the model of activation dynamics proposed by Hatze (Myocybernetic Control Models of Skeletal Muscle, University of South Africa, Pretoria, 1981, pp. 31-42) indicated that this model captures the main characteristics of LDCS well. It was shown that LDCS accounts for the experimentally observed shifts in optimum length at sub-maximal stimulation levels. Furthermore, it was shown that in conditions with low-to-medium muscle stimulation, the contribution of LDCS to the total amount of stiffness provided by the muscle is substantial. It was concluded that LDCS is an important muscle property and should be taken into account in studies concerning motor control.

Length-dependent Ca2+ activation in cardiac muscle: some remaining questions

The steep relationship between systolic force and end diastolic volume in cardiac muscle (Frank-Starling relation) is, to a large extent, based on length-dependent changes in myofilament Ca(2+) sensitivity. How sarcomere length modulates Ca(2+) sensitivity is still a topic of active investigation. Two general themes have emerged in recent years. On the one hand, there is a large body of evidence indicating that length-dependent changes in lattice spacing determine changes in Ca(2+) sensitivity for a given set of conditions. A model has been put forward in which the number of strong-binding cross-bridges that are formed is directly related to the proximity of the myosin heads to binding sites on actin. On the other hand, there is also a body of evidence suggesting that lattice spacing and Ca(2+) sensitivity are not tightly linked and that there is a length-sensing element in the sarcomere, which can modulate actin-myosin interactions independent of changes in lattice spacing. In this review, we examine the evidence that has been cited in support of these viewpoints. Much recent progress has been based on the combination of mechanical measurements with X-ray diffraction analysis of lattice spacing and cross-bridge interaction with actin. Compelling evidence indicates that the relationship between sarcomere length and lattice spacing is influenced by the elastic properties of titin and that changes in lattice spacing directly modulate cross-bridge interactions with thin filaments. However, there is also evidence that the precise relationship between Ca(2+) sensitivity and lattice spacing can be altered by changes in protein isoform expression, protein phosphorylation, modifiers of cross-bridge kinetics, and changes in titin compliance. Hence although there is no unique relationship between Ca(2+) sensitivity and lattice spacing the evidence strongly suggests that under any given set of physiological circumstances variation in lattice spacing is the major determinant of length-dependent changes in Ca(2+) sensitivity.

Low-frequency depression of tension in the cat gastrocnemius muscle after eccentric exercise

Subjecting a muscle to a series of eccentric contractions in which the contracting muscle is lengthened results in a number of changes in its mechanical properties. These include a fall in isometric tension that is particularly pronounced during low-frequency stimulation, a phenomenon known as low-frequency depression (LFD). Reports of LFD have not taken into account the shift in optimum length for active tension generation to longer muscle lengths that takes place after eccentric contractions. Given the length dependence of the stimulation frequency-tension curve, we tested the hypothesis that the change in this relationship after eccentric exercise is due to the shift in optimum length. We measured LFD by recording tension in response to a linearly increasing rate of stimulation of the nerve to medial gastrocnemius of anesthetized cats, over the range 0-100 pulses per second. Tension responses were measured before and after 50 eccentric contractions consisting of 6-mm stretches starting at 3 mm below optimum length and finishing at 3 mm above it. An index of LFD was derived from the tension responses to ramp stimulation. It was found that LFD after the eccentric contractions was partly, but not entirely, due to changes in the muscle's optimum length. An additional factor was the effect of fatigue. These observations led to the conclusion that the muscle length dependence of LFD was reduced by eccentric contractions. All of this means that after eccentric exercise the tension deficit at low rates of muscle activation is likely to be less severe than first thought.

Hystereses in the force-length relation and regulation of cross-bridge recruitment in tetanized rat trabeculae

Various mechanisms have been suggested to explain cardiac force-length Ca2+relations. The existence of a cooperativity mechanism, whereby cross-bridge (XB) recruitment is affected by the number of active XBs, suggests that the force response to length oscillations should lag length oscillations. Consequently, the oscillatory force response should be larger during shortening than during lengthening. To test this prediction, force responses to large-sarcomere length (SL) oscillations (36.7 ± 16.0 nm) at different SLs ( n = 6) and frequencies ( n = 7) were studied in intact tetanized trabeculae dissected from rat right ventricle ( n = 13). Stable tetani were obtained by utilizing 30 μM cyclopiazonic acid in Krebs-Henseleit solution containing 6 mM extracellular Ca2+at 25°C. SL was measured by laser diffraction techniques (Dalsa). Force was measured by silicone strain gauge. Instantaneous dynamic stiffness during large oscillations was measured by superimposing additional fast (50 or 200 Hz) and small-amplitude (2.25 ± 0.25 nm) oscillations. The force responses lagged the SL oscillations at slow frequencies (112 ± 41 ms at 1 Hz), and counterclockwise hystereses were obtained in the force-length plane: the force was higher during shortening than during lengthening. The delay in the force response decreased as the frequency of the SL oscillation was increased. Clockwise hysteresis, where the force preceded the SL, was obtained at frequencies >4 Hz. Similar hysteresis characteristics were obtained in the force-SL and stiffness-SL planes. Maximal lag was observed at the shortest SL, and the delay decreased with sarcomere elongation: 131.1 ± 31.7 ms at 1.78 ± 0.03 μm vs. 14.7 ± 18.5 ms at 1.99 ± 0.015 μm. The results establish the ability of cardiac fiber to adapt XB recruitment to changes in prevailing loading conditions. This study supports the stipulated existence of a cooperativity mechanism that regulates XB recruitment and highlights an additional method to characterize regulation of the force-length relation.

Limiting mechanisms of force production after repetitive dynamic contractions in human triceps surae

The influence of repetitive dynamic fatiguing contractions on the neuromuscular characteristics of the human triceps surae was investigated in 10 subjects. The load was 50% of the torque produced during a maximal voluntary contraction, and the exercise ended when the ankle range of motion declined to 50% of control. The maximal torque of the triceps surae and the electromyographic (EMG) activities of the soleus and medial gastrocnemius were studied in response to voluntary and electrically induced contractions before and after the fatiguing task and after 5 min of recovery. Reflex activities were also tested by recording the Hoffmann reflex (H reflex) and tendon reflex (T reflex) in the soleus muscle. The results indicated that whereas the maximal voluntary contraction torque, tested in isometric conditions, was reduced to a greater extent (P < 0.05) at 20 degrees of plantar flexion (-33%) compared with the neutral position (-23%) of the ankle joint, the EMG activity of both muscles was not significantly reduced after fatigue. Muscle activation, tested by the interpolated-twitch method or the ratio of the voluntary EMG to the amplitude of the muscle action potential (M-wave), as well as the neuromuscular transmission and sarcolemmal excitation, tested by the M-wave amplitude, did not change significantly after the fatiguing exercise. Although the H and T reflexes declined slightly (10-13%; P < 0.05) after fatigue, these adjustments did not appear to have a direct deleterious effect on muscle activation. In contrast, alterations in the mechanical twitch time course and postactivation potentiation indicated that intracellular Ca(2+)-controlled excitation-contraction coupling processes most likely played a major role in the force decrease after dynamic fatiguing contractions performed for short duration.