A novel three-filament model of force generation in eccentric contraction of skeletal muscles

Maximal active force in skinned muscle fibres from children with cerebral palsy

The aim of this study was to gain insight into the origins of muscle weakness in children with cerebral palsy (CP) by investigating active force in single muscle fibres isolated from the adductor longus (AL) of children with CP. Single skinned muscle fibres (n = 43, from 11 children with CP) were isolated and tested for their maximal active stress, instantaneous stiffness, and the ratio of active stress to stiffness at a sarcomere length (SL) of 2.4 µm, and passive stress at SLs of 2.4, 2.6, 2.8, 3.0, 3.2, and 3.4 µm. The muscle biopsies were tested for their total myofibrillar protein content using a BCA assay, and myosin heavy chain, actin, titin and nebulin content using gel electrophoresis. Muscle biopsies from the vastus lateralis of healthy adults (HA; n = 19 fibres from 4 subjects) were used for comparison. The maximal active stress and the instantaneous stiffness, expressed as active elastic modulus, were lower in the CP fibres compared to the HA fibres (79 ± 4 vs. 170 ± 11 kPa, and 5479 ± 381 vs. 8943 ± 402 kPa, respectively). The maximal active stress to stiffness ratio was not different between CP and HA fibres (0.016 ± 0.001 vs. 0.020 ± 0.002). Actin, titin and nebulin content was reduced in the CP compared to the HA samples. Passive stress was also reduced in the CP fibres at SLs of 2.8, 3.0, 3.2 and 3.6 µm. These results suggest that the contractile ability of muscles from children with CP is compromised at the fibre level and this is likely the result of a decrease in sarcomeric proteins such as actin, titin and nebulin.

Consecutive SSCs increase the SSC effect in skinned rat muscle fibres

Muscle function is essential for generating force and movement, with stretch-shortening cycles (SSCs) playing a fundamental role in the economy of everyday locomotion. Compared with pure shortening contractions, the SSC effect is characterised by increased force, work, and power output during the SSC shortening phase. Few studies have investigated whether SSC effects transfer across consecutive SSCs. Therefore, we investigated SSC effects over three consecutive SSCs in skinned rat muscle fibres by analysing the isometric force immediately before stretch onset (Fonset), the peak force at the end of stretching (Fpeak), and the minimum force at the end of shortening (Fmin), along with mechanical (WorkSSC) and shortening work (WorkSHO) at different activation levels (20%, 60%, and 100%). Each SSC was followed by an isometric hold phase, allowing force to return to a steady state. Results indicated an increase in both Fpeak (20.3%) and WorkSSC (60.9%) from SSC1 to SSC3 across all activation levels tested. At 20% and 60% activation, Fonset, Fmin, and WorkSHO increased (range: 4.5-28.5%) from SSC1 to SSC3. However, at 100% activation, Fonset and WorkSHO remained unchanged, while Fmin decreased (- 8.5%) from SSC1 to SSC3. These results suggest that the increase in SSC effects at submaximal activation may be primarily due to increased cross-bridge forces. The absence of increases in Fonset, Fmin, and WorkSHO at 100% activation suggests that increases in Fpeak and WorkSSC may not be attributed to increased cross-bridge force but could instead be caused by additional effects, possibly involving modulation of non-cross-bridge structures, likely titin, and their stiffness.

Residual force depression is affected by muscle length

The isometric force attained after active shortening is smaller than that attained during purely isometric contractions, although the sarcomere length and activation level are the same. This phenomenon is known as residual force depression. This study aimed to examine whether the magnitude of residual force depression is affected by muscle length. Single-skinned fibers obtained from the rabbit psoas muscle (n = 8) were used in this study. We measured the isometric forces at an average sarcomere length of 2.1, 2.4, and 2.7 μm, and the isometric forces attained after active shortening (from 2.7 to 2.4 μm, and from 2.4 to 2.1 μm) to calculate the magnitude of residual force depression attained at both long (2.4 μm) and short (2.1 μm) length conditions. The magnitude of residual force depression was significantly larger in the long than short condition (p = 0.046). Although not statistically significant, the mean force attained during shortening was greater in the long than in the short condition (p = 0.074, note that all fibers showed larger mechanical work in the long condition). This tendency of difference in force (mechanical work attained during shortening) between the conditions is one of the reasons for muscle length-dependent residual force depression; however, some fibers showed small differences in mechanical work and large differences in residual force depression between the conditions, indicating that the magnitude of mechanical work did not simply explain the magnitude of residual force depression.

Phenomenological Muscle Constitutive Model With Actin-Titin Binding for Simulating Active Stretching

The force produced by a muscle depends on its contractile history, yet human movement simulations typically employ muscle models that define the force-length relationship from measurements of fiber force during isometric contractions. In these muscle models, the total force-length curve can have a negative slope at fiber lengths greater than the fiber length at which peak isometric force is produced. This region of negative stiffness can cause numerical instability in simulations. Experiments have found that the steady-state force in a muscle fiber following active stretching is greater than the force produced during a purely isometric contraction. This behavior is called residual force enhancement. We present a constitutive model that exhibits force enhancement, implemented as a hyperelastic material in the febio finite element software. There is no consensus on the mechanisms responsible for force enhancement; we adopt the assumption that the passive fiber force depends on the sarcomere length at the instant that the muscle is activated above a threshold. We demonstrate the numerical stability of our model using an eigenvalue analysis and by simulating a muscle whose fibers are of different lengths. We then use a three-dimensional muscle geometry to verify the effect of force enhancement on the development of stress and the distribution of fiber lengths. Our proposed muscle material model is one of the few models available that exhibits force enhancement and is suitable for simulations of active lengthening. We provide our implementation in febio so that others can reproduce and extend our results.

Impact of lengthening velocity on the generation of eccentric force by slow-twitch muscle fibers in long stretches

After an initial increase, isovelocity elongation of a muscle fiber can lead to diminishing (referred to as Give in the literature) and subsequently increasing force. How the stretch velocity affects this behavior in slow-twitch fibers remains largely unexplored. Here, we stretched fully activated individual rat soleus muscle fibers from 0.85 to 1.3 optimal fiber length at stretch velocities of 0.01, 0.1, and 1 maximum shortening velocity, vmax, and compared the results with those of rat EDL fast-twitch fibers obtained in similar experimental conditions. In soleus muscle fibers, Give was 7%, 18%, and 44% of maximum isometric force for 0.01, 0.1, and 1 vmax, respectively. As in EDL fibers, the force increased nearly linearly in the second half of the stretch, although the number of crossbridges decreased, and its slope increased with stretch velocity. Our findings are consistent with the concept of a forceful detachment and subsequent crossbridge reattachment in the stretch's first phase and a strong viscoelastic titin contribution to fiber force in the second phase of the stretch. Interestingly, we found interaction effects of stretch velocity and fiber type on force parameters in both stretch phases, hinting at fiber type-specific differences in crossbridge and titin contributions to eccentric force. Whether fiber type-specific combined XB and non-XB models can explain these effects or if they hint at some not fully understood properties of muscle contraction remains to be shown. These results may stimulate new optimization perspectives in sports training and provide a better understanding of structure-function relations of muscle proteins.

A three filament mechanistic model of musculotendon force and impedance

The force developed by actively lengthened muscle depends on different structures across different scales of lengthening. For small perturbations, the active response of muscle is well captured by a linear-time-invariant (LTI) system: a stiff spring in parallel with a light damper. The force response of muscle to longer stretches is better represented by a compliant spring that can fix its end when activated. Experimental work has shown that the stiffness and damping (impedance) of muscle in response to small perturbations is of fundamental importance to motor learning and mechanical stability, while the huge forces developed during long active stretches are critical for simulating and predicting injury. Outside of motor learning and injury, muscle is actively lengthened as a part of nearly all terrestrial locomotion. Despite the functional importance of impedance and active lengthening, no single muscle model has all these mechanical properties. In this work, we present the viscoelastic-crossbridge active-titin (VEXAT) model that can replicate the response of muscle to length changes great and small. To evaluate the VEXAT model, we compare its response to biological muscle by simulating experiments that measure the impedance of muscle, and the forces developed during long active stretches. In addition, we have also compared the responses of the VEXAT model to a popular Hill-type muscle model. The VEXAT model more accurately captures the impedance of biological muscle and its responses to long active stretches than a Hill-type model and can still reproduce the force-velocity and force-length relations of muscle. While the comparison between the VEXAT model and biological muscle is favorable, there are some phenomena that can be improved: the low frequency phase response of the model, and a mechanism to support passive force enhancement.

Force re-development after shortening reveals a role for titin in stretch-shortening performance enhancement in skinned muscle fibres

Stretch-shortening cycles (SSCs) involve muscle lengthening (eccentric contractions) instantly followed by shortening (concentric contractions). This combination enhances force, work and power output compared with pure shortening contractions, which is known as the SSC effect. Recent evidence indicates both cross-bridge (XB)-based and non-XB-based (e.g. titin) structures contribute to this effect. This study analysed force re-development following SSCs and pure shortening contractions to gain further insight into the roles of XB and non-XB structures regarding the SSC effect. Experiments were conducted on rat soleus muscle fibres (n=16) with different SSC velocities (30%, 60% and 85% of maximum shortening velocity) and constant stretch-shortening magnitudes (18% of optimum length). The XB inhibitor blebbistatin was used to distinguish between XB and non-XB contributions to force generation. The results showed SSCs led to significantly greater [mean±s.d. 1.02±0.15 versus 0.68±0.09 (ΔF/Δt); t62=8.61, P<0.001, d=2.79) and faster (75 ms versus 205 ms; t62=-6.37, P<0.001, d=-1.48) force re-development compared with pure shortening contractions in the control treatment. In the blebbistatin treatment, SSCs still resulted in greater [0.11±0.03 versus 0.06±0.01 (ΔF/Δt); t62=8.00, P<0.001, d=2.24) and faster (3010±1631 versus 7916±3230 ms; t62=-8.00, P<0.001, d=-1.92) force re-development compared with pure shortening contractions. These findings deepen our understanding of the SSC effect, underscoring the involvement of non-XB structures such as titin in modulating force production. This modulation is likely to involve complex mechanosensory coupling from stretch to signal transmission during muscle contraction.

Muscle short-range stiffness behaves like a maxwell element, not a spring: Implications for joint stability

INTRODUCTION

Muscles play a critical role in supporting joints during activities of daily living, owing, in part, to the phenomenon of short-range stiffness. Briefly, when an active muscle is lengthened, bound cross-bridges are stretched, yielding forces greater than what is predicted from the force length relationship. For this reason, short-range stiffness has been proposed as an attractive mechanism for providing joint stability. However, there has yet to be a forward dynamic simulation employing a cross-bridge model, that demonstrates this stabilizing role. Therefore, the purpose of this investigation was to test whether Huxley-type muscle elements, which exhibit short-range stiffness, can stabilize a joint while at constant activation.

METHODS

We analyzed the stability of an inverted pendulum (moment of inertia: 2.7 kg m2) supported by Huxley-type muscle models that reproduce the short-range stiffness phenomenon. We calculated the muscle forces that would provide sufficient short-range stiffness to stabilize the system based in minimizing the potential energy. Simulations consisted of a 50 ms long, 5 Nm square-wave perturbation, with numerical simulations carried out in ArtiSynth.

RESULTS

Despite the initial analysis predicting shared activity of antagonist and agonist muscles to maintain stable equilibrium, the inverted pendulum model was not stable, and did not maintain an upright posture even with fully activated muscles.

DISCUSSION & CONCLUSION

Our simulations suggested that short-range stiffness cannot be solely responsible for joint stability, even for modest perturbations. We argue that short-range stiffness cannot achieve stability because its dynamics do not behave like a typical spring. Instead, an alternative conceptual model for short-range stiffness is that of a Maxwell element (spring and damper in series), which can be obtained as a first-order approximation to the Huxley model. We postulate that the damping that results from short-range stiffness slows down the mechanical response and allows the central nervous system time to react and stabilize the joint. We speculate that other mechanisms, like reflexes or residual force enhancement/depression, may also play a role in joint stability. Joint stability is due to a combination of factors, and further research is needed to fully understand this complex system.

Unlocking the benefit of active stretch: the eccentric muscle action, not the preload, maximizes muscle-tendon unit stretch-shortening cycle performance

Stretch-shortening cycles (SSCs) outperform shortening contractions preceded by isometric contractions in terms of enhanced force/torque, work, and power production during shortening. This so-called SSC effect is presumably related to the active muscle stretch before shortening in SSCs. However, it remains unclear whether the effects of stretch-induced higher preload level or stretch-induced history dependence maximize the SSC effect. Therefore, we analyzed fascicle behavior, muscle-tendon unit (MTU) shortening work, and torque/force (n = 12 participants) via ultrasound and dynamometry during electrically stimulated submaximal plantar flexion contractions from 10° plantarflexion to 15° dorsiflexion. To elucidate the effects of preload level and preload modality (i.e., contraction type) on shortening performance, muscle-tendon unit shortening was preceded by fixed-end (SHO), active stretch (SSC), and preload-matched fixed-end (MATCHED) contractions. Before shortening, MATCHED and SCC had the same preload level (1% torque difference), similar joint position, and muscle fascicle lengths. Compared with SHO, shortening work was significantly (P < 0.001, partial η2 = 0.749) increased by 85% and 55% for SSC and MATCHED, respectively, with SSC shortening work being significantly higher than MATCHED (P = 0.016). This indicates that preload contributes by 65% to the overall SSC effect so that 35% needs to be referred to stretched-induced history-dependent mechanisms. In addition, SSC showed larger fascicle forces at the end of shortening (P < 0.001) and 20% less depressed isometric torque following shortening compared with MATCHED (P < 0.001). As potential decoupling effects by the series elastic element were controlled by matching the preload levels, we conclude that the difference between SSC and MATCHED is related to stretch-induced long-lasting history-dependent effects.NEW & NOTEWORTHY Using a torque-matched preload protocol, we found that 2/3 of the performance enhancement in muscle-tendon unit stretch-shortening cycles (SSCs) is caused by the increased preload level. The remaining 1/3 is owed to the long-lasting history-dependent effects triggered during the stretch in SSCs. This increased performance output is attributed to passive elastic structures within the contractile element that do not require additional muscle activation, therefore contributing to the higher efficiency of the neuromuscular system in SSCs.

The effect of muscle ultrastructure on the force, displacement and work capacity of skeletal muscle

Skeletal muscle powers animal movement through interactions between the contractile proteins, actin and myosin. Structural variation contributes greatly to the variation in mechanical performance observed across muscles. In vertebrates, gross structural variation occurs in the form of changes in the muscle cross-sectional area : fibre length ratio. This results in a trade-off between force and displacement capacity, leaving work capacity unaltered. Consequently, the maximum work per unit volume-the work density-is considered constant. Invertebrate muscle also varies in muscle ultrastructure, i.e. actin and myosin filament lengths. Increasing actin and myosin filament lengths increases force capacity, but the effect on muscle fibre displacement, and thus work, capacity is unclear. We use a sliding-filament muscle model to predict the effect of actin and myosin filament lengths on these mechanical parameters for both idealized sarcomeres with fixed actin : myosin length ratios, and for real sarcomeres with known filament lengths. Increasing actin and myosin filament lengths increases stress without reducing strain capacity. A muscle with longer actin and myosin filaments can generate larger force over the same displacement and has a higher work density, so seemingly bypassing an established trade-off. However, real sarcomeres deviate from the idealized length ratio suggesting unidentified constraints or selective pressures.

Molecular mechanisms of muscle contraction: A historical perspective

Studies of muscle structure and function can be traced to at least 2,000 years ago. However, the modern era of muscle contraction mechanisms started in the 1950s with the classic works by AF Huxley and HE Huxley, both born in the United Kingdom, but not related and working independently. HE Huxley was the first to suggest that muscle contraction occurred through the sliding of two sets of filamentous structures (actin or thin filaments and myosin or thick filaments). AF Huxley then developed a biologically inspired mathematical model suggesting a possible molecular mechanism of how this sliding of actin and myosin might take place. This model then evolved from a two-state to a multi-state model of myosin-actin interactions, and from one that suggested a linear motor causing the sliding to a rotating motor. This model, the cross-bridge model of muscle contraction, is still widely used in biomechanics, and even the more sophisticated cross-bridge models of today still contain many of the features originally proposed by AF Huxley. In 2002, we discovered a hitherto unknown property of muscle contraction that suggested the involvement of passive structures in active force production, the so-called passive force enhancement. It was quickly revealed that this passive force enhancement was caused by the filamentous protein titin, and the three-filament (actin, myosin, and titin) sarcomere model of muscle contraction evolved. There are many suggestions of how these three proteins interact to cause contraction and produce active force, and one such suggestion is described here, but the molecular details of this proposed mechanism still need careful evaluation.

Stretching the story of titin and muscle function

The discovery of the giant protein titin, also known as connectin, dates almost half a century back. In this review, I recapitulate major advances in the discovery of the titin filaments and the recognition of their properties and function until today. I briefly discuss how our understanding of the layout and interactions of titin in muscle sarcomeres has evolved and review key facts about the titin sequence at the gene (TTN) and protein levels. I also touch upon properties of titin important for the stability of the contractile units and the assembly and maintenance of sarcomeric proteins. The greater part of my discussion centers around the mechanical function of titin in skeletal muscle. I cover milestones of research on titin's role in stretch-dependent passive tension development, recollect the reasons behind the enormous elastic diversity of titin, and provide an update on the molecular mechanisms of titin elasticity, details of which are emerging even now. I reflect on current knowledge of how muscle fibers behave mechanically if titin stiffness is removed and how titin stiffness can be dynamically regulated, such as by posttranslational modifications or calcium binding. Finally, I highlight novel and exciting, but still controversially discussed, insight into the role titin plays in active tension development, such as length-dependent activation and contraction from longer muscle lengths.

The history-dependent features of muscle force production: A challenge to the cross-bridge theory and their functional implications

The cross-bridge theory predicts that muscle force is determined by muscle length and the velocity of active muscle length changes. However, before the formulation of the cross-bridge theory, it had been observed that the isometric force at a given muscle length is enhanced or depressed depending on active muscle length changes before that given length is reached. These enhanced and depressed force states are termed residual force enhancement (rFE) and residual force depression (rFD), respectively, and together they are known as the history-dependent features of muscle force production. In this review, we introduce early attempts in explaining rFE and rFD before we discuss more recent research from the past 25 years which has contributed to a better understanding of the mechanisms underpinning rFE and rFD. Specifically, we discuss the increasing number of findings on rFE and rFD which challenge the cross-bridge theory and propose that the elastic element titin plays a role in explaining muscle history-dependence. Accordingly, new three-filament models of force production including titin seem to provide better insight into the mechanism of muscle contraction. Complementary to the mechanisms behind muscle history-dependence, we also show various implications for muscle history-dependence on in-vivo human muscle function such as during stretch-shortening cycles. We conclude that titin function needs to be better understood if a new three-filament muscle model which includes titin, is to be established. From an applied perspective, it remains to be elucidated how muscle history-dependence affects locomotion and motor control, and whether history-dependent features can be changed by training.

Eccentric muscle contractions: from single muscle fibre to whole muscle mechanics

Eccentric muscle loading encompasses several unique features compared to other types of contractions. These features include increased force, work, and performance at decreased oxygen consumption, reduced metabolic cost, improved energy efficiency, as well as decreased muscle activity. This review summarises explanatory approaches to long-standing questions in terms of muscular contraction dynamics and molecular and cellular mechanisms underlying eccentric muscle loading. Moreover, this article intends to underscore the functional link between sarcomeric components, emphasising the fundamental role of titin in skeletal muscle. The giant filament titin reveals versatile functions ranging from sarcomere organisation and maintenance, providing passive tension and elasticity, and operates as a mechanosensory and signalling platform. Structurally, titin consists of a viscoelastic spring segment that allows activation-dependent coupling to actin. This titin-actin interaction can explain linear force increases in active lengthening experiments in biological systems. A three-filament model of skeletal muscle force production (mediated by titin) is supposed to overcome significant deviations between experimental observations and predictions by the classic sliding-filament and cross-bridge theories. Taken together, this review intends to contribute to a more detailed understanding of overall muscle behaviour and force generation-from a microscopic sarcomere level to a macroscopic multi-joint muscle level-impacting muscle modelling, the understanding of muscle function, and disease.

Force potentiation during eccentric contractions in rat skeletal muscle

Postactivation potentiation refers to an acute enhancement of contractile properties following muscle activity. Previously, the effects of prior muscle activation on eccentric force at tetanic activation frequencies have only been sparsely reported. This paper aimed to study acute activity-induced effects on eccentric force of slow and fast-twitch muscles and characterize them in relation to postactivation potentiation. We elicited eccentric contractions in isolated rat extensor digitorum longus and soleus muscles by actively lengthening muscles at a constant velocity. We assessed contractile properties by measuring force over shortly interspaced, identical eccentric, and isometric contractions. We then analyzed stretch force, isometric peak force, rate of force development, and relaxation times. Finally, we compared the time courses for the development and cessation of changes in stretch force to known features of postactivation potentiation. In extensor digitorum longus, muscles stretch force consistently increased in a contraction-to-contraction manner by up to 49% [95% confidence interval (CI): 35-64%] whereas isometric peak force simultaneously showed minor declines (8%, 95% CI: 5-10%). The development and cessation of eccentric force potentiation coincided with the development of twitch potentiation and increases in rate of force development. In soleus muscles we found no consistent eccentric potentiation. Characterization of the increase in eccentric force revealed that force only increased in the very beginning of an active stretch. Eccentric force at tetanic activation frequencies potentiates substantially in extensor digitorum longus muscles over consecutive contractions with a time course coinciding with postactivation potentiation. Such eccentric potentiation may be important in sport performance.NEW & NOTEWORTHY Force during eccentric contractions can increase to a magnitude that may have profound consequences for our understanding of skeletal muscle locomotion. This increase in eccentric force occurs over consecutive, shortly interspaced, tetanic contractions in rat extensor digitorum longus muscles-not in rat soleus muscles-and coincides with well-known traits of postactivation potentiation. Eccentric force potentiation may significantly enhance muscle performance in activities involving stretch-shortening cycles.

Numerical instability of Hill-type muscle models

Hill-type muscle models are highly preferred as phenomenological models for musculoskeletal simulation studies despite their introduction almost a century ago. The use of simple Hill-type models in simulations, instead of more recent cross-bridge models, is well justified since computationally 'light-weight'-although less accurate-Hill-type models have great value for large-scale simulations. However, this article aims to invite discussion on numerical instability issues of Hill-type muscle models in simulation studies, which can lead to computational failures and, therefore, cannot be simply dismissed as an inevitable but acceptable consequence of simplification. We will first revisit the basic premises and assumptions on the force-length and force-velocity relationships that Hill-type models are based upon, and their often overlooked but major theoretical limitations. We will then use several simple conceptual simulation studies to discuss how these numerical instability issues can manifest as practical computational problems. Lastly, we will review how such numerical instability issues are dealt with, mostly in an ad hoc fashion, in two main areas of application: musculoskeletal biomechanics and computer animation.

Effects of shortening velocity on the stiffness to force ratio during isometric force redevelopment suggest mechanisms of residual force depression

Although the phenomenon of residual force depression has been known for decades, the mechanisms remain elusive. In the present study, we investigated mechanisms of residual force depression by measuring the stiffness to force ratio during force redevelopment after shortening at different velocities. The results showed that the slope of the relationship between muscle stiffness and force decreased with decreasing shortening velocity, and the y-intercept increased with decreasing shortening velocity. The differing slopes and y-intercepts indicate that the stiffness to force ratio during isometric force redevelopment depends on the active shortening velocity at a given muscle length and activation level. The greater stiffness to force ratio after active shortening can potentially be explained by weakly-bound cross bridges in the new overlap zone. However, weakly-bound cross bridges are insufficient to explain the reduced slope at the slowest shortening velocity because the reduced velocity should increase the proportion of weakly- to strongly-bound cross bridges, thereby increasing the slope. In addition, if actin distortion caused by active shortening recovers during the force redevelopment period, then the resulting slope should be similar to the non-linear slope of force redevelopment over time. Alternatively, we suggest that a tunable elastic element, such as titin, could potentially explain the results.

Sensitivity of muscle force response of a two-state cross-bridge model to variations in model parameters

Muscle models based on the cross-bridge theory (Huxley-type models) are frequently used to calculate muscle forces for different contractile conditions. Dynamic and nonlinear characteristics of muscle forces produced during isometric, concentric, and eccentric contractions can be represented to a limited extent by using cross-bridge models. Cross-bridge models use various parameters to simulate force responses. However, there remains uncertainty as to the effect of changes in model parameters on force responses in Huxley-type models. In this study, we aimed to analyze the sensitivity of force response to changes in model parameters in Huxley-type models. A two-state Huxley model was used to determine the cross-bridge attachment distributions and forces for shortening and lengthening contractions. Sensitivity of muscle force to changes in attachment rate, detachment rate, and cross-bridge binding distance was examined within a range of ±20% of the nominal value using Monte Carlo simulations. Changes in the detachment rate influenced the predicted muscle forces the most for lengthening contractions, while changes in attachment rate and binding distance affected forces the most for shortening contractions. These results show once more the asymmetry between shortening and lengthening contractions and the difficulty in using a single cross-bridge model to predict forces during shortening and elongation accurately.

Active muscle stiffness is reduced during rapid unloading in muscles from TtnD112-158 mice with a large deletion to PEVK titin

Evidence suggests that the giant muscle protein, titin functions as a tunable spring in active muscle. However, the mechanisms for increasing titin stiffness with activation are not well understood. Previous studies have suggested that during muscle activation, titin binds to actin which engages the PEVK region of titin thereby increasing titin stiffness. In this study, we investigated the role of PEVK titin in active muscle stiffness during rapid unloading. We measured elastic recoil of active and passive soleus muscles from TtnD112-158 mice characterized by a 75% deletion of PEVK titin and increased passive stiffness. We hypothesized that activated TtnD112-158 muscles are more stiff than wild type muscles due to the increased stiffness of PEVK titin. Using a servomotor force lever, we compared the stress–strain relationships of elastic elements in active and passive muscles during rapid unloading and quantified the change in stiffness upon activation. Results show that the elastic modulus of TtnD112-158 muscles increased with activation. However, elastic elements developed force at 7% longer lengths and exhibited 50% lower active stiffness in TtnD112-158 soleus muscles than wild type muscles. Thus, despite having a shorter, stiffer PEVK segment, during rapid unloading, TtnD112-158 soleus muscles exhibited reduced active stiffness compared to wild type soleus muscles. These results are consistent with the idea that PEVK titin contributes to active muscle stiffness, however, the reduction in active stiffness of TtnD112-158 muscles suggests that other mechanisms compensate for the increased PEVK stiffness.

What Can We Learn from Single Sarcomere and Myofibril Preparations?

Sarcomeres are the smallest functional contractile unit of muscle, and myofibrils are striated muscle organelles that are comprised of sarcomeres that are strictly aligned in series. Furthermore, passive forces in sarcomeres and myofibrils are almost exclusively produced by the structural protein titin, and all contractile, regulatory, and structural proteins are in their natural configuration. For these mechanical and structural reasons single sarcomere and myofibril preparations are arguably the most powerful to answer questions on the mechanisms of striated muscle contraction. We developed and optimized single myofibril research over the past 20 years and were the first to mechanically isolate and test single sarcomeres. The results from this research led to the uncovering of the crucial role of titin in muscle contraction, first molecular explanations for the origins of the passive and the residual force enhancement properties of skeletal and cardiac muscles, the discovery of sarcomere length stability on the descending limb of the force-length relationship, and culminating in the formulation of the three-filament theory of muscle contraction that, aside from actin and myosin, proposes a crucial role of titin in active force production. Aside from all the advantages and possibilities that single sarcomere and myofibril preparations offer, there are also disadvantages. These include the fragility of the preparation, the time-consuming training to master these preparations, the limited spatial resolution for length and force measurements, and the unavailability of commercial systems for single sarcomere/myofibril research. Ignoring the mechanics that govern serially linked systems, not considering the spatial resolution and associated accuracies of myofibril systems, and neglecting the fragility of myofibril preparations, has led to erroneous interpretations of results and misleading conclusions. Here, we will attempt to describe the methods and possible applications of single sarcomere/myofibril research and discuss the advantages and disadvantages by focusing on specific applications. It is hoped that this discussion may contribute to identifying the enormous potential of single sarcomere/myofibril research in discovering the secrets of muscle contraction.

The titin N2B and N2A regions: biomechanical and metabolic signaling hubs in cross-striated muscles

Muscle specific signaling has been shown to originate from myofilaments and their associated cellular structures, including the sarcomeres, costameres or the cardiac intercalated disc. Two signaling hubs that play important biomechanical roles for cardiac and/or skeletal muscle physiology are the N2B and N2A regions in the giant protein titin. Prominent proteins associated with these regions in titin are chaperones Hsp90 and αB-crystallin, members of the four-and-a-half LIM (FHL) and muscle ankyrin repeat protein (Ankrd) families, as well as thin filament-associated proteins, such as myopalladin. This review highlights biological roles and properties of the titin N2B and N2A regions in health and disease. Special emphasis is placed on functions of Ankrd and FHL proteins as mechanosensors that modulate muscle-specific signaling and muscle growth. This region of the sarcomere also emerged as a hotspot for the modulation of passive muscle mechanics through altered titin phosphorylation and splicing, as well as tethering mechanisms that link titin to the thin filament system.

Titin N2A Domain and Its Interactions at the Sarcomere

Titin is a giant protein in the sarcomere that plays an essential role in muscle contraction with actin and myosin filaments. However, its utility goes beyond mechanical functions, extending to versatile and complex roles in sarcomere organization and maintenance, passive force, mechanosensing, and signaling. Titin’s multiple functions are in part attributed to its large size and modular structures that interact with a myriad of protein partners. Among titin’s domains, the N2A element is one of titin’s unique segments that contributes to titin’s functions in compliance, contraction, structural stability, and signaling via protein–protein interactions with actin filament, chaperones, stress-sensing proteins, and proteases. Considering the significance of N2A, this review highlights structural conformations of N2A, its predisposition for protein–protein interactions, and its multiple interacting protein partners that allow the modulation of titin’s biological effects. Lastly, the nature of N2A for interactions with chaperones and proteases is included, presenting it as an important node that impacts titin’s structural and functional integrity.

Force-velocity and tension transient measurements from Drosophila jump muscle reveal the necessity of both weakly-bound cross-bridges and series elasticity in models of muscle contraction

Muscle contraction is a fundamental biological process where molecular interactions between the myosin molecular motor and actin filaments result in contraction of a whole muscle, a process spanning size scales differing in eight orders of magnitude. Since unique behavior is observed at every scale in between these two extremes, to fully understand muscle function it is vital to develop multi-scale models. Based on simulations of classic measurements of muscle heat generation as a function of work, and shortening rate as a function of applied force, we hypothesize that a model based on molecular measurements must be modified to include a weakly-bound interaction between myosin and actin in order to fit measurements at the muscle fiber or whole muscle scales. This hypothesis is further supported by the model's need for a weakly-bound state in order to qualitatively reproduce the force response that occurs when a muscle fiber is rapidly stretched a small distance. We tested this hypothesis by measuring steady-state force as a function of shortening velocity, and the force transient caused by a rapid length step in Drosophila jump muscle fibers. Then, by performing global parameter optimization, we quantitatively compared the predictions of two mathematical models, one lacking a weakly-bound state and one with a weakly-bound state, to these measurements. Both models could reproduce our force-velocity measurements, but only the model with a weakly-bound state could reproduce our force transient measurements. However, neither model could concurrently fit both measurements. We find that only a model that includes weakly-bound cross-bridges with force-dependent detachment and an elastic element in series with the cross-bridges is able to fit both of our measurements. This result suggests that the force response after stretch is not a reflection of distinct steps in the cross-bridge cycle, but rather arises from the interaction of cross-bridges with a series elastic element. Additionally, the model suggests that the curvature of the force-velocity relationship arises from a combination of the force-dependence of weakly- and strongly-bound cross-bridges. Overall, this work presents a minimal cross-bridge model that has predictive power at the fiber level.

Power Amplification Increases With Contraction Velocity During Stretch-Shortening Cycles of Skinned Muscle Fibers

Muscle force, work, and power output during concentric contractions (active muscle shortening) are increased immediately following an eccentric contraction (active muscle lengthening). This increase in performance is known as the stretch-shortening cycle (SSC)-effect. Recent findings demonstrate that the SSC-effect is present in the sarcomere itself. More recently, it has been suggested that cross-bridge (XB) kinetics and non-cross-bridge (non-XB) structures (e.g., titin and nebulin) contribute to the SSC-effect. As XBs and non-XB structures are characterized by a velocity dependence, we investigated the impact of stretch-shortening velocity on the SSC-effect. Accordingly, we performed in vitro isovelocity ramp experiments with varying ramp velocities (30, 60, and 85% of maximum contraction velocity for both stretch and shortening) and constant stretch-shortening magnitudes (17% of the optimum sarcomere length) using single skinned fibers of rat soleus muscles. The different contributions of XB and non-XB structures to force production were identified using the XB-inhibitor Blebbistatin. We show that (i) the SSC-effect is velocity-dependent-since the power output increases with increasing SSC-velocity. (ii) The energy recovery (ratio of elastic energy storage and release in the SSC) is higher in the Blebbistatin condition compared with the control condition. The stored and released energy in the Blebbistatin condition can be explained by the viscoelastic properties of the non-XB structure titin. Consequently, our experimental findings suggest that the energy stored in titin during the eccentric phase contributes to the SSC-effect in a velocity-dependent manner.

The effects of an activation-dependent increase in titin stiffness on whole muscle properties using finite element modeling

Active state titin's effects have been studied predominantly in sarcomere or muscle fiber segment level and an understanding of its functional effects in the context of a whole muscle, and the mechanism of those is lacking. By representing experimentally observed calcium induced stiffening and actin-titin interaction induced reduced free spring length effects of active state titin in our linked fiber-matrix mesh finite element model, our aim was to study the mechanism of effects and particularly to determine the functionally more effective active state titin model. Isolated EDL muscle of the rat was modeled and three cases were studied: passive state titin (no change in titin constitutive equation in the active state), active state titin-I (constitutive equation involves a higher stiffness in the active state) and active state titin-II (constitutive equation also involves a strain shift coefficient accounting for titin's reduced free spring length). Isometric muscle lengthening was imposed (initial to long length, l_m = 28.7 mm to 32.7 mm). Compared to passive state titin, (i) active state titin-I and II elevates muscle total (l_m = 32.7 mm: 14% and 29%, respectively) and active (l_m = 32.7 mm: 37.5% and 77.4%, respectively) forces, (ii) active state titin-II also shifts muscle's optimum length to a longer length (l_m = 29.6 mm), (iii) active state titin-I and II limits sarcomere shortening (l_m = 32.7 mm: up to 10% and 20%, respectively). Such shorter sarcomere effect characterizes active state titin's mechanism of effects. These effects become more pronounced and functionally more effective if not only calcium induced stiffening but also a reduced free spring length of titin is accounted for.

Immunohistochemical evidence of striated muscle cells within midfacial superficial musculoaponeurotic system

INTRODUCTION

The superficial musculoaponeurotic system (SMAS) is a controversial functional fibro-adipose layer that connects the mimic muscles to the skin and is involved in a variety of facial mimic expressions. The presence of muscle fibers within SMAS fibrous septa is hypothetical. The present study analyzed SMAS fibrous septa composition for the existence of striated muscle cells.

METHODS

Histological serial sections of the sample borders (n=107) of 19 in sano-resected and diagnosed cutaneous tumors of the midfacial region were investigated. Immunohistochemical (actin and myosin) and hematoxylin and eosin staining were performed to detect striated muscle cells in SMAS fibrous septa.

RESULTS

A fibro-neuro-musculo-vascular functional unit within SMAS fibrous septa was demonstrated. SMAS striated muscle cells were morphologically independent from preparotideal and periorbital mimic muscles. Intraseptal blood vessels draining the superficial and deep SMAS vascular system were described.

CONCLUSIONS

Striated muscle cells were demonstrated within SMAS fibrous septa. Nerve cells and vascular tissue together with the SMAS fibro-muscular meshwork demonstrated an autonomous operating functional unit that hypothetical modulated individual mimic expression contributing to the diversity of mimic expression. The SMAS develops with mimic muscle contractions as a synergetic effect during facial crease and fold formation processes.

New Model for Stacking Monomers in Filamentous Actin from Skeletal Muscles of Oryctolagus cuniculus

To date, some scientific evidence (limited proteolysis, mass spectrometry analysis, electron microscopy (EM)) has accumulated, which indicates that the generally accepted model of double-stranded of filamentous actin (F-actin) organization in eukaryotic cells is not the only one. This entails an ambiguous understanding of many of the key cellular processes in which F-actin is involved. For a detailed understanding of the mechanism of F-actin assembly and actin interaction with its partners, it is necessary to take into account the polymorphism of the structural organization of F-actin at the molecular level. Using electron microscopy, limited proteolysis, mass spectrometry, X-ray diffraction, and structural modeling we demonstrated that F-actin presented in the EM images has no double-stranded organization, the regions of protease resistance are accessible for action of proteases in F-actin models. Based on all data, a new spatial model of filamentous actin is proposed, and the F-actin polymorphism is discussed.

Chronic Undernutrition Differentially Changes Muscle Fiber Types Organization and Distribution in the EDL Muscle Fascicles

Fiber type composition, organization, and distribution are key elements in muscle functioning. These properties can be modified by intrinsic and/or extrinsic factors, such as undernutrition and injuries. Currently, there is no methodology to quantitatively analyze such modifications. On one hand, we propose a fractal approach to determine fiber type organization, using the fractal correlation method in software Fractalyse. On the other hand, we applied the kernel methodology from machine learning to build radial-basis functions for the spatial distribution of fibers (distribution functions), by dividing into square cells a two-dimensional binary image for the spatial distribution of fibers from a muscle fascicle and mounting on each cell a radial-basis function in such a way that the sum of all cell functions creates a smooth version of the fiber histogram on the cell grid. The distribution functions thus created belong in a reproducing kernel Hilbert space which permits us to regard them as vectors and measure distances and angles between them. In the present study, we analyze fiber type organization and distribution in fascicles (F2, F3, F4, and F5) of the extensor digitorum longus muscle (EDLm) from control and undernourished male rats. Fibers were classified according to the ATPase activity in slow, intermediate, and fast. Then, (x, y) coordinates of fibers were used to build binary images and distribution functions for each fiber type and both conditions. The fractal organization analysis showed that fast and intermediate fibers, from both groups, had a fractal organization within the four fascicles, i.e., the fiber assembly is distributed in clusters. We also show that chronic undernutrition altered the organization of fast fibers in the F3, although it still is considered a fractal organization. Distribution function analysis showed that each fiber type (slow, intermediate, and fast) has a unique distribution within the fascicles, in both conditions. However, chronic undernutrition modified the intra-fascicular fiber type distributions, except in the F2. Altogether, these results showed that the methodology herein proposed allows for analyzing fiber type organization and distribution modifications. On the other side, we show that chronic undernutrition alters not only the fiber type composition but also the organization and distribution, which could affect the muscle functioning, and ultimately, its behavior (e.g., locomotion).

Evaluation of Non-Invasive Ankle Joint Effort Prediction Methods for Use in Neurorehabilitation Using Electromyography and Ultrasound Imaging

OBJECTIVE

Reliable measurement of voluntary human effort is essential for effective and safe interaction between the wearer and an assistive robot. Existing voluntary effort prediction methods that use surface electromyography (sEMG) are susceptible to prediction inaccuracies due to non-selectivity in measuring muscle responses. This technical challenge motivates an investigation into alternative non-invasive effort prediction methods that directly visualize the muscle response and improve effort prediction accuracy. The paper is a comparative study of ultrasound imaging (US)-derived neuromuscular signals and sEMG signals for their use in predicting isometric ankle dorsiflexion moment. Furthermore, the study evaluates the prediction accuracy of model-based and model-free voluntary effort prediction approaches that use these signals.

METHODS

The study evaluates sEMG signals and three US imaging-derived signals: pennation angle, muscle fascicle length, and echogenicity and three voluntary effort prediction methods: linear regression (LR), feedforward neural network (FFNN), and Hill-type neuromuscular model (HNM).

RESULTS

In all the prediction methods, pennation angle and fascicle length significantly improve the prediction accuracy of dorsiflexion moment, when compared to echogenicity. Also, compared to LR, both FFNN and HNM improve dorsiflexion moment prediction accuracy.

CONCLUSION

The findings indicate FFNN or HNM approach and using pennation angle or fascicle length predict human ankle movement intent with higher accuracy.

SIGNIFICANCE

The accurate ankle effort prediction will pave the path to safe and reliable robotic assistance in patients with drop foot.

Cross-Bridges and Sarcomeric Non-cross-bridge Structures Contribute to Increased Work in Stretch-Shortening Cycles

Stretch-shortening cycles (SSCs) refer to the muscle action when an active muscle stretch is immediately followed by active muscle shortening. This combination of eccentric and concentric contractions is the most important type of daily muscle action and plays a significant role in natural locomotion such as walking, running or jumping. SSCs are used in human and animal movements especially when a high movement speed or economy is required. A key feature of SSCs is the increase in muscular force and work during the concentric phase of a SSC by more than 50% compared with concentric muscle actions without prior stretch (SSC-effect). This improved muscle capability is related to various mechanisms, including pre-activation, stretch-reflex responses and elastic recoil from serial elastic tissues. Moreover, it is assumed that a significant contribution to enhanced muscle capability lies in the sarcomeres itself. Thus, we investigated the force output and work produced by single skinned fibers of rat soleus muscles during and after ramp contractions at a constant velocity. Shortening, lengthening, and SSCs were performed under physiological boundary conditions with 85% of the maximum shortening velocity and stretch-shortening magnitudes of 18% of the optimum muscle length. The different contributions of cross-bridge (XB) and non-cross-bridge (non-XB) structures to the total muscle force were identified by using Blebbistatin. The experiments revealed three main results: (i) partial detachment of XBs during the eccentric phase of a SSC, (ii) significantly enhanced forces and mechanical work during the concentric phase of SSCs compared with shortening contractions with and without XB-inhibition, and (iii) no residual force depression after SSCs. The results obtained by administering Blebbistatin propose a titin-actin interaction that depends on XB-binding or active XB-based force production. The findings of this study further suggest that enhanced forces generated during the active lengthening phase of SSCs persist during the subsequent shortening phase, thereby contributing to enhanced work. Accordingly, our data support the hypothesis that sarcomeric mechanisms related to residual force enhancement also contribute to the SSC-effect. The preload of the titin molecule, acting as molecular spring, might be part of that mechanism by increasing the mechanical efficiency of work during physiological SSCs.

N2A Titin: Signaling Hub and Mechanical Switch in Skeletal Muscle

Since its belated discovery, our understanding of the giant protein titin has grown exponentially from its humble beginning as a sarcomeric scaffold to recent recognition of its critical mechanical and signaling functions in active muscle. One uniquely useful model to unravel titin’s functions, muscular dystrophy with myositis (mdm), arose spontaneously in mice as a transposon-like LINE repeat insertion that results in a small deletion in the N2A region of titin. This small deletion profoundly affects hypertrophic signaling and muscle mechanics, thereby providing insights into the function of this specific region and the consequences of its dysfunction. The impact of this mutation is profound, affecting diverse aspects of the phenotype including muscle mechanics, developmental hypertrophy, and thermoregulation. In this review, we explore accumulating evidence that points to the N2A region of titin as a dynamic “switch” that is critical for both mechanical and signaling functions in skeletal muscle. Calcium-dependent binding of N2A titin to actin filaments triggers a cascade of changes in titin that affect mechanical properties such as elastic energy storage and return, as well as hypertrophic signaling. The mdm phenotype also points to the existence of as yet unidentified signaling pathways for muscle hypertrophy and thermoregulation, likely involving titin’s PEVK region as well as the N2A signalosome.

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

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

Titin: A Tunable Spring in Active Muscle

Muscle has conventionally been viewed as a motor that converts chemical to kinetic energy in series with a passive spring, but new insights emerge when muscle is viewed as a composite material whose elastic elements are tuned by activation. New evidence demonstrates that calcium-dependent binding of N2A titin to actin increases titin stiffness in active skeletal muscles, which explains many long-standing enigmas of muscle physiology.

Effects of a titin mutation on force enhancement and force depression in mouse soleus muscles

The active isometric force produced by muscles varies with muscle length in accordance with the force-length relationship. Compared with isometric contractions at the same final length, force increases after active lengthening (force enhancement) and decreases after active shortening (force depression). In addition to cross-bridges, titin has been suggested to contribute to force enhancement and depression. Although titin is too compliant in passive muscles to contribute to active tension at short sarcomere lengths on the ascending limb and plateau of the force-length relationship, recent evidence suggests that activation increases titin stiffness. To test the hypothesis that titin plays a role in force enhancement and depression, we investigated isovelocity stretching and shortening in active and passive wild-type and mdm (muscular dystrophy with myositis) soleus muscles. Skeletal muscles from mdm mice have a small deletion in the N2A region of titin and show no increase in titin stiffness during active stretch. We found that: (1) force enhancement and depression were reduced in mdm soleus compared with wild-type muscles relative to passive force after stretch or shortening to the same final length; (2) force enhancement and force depression increased with amplitude of stretch across all activation levels in wild-type muscles; and (3) maximum shortening velocity of wild-type and mdm muscles estimated from isovelocity experiments was similar, although active stress was reduced in mdm compared with wild-type muscles. The results of this study suggest a role for titin in force enhancement and depression, which contribute importantly to muscle force during natural movements.

Current Understanding of Residual Force Enhancement: Cross-Bridge Component and Non-Cross-Bridge Component

Muscle contraction is initiated by the interaction between actin and myosin filaments. The sliding of actin filaments relative to myosin filaments is produced by cross-bridge cycling, which is governed by the theoretical framework of the cross-bridge theory. The cross-bridge theory explains well a number of mechanical responses, such as isometric and concentric contractions. However, some experimental observations cannot be explained with the cross-bridge theory; for example, the increased isometric force after eccentric contractions. The steady-state, isometric force after an eccentric contraction is greater than that attained in a purely isometric contraction at the same muscle length and same activation level. This well-acknowledged and universally observed property is referred to as residual force enhancement (rFE). Since rFE cannot be explained by the cross-bridge theory, alternative mechanisms for explaining this force response have been proposed. In this review, we introduce the basic concepts of sarcomere length non-uniformity and titin elasticity, which are the primary candidates that have been used for explaining rFE, and discuss unresolved problems regarding these mechanisms, and how to proceed with future experiments in this exciting area of research.

Calcium-dependent titin-thin filament interactions in muscle: observations and theory

Gaps in our understanding of muscle mechanics demonstrate that the current model is incomplete. Increasingly, it appears that a role for titin in active muscle contraction might help to fill these gaps. While such a role for titin is increasingly accepted, the underlying molecular mechanisms remain unclear. The goals of this paper are to review recent studies demonstrating Ca²⁺-dependent interactions between N2A titin and actin in vitro, to explore theoretical predictions of muscle behavior based on this interaction, and to review experimental data related to the predictions. In a recent study, we demonstrated that Ca²⁺ increases the association constant between N2A titin and F-actin; that Ca²⁺ increases rupture forces between N2A titin and F-actin; and that Ca²⁺ and N2A titin reduce sliding velocity of F-actin and reconstituted thin filaments in motility assays. Preliminary data support a role for Ig83, but other Ig domains in the N2A region may also be involved. Two mechanical consequences are inescapable if N2A titin binds to thin filaments in active muscle sarcomeres: (1) the length of titin's freely extensible I-band should decrease upon muscle activation; and (2) binding between N2A titin and thin filaments should increase titin stiffness in active muscle. Experimental observations demonstrate that these properties characterize wild type muscles, but not muscles from mdm mice with a small deletion in N2A titin, including part of Ig83. Given the new in vitro evidence for Ca²⁺-dependent binding between N2A titin and actin, it is time for skepticism to give way to further investigation.

Passive force enhancement in striated muscle

Passive force enhancement is defined as the increase in passive, steady-state, isometric force of an actively stretched muscle compared with the same muscle stretched passively to that same length. Passive force enhancement is long lasting, increases with increasing muscle length and increasing stretch magnitudes, contributes to the residual force enhancement in skeletal and cardiac muscle, and is typically only observed at muscle lengths at which passive forces occur naturally. Passive force enhancement is typically equal to or smaller than the total residual force enhancement, it persists when a muscle is deactivated and reactivated, but can be abolished instantaneously when a muscle is shortened quickly from its stretched length. There is strong evidence that the passive force enhancement is caused by the filamentous sarcomeric protein titin, although the detailed molecular mechanisms underlying passive force enhancement remain unknown. Here I propose a tentative mechanism based on experimental evidence that associates passive force enhancement with the shortening of titin's free spring length in the I-band region of sarcomeres. I suggest that this shortening is accomplished by titin binding to actin and that the trigger for titin-actin interactions is associated with the formation of strongly bound cross bridges between actin and myosin that exposes actin attachment sites for titin through movement of the regulatory proteins troponin and tropomyosin.

Extensive eccentric contractions in intact cardiac trabeculae: revealing compelling differences in contractile behaviour compared to skeletal muscles

Force enhancement (FE) is a phenomenon that is present in skeletal muscle. It is characterized by progressive forces upon active stretching-distinguished by a linear rise in force-and enhanced isometric force following stretching (residual FE (RFE)). In skeletal muscle, non-cross-bridge (XB) structures may account for this behaviour. So far, it is unknown whether differences between non-XB structures within the heart and skeletal muscle result in deviating contractile behaviour during and after eccentric contractions. Thus, we investigated the force response of intact cardiac trabeculae during and after isokinetic eccentric muscle contractions (10% of maximum shortening velocity) with extensive magnitudes of stretch (25% of optimum muscle length). The different contributions of XB and non-XB structures to the total muscle force were revealed by using an actomyosin inhibitor. For cardiac trabeculae, we found that the force-length dynamics during long stretch were similar to the total isometric force-length relation. This indicates that no (R)FE is present in cardiac muscle while stretching the muscle from 0.75 to 1.0 optimum muscle length. This finding is in contrast with the results obtained for skeletal muscle, in which (R)FE is present. Our data support the hypothesis that titin stiffness does not increase with activation in cardiac muscle.

Evolution of the Highly Repetitive PEVK Region of Titin Across Mammals

The protein titin plays a key role in vertebrate muscle where it acts like a giant molecular spring. Despite its importance and conservation over vertebrate evolution, a lack of high quality annotations in non-model species makes comparative evolutionary studies of titin challenging. The PEVK region of titin—named for its high proportion of Pro-Glu-Val-Lys amino acids—is particularly difficult to annotate due to its abundance of alternatively spliced isoforms and short, highly repetitive exons. To understand PEVK evolution across mammals, we developed a bioinformatics tool, PEVK_Finder, to annotate PEVK exons from genomic sequences of titin and applied it to a diverse set of mammals. PEVK_Finder consistently outperforms standard annotation tools across a broad range of conditions and improves annotations of the PEVK region in non-model mammalian species. We find that the PEVK region can be divided into two subregions (PEVK-N, PEVK-C) with distinct patterns of evolutionary constraint and divergence. The bipartite nature of the PEVK region has implications for titin diversification. In the PEVK-N region, certain exons are conserved and may be essential, but natural selection also acts on particular codons. In the PEVK-C, exons are more homogenous and length variation of the PEVK region may provide the raw material for evolutionary adaptation in titin function. The PEVK-C region can be further divided into a highly repetitive region (PEVK-CA) and one that is more variable (PEVK-CB). Taken together, we find that the very complexity that makes titin a challenge for annotation tools may also promote evolutionary adaptation.

Muscle Function from Organisms to Molecules

Gaps in our understanding of muscle contraction at the molecular level limit the ability to predict in vivo muscle forces in humans and animals during natural movements. Because muscles function as motors, springs, brakes, or struts, it is not surprising that uncertainties remain as to how sarcomeres produce these different behaviors. Current theories fail to explain why a single extra stimulus, added shortly after the onset of a train of stimuli, doubles the rate of force development. When stretch and doublet stimulation are combined in a work loop, muscle force doubles and work increases by 50% per cycle, yet no theory explains why this occurs. Current theories also fail to predict persistent increases in force after stretch and decreases in force after shortening. Early studies suggested that all of the instantaneous elasticity of muscle resides in the cross-bridges. Subsequent cross-bridge models explained the increase in force during active stretch, but required ad hoc assumptions that are now thought to be unreasonable. Recent estimates suggest that cross-bridges account for only ∼12% of the energy stored by muscles during active stretch. The inability of cross-bridges to account for the increase in force that persists after active stretching led to development of the sarcomere inhomogeneity theory. Nearly all predictions of this theory fail, yet the theory persists. In stretch-shortening cycles, muscles with similar activation and contractile properties function as motors or brakes. A change in the phase of activation relative to the phase of length changes can convert a muscle from a motor into a spring or brake. Based on these considerations, it is apparent that the current paradigm of muscle mechanics is incomplete. Recent advances in our understanding of giant muscle proteins, including twitchin and titin, allow us to expand our vision beyond cross-bridges to understand how muscles contribute to the biomechanics and control of movement.

A Spatially Explicit Model Shows How Titin Stiffness Modulates Muscle Mechanics and Energetics

In striated muscle, the giant protein titin spans the entire length of a half-sarcomere and extends from the backbone of the thick filament, reversibly attaches to the thin filaments, and anchors to the dense protein network of the z-disk capping the end of the half-sarcomere. However, little is known about the relationship between the basic mechanical properties of titin and muscle contractility. Here, we build upon our previous multi-filament, spatially explicit computational model of the half-sarcomere by incorporating the nonlinear mechanics of titin filaments in the I-band. We vary parameters of the nonlinearity to understand the effects of titin stiffness on contraction dynamics and efficiency. We do so by simulating isometric contraction for a range of sarcomere lengths (SLs; 1.6-3.25 µm). Intermediate values of titin stiffness accurately reproduce the passive force-SL relation for skeletal muscle. The maximum force-SL relation is not affected by titin for SL≤2.5 µm. However, as titin stiffness increases, maximum force for the four thick filament system at SL = 3.0 µm significantly decreases from 103.2 ± 2 to 58.8 ± 1 pN. Additionally, by monitoring ATP consumption, we measure contraction efficiency as a function of titin stiffness. We find that at SL = 3.0 µm, efficiency significantly decreases from 13.9 ± 0.4 to 7.0 ± 0.3 pN/ATP when increasing titin stiffness, with little or no effect below 2.5 µm. Taken together, our results suggest that, despite an increase in the fraction of motors bound to actin along the descending limb when titin is stiffer, the force-generating capacity of the motors is reduced. These results suggest that titin stiffness has the potential to affect contractile efficiency.

Analysis of Titin in Red and White Muscles: Crucial Role on Muscle Contractions Using a Fish Model

Several studies have compared molecular components between red and white skeletal muscles in mammals. However, mammalian skeletal muscles are composed of mixed types of muscle fibers. In the current study, we analyzed and compared the distributions of titin, lipid, phosphate ions, and fatty acid levels in red and white muscles using a fish model (Tilapia), which is rich in red and white muscles, and these are well separated. Oil-red O staining showed that red muscle had more-abundant lipids than did white muscle. A time-of-flight secondary-ion mass spectrometric (TOF-SIMS) analysis revealed that red muscle possessed high levels of palmitic acid and oleic acid, but white muscle contained more phosphate ions. Moreover, elastica-van Gieson (EVG) and Mito-Tracker green FM staining showed that collagen and elastic fibers were highly, respectively, distributed in connective tissues and mitochondria in red muscle. An electron micrographic analysis indicated that red muscle had a relatively higher number of mitochondria and longer sarcomere lengths and Z-line widths, while myofibril diameters were thicker in white muscle. Myofibrillar proteins separated by SDS-PAGE showed that the major giant protein, titin, was highly expressed in white muscle than in red muscle. Furthermore, ratios of titin to myosin heavy chain (MHC) (titin/MHC) were about 1.3 times higher in white muscle than red muscle. We postulated that white muscle is fit for short and strong contractile performance due to high levels of titin and condensed sarcomeres, whereas red muscle is fit for low intensity and long-lasting activity due to high levels of lipids and mitochondria and long sarcomeres.

Calcium increases titin N2A binding to F-actin and regulated thin filaments

Mutations in titin are responsible for many cardiac and muscle diseases, yet the underlying mechanisms remain largely unexplained. Numerous studies have established roles for titin in muscle function, and Ca²⁺-dependent interactions between titin and actin have been suggested to play a role in muscle contraction. The present study used co-sedimentation assays, dynamic force spectroscopy (DFS), and in vitro motility (IVM) assays to determine whether the N2A region of titin, overlooked in previous studies, interacts with actin in the presence of Ca²⁺. Co-sedimentation demonstrated that N2A – F-actin binding increases with increasing protein and Ca²⁺ concentration, DFS demonstrated increased rupture forces and decreased k_off in the presence of Ca²⁺, and IVM demonstrated a Ca²⁺-dependent reduction in motility of F-actin and reconstituted thin filaments in the presence of N2A. These results indicate that Ca²⁺ increases the strength and stability of N2A – actin interactions, supporting the hypothesis that titin plays a regulatory role in muscle contraction. The results further support a model in which N2A – actin binding in active muscle increases titin stiffness, and that impairment of this mechanism contributes to the phenotype in muscular dystrophy with myositis. Future studies are required to determine whether titin – actin binding occurs in skeletal muscle sarcomeres in vivo.

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.

The multiple roles of titin in muscle contraction and force production

Titin is a filamentous protein spanning the half-sarcomere, with spring-like properties in the I-band region. Various structural, signaling, and mechanical functions have been associated with titin, but not all of these are fully elucidated and accepted in the scientific community. Here, I discuss the primary mechanical functions of titin, including its accepted role in passive force production, stabilization of half-sarcomeres and sarcomeres, and its controversial contribution to residual force enhancement, passive force enhancement, energetics, and work production in shortening muscle. Finally, I provide evidence that titin is a molecular spring whose stiffness changes with muscle activation and actin-myosin-based force production, suggesting a novel model of force production that, aside from actin and myosin, includes titin as a "third contractile" filament. Using this three-filament model of sarcomeres, the stability of (half-) sarcomeres, passive force enhancement, residual force enhancement, and the decrease in metabolic energy during and following eccentric contractions can be explained readily.

Neural and musculotendinous mechanisms underpinning age-related force reductions

Ageing leads to substantial force production capacity reductions, which is an indicator of frailty and disability, and a mortality predictor in elders. Understanding the age-dependent neuromuscular mechanisms underlying force reductions can optimize healthcare professionals' exercise protocol choices for patients and allows researchers to investigate new interventions to mitigate these reductions. Our primary goal was to provide an updated review about the main neural and musculotendinous mechanisms underpinning age-related reductions in force capacity. Our secondary goal was to summarize how aerobic and strength training can lessen these age-related reductions. This review suggests that several steps in the force production pathway, from cortical to muscular mechanisms, are negatively affected by ageing. However, combining aerobic and strength training can attenuate these effects. Strength training (i.e. moderate to high- intensity, progressive volume, accentuated eccentric loading and fast concentric contraction velocity) can increase overall force production capacity by producing beneficial neural and musculotendinous adaptations. Additionally, aerobic training (i.e. moderate and high intensities) plays an essential role in preserving the structure and function of the neuromuscular system.

Basic science and clinical use of eccentric contractions: History and uncertainties

The peculiar attributes of muscles that are stretched when active have been noted for nearly a century. Understandably, the focus of muscle physiology has been primarily on shortening and isometric contractions, as eloquently revealed by A.V. Hill and subsequently by his students. When the sliding filament theory was introduced by A.F. Huxley and H.E. Huxley, it was a relatively simple task to link Hill's mechanical observations to the actions of the cross bridges during these shortening and isometric contractions. In contrast, lengthening or eccentric contractions have remained somewhat enigmatic. Dismissed as necessarily causing muscle damage, eccentric contractions have been much more difficult to fit into the cross-bridge theory. The relatively recent discovery of the giant elastic sarcomeric filament titin has thrust a previously missing element into any discussion of muscle function, in particular during active stretch. Indeed, the unexpected contribution of giant elastic proteins to muscle contractile function is highlighted by recent discoveries that twitchin-actin interactions are responsible for the "catch" property of invertebrate muscle. In this review, we examine several current theories that have been proposed to account for the properties of muscle during eccentric contraction. We ask how well each of these explains existing data and how an elastic filament can be incorporated into the sliding filament model. Finally, we review the increasing body of evidence for the benefits of including eccentric contractions into a program of muscle rehabilitation and strengthening.