A non-cross-bridge stiffness in activated frog muscle fibers

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.

Titin activates myosin filaments in skeletal muscle by switching from an extensible spring to a mechanical rectifier

Titin is a molecular spring in parallel with myosin motors in each muscle half-sarcomere, responsible for passive force development at sarcomere length (SL) above the physiological range (>2.7 μm). The role of titin at physiological SL is unclear and is investigated here in single intact muscle cells of the frog (Rana esculenta), by combining half-sarcomere mechanics and synchrotron X-ray diffraction in the presence of 20 μM para-nitro-blebbistatin, which abolishes the activity of myosin motors and maintains them in the resting state even during activation of the cell by electrical stimulation. We show that, during cell activation at physiological SL, titin in the I-band switches from an SL-dependent extensible spring (OFF-state) to an SL-independent rectifier (ON-state) that allows free shortening while resisting stretch with an effective stiffness of ~3 pN nm^-1 per half-thick filament. In this way, I-band titin efficiently transmits any load increase to the myosin filament in the A-band. Small-angle X-ray diffraction signals reveal that, with I-band titin ON, the periodic interactions of A-band titin with myosin motors alter their resting disposition in a load-dependent manner, biasing the azimuthal orientation of the motors toward actin. This work sets the stage for future investigations on scaffold and mechanosensing-based signaling functions of titin in health and disease.

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.

Muscle as a tunable material: implications for achieving muscle-like function in robotic prosthetic devices

An ideal prosthesis should perform as well as or better than the missing limb it was designed to replace. Although this ideal is currently unattainable, recent advances in design have significantly improved the function of prosthetic devices. For the lower extremity, both passive prostheses (which provide no added power) and active prostheses (which add propulsive power) aim to emulate the dynamic function of the ankle joint, whose adaptive, time-varying resistance to applied forces is essential for walking and running. Passive prostheses fail to normalize energetics because they lack variable ankle impedance that is actively controlled within each gait cycle. By contrast, robotic prostheses can normalize energetics for some users under some conditions. However, the problem of adaptive and versatile control remains a significant issue. Current prosthesis-control algorithms fail to adapt to changes in gait required for walking on level ground at different speeds or on ramps and stairs. A new paradigm of 'muscle as a tunable material' versus 'muscle as a motor' offers insights into the adaptability and versatility of biological muscles, which may provide inspiration for prosthesis design and control. In this new paradigm, neural activation tunes muscle stiffness and damping, adapting the response to applied forces rather than instructing the timing and amplitude of muscle force. A mechanistic understanding of muscle function is incomplete and would benefit from collaboration between biologists and engineers. An improved understanding of the adaptability of muscle may yield better models as well as inspiration for developing prostheses that equal or surpass the functional capabilities of biological limbs across a wide range of conditions.

Non-cross Bridge Viscoelastic Elements Contribute to Muscle Force and Work During Stretch-Shortening Cycles: Evidence From Whole Muscles and Permeabilized Fibers

The sliding filament-swinging cross bridge theory of skeletal muscle contraction provides a reasonable description of muscle properties during isometric contractions at or near maximum isometric force. However, it fails to predict muscle force during dynamic length changes, implying that the model is not complete. Mounting evidence suggests that, along with cross bridges, a Ca²⁺-sensitive viscoelastic element, likely the titin protein, contributes to muscle force and work. The purpose of this study was to develop a multi-level approach deploying stretch-shortening cycles (SSCs) to test the hypothesis that, along with cross bridges, Ca²⁺-sensitive viscoelastic elements in sarcomeres contribute to force and work. Using whole soleus muscles from wild type and mdm mice, which carry a small deletion in the N2A region of titin, we measured the activation- and phase-dependence of enhanced force and work during SSCs with and without doublet stimuli. In wild type muscles, a doublet stimulus led to an increase in peak force and work per cycle, with the largest effects occurring for stimulation during the lengthening phase of SSCs. In contrast, mdm muscles showed neither doublet potentiation features, nor phase-dependence of activation. To further distinguish the contributions of cross bridge and non-cross bridge elements, we performed SSCs on permeabilized psoas fiber bundles activated to different levels using either [Ca²⁺] or [Ca²⁺] plus the myosin inhibitor 2,3-butanedione monoxime (BDM). Across activation levels ranging from 15 to 100% of maximum isometric force, peak force, and work per cycle were enhanced for fibers in [Ca²⁺] plus BDM compared to [Ca²⁺] alone at a corresponding activation level, suggesting a contribution from Ca²⁺-sensitive, non-cross bridge, viscoelastic elements. Taken together, our results suggest that a tunable viscoelastic element such as titin contributes to: (1) persistence of force at low [Ca²⁺] in doublet potentiation; (2) phase- and length-dependence of doublet potentiation observed in wild type muscles and the absence of these effects in mdm muscles; and (3) increased peak force and work per cycle in SSCs. We conclude that non-cross bridge viscoelastic elements, likely titin, contribute substantially to muscle force and work, as well as the phase-dependence of these quantities, during dynamic length changes.

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.

Force enhancement after stretch of isolated myofibrils is increased by sarcomere length non-uniformities

When a muscle is stretched during a contraction, the resulting steady-state force is higher than the isometric force produced at a comparable sarcomere length. This phenomenon, also referred to as residual force enhancement, cannot be readily explained by the force-sarcomere length relation. One of the most accepted mechanisms for the residual force enhancement is the development of sarcomere length non-uniformities after an active stretch. The aim of this study was to directly investigate the effect of non-uniformities on the force-producing capabilities of isolated myofibrils after they are actively stretched. We evaluated the effect of depleting a single A-band on sarcomere length non-uniformity and residual force enhancement. We observed that sarcomere length non-uniformity was effectively increased following A-band depletion. Furthermore, isometric forces decreased, while the percent residual force enhancement increased compared to intact myofibrils (5% vs. 20%). We conclude that sarcomere length non-uniformities are partially responsible for the enhanced force production after stretch.

Differences in stretch-shortening cycle and residual force enhancement between muscles

It has been suggested that cross bridge kinetics and residual force enhancement (RFE) affect force in the stretch-shortening cycle (SSC). Because cross bridge kinetics and titin isoforms, which are thought to be related to RFE, differ between muscles, the SSC effect may be also muscle-dependent. Thus, we compared the SSC effect between psoas and soleus muscles, which have a distinct fiber type distribution and different titin isoforms. Four tests (SSC, SSC control, RFE, RFE control) were conducted using isolated, skinned fibers of psoas and soleus. In the SSC tests, fibers were activated at an average sarcomere length of 2.4 μm, stretched to 3.0 μm, and shortened to 2.4 μm. In the SSC control tests, fibers were activated at an average sarcomere length of 3.0 μm and then shortened to 2.4 μm. The relative increase in mechanical work obtained during shortening between tests was defined as the SSC effect. In the RFE tests, fibers were activated at an average sarcomere length of 2.4 μm and then stretched to 3.0 μm, while the RFE control tests consisted of an isometric contraction at 3.0 μm. The difference in steady-state isometric force between tests was defined as RFE. The SSC effect was greater in soleus than in psoas, while the RFE was the same for both muscles. Since the SSC effect was greater in soleus, while the RFE was the same, the observed greater SSC effect is probably not directly caused by RFE, but may be related to differences in cross bridge kinetics.

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.

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.

Contracting striated muscle has a dynamic I-band spring with an undamped stiffness 100 times larger than the passive stiffness

KEY POINTS

Fast sarcomere-level mechanics in contracting intact fibres from frog skeletal muscle reveal an I-band spring with an undamped stiffness 100 times larger than the known static stiffness. This undamped stiffness remains constant in the range of sarcomere length 2.7-3.1 µm, showing the ability of the I-band spring to adapt its length to the width of the I-band. The stiffness and tunability of the I-band spring implicate titin as a force contributor that, during contraction, allows weaker half-sarcomeres to equilibrate with in-series stronger half-sarcomeres, preventing the development of sarcomere length inhomogeneity. This work opens new possibilities for the detailed in situ description of the structural-functional basis of muscle dysfunctions related to mutations or site-directed mutagenesis in titin that alter the I-band stiffness.

ABSTRACT

Force and shortening in the muscle sarcomere are due to myosin motors from thick filaments pulling nearby actin filaments toward the sarcomere centre. Thousands of serially linked sarcomeres in muscle make the shortening (and the shortening speed) macroscopic, while the intrinsic instability of in-series force generators is likely prevented by the cytoskeletal protein titin that connects the thick filament with the sarcomere end, working as an I-band spring that accounts for the rise of passive force with sarcomere length (SL). However, current estimates of titin stiffness, deduced from the passive force-SL relation and single molecule mechanics, are much smaller than what is required to avoid the development of large inhomogeneities among sarcomeres. In this work, using 4 kHz stiffness measurements on a population of sarcomeres selected along an intact fibre isolated from frog skeletal muscle contracting at different SLs (temperature 4°C), we measure the undamped stiffness of an I-band spring that at SL > 2.7 µm attains a maximum constant value of ∼6 pN nm-1 per half-thick filament, two orders of magnitude larger than expected from titin-related passive force. We conclude that a titin-like dynamic spring in the I-band, made by an undamped elastic element in-series with damped elastic elements, adapts its length to the SL with kinetics that provide force balancing among serially linked sarcomeres during contraction. In this way, the I-band spring plays a fundamental role in preventing the development of SL inhomogeneity.

A reduction in compliance or activation level reduces residual force depression in human tibialis anterior

AIM

We investigated if residual force depression (rFD) is present during voluntary fixed-end contractions of human tibialis anterior (TA) and whether reducing TA's activation level after active shortening could reduce rFD.

METHODS

Ten participants performed fixed-end dorsiflexion contractions to a low, moderate or high level while electromyography (EMG), dorsiflexion force and TA ultrasound images were recorded. Contractions were force- or EMG-matched and after the low or high contraction level was attained, participants respectively increased or decreased their force/EMG to a moderate level. Participants also performed moderate level contractions while the TA muscle-tendon unit (MTU) was lengthened during the force/EMG rise to the reference MTU length.

RESULTS

Equivalent fascicle shortening over moderate and low to moderate level contractions did not alter EMG (P = 0.45) or dorsiflexion force (P = 0.47) at the moderate level. Greater initial fascicle shortening magnitudes (1.7 mm; P ≤ 0.01) to the high contraction level did not alter EMG (P = 0.45) or dorsiflexion force (P = 0.30) at the subsequent moderate level compared with moderate level contractions. TA MTU lengthening during the initial force/EMG rise reduced TA fascicle shortening (-2.5 mm; P ≤ 0.01), which reduced EMG (-3.9% MVC; P < 0.01) and increased dorsiflexion force (3.7% MVC; P < 0.01) at the moderate level compared with fixed-end moderate level contractions.

CONCLUSION

rFD is present during fixed-end dorsiflexion contractions because fascicles actively shorten as force/EMG increases and rFD can be reduced by reducing the effective MTU compliance. A reduction in muscle activation level also reduces rFD by potentially triggering residual force enhancement-related mechanisms as force drops and some fascicles actively lengthen.

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.

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.

Mechanical parameters of the molecular motor myosin II determined in permeabilised fibres from slow and fast skeletal muscles of the rabbit

KEY POINTS

The different performance of slow and fast muscles is mainly attributed to diversity of the myosin heavy chain (MHC) isoform expressed within them. In this study fast sarcomere-level mechanics has been applied to Ca²⁺ -activated single permeabilised fibres isolated from soleus (containing the slow myosin isoform) and psoas (containing the fast myosin isoform) muscles of rabbit for a comparative definition of the mechano-kinetics of force generation by slow and fast myosin isoforms in situ. The stiffness and the force of the slow myosin isoform are three times smaller than those of the fast isoform, suggesting that the stiffness of the myosin motor is a determinant of the isoform-dependent functional diversity between skeletal muscles. These results open the question of the mechanism that can reconcile the reduced performance of the slow MHC with the higher efficiency of the slow muscle.

ABSTRACT

The skeletal muscle exhibits large functional differences depending on the myosin heavy chain (MHC) isoform expressed in its molecular motor, myosin II. The differences in the mechanical features of force generation by myosin isoforms were investigated in situ by using fast sarcomere-level mechanical methods in permeabilised fibres (sarcomere length 2.4 μm, temperature 12°C, 4% dextran T-500) from slow (soleus, containing the MHC-1 isoform) and fast (psoas, containing the MHC-2X isoform) skeletal muscle of the rabbit. The stiffness of the half-sarcomere was determined at the plateau of Ca²⁺ -activated isometric contractions and in rigor and analysed with a model that accounted for the filament compliance to estimate the stiffness of the myosin motor (ε). ε was 0.56 ± 0.04 and 1.70 ± 0.37 pN nm^-1 for the slow and fast isoform, respectively, while the average strain per attached motor (s₀ ) was similar (∼3.3 nm) in both isoforms. Consequently the force per motor (F₀  = εs₀ ) was three times smaller in the slow isoform than in the fast isoform (1.89 ± 0.43 versus 5.35 ± 1.51 pN). The fraction of actin-attached motors responsible for maximum isometric force at saturating Ca²⁺ (T_0,4.5 ) was 0.47 ± 0.09 in soleus fibres, 70% larger than that in psoas fibres (0.29 ± 0.08), so that F₀ in slow fibres was decreased by only 53%. The lower stiffness and force of the slow myosin isoform open the question of the molecular basis of the higher efficiency of slow muscle with respect to fast muscle.

Residual Force Enhancement Following Eccentric Contractions: A New Mechanism Involving Titin

Eccentric muscle properties are not well characterized by the current paradigm of the molecular mechanism of contraction: the cross-bridge theory. Findings of force contributions by passive structural elements a decade ago paved the way for a new theory. Here, we present experimental evidence and theoretical support for the idea that the structural protein titin contributes to active force production, thereby explaining many of the unresolved properties of eccentric muscle contraction.

Residual force enhancement is regulated by titin in skeletal and cardiac myofibrils

KEY POINTS

When a skeletal muscle is stretched while it contracts, the muscle produces a relatively higher force than the force from an isometric contraction at the same length: a phenomenon referred to as residual force enhancement. Residual force enhancement is puzzling because it cannot be directly explained by the classical force-length relationship and the sliding filament theory of contraction, the main paradigms in the muscle field. We used custom-built instruments to measure residual force enhancement in skeletal myofibrils, and, for the first time, in cardiac myofibrils. Our data report that residual force enhancement is present in skeletal muscles, but not cardiac muscles, and is regulated by the different isoforms of the titin protein filaments.

ABSTRACT

When a skeletal muscle contracts isometrically, the muscle produces a force that is relative to the final isometric sarcomere length (SL). However, when the same final SL is reached by stretching the muscle while it contracts, the muscle produces a relatively higher force: a phenomenon commonly referred to as residual force enhancement. In this study, we investigated residual force enhancement in rabbit skeletal psoas myofibrils and, for the first time, cardiac papillary myofibrils. A custom-built atomic force microscope was used in experiments that stretched myofibrils before and after inhibiting myosin and actin interactions to determine whether the different cardiac and skeletal titin isoforms regulate residual force enhancement. At SLs ranging from 2.24 to 3.13 μm, the skeletal myofibrils enhanced the force by an average of 9.0%, and by 29.5% after hindering myosin and actin interactions. At SLs ranging from 1.80 to 2.29 μm, the cardiac myofibrils did not enhance the force before or after hindering myosin and actin interactions. We conclude that residual force enhancement is present only in skeletal muscles and is dependent on the titin isoforms.

Physiological Mechanisms of Eccentric Contraction and Its Applications: A Role for the Giant Titin Protein

When active muscles are stretched, our understanding of muscle function is stretched as well. Our understanding of the molecular mechanisms of concentric contraction has advanced considerably since the advent of the sliding filament theory, whereas mechanisms for increased force production during eccentric contraction are only now becoming clearer. Eccentric contractions play an important role in everyday human movements, including mobility, stability, and muscle strength. Shortly after the sliding filament theory of muscle contraction was introduced, there was a reluctant recognition that muscle behaved as if it contained an "elastic" filament. Jean Hanson and Hugh Huxley referred to this structure as the "S-filament," though their concept gained little traction. This additional filament, the giant titin protein, was identified several decades later, and its roles in muscle contraction are still being discovered. Recent research has demonstrated that, like activation of thin filaments by calcium, titin is also activated in muscle sarcomeres by mechanisms only now being elucidated. The mdm mutation in mice appears to prevent activation of titin, and is a promising model system for investigating mechanisms of titin activation. Titin stiffness appears to increase with muscle force production, providing a mechanism that explains two fundamental properties of eccentric contractions: their high force and low energetic cost. The high force and low energy cost of eccentric contractions makes them particularly well suited for athletic training and rehabilitation. Eccentric exercise is commonly prescribed for treatment of a variety of conditions including sarcopenia, osteoporosis, and tendinosis. Use of eccentric exercise in rehabilitation and athletic training has exploded to include treatment for the elderly, as well as muscle and bone density maintenance for astronauts during long-term space travel. For exercise intolerance and many types of sports injuries, experimental evidence suggests that interventions involving eccentric exercise are demonstrably superior to conventional concentric interventions. Future work promises to advance our understanding of the molecular mechanisms that confer high force and low energy cost to eccentric contraction, as well as signaling mechanisms responsible for the beneficial effects of eccentric exercise in athletic training and rehabilitation.

Eccentric contraction: unraveling mechanisms of force enhancement and energy conservation

During the past century, physiologists have made steady progress in elucidating the molecular mechanisms of muscle contraction. However, this progress has so far failed to definitively explain the high force and low energy cost of eccentric muscle contraction. Hypotheses that have been proposed to explain increased muscle force during active stretch include cross-bridge mechanisms, sarcomere and half-sarcomere length non-uniformity, and engagement of a structural element upon muscle activation. The available evidence suggests that force enhancement results from an interaction between an elastic element in muscle sarcomeres, which is engaged upon activation, and the cross-bridges, which interact with the elastic elements to regulate their length and stiffness. Similarities between titin-based residual force enhancement in vertebrate muscle and twitchin-based 'catch' in invertebrate muscle suggest evolutionary homology. The winding filament hypothesis suggests plausible molecular mechanisms for effects of both Ca(2+) influx and cross-bridge cycling on titin in active muscle. This hypothesis proposes that the N2A region of titin binds to actin upon Ca(2+) influx, and that the PEVK region of titin winds on the thin filaments during force development because the cross-bridges not only translate but also rotate the thin filaments. Simulations demonstrate that a muscle model based on the winding filament hypothesis can predict residual force enhancement on the descending limb of the length-tension curve in muscles during eccentric contraction. A kinematic model of titin winding based on sarcomere geometry makes testable predictions about titin isoforms in different muscles. Ongoing research is aimed at testing these predictions and elucidating the biochemistry of the underlying protein interactions.

Non-crossbridge stiffness in active muscle fibres

Stretching of an activated skeletal muscle induces a transient tension increase followed by a period during which the tension remains elevated well above the isometric level at an almost constant value. This excess of tension in response to stretching has been called 'static tension' and attributed to an increase in fibre stiffness above the resting value, named 'static stiffness'. This observation was originally made, by our group, in frog intact muscle fibres and has been confirmed more recently, by us, in mammalian intact fibres. Following stimulation, fibre stiffness starts to increase during the latent period well before crossbridge force generation and it is present throughout the whole contraction in both single twitches and tetani. Static stiffness is dependent on sarcomere length in a different way from crossbridge force and is independent of stretching amplitude and velocity. Static stiffness follows a time course which is distinct from that of active force and very similar to the myoplasmic calcium concentration time course. We therefore hypothesize that static stiffness is due to a calcium-dependent stiffening of a non-crossbridge sarcomere structure, such as the titin filament. According to this hypothesis, titin, in addition to its well-recognized role in determining the muscle passive tension, could have a role during muscle activity.

Skeletal muscle tissue in movement and health: positives and negatives

The history of muscle physiology is a wonderful lesson in ‘the scientific method’; our functional hypotheses have been limited by our ability to decipher (observe) muscle structure. The simplistic understanding of how muscles work made a large leap with the remarkable insights of A. V. Hill, who related muscle force and power to shortening velocity and energy use. However, Hill's perspective was largely limited to isometric and isotonic contractions founded on isolated muscle properties that do not always reflect how muscles function in vivo. Robert Josephson incorporated lengthening contractions into a work loop analysis that shifted the focus to dynamic muscle function, varying force, length and work done both by and on muscle during a single muscle work cycle. It became apparent that muscle is both a force generator and a spring. Titin, the missing filament in the sliding filament model, is a muscle spring, which functions very differently in cardiac versus skeletal muscle; its possible role in these two muscle types is discussed relative to their contrasting function. The good news for those of us who choose to work on skeletal muscle is that muscle has been reluctant to reveal all of its secrets.

Effects of activation on the elastic properties of intact soleus muscles with a deletion in titin

Titin has long been known to contribute to muscle passive tension. Recently, it was also demonstrated that titin-based stiffness increases upon Ca2+-activation of wildtype mouse psoas myofibrils stretched beyond overlap of the thick and thin filaments. In addition, this increase in titin-based stiffness upon activation was impaired in single psoas myofibrils from mdm mice with a deletion in titin. Here, we investigate the effects of muscle activation on elastic properties of intact soleus muscles from wildtype and mdm mice to determine whether titin may contribute to active muscle stiffness. Using load-clamp experiments, we compared the stress-strain relationships of elastic elements in active and passive muscles during unloading, and quantified the change in stiffness upon activation. We used the mdm mutation, characterized by a deletion in the N2A region of the Ttn gene, to test the hypothesis that titin contributes to active muscle stiffness. Results show that the elastic modulus of wildtype muscles increases upon activation. Elastic elements began to develop force at lengths that were 15% shorter in active than in passive soleus, and there was a 2.9-fold increase in the slope of the stress - strain relationship. In contrast, mdm soleus showed no effect of activation on the slope or intercept of the stress - strain relationship. These results from intact soleus muscles are qualitatively and quantitatively similar to results from single wildtype psoas myofibrils stretched beyond overlap of the thick and thin filaments. Therefore, it is likely that titin plays a role in the increase of stiffness during rapid unloading that we observed in intact soleus muscles upon activation. The results from intact mdm soleus muscles are also consistent with impaired titin activation observed in single mdm psoas myofibrils stretched beyond filament overlap, further suggesting that the mechanism of titin activation is impaired in skeletal muscles from mdm mice. These results are consistent with the idea that, in addition to the thin filaments, titin is activated upon Ca2+-influx in skeletal muscle.

The increase in non-cross-bridge forces after stretch of activated striated muscle is related to titin isoforms

Skeletal muscles present a non-cross-bridge increase in sarcomere stiffness and tension on Ca(2+) activation, referred to as static stiffness and static tension, respectively. It has been hypothesized that this increase in tension is caused by Ca(2+)-dependent changes in the properties of titin molecules. To verify this hypothesis, we investigated the static tension in muscles containing different titin isoforms. Permeabilized myofibrils were isolated from the psoas, soleus, and heart ventricle from the rabbit, and tested in pCa 9.0 and pCa 4.5, before and after extraction of troponin C, thin filaments, and treatment with the actomyosin inhibitor blebbistatin. The myofibrils were tested with stretches of different amplitudes in sarcomere lengths varying between 1.93 and 3.37 μm for the psoas, 2.68 and 4.21 μm for the soleus, and 1.51 and 2.86 μm for the ventricle. Using gel electrophoresis, we confirmed that the three muscles tested have different titin isoforms. The static tension was present in psoas and soleus myofibrils, but not in ventricle myofibrils, and higher in psoas myofibrils than in soleus myofibrils. These results suggest that the increase in the static tension is directly associated with Ca(2+)-dependent change in titin properties and not associated with changes in titin-actin interactions.

From Tusko to Titin: the role for comparative physiology in an era of molecular discovery

As we approach the centenary of the term "comparative physiology," we reexamine its role in modern biology. Finding inspiration in Krogh's classic 1929 paper, we first look back to some timeless contributions to the field. The obvious and fascinating variation among animals is much more evident than is their shared physiological unity, which transcends both body size and specific adaptations. The "unity in diversity" reveals general patterns and principles of physiology that are invisible when examining only one species. Next, we examine selected contemporary contributions to comparative physiology, which provides the context in which reductionist experiments are best interpreted. We discuss the sometimes surprising insights provided by two comparative "athletes" (pronghorn and rattlesnakes), which demonstrate 1) animals are not isolated molecular mechanisms but highly integrated physiological machines, a single "rate-limiting" step may be exceptional; and 2) extremes in nature are rarely the result of novel mechanisms, but rather employ existing solutions in novel ways. Furthermore, rattlesnake tailshaker muscle effectively abolished the conventional view of incompatibility of simultaneous sustained anaerobic glycolysis and oxidative ATP production. We end this review by looking forward, much as Krogh did, to suggest that a comparative approach may best lend insights in unraveling how skeletal muscle stores and recovers mechanical energy when operating cyclically. We discuss and speculate on the role of the largest known protein, titin (the third muscle filament), as a dynamic spring capable of storing and recovering elastic recoil potential energy in skeletal muscle.

Non-crossbridge forces in activated striated muscles: a titin dependent mechanism of regulation?

When skeletal muscles are stretched during activation in the absence of myosin-actin interactions, the force increases significantly. The force remains elevated throughout the activation period. The mechanism behind this non-crossbridge force, referred to as static tension, is unknown and generates debate in the literature. It has been suggested that the static tension is caused by Ca(2+)-induced changes in the properties of titin molecules that happens during activation and stretch, but a comprehensive evaluation of such possibility is still lacking. This paper reviews the general characteristics of the static tension, and evaluates the proposed mechanism by which titin may change the force upon stretch. Evidence is presented suggesting that an increase in intracellular Ca(2+) concentration leads to Ca(2+) binding to the PEVK region of titin. Such binding increases titin stiffness, which increases the overall sarcomere stiffness and causes the static tension. If this form of Ca(2+)-induced increase in titin stiffness is confirmed in future studies, it may have large implications for understating of the basic mechanisms of muscle contraction.

Force enhancement after stretch in mammalian muscle fiber: no evidence of cross-bridge involvement

Stretching of activated skeletal muscles induces a force increase above the isometric level persisting after stretch, known as residual force enhancement (RFE). RFE has been extensively studied; nevertheless, its mechanism remains debated. Unlike previous RFE studies, here the excess of force after stretch, termed static tension (ST), was investigated with fast stretches (amplitude: 3-4% sarcomere length; duration: 0.6 ms) applied at low tension during the tetanus rise in fiber bundles from flexor digitorum brevis (FDB) mouse muscle at 30°C. ST was measured at sarcomere length between 2.6 and 4.4 μm in normal and N-benzyl-p-toluene sulphonamide (BTS)-added (10 μM) Tyrode solution. The results showed that ST has the same characteristics and it is equivalent to RFE. ST increased with sarcomere length, reached a peak at 3.5 μm, and decreased to zero at ∼4.5 μm. At 4 μm, where active force was zero, ST was still 50% of maximum. BTS reduced force by ∼75% but had almost no effect on ST. Following stimulation, ST developed earlier than force, with a time course similar to internal Ca(2+) concentration: it was present 1 ms after the stimulus, at zero active force, and peaked at ∼3-ms delay. At 2.7 μm, activation increased the passive sarcomere stiffness by a factor of ∼7 compared with the relaxed state All our data indicate that ST, or RFE, is independent of the cross-bridge presence and it is due to the Ca(2+)-induced stiffening of a sarcomeric structure identifiable with titin.

Phosphate and acidosis act synergistically to depress peak power in rat muscle fibers

Skeletal muscle fatigue is characterized by the buildup of H(+) and inorganic phosphate (Pi), metabolites that are thought to cause fatigue by inhibiting muscle force, velocity, and power. While the individual effects of elevated H(+) or Pi have been well characterized, the effects of simultaneously elevating the ions, as occurs during fatigue in vivo, are still poorly understood. To address this, we exposed slow and fast rat skinned muscle fibers to fatiguing levels of H(+) (pH 6.2) and Pi (30 mM) and determined the effects on contractile properties. At 30°C, elevated Pi and low pH depressed maximal shortening velocity (Vmax) by 15% (4.23 to 3.58 fl/s) in slow and 31% (6.24 vs. 4.55 fl/s) in fast fibers, values similar to depressions from low pH alone. Maximal isometric force dropped by 36% in slow (148 to 94 kN/m(2)) and 46% in fast fibers (148 to 80 kN/m(2)), declines substantially larger than what either ion exerted individually. The strong effect on force combined with the significant effect on velocity caused peak power to decline by over 60% in both fiber types. Force-stiffness ratios significantly decreased with pH 6.2 + 30 mM Pi in both fiber types, suggesting these ions reduced force by decreasing the force per bridge and/or increasing the number of low-force bridges. The data indicate the collective effects of elevating H(+) and Pi on maximal isometric force and peak power are stronger than what either ion exerts individually and suggest the ions act synergistically to reduce muscle function during fatigue.

A model for creating a single stretch injury in murine biarticular muscle

Background

We developed a single stretch injury model to create damage near the musculotendinous junction (MTJ) of the gastrocnemius muscle in mice. Our hypothesis was that magnitude of muscle injury could be controlled by stepped shortening of the Achilles tendon (AT) prior to a lengthening contraction. Increased shortening would result in a greater isometric torque deficit and morphological damage 24 hours post-injury.

Methods

Sixteen mice were randomly assigned to sham or injury predicated on stepped increases in AT shortening. The AT was exposed and placed in a customized stainless steel roller-clamp system to achieve a specific level of shortening; 0 mm (resting length), 0.7 mm or 1.4 mm. Plantar flexors were stimulated to tetany with a needle electrode and then actively lengthened at 450°/sec from neutral to 75° of dorsiflexion. Passive and isometric torques were measured pre- and immediately post-injury. Isometric torque was measured again 24 h post-injury. Peak isokinetic torque was recorded during eccentric injury.

Results

Injury resulted in decreased passive and immediate absolute isometric torque only when induced with AT shortening. The percentage of pre-injury isometric torque was significantly lower in the AT shortened groups immediately and 24 h post-injury, but was unaffected by the level of shortening. Relative isometric torque deficits were noted in the 0 mm group only 24 h post-injury. Peak isokinetic torque during injury was similar in all groups. Histological evaluation 24 h post-injury revealed increased morphological damage near the MTJ in the AT shortened groups.

Conclusion

Single stretch with AT shortening created morphological damage near the MTJ and isometric torque deficits immediately and 24 h post-injury, but the magnitude of damage could not be titrated with stepped increases in AT shortening. This model provides an opportunity to utilize transgenic mice in order to elucidate inflammatory mediators that promote regeneration and inhibit fibrosis in order to optimize therapeutic interventions for complete functional recovery.

The non-linear elasticity of the muscle sarcomere and the compliance of myosin motors

Force in striated muscle is due to attachment of the heads of the myosin, the molecular motors extending from the myosin filament, to the actin filament in each half-sarcomere, the functional unit where myosin motors act in parallel. Mechanical and X-ray structural evidence indicates that at the plateau of isometric contraction (force T0), less than half of the elastic strain of the half-sarcomere is due to the strain in the array of myosin motors (s), with the remainder being accounted for by the compliance of filaments acting as linear elastic elements in series with the motor array. Early during the development of isometric force, however, the half-sarcomere compliance has been found to be less than that expected from the linear elastic model assumed above, and this non-linearity may affect the estimate of s. This question is investigated here by applying nanometre-microsecond-resolution mechanics to single intact fibres from frog skeletal muscle at 4 °C, to record the mechanical properties of the half-sarcomere throughout the development of force in isometric contraction. The results are interpreted with mechanical models to estimate the compliance of the myosin motors. Our conclusions are as follows: (i) early during the development of an isometric tetanus, an elastic element is present in parallel with the myosin motors, with a compliance of ∼200 nm MPa(-1) (∼20 times larger than the compliance of the motor array at T0); and (ii) during isometric contraction, s is 1.66 ± 0.05 nm, which is not significantly different from the value estimated with the linear elastic model.

Muscle residual force enhancement: a brief review

Muscle residual force enhancement has been observed in different muscle preparations for more than half a century. Nonetheless, its mechanism remains unclear; to date, there are three generally accepted hypotheses: 1) sarcomere length non-uniformity, 2) engagement of passive elements, and 3) an increased number of cross-bridges. The first hypothesis uses sarcomere non-homogeneity and instability to explain how "weak" sarcomeres would convey the higher tension generated by an enhanced overlap from "stronger" sarcomeres, allowing the whole system to produce higher forces than predicted by the force-length relationship; non-uniformity provides theoretical support for a large amount of the experimental data. The second hypothesis suggests that passive elements within the sarcomeres (i.e., titin) could gain strain upon calcium activation followed by stretch. Finally, the third hypothesis suggests that muscle stretch after activation would alter cross-bridge kinetics to increase the number of attached cross-bridges. Presently, we cannot completely rule out any of the three hypotheses. Different experimental results suggest that the mechanisms on which these three hypotheses are based could all coexist.

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

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

The mechanisms of the residual force enhancement after stretch of skeletal muscle: non-uniformity in half-sarcomeres and stiffness of titin

When activated skeletal muscles are stretched, the force increases significantly. After the stretch, the force decreases and reaches a steady-state level that is higher than the force produced at the corresponding length during purely isometric contractions. This phenomenon, referred to as residual force enhancement, has been observed for more than 50 years, but the mechanism remains elusive, generating considerable debate in the literature. This paper reviews studies performed with single muscle fibres, myofibrils and sarcomeres to investigate the mechanisms of the stretch-induced force enhancement. First, the paper summarizes the characteristics of force enhancement and early hypotheses associated with non-uniformity of sarcomere length. Then, it reviews new evidence suggesting that force enhancement can also be associated with sarcomeric structures. Finally, this paper proposes that force enhancement is caused by: (i) half-sarcomere non-uniformities that will affect the levels of passive forces and overlap between myosin and actin filaments, and (ii) a Ca(2+)-induced stiffness of titin molecules. These mechanisms are compatible with most observations in the literature, and can be tested directly with emerging technologies in the near future.

Residual force enhancement after stretch in striated muscle. A consequence of increased myofilament overlap?

When skeletal muscle is stretched above optimal sarcomere length during tetanic activity there is an increase in force that stays above the isometric force level throughout the activity period. This long-lasting increase in contractile force, generally referred to as 'residual force enhancement after stretch' (FE(resid)), has been studied in great detail in various muscle preparations over more than half a century. Substantial evidence has been presented to show that non-uniform sarcomere behaviour plays a major part in the development of FE(resid). However, in a great number of recent studies the role of sarcomere non-uniformity has been challenged and alternative mechanisms have instead been proposed to explain the increase in force such as enhancement of cross-bridge function and/or strengthening of parallel elastic elements along the muscle fibres. This article presents a short review of the salient features of FE(resid) and provides evidence that non-uniform sarcomere behaviour is indeed likely to play a major role in the development of FE(resid). Electron microscopical studies of fibres rapidly fixed after active stretch demonstrate that, dispersed in the preparation, there are assymetrical length changes within the two halves of myofibrillar sarcomeres resulting in greater filament overlap in one half of the sarcomere than in the opposite sarcomere half. Sarcomere halves with increased filament overlap will consequently be in a situation where they are able to produce a greater force than that recorded in the isometric control. Weaker regions in series will be able to keep the enhanced force by recruitment of elastic elements.

A non-cross-bridge, static tension is present in permeabilized skeletal muscle fibers after active force inhibition or actin extraction

When activated muscle fibers are stretched, there is a long-lasting increase in the force. This phenomenon, referred to as "residual force enhancement," has characteristics similar to those of the "static tension," a long-lasting increase in force observed when muscles are stretched in the presence of Ca(2+) but in the absence of myosin-actin interaction. Independent studies have suggested that these two phenomena have a common mechanism and are caused either by 1) a Ca(2+)-induced stiffening of titin or by 2) promoting titin binding to actin. In this study, we performed two sets of experiments in which activated fibers (pCa(2+) 4.5) treated with the myosin inhibitor blebbistatin were stretched from 2.7 to 2.8 μm at a speed of 40 L(o)/s, first, after partial extraction of TnC, which inhibits myosin-actin interactions, or, second, after treatment with gelsolin, which leads to the depletion of thin (actin) filaments. We observed that the static tension, directly related with the residual force enhancement, was not changed after treatments that inhibit myosin-actin interactions or that deplete fibers from troponin C and actin filaments. The results suggest that the residual force enhancement is caused by a stiffening of titin upon muscle activation but not with titin binding to actin. This finding indicates the existence of a Ca(2+)-regulated, titin-based stiffness in skeletal muscles.

Mechanisms Of Residual Force Enhancement In Skeletal Muscle: Insights From Experiments And Mathematical Models

A skeletal muscle that is stretched while contracting will produce more force at steady state than if it is stretched passively and then stimulated to contract. This phenomenon is known as residual force enhancement and has been widely studied since its description more than sixty years ago. The idea that the mechanical properties of a muscle are governed not just by its present length but also by its length at earlier time points has far reaching implications since muscles stretch and shorten routinely in normal use. In this review, we present the experimental and theoretical advances that have been made toward understanding the mechanisms that underlie residual force enhancement. In the past ten years, experiments and models have focused on essentially three candidate mechanisms for residual force enhancement: (half-) sarcomere inhomogeneity, activity of so-called 'passive' mechanical elements in the sarcomere (titin), and the intrinsic properties of myosin crossbridges. Evidence, both computational and experimental, is accumulating for each of these mechanisms such that a final description of the phenomenon seems attainable in the near future. We conclude that computational models that incorporate more than one putative mechanism may ultimately facilitate reconciliation of the growing number of ideas and experimental data in this field.

Force produced by isolated sarcomeres and half-sarcomeres after an imposed stretch

When a stretch is imposed to activated muscles, there is a residual force enhancement that persists after the stretch; the force is higher than that produced during an isometric contraction in the corresponding length. The mechanisms behind the force enhancement remain elusive, and there is disagreement if it represents a sarcomeric property, or if it is associated with length nonuniformities among sarcomeres and half-sarcomeres. The purpose of this study was to investigate the effects of stretch on single sarcomeres and myofibrils with predetermined numbers of sarcomeres (n = 2, 3. . . , 8) isolated from the rabbit psoas muscle. Sarcomeres were attached between two precalibrated microneedles for force measurements, and images of the preparations were projected onto a linear photodiode array for measurements of half-sarcomere length (SL). Fully activated sarcomeres were subjected to a stretch (5-10% of initial SL, at a speed of 0.3 μm·s(-1)·SL(-1)) after which they were maintained isometric for at least 5 s before deactivation. Single sarcomeres showed two patterns: 31 sarcomeres showed a small level of force enhancement after stretch (10.46 ± 0.78%), and 28 sarcomeres did not show force enhancement (-0.54 ± 0.17%). In these preparations, there was not a strong correlation between the force enhancement and half-sarcomere length nonuniformities. When three or more sarcomeres arranged in series were stretched, force enhancement was always observed, and it increased linearly with the degree of half-sarcomere length nonuniformities. The results show that the residual force enhancement has two mechanisms: 1) stretch-induced changes in sarcomeric structure(s); we suggest that titin is responsible for this component, and 2) stretch-induced nonuniformities of half-sarcomere lengths, which significantly increases the level of force enhancement.

A mathematical model of muscle containing heterogeneous half-sarcomeres exhibits residual force enhancement

A skeletal muscle fiber that is stimulated to contract and then stretched from L₁ to L₂ produces more force after the initial transient decays than if it is stimulated at L₂. This behavior has been well studied experimentally, and is known as residual force enhancement. The underlying mechanism remains controversial. We hypothesized that residual force enhancement could reflect mechanical interactions between heterogeneous half-sarcomeres. To test this hypothesis, we subjected a computational model of interacting heterogeneous half-sarcomeres to the same activation and stretch protocols that produce residual force enhancement in real preparations. Following a transient period of elevated force associated with active stretching, the model predicted a slowly decaying force enhancement lasting >30 seconds after stretch. Enhancement was on the order of 13% above isometric tension at the post-stretch muscle length, which agrees well with experimental measurements. Force enhancement in the model was proportional to stretch magnitude but did not depend strongly on the velocity of stretch, also in agreement with experiments. Even small variability in the strength of half-sarcomeres (2.1% standard deviation, normally distributed) was sufficient to produce a 5% force enhancement over isometric tension. Analysis of the model suggests that heterogeneity in half-sarcomeres leads to residual force enhancement by storing strain energy introduced during active stretch in distributions of bound cross-bridges. Complex interactions between the heterogeneous half-sarcomeres then dissipate this stored energy at a rate much slower than isolated cross-bridges would cycle. Given the variations in half-sarcomere length that have been observed in real muscle preparations and the stochastic variability inherent in all biological systems, half-sarcomere heterogeneity cannot be excluded as a contributing source of residual force enhancement.

Textbooks often state that the force produced by a contracting muscle depends on its length. Nearly 60 years ago, it was discovered that this length-tension relationship is violated if the muscle is stretched to a given length while contracting, in which case the muscle produces more force than if it was stretched to the given length prior to contraction. This effect is known as residual force enhancement, and its mechanism remains controversial. Understanding residual force enhancement is important because it potentially affects outcomes of many in vivo and in vitro experiments where contracting muscles or muscle preparations are stretched. In this work, we use a computational model of half-sarcomeres connected in series to show that residual force enhancement is an emergent behavior of the contractile system when the half-sarcomeres are not completely identical. Force enhancement in the model shares several key properties with the phenomenon observed in real muscle, including independence from the rate of stretch and proportionality to stretch magnitude. Enhancement in the model is produced by a previously undescribed mechanism in which complex interactions between the heterogeneous half-sarcomeres dissipate strain-energy from the imposed stretch at very slow rates, creating a long-lasting, enhanced level of force.

Impact of myocyte strain on cardiac myofilament activation

When cardiac myocytes are stretched by a longitudinal strain, they develop proportionally more active force at a given sub-maximal Ca(2+) concentration than they did at the shorter length. This is known as length-dependent activation. It is one of the most important contributors to the Frank-Starling relationship, a critical part of normal cardiovascular function. Despite intense research efforts, the mechanistic basis of the Frank-Starling relationship remains unclear. Potential mechanisms involving myofibrillar lattice spacing, titin-based effects, and cooperative activation have all been proposed. This review summarizes some of these mechanisms and discusses two additional potential theories that reflect the effects of localized strains that occur within and between half-sarcomeres. The main conclusion is that the Frank-Starling relationship is probably the integrated result of many interacting molecular mechanisms. Multiscale computational modeling may therefore provide the best way of determining the key processes that underlie length-dependent activation and their relative strengths.

Thick-filament strain and interfilament spacing in passive muscle: effect of titin-based passive tension

We studied the effect of titin-based passive tension on sarcomere structure by simultaneously measuring passive tension and low-angle x-ray diffraction patterns on passive fiber bundles from rabbit skinned psoas muscle. We used a stretch-hold-release protocol with measurement of x-ray diffraction patterns at various passive tension levels during the hold phase before and after passive stress relaxation. Measurements were performed in relaxing solution without and with dextran T-500 to compress the lattice toward physiological levels. The myofilament lattice spacing was measured in the A-band (d(1,0)) and Z-disk (d(Z)) regions of the sarcomere. The axial spacing of the thick-filament backbone was determined from the sixth myosin meridional reflection (M6) and the equilibrium positions of myosin heads from the fourth myosin layer line peak position and the I(1,1)/I(1,0) intensity ratio. Total passive tension was measured during the x-ray experiments, and a differential extraction technique was used to determine the relations between collagen- and titin-based passive tension and sarcomere length. Within the employed range of sarcomere lengths (∼2.2-3.4 μm), titin accounted for >80% of passive tension. X-ray results indicate that titin compresses both the A-band and Z-disk lattice spacing with viscoelastic behavior when fibers are swollen after skinning, and elastic behavior when the lattice is reduced with dextran. Titin also increases the axial thick-filament spacing, M6, in an elastic manner in both the presence and absence of dextran. No changes were detected in either I(1,1)/I(1,0) or the position of peaks on the fourth myosin layer line during passive stress relaxation. Passive tension and M6 measurements were converted to thick-filament compliance, yielding a value of ∼85 m/N, which is several-fold larger than the thick-filament compliance determined by others during the tetanic tension plateau of activated intact muscle. This difference can be explained by the fact that thick filaments are more compliant at low tension (passive muscle) than at high tension (tetanic tension). The implications of our findings are discussed.

Fiber-type dependence of stretch-induced force enhancement in rat skeletal muscle

When an active muscle is stretched, the force increases due to strain of contractile and noncontractile proteins. We examined this force enhancement in rat extensor digitorum longus (EDL) and soleus muscles, which differ in their composition of these proteins, and their susceptibility to damage. Small stretches were applied at different velocities during isometric contractions from which we quantified the velocity-dependent contractile and velocity-independent noncontractile contributions to force enhancement. Whereas the contractile contribution was significantly greater in soleus than EDL, the noncontractile force enhancement was significantly greater in EDL than soleus, and increased ≈6-fold after damaging eccentric contractions. The increased contractile stiffness may be functionally beneficial in slow muscle, as resistance to lengthening is fundamental to maintaining posture. Following stretch-induced muscle damage this capacity is compromised, leading to increased strain of noncontractile proteins that may facilitate the activation of signaling pathways involved in muscle adaptation to injury.