Dynamic behaviour of half-sarcomeres during and after stretch in activated rabbit psoas myofibrils: sarcomere asymmetry but no 'sarcomere popping'

Levosimendan's Effects on Length-Dependent Activation in Murine Fast-Twitch Skeletal Muscle

Levosimendan's calcium sensitizing effects in heart muscle cells are well established; yet, its potential impact on skeletal muscle cells has not been evidently determined. Despite controversial results, levosimendan is still expected to interact with skeletal muscle through off-target sites (further than troponin C). Adding to this debate, we investigated levosimendan's acute impact on fast-twitch skeletal muscle biomechanics in a length-dependent activation study by submersing single muscle fibres in a levosimendan-supplemented solution. We employed our MyoRobot technology to investigate the calcium sensitivity of skinned single muscle fibres alongside their stress-strain response in the presence or absence of levosimendan (100 µM). While control data are in agreement with the theory of length-dependent activation, levosimendan appears to shift the onset of the 'descending limb' of active force generation to longer sarcomere lengths without notably improving myofibrillar calcium sensitivity. Passive stretches in the presence of levosimendan yielded over twice the amount of enlarged restoration stress and Young's modulus in comparison to control single fibres. Both effects have not been described before and may point towards potential off-target sites of levosimendan.

Characterizing residual and passive force enhancements in cardiac myofibrils

Residual force enhancement (RFE), an increase in isometric force after active stretching of a muscle compared with the purely isometric force at the corresponding length, has been consistently observed throughout the structural hierarchy of skeletal muscle. Similar to RFE, passive force enhancement (PFE) is also observable in skeletal muscle and is defined as an increase in passive force when a muscle is deactivated after it has been actively stretched compared with the passive force following deactivation of a purely isometric contraction. These history-dependent properties have been investigated abundantly in skeletal muscle, but their presence in cardiac muscle remains unresolved and controversial. The purpose of this study was to investigate whether RFE and PFE exist in cardiac myofibrils and whether the magnitudes of RFE and PFE increase with increasing stretch magnitudes. Cardiac myofibrils were prepared from the left ventricles of New Zealand White rabbits, and the history-dependent properties were tested at three different final average sarcomere lengths (n = 8 for each), 1.8, 2, and 2.2 μm, while the stretch magnitude was kept at 0.2 μm/sarcomere. The same experiment was repeated with a final average sarcomere length of 2.2 μm and a stretching magnitude of 0.4 μm/sarcomere (n = 8). All 32 cardiac myofibrils exhibited increased forces after active stretching compared with the corresponding purely isometric reference conditions (p < 0.05). Furthermore, the magnitude of RFE was greater when myofibrils were stretched by 0.4 compared with 0.2 μm/sarcomere (p < 0.05). We conclude that, like in skeletal muscle, RFE and PFE are properties of cardiac myofibrils and are dependent on stretch magnitude.

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.

Effects of Hydrostatic-Pressure on Muscle Contraction: A Look Back on Some Experimental Findings

Findings from experiments that used hydrostatic pressure changes to analyse the process of skeletal muscle contraction are re-examined. The force in resting muscle is insensitive to an increase in hydrostatic pressure from 0.1 MPa (atmospheric) to 10 MPa, as also found for force in rubber-like elastic filaments. The force in rigour muscle rises with increased pressure, as shown experimentally for normal elastic fibres (e.g., glass, collagen, keratin, etc.). In submaximal active contractions, high pressure leads to tension potentiation. The force in maximally activated muscle decreases with increased pressure: the extent of this force decrease in maximal active muscle is sensitive to the concentration of products of ATP hydrolysis (Pi-inorganic phosphate and ADP-adenosine diphosphate) in the medium. When the increased hydrostatic pressure is rapidly decreased, the force recovered to the atmospheric level in all cases. Thus, the resting muscle force remained the same: the force in the rigour muscle decreased in one phase and that in active muscle increased in two phases. The rate of rise of active force on rapid pressure release increased with the concentration of Pi in the medium, indicating that it is coupled to the Pi release step in the ATPase-driven crossbridge cycle in muscle. Pressure experiments on intact muscle illustrate possible underlying mechanisms of tension potentiation and causes of muscle fatigue.

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.

Contractile State Dependent Sarcomere Length Variability in Isolated Guinea-Pig Cardiomyocytes

Cardiomyocytes contract keeping their sarcomere length (SL) close to optimal values for force generation. Transmural heterogeneity in SL across the ventricular wall coordinates the contractility of the whole-ventricle. SL heterogeneity (variability) exists not only at the tissue (macroscale) level, but also presents at the level of a single cardiomyocyte (microscale level). However, transmural differences in intracellular SL variability and its possible dependence on the state of contraction (e.g. end-diastole or end-systole) have not been previously reported. In the present study, we studied three aspects of sarcomere-to-sarcomere variability in intact cardiomyocytes isolated from the left ventricle of healthy guinea-pig: 1) transmural differences in SL distribution between subepi- (EPI) and subendocardial (ENDO) cardiomyocytes; 2) the dependence of intracellular variability in SL upon the state of contraction; 3) local differences in SL variability, comparing SL distributions between central and peripheral regions within the cardiomyocyte. To characterize the intracellular variability of SL, we used different normality tests for the assessment of SL distributions, as well as nonparametric coefficients to quantify the variability. We found that individual SL values in the end-systolic state of contraction followed a normal distribution to a lesser extent as compared to the end-diastolic state of contraction (∼1.3-fold and ∼1.6-fold in ENDO and EPI, respectively). The relative and absolute coefficients of sarcomere-to-sarcomere variability in end-systolic SL were significantly greater (∼1.3-fold) as compared to end-diastolic SL. This was independent of both the transmural region across the left ventricle and the intracellular region within the cardiomyocyte. We conclude that the intracellular variability in SL, which exists in normal intact guinea-pig cardiomyocytes, is affected by the contractile state of the myocyte. This phenomenon may play a role in inter-sarcomere communication in the beating heart.

Effect of Active Lengthening and Shortening on Small-Angle X-ray Reflections in Skinned Skeletal Muscle Fibres

Our purpose was to use small-angle X-ray diffraction to investigate the structural changes within sarcomeres at steady-state isometric contraction following active lengthening and shortening, compared to purely isometric contractions performed at the same final lengths. We examined force, stiffness, and the 1,0 and 1,1 equatorial and M3 and M6 meridional reflections in skinned rabbit psoas bundles, at steady-state isometric contraction following active lengthening to a sarcomere length of 3.0 µm (15.4% initial bundle length at 7.7% bundle length/s), and active shortening to a sarcomere length of 2.6 µm (15.4% bundle length at 7.7% bundle length/s), and during purely isometric reference contractions at the corresponding sarcomere lengths. Compared to the reference contraction, the isometric contraction after active lengthening was associated with an increase in force (i.e., residual force enhancement) and M3 spacing, no change in stiffness and the intensity ratio I_1,1/I_1,0, and decreased lattice spacing and M3 intensity. Compared to the reference contraction, the isometric contraction after active shortening resulted in decreased force, stiffness, I_1,1/I_1,0, M3 and M6 spacings, and M3 intensity. This suggests that residual force enhancement is achieved without an increase in the proportion of attached cross-bridges, and that force depression is accompanied by a decrease in the proportion of attached cross-bridges. Furthermore, the steady-state isometric contraction following active lengthening and shortening is accompanied by an increase in cross-bridge dispersion and/or a change in the cross-bridge conformation compared to the reference contractions.

Sarcomere length measurement reliability in single myofibrils

Sarcomere length non-uniformities occur at all structural levels of skeletal muscles and have been associated with important mechanical properties. Changes in sarcomere length non-uniformities in the nano- and sub-nanometer range have been used to explain muscle properties and contractile mechanisms. Typically, these measurements rely on light microscopy with a limited spatial resolution. One critical aspect in sarcomere length determination is the relatively arbitrary choice of intensity thresholds used to delineate sarcomere structures, such as A-bands or Z-lines. In experiments, these structures are typically distorted, intensity profiles vary, and baselines drift, resulting in asymmetric intensity patterns, causing changes in the centroid location of these structures depending on threshold choice, resulting in changes of sarcomere lengths. The purpose of this study was to determine the changes in (half-) sarcomere lengths associated with small changes in the A-band threshold choice. Sarcomere and half-sarcomere length changes for minute variations in A-band threshold were 28 nm (±28 nm) and 18 nm (±22 nm), respectively, and for the entire feasible range of thresholds across A-bands were 123 nm (±88 nm) and 99 nm (±105 nm), respectively. We conclude from these results that (half-) sarcomere lengths in the nanometer range obtained with light microcopy are noise, and the functional implications associated with such data should be discarded. We suggest that a functional resolution for sarcomere length of 100 nm (0.1 µm) is reasonable and 50 nm (0.05 µm) might be possible under ideal conditions.

Structure-Function Relationships in Muscle Fibres: MyoRobot online Assessment of Muscle Fibre Elasticity and Sarcomere Length Distributions

OBJECTIVE

Muscle biomechanics is set by the spacing of repetitive striation patterns of individual sarcomeres within single muscle fibres of stacked myofibrils. Sarcomere lengths (SL) are rather unequally distributed than of equal distance. This non-uniformity may affect both, force production as well as passive-elastic deformation. However, online recording of SL during axially imposed strains is cumbersome due to a lack of compact technologies.

METHODS

To fuse SL pattern recognition with restoration force assessments during quasi-static axial stretch, we implemented live tracking of SL distributions simultaneous to voice-coil actuated stretch and restoration force recordings in our MyoRobot 2.0 automated biomechatronics platform. Both were obtained online during stretchrelaxation cycles of murine single muscle fibres.

RESULTS

Under quasi-static stretch conditions (∼1 μm/s fibre length changes), almost no apparent hysteresis was detected in single fibres. SL showed a non-uniform distribution. While mean SL varied between 2.6 μm and 3.4 μm upon 140% stretch, two populations of fibres were noticed: one showing a minor change in SL distribution with stretch, and one becoming more equally distributed upon stretch.

CONCLUSION

A roughly 5% SL variability under rest either diminishes or remains almost unaltered upon elastic axial deformation. This may reflect differential impact of mostly extra-sarcomeric components to stretch in this stretch range.

SIGNIFICANCE

The augmented functionality of the MyoRobot 2.0 towards online sarcomere analyses within single fibres shall provide a valuable tool for the muscle community to study the contribution of serial elastic and force producing elements in health and disease models.

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.

Residual and passive force enhancement in skinned cardiac fibre bundles

In skeletal muscle, steady-state force is consistently greater following active stretch than during a purely isometric contraction at the same length (residual force enhancement; RFE). Similarly, when deactivated, the force remains higher following active stretch than following an isometric condition (passive force enhancement; PFE). RFE and PFE have been associated with the sarcomere protein titin, but skeletal and cardiac titin have different structures, and results regarding RFE in cardiac muscle have been inconsistent and contradictory. Therefore, the purpose of this study was to determine if cardiac muscle exhibits RFE and PFE. Skinned fibre bundles (n = 10) were activated isometrically at a sarcomere length of 2.2 μm and actively stretched by 15% of their length. The resultant active and passive forces were compared to the corresponding forces obtained for purely isometric contractions at the long length. RFE was observed in all fibre bundles, averaging 5.5 ± 2.5% (ranging from 2.3 to 9.4%). PFE was observed in nine of the ten bundles, averaging 11.1 ± 6.5% (ranging from -2.1 to 18.7%). Stiffness was not different between the active isometric and the force enhanced conditions, but was higher following deactivation from the force-enhanced compared to the isometric reference state. We conclude that there is RFE and PFE in cardiac muscle. We speculate that cardiac muscle has the same RFE capability as skeletal muscle, and that the most likely mechanism for the RFE and PFE is the engagement of a passive structural element during active stretching.

Force generated by myosin cross-bridges is reduced in myofibrils exposed to ROS/RNS

Skeletal muscle weakness is associated with oxidative stress and oxidative posttranslational modifications on contractile proteins. There is indirect evidence that reactive oxygen/nitrogen species (ROS/RNS) affect skeletal muscle myofibrillar function, although the details of the acute effects of ROS/RNS on myosin-actin interactions are not known. In this study, we examined the effects of peroxynitrite (ONOO−) on the contractile properties of individual skeletal muscle myofibrils by monitoring myofibril-induced displacements of an atomic force cantilever upon activation and relaxation. The isometric force decreased by ~50% in myofibrils treated with the ONOO− donor (SIN-1) or directly with ONOO−, which was independent of the cross-bridge abundancy condition (i.e., rigor or relaxing condition) during SIN-1 or ONOO− treatment. The force decrease was attributed to an increase in the cross-bridge detachment rate ( gapp) in combination with a conservation of the force redevelopment rate (kTr) and hence, an increase in the population of cross-bridges transitioning from force-generating to non-force-generating cross-bridges during steady-state. Taken together, the results of this study provide important information on how ROS/RNS affect myofibrillar force production which may be of importance for conditions where increased oxidative stress is part of the pathophysiology.

On sarcomere length stability during isometric and post-active-stretch isometric contractions

Sarcomere length (SL) instability and SL non-uniformity have been used to explain fundamental properties of skeletal muscles, such as creep, force depression following active muscle shortening, and residual force enhancement following active stretching of muscles. Regarding residual force enhancement, it has been argued that active muscle stretching causes SL instability, thereby increasing SL non-uniformity. However, we recently showed that SL non-uniformity is not increased by active muscle stretching, but it remains unclear if SL stability is affected by active stretching. Here, we used single myofibrils of rabbit psoas and measured SL non-uniformity and SL instability during isometric contractions and for isometric contractions following active stretching at average SLs corresponding to the descending limb of the force-length relationship. We defined isometric contractions as contractions during which mean SL remained constant. SL instability was quantified by the rate of change of individual SLs over the course of steady state, isometric force; and SL non-uniformity was defined as deviations of SLs from the mean SL at an instant of time. We found that while the mean SL remained constant during isometric contraction, by definition, individual SLs did not. SLs were more stable in the force-enhanced, isometric state following active stretching compared to the isometric reference state. We also found that SL instability was not correlated with the rate of change of SL non-uniformity. Also, SL non-uniformity was not different in the isometric and the post-stretch isometric contractions. We conclude that since SL is more stable but similarly non-uniform in the force-enhanced compared to the corresponding isometric reference contraction, it appears unlikely that either SL instability or SL non-uniformity contribute to the residual force enhancement property of skeletal muscle.

Single sarcomere contraction dynamics in a whole muscle

The instantaneous sarcomere length (SL) is regarded as an important indicator of the functional properties of striated muscle. Previously, we found greater sarcomere elongations at the distal end compared to the mid-portion in the mouse tibialis anterior (TA) when the muscle was stretched passively. Here, we wanted to see if SL dispersions increase with activation, as has been observed in single myofibrils, and if SL dispersions differ for different locations in a muscle. Sarcomere lengths were measured at a mid- and a distal location of the TA in live mice using second harmonic generation imaging. Muscle force was measured using a tendon force transducer. We found that SL dispersions increased substantially from the passive to the active state, and were the same for the mid- and distal portions of TA. Sarcomere length non-uniformities within a segment of ~30 serial sarcomeres were up to 1.0 µm. We conclude from these findings that passive, mean SLs obtained from a single location are not necessarily representative of the distribution of SL in active muscle, and thus may be misinterpreted when deriving muscle mechanical properties, such as the force-length relationship. In view of these findings, it seems crucial to determine how SL distributions within a muscle relate to the most fundamental properties of muscle, such as the maximal isometric force.

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.

Titin-mediated thick filament activation stabilizes myofibrils on the descending limb of their force-length relationship

PURPOSE

The aim of this study was to extend current half-sarcomere models by involving a recently found force-mediated activation of the thick filament and analyze the effect of this mechanosensing regulation on the length stability of half-sarcomeres arranged in series.

METHODS

We included a super-relaxed state of myosin motors and its force-dependent activation in a conventional cross-bridge model. We simulated active stretches of a sarcomere consisting of 2 non-uniform half-sarcomeres on the descending limb of the force-length relationship.

RESULTS

The mechanosensing model predicts that, in a passive sarcomere on the descending limb of the force-length relationship, the longer half-sarcomere has a higher fraction of myosin motors in the on-state than the shorter half-sarcomere. The difference in the number of myosin motors in the on-state ensures that upon calcium-mediated thin filament activation, the force-dependent thick filament activation keeps differences in active force within 20% during an active stretch. In the classical cross-bridge model, the corresponding difference exceeds 80%, leading to great length instabilities.

CONCLUSION

Our simulations suggest that, in contrast to the classical cross-bridge model, the mechanosensing regulation is able to stabilize a system of non-uniform half-sarcomeres arranged in series on the descending limb of the force-length relationship.

A continuum-mechanical skeletal muscle model including actin-titin interaction predicts stable contractions on the descending limb of the force-length relation

Contractions on the descending limb of the total (active + passive) muscle force-length relationship (i. e. when muscle stiffness is negative) are expected to lead to vast half-sarcomere-length inhomogeneities. This is however not observed in experiments-vast half-sarcomere-length inhomogeneities can be absent in myofibrils contracting in this range, and initial inhomogeneities can even decrease. Here we show that the absence of half-sarcomere-length inhomogeneities can be predicted when considering interactions of the semi-active protein titin with the actin filaments. Including a model of actin-titin interactions within a multi-scale continuum-mechanical model, we demonstrate that stability, accurate forces and nearly homogeneous half-sarcomere lengths can be obtained on the descending limb of the static total force-length relation. This could be a key to durable functioning of the muscle because large local stretches, that might harm, for example, the transverse-tubule system, are avoided.

Microfluidic perfusion shows intersarcomere dynamics within single skeletal muscle myofibrils

The sarcomere is the smallest functional unit of myofibrils in striated muscles. Sarcomeres are connected in series through a network of elastic and structural proteins. During myofibril activation, sarcomeres develop forces that are regulated through complex dynamics among their structures. The mechanisms that regulate intersarcomere dynamics are unclear, which limits our understanding of fundamental muscle features. Such dynamics are associated with the loss in forces caused by mechanical instability encountered in muscle diseases and cardiomyopathy and may underlie potential target treatments for such conditions. In this study, we developed a microfluidic perfusion system to control one sarcomere within a myofibril, while measuring the individual behavior of all sarcomeres. We found that the force from one sarcomere leads to adjustments of adjacent sarcomeres in a mechanism that is dependent on the sarcomere length and the myofibril stiffness. We concluded that the cooperative work of the contractile and the elastic elements within a myofibril rules the intersarcomere dynamics, with important consequences for muscle contraction.

Sarcomere mechanics in striated muscles: from molecules to sarcomeres to cells

Muscle contraction is commonly associated with the cross-bridge and sliding filament theories, which have received strong support from experiments conducted over the years in different laboratories. However, there are studies that cannot be readily explained by the theories, showing 1) a plateau of the force-length relation extended beyond optimal filament overlap, and forces produced at long sarcomere lengths that are higher than those predicted by the sliding filament theory; 2) passive forces at long sarcomere lengths that can be modulated by activation and Ca²⁺, which changes the force-length relation; and 3) an unexplained high force produced during and after stretch of activated muscle fibers. Some of these studies even propose "new theories of contraction." While some of these observations deserve evaluation, many of these studies present data that lack a rigorous control and experiments that cannot be repeated in other laboratories. This article reviews these issues, looking into studies that have used intact and permeabilized fibers, myofibrils, isolated sarcomeres, and half-sarcomeres. A common mechanism associated with sarcomere and half-sarcomere length nonuniformities and a Ca²⁺-induced increase in the stiffness of titin is proposed to explain observations that derive from these studies.

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.

The role of sarcomere length non-uniformities in residual force enhancement of skeletal muscle myofibrils

The sarcomere length non-uniformity theory (SLNT) is a widely accepted explanation for residual force enhancement (RFE). RFE is the increase in steady-state isometric force following active muscle stretching. The SLNT predicts that active stretching of a muscle causes sarcomere lengths (SL) to become non-uniform, with some sarcomeres stretched beyond actin-myosin filament overlap (popping), causing RFE. Despite being widely known, this theory has never been directly tested. We performed experiments on isolated rabbit muscle myofibrils (n = 12) comparing SL non-uniformities for purely isometric reference contractions (I-state) and contractions following active stretch producing RFE (FE-state). Myofibrils were activated isometrically along the descending limb of the force-length relationship (mean ± 1 standard deviation (SD) = 2.8 ± 0.3 µm sarcomere(-1)). Once the I-state was reached, myofibrils were shortened to an SL on the plateau of the force-length relationship (2.4 µm sarcomere(-1)), and then were actively stretched to the reference length (2.9 ± 0.3 µm sarcomere(-1)). We observed RFE in all myofibrils (39 ± 15%), and saw varying amounts of non-uniformity (1 SD = 0.9 ± 0.5 µm) that was not significantly correlated with the amount of RFE, but through pairwise comparisons was found to be significantly greater than the non-uniformity measured for the I-state (0.7 ± 0.4 µm). Three myofibrils exhibited no increase in non-uniformity. Active stretching was accompanied by sarcomere popping in four myofibrils, and seven had popped sarcomeres in the I-state. These results suggest that, while non-uniformities are present with RFE, they are also present in the I-state. Furthermore, non-uniformity is not associated with the magnitude of RFE, and myofibrils that had no increase in non-uniformity with stretch still showed normal RFE. Therefore, it appears that SL non-uniformity is a normal associate of muscle contraction, but does not contribute to RFE following active stretching of isolated skeletal muscle myofibrils.

MgADP activation contributes to force enhancement during fast stretch of isolated skeletal myofibrils

BACKGROUND

When an activated muscle is rapidly stretched, force rises and peaks while muscle lengthens. The peak force is normally called critical-force (Pc). The mechanism behind this increase in force is not well understood, but it has been associated with crossbridges operating in different states.

METHODS

Myofibrils were attached between a cantilever and a micro-needle, and activated with Ca(2+) or MgADP. During activation, the myofibrils were stretched by 3% SLo at 10 SLo·s(-1). A crossbridge model was developed to better understand the effects of MgADP in myofibrils activation.

RESULTS

Despite a similar stretch magnitude, MgADP activation produced a higher Pc (1.37 ± 0.07 P/Po) than Ca(2+) activation (Pc = 1.23 ± 0.03 P/Po). These results suggest that myofibrils activated with MgADP become stiffer than myofibrils activated with Ca(2+).

CONCLUSIONS

MgADP induces a fraction of crossbridges to form a "rigor-like" state that precedes ADP release, and that may not contribute to isometric forces. Such interpretation was strengthened by the results obtained with the developed crossbridge model, which showed that MgADP bias crossbridges into the rigor-like state. This state would be crucial to initiate a cooperative activation of crossbridges and actin, and to resist to unbinding from actin when the myofibrils are stretched.

SIGNIFICANCE

Our results suggest a new mechanism contributing for force output during stretch, which underlies basic mechanisms of muscle contraction.

Poorly understood aspects of striated muscle contraction

Muscle contraction results from cyclic interactions between the contractile proteins myosin and actin, driven by the turnover of adenosine triphosphate (ATP). Despite intense studies, several molecular events in the contraction process are poorly understood, including the relationship between force-generation and phosphate-release in the ATP-turnover. Different aspects of the force-generating transition are reflected in the changes in tension development by muscle cells, myofibrils and single molecules upon changes in temperature, altered phosphate concentration, or length perturbations. It has been notoriously difficult to explain all these events within a given theoretical framework and to unequivocally correlate observed events with the atomic structures of the myosin motor. Other incompletely understood issues include the role of the two heads of myosin II and structural changes in the actin filaments as well as the importance of the three-dimensional order. We here review these issues in relation to controversies regarding basic physiological properties of striated muscle. We also briefly consider actomyosin mutation effects in cardiac and skeletal muscle function and the possibility to treat these defects by drugs.

Contraction induced muscle injury: towards personalized training and recovery programs

Skeletal muscles can be injured by their own contractions. Such contraction-induced injury, often accompanied by delayed onset of muscle soreness, is a leading cause of the loss of mobility in the rapidly increasing population of elderly people. Unlike other types of muscle injuries which hurt almost exclusively those who are subjected to intensive exercise such as professional athletes and soldiers in training, contraction induced injury is a phenomenon which may be experienced by people of all ages while performing a variety of daily-life activities. Subjects that experience contraction induced injury report on soreness that usually increases in intensity in the first 24 h after the activity, peaks from 24 to 72 h, and then subsides and disappears in a few days. Despite their clinical importance and wide influence, there are almost no studies, clinical, experimental or computational, that quantitatively relate between the extent of contraction induced injury and activity factors, such as number of repetitions, their frequency and magnitude. The lack of such quantitative information is even more emphasized by the fact that contraction induced injury can be used, if moderate and controlled, to improve muscle performance in the long term. Thus, if properly understood and carefully implemented, contraction induced injury can be used for the purpose of personalized training and recovery programs. In this paper, we review experimental, clinical, and theoretical works, attempting towards drawing a more quantitative description of contraction induced injury and related phenomena.

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.

Mechanisms of enhanced force production in lengthening (eccentric) muscle contractions

In contrast to isometric and shortening contractions, many observations made on actively lengthening muscles cannot be readily explained with the sliding filament and cross-bridge theory. Specifically, residual force enhancement, the persistent increase in force following active muscle lengthening, beyond what one would expect based on muscle length, has not been explained satisfactorily. Here, we summarize the experimental evidence on residual force enhancement, critically evaluate proposed mechanisms for the residual force enhancement, and propose a mechanism for residual force enhancement that explains all currently agreed upon experimental observations. The proposed mechanism is based on the engagement of the structural protein titin upon muscle activation and an increase in titin's resistance to active compared with passive stretching. This change in resistance from the passive to the active state is suggested to be based on 1) calcium binding by titin upon activation, 2) binding of titin to actin upon activation, and 3) as a consequence of titin-actin binding—a shift toward stiffer titin segments that are used in active compared with passive muscle elongation. Although there is some experimental evidence for the proposed mechanism, it must be stressed that much of the details proposed here remain unclear and should provide ample research opportunities for scientists in the future. Nevertheless, the proposed mechanism for residual force enhancement explains all basic findings in this area of research.

Variation in isometric force after active shortening and lengthening and their mechanisms: a review

Introduction The isometric force history dependence of skeletal muscle has been studied along the last one hundred years. Several theories have been formulated to explain and establish the causes of the phenomenon, but not successfully, as they have not been fully accepted and demonstrated, and much controversy on such a subject still remains. Objective To present a systematic literature review on the dynamics of the mechanisms of force depression and force enhancement after active shortening and lengthening, respectively, identifying the key variables involved in the phenomenon, and to date to present the main theories and hypothesis developed trying to explaining it. Method The procedure of literature searching complied the major databases, including articles either, those which directly investigated the phenomena of force depression and force enhancement or those which presented possible causes and mechanisms associated with their respective events, from the earliest studies published until the year of 2010. Results 97 references were found according to the criteria used. Conclusion Based on this review, it is suggested that the theory of stress inhibition of actin-myosin cross-bridges is that better explain the phenomenon of force depression. Whereas regarding the force enhancement phenomenon, one theory have been well accepted, the increased number of actin-myosin cross-bridges in strong binding state influenced by the recruitment of passive elastic components, which hole is attributed to the titin filament.

Force produced after stretch in sarcomeres and half-sarcomeres isolated from skeletal muscles

The goal of this study was to evaluate if isolated sarcomeres and half-sarcomeres produce a long-lasting increase in force after a stretch is imposed during activation. Single and half-sarcomeres were isolated from myofibrils using micro-needles, which were also used for force measurements. After full force development, both preparations were stretched by different magnitudes. The sarcomere length (SL) or half-sarcomere length variations (HSL) were extracted by measuring the initial and final distances from the Z-line to the adjacent Z-line or to a region externally adjacent to the M-line of the sarcomere, respectively. Half-sarcomeres generated approximately the same amount of isometric force (29.0 ± SD 15.5 nN·μm⁻²) as single sarcomeres (32.1 ± SD 15.3 nN·μm⁻²) when activated. In both cases, the steady-state forces after stretch were higher than the forces during isometric contractions at similar conditions. The results suggest that stretch-induced force enhancement is partly caused by proteins within the half-sarcomere.

Phosphorylation of myosin regulatory light chain has minimal effect on kinetics and distribution of orientations of cross bridges of rabbit skeletal muscle

Force production in muscle results from ATP-driven cyclic interactions of myosin with actin. A myosin cross bridge consists of a globular head domain, containing actin and ATP-binding sites, and a neck domain with the associated light chain 1 (LC1) and the regulatory light chain (RLC). The actin polymer serves as a "rail" over which myosin translates. Phosphorylation of the RLC is thought to play a significant role in the regulation of muscle relaxation by increasing the degree of skeletal cross-bridge disorder and increasing muscle ATPase activity. The effect of phosphorylation on skeletal cross-bridge kinetics and the distribution of orientations during steady-state contraction of rabbit muscle is investigated here. Because the kinetics and orientation of an assembly of cross bridges (XBs) can only be studied when an individual XB makes a significant contribution to the overall signal, the number of observed XBs was minimized to ∼20 by limiting the detection volume and concentration of fluorescent XBs. The autofluorescence and photobleaching from an ex vivo sample was reduced by choosing a dye that was excited in the red and observed in the far red. The interference from scattering was eliminated by gating the signal. These techniques decrease large uncertainties associated with determination of the effect of phosphorylation on a few molecules ex vivo with millisecond time resolution. In spite of the remaining uncertainties, we conclude that the state of phosphorylation of RLC had no effect on the rate of dissociation of cross bridges from thin filaments, on the rate of myosin head binding to thin filaments, and on the rate of power stroke. On the other hand, phosphorylation slightly increased the degree of disorder of active cross bridges.

Sarcomere lengths in human extensor carpi radialis brevis measured by microendoscopy

INTRODUCTION

Second-harmonic generation microendoscopy is a minimally invasive technique to image sarcomeres and measure their lengths in humans, but motion artifact and low signal have limited the use of this novel technique.

METHODS

We discovered that an excitation wavelength of 960 nm maximized image signal; this enabled an image acquisition rate of 3 frames/s, which decreased motion artifact. We then used microendoscopy to measure sarcomere lengths in the human extensor carpi radialis brevis with the wrist at 45° extension and 45° flexion in 7 subjects. We also measured the variability in sarcomere lengths within single fibers.

RESULTS

Average sarcomere lengths in 45° extension were 2.93±0.29 μm (±SD) and increased to 3.58±0.19 μm in 45° flexion. Within single fibers the standard deviation of sarcomere lengths in series was 0.20 μm.

CONCLUSIONS

Microendoscopy can be used to measure sarcomere lengths at different body postures. Lengths of sarcomeres in series within a fiber vary substantially.

Force enhancement in lengthening contractions of cat soleus muscle in situ: transient and steady-state aspects

Force enhancement (FE) associated with lengthening is a well-accepted phenomenon of active skeletal muscle, but the underlying mechanism(s) remain unknown. Similar to force depression (FD) following active shortening, the mechanism of FE may be attributed, at least in part, to cross-bridge kinetics. To examine this relationship, a post hoc analysis was performed on the transient force relaxation phase of previous in-situ FE experiments in soleus muscle-tendon units of anesthetized cats. For each muscle (n = 8), nine eccentric lengthenings (3 amplitudes, 3 velocities) were performed while tetanically stimulated (3T at 30 Hz, 3× α motorneuron, 35 ± 1°C). To determine transient aspects of FE, the period immediately following stretching was fit with an exponential decay function (R (2) > 0.95). Statistical analyses revealed that total steady-state FE (FESS) increased with stretching amplitude and applied mechanical work. A positive relationship was observed between the active FESS and rate of force decay (k), indicating that a kinetic mechanism may explain active FE. However, for all muscles and stretch conditions, there was no correlation between the total amount of FESS and rate of decay. Therefore, FE cannot be explained solely by an active FE mechanism involving the interaction of actin and myosin. Rather, these findings suggest a combination of underlying mechanisms, including a kinetic mechanism for active FE, contributions of a passive elastic element, and possibly an activatable passive component operating outside of actin-myosin cross-bridging. Moreover, this transient analysis identifies that FE is not simply the opposite of FD, and its underlying mechanism(s) cannot simply be the opposite in nature.

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.

Increased residual force enhancement in older adults is associated with a maintenance of eccentric strength

Despite an age-related loss of voluntary isometric and concentric strength, muscle strength is well maintained during lengthening muscle actions (i.e., eccentric strength) in old age. Additionally, in younger adults during lengthening of an activated skeletal muscle, the force level observed following the stretch is greater than the isometric force at the same muscle length. This feature is termed residual force enhancement (RFE) and is believed to be a combination of active and passive components of the contractile apparatus. The purpose of this study was to provide an initial assessment of RFE in older adults and utilize aging as a muscle model to explore RFE in a system in which isometric force production is compromised, but structural mechanisms of eccentric strength are well-maintained. Therefore, we hypothesised that older adults will experience greater RFE compared with young adults. Following a reference maximal voluntary isometric contraction (MVC) of the dorsiflexors in 10 young (26.1±2.7y) and 10 old (76.0±6.5y) men, an active stretch was performed at 15°/s over a 30° ankle joint excursion ending at the same muscle length as the reference MVCs (40° of plantar flexion). Any additional torque compared with the reference MVC therefore represented RFE. In older men RFE was ∼2.5 times greater compared to young. The passive component of force enhancement contributed ∼37% and ∼20% to total force enhancement, in old and young respectively. The positive association (R² = 0.57) between maintained eccentric strength in old age and RFE indicates age-related mechanisms responsible for the maintenance of eccentric strength likely contributed to the observed elevated RFE. Additionally, as indicated by the greater passive force enhancement, these mechanisms may be related to increased muscle series elastic stiffness in old age.

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).

ATP binding and cross-bridge detachment steps during full Ca²⁺ activation: comparison of myofibril and muscle fibre mechanics by sinusoidal analysis

Single myofibrils 50–60 μm length and 2–3 μm diameter were isolated from rabbit psoas muscle fibres, and cross-bridge kinetics were studied by small perturbations of the length (∼0.2%) over a range of 15 frequencies (1–250 Hz). The experiments were performed at 15◦C in the presence of 0.05–10 mM MgATP, 8mM phosphate (Pi), 200 mM ionic strength with KAc (acetate), pCa 4.35–4.65, and pH 7.0. Two exponential processes, B and C, were resolved in tension transients. Their apparent rate constants (2πb and 2πc) increased as the [MgATP] was raised from 0.05 mM to 1mM, and then reached saturation at [MgATP] ≥ 1. Given that these rate constants were similar (c/b ∼1.7) at [Pi] ≥ 4 mM, they were combined to achieve an accurate estimate of the kinetic constants: their sum and product were analysed as functions of [MgATP]. These analyses yielded K1 =2.91 ± 0.31 mM −1, k2 =288 ± 36 s−1, and k−2 =10 ± 21 s−1 (±95% confidence limit, n =13 preparations), based on the cross-bridge model: AM+ATP ↔ (step 1) AM.ATP ↔ (step 2) A+M.ATP, where K1 is the ATP association constant (step 1), k2 is the rate constant of the cross-bridge detachment (step 2), and k−2 is the rate constant of its reversal step. These kinetic constants are respectively comparable to those observed in single fibres from rabbit psoas (K1 =2.35 ± 0.31 mM −1, k2 =243 ± 22 s−1, and k−2 =6 ± 14 s−1; n =8 preparations) when analysed by the same methods and under the same experimental conditions. These values are respectively not significantly different from those obtained in myofibrils, indicating that the same kinetic constants can be deduced from myofibril and muscle fibre studies, in terms of ATP binding and cross-bridge detachments steps. The fact that K1 in myofibrils is 1.2 times that in fibres (P≈0.05) may be explained by a small concentration gradient of ATP, ADP and/or Pi in single fibres.

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.

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.

Is titin a 'winding filament'? A new twist on muscle contraction

Recent studies have demonstrated a role for the elastic protein titin in active muscle, but the mechanisms by which titin plays this role remain to be elucidated. In active muscle, Ca(2+)-binding has been shown to increase titin stiffness, but the observed increase is too small to explain the increased stiffness of parallel elastic elements upon muscle activation. We propose a 'winding filament' mechanism for titin's role in active muscle. First, we hypothesize that Ca(2+)-dependent binding of titin's N2A region to thin filaments increases titin stiffness by preventing low-force straightening of proximal immunoglobulin domains that occurs during passive stretch. This mechanism explains the difference in length dependence of force between skeletal myofibrils and cardiac myocytes. Second, we hypothesize that cross-bridges serve not only as motors that pull thin filaments towards the M-line, but also as rotors that wind titin on the thin filaments, storing elastic potential energy in PEVK during force development and active stretch. Energy stored during force development can be recovered during active shortening. The winding filament hypothesis accounts for force enhancement during stretch and force depression during shortening, and provides testable predictions that will encourage new directions for research on mechanisms of muscle contraction.