The force-length relationship of mechanically isolated sarcomeres

Gaining new understanding of sarcomere length non-uniformities in skeletal muscles

Sarcomere lengths are non-uniform on all structural levels of mammalian skeletal muscle. These non-uniformities have been associated with a variety of mechanical properties, including residual force enhancement and depression, creep, increased force capacity, and extension of the plateau of the force-length relationship. However, the nature of sarcomere length non-uniformities has not been explored systematically. The purpose of this study was to determine the properties of sarcomere length non-uniformities in active and passive muscle. Single myofibrils of rabbit psoas (n = 20; with 412 individual sarcomeres) were subjected to three activation/deactivation cycles and individual sarcomere lengths were measured at 4 passive and 3 active points during the activation/deactivation cycles. The myofibrils were divided into three groups based on their initial average sarcomere lengths: short, intermediate, and long average sarcomere lengths of 2.7, 3.2, and 3.6 µm. The primary results were that sarcomere length non-uniformities did not occur randomly but were governed by some structural and/or contractile properties of the sarcomeres and that sarcomere length non-uniformities increased when myofibrils went from the passive to the active state. We propose that the mechanisms that govern the systematic sarcomere lengths non-uniformities observed in active and passive myofibrils may be associated with the variable number of contractile proteins and the variable number and the adjustable stiffness of titin filaments in individual sarcomeres.

In vivo imaging of skeletal muscle form and function: 50 years of insight

Skeletal muscle form and function has fascinated scientists for centuries. Our understanding of muscle function has long been driven by advancements in imaging techniques. For example, the sliding filament theory of muscle, which is now widely leveraged in biomechanics research, stemmed from observations made possible by scanning electron microscopy. Over the last 50 years, advancing in medical imaging, combined with ingenuity and creativity of biomechanists, have provide a wealth of new and important insights into in vivo human muscle function. Incorporation of in vivo imaging has also advanced computational modeling and allowed our research to have an impact in many clinical populations. While this review does not provide a comprehensive or meta-analysis of the all the in vivo muscle imaging work over the last five decades, it provides a narrative about the past, present, and future of in vivo muscle imaging.

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.

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.

Relationship of muscle morphology to hip displacement in cerebral palsy: a pilot study investigating changes intrinsic to the sarcomere

BACKGROUND

Cerebral palsy (CP) is the most common cause of childhood disability, typified by a static encephalopathy with peripheral musculoskeletal manifestations-most commonly related to spasticity-that are progressive with age. Hip displacement is one of the most common manifestations, observed to lead to painful degenerative arthritis over time. Despite the key role that spasticity-related adductor muscle contractures are thought to play in the development of hip displacement in CP, basic science research in this area to date has been limited. This study was initiated to correlate hip adductor muscle changes intrinsic to the sarcomere-specifically, titin isoforms and sarcomere length-to the severity of hip displacement in children with spastic cerebral palsy.

METHODS

Single gracilis muscle biopsies were obtained from children with CP (Gross Motor Function Classification System (GMFCS) III-V; n = 10) who underwent adductor muscle release surgery for the treatment of hip displacement. Gel electrophoresis was used to estimate titin molecular weight. Sarcomere lengths were measured from muscle fascicles using laser diffraction. The severity of hip displacement was determined by measuring by Reimers migration percentage (MP) from anteroposterior pelvic x-rays. Correlation analyses between titin, sarcomere lengths, and MP were performed.

RESULTS

The mean molecular weight of titin was 3588 kDa. The mean sarcomere length was 3.51 μm. Increased MP was found to be associated with heavier isoforms of titin (R2 = 0.65, p < 0.05) and with increased sarcomere lengths (R2 = 0.65, p < 0.05). Heavier isoforms of titin were also associated with increased sarcomere lengths (R2 = 0.80, p < 0.05).

CONCLUSIONS

Our results suggest that both larger titin isoforms and sarcomere lengths are positively correlated with increased severity of hip displacement and may represent adaptations in response to concomitant increases in spasticity and muscle shortening.

TRIAL REGISTRATION

As this study does not report the results of a health care intervention on human participants, it has not been registered.

Stiffness of hip adductor myofibrils is decreased in children with spastic cerebral palsy

Cerebral palsy (CP) is the result of a static brain lesion which causes spasticity and muscle contracture. The source of the increased passive stiffness in patients is not understood and while whole muscle down to single muscle fibres have been investigated, the smallest functional unit of muscle (the sarcomere) has not been. Muscle biopsies (adductor longus and gracilis) from pediatric patients were obtained (CP n = 9 and control n = 2) and analyzed for mechanical stiffness, in-vivo sarcomere length and titin isoforms. Adductor longus muscle was the focus of this study and the results for sarcomere length showed a significant increase in length for CP (3.6 µm) compared to controls (2.6 µm). Passive stress at the same sarcomere length for CP compared to control was significantly lower in CP and the elastic modulus for the physiological range of muscle was lower in CP compared to control (98.2 kPa and 166.1 kPa, respectively). Our results show that CP muscle at its most reduced level (the myofibril) is more compliant compared to normal, which is completely opposite to what is observed at higher structural levels (single fibres, muscle fibre bundles and whole muscle). It is noteworthy that at the in vivo sarcomere length in CP, the passive forces are greater than normal, purely as a functional of these more compliant sarcomeres operating at long lengths. Titin isoforms were not different between CP and non-CP adductor longus but titin:nebulin was reduced in CP muscle, which may be due to titin loss or an over-expression of nebulin in CP muscles.

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.

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.

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

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

The 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.

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.

Bending, twisting and beating trunk robot bioinspired from the '3 + 0' axoneme

The axoneme is the skeleton and motor axis of flagella and cilia in eukaryotic organisms. Basically it consists of a series of longitudinal fibers (outer doublets of microtubules) that design a cylinder and whose sliding, due to the coordinated activities of dedicated molecular motors (the dynein arms), is converted into a bending because outer doublets pairs are stabilized by elastic links (the nexine molecules). In spite of these interesting mechanical properties, mechanical and robotics engineers have never considered this amazing molecular machinery as a model. The aim of this paper is to propose the robotic design and the kinematic modeling of the '3 + 0' axoneme that makes motile the flagellum of Diplauxis hatti, the simplest that exists. The model that we propose bends and twists and combines the two movements. It is able to propagate wave trains that could be involved in the development of biomimetic actuators of various mechanisms such as (sub)aquatic robotic propellers as well as robotic trunks.

Cortical and spinal excitability during and after lengthening contractions of the human plantar flexor muscles performed with maximal voluntary effort

This study was designed to investigate the sites of potential specific modulations in the neural control of lengthening and subsequent isometric maximal voluntary contractions (MVCs) versus purely isometric MVCs of the plantar flexor muscles, when there is enhanced torque during and following stretch. Ankle joint torque during maximum voluntary plantar flexion was measured by a dynamometer when subjects (n = 10) lay prone on a bench with the right ankle tightly strapped to a foot-plate. Neural control was analysed by comparing soleus motor responses to electrical nerve stimulation (M-wave, V-wave), electrical stimulation of the cervicomedullary junction (CMEP) and transcranial magnetic stimulation of the motor cortex (MEP). Enhanced torque of 17±8% and 9±8% was found during and 2.5–3 s after lengthening MVCs, respectively. Cortical and spinal responsiveness was similar to that in isometric conditions during the lengthening MVCs, as shown by unchanged MEPs, CMEPs and V-waves, suggesting that the major voluntary motor pathways are not subject to substantial inhibition. Following the lengthening MVCs, enhanced torque was accompanied by larger MEPs (p≤0.05) and a trend to greater V-waves (p≤0.1). In combination with stable CMEPs, increased MEPs suggest an increase in cortical excitability, and enlarged V-waves indicate greater motoneuronal output or increased stretch reflex excitability. The new results illustrate that neuromotor pathways are altered after lengthening MVCs suggesting that the underlying mechanisms of the enhanced torque are not purely mechanical in nature.

Pediatric orbital floor trapdoor fractures: outcomes and CT-based morphologic assessment of the inferior rectus muscle

INTRODUCTION

Trauma to the pediatric orbit may produce a unique fracture in which entrapment of the periorbital tissue and/or inferior rectus muscle may occur due to a "trap-door" effect of the compliant orbital floor. This study was designed to assess the outcome following the surgical management of orbital trapdoor fractures in children and to examine alterations in the morphology of the inferior rectus (IR) muscle.

METHODOLOGY

Outcome assessment on patients undergoing surgery at the Hospital For Sick Children, Toronto with symptomatic orbital floor trapdoor fractures over a 10-year period and a CT-based morphometric analysis of the inferior rectus muscle were performed.

RESULTS

18 patients (5F, 13M) mean age 12.6 years (range 8.3-16.6 years) underwent surgical exploration (average time to surgery 9.7 ± 3.5 days (range 1-45 days). Follow-up was 15.4 months (range 6-36 months). All patients noted improvement in extra-ocular muscle (EOM) range of motion post-operatively: 7 patients had normal EOM with no diplopia; 9 patients had minimal diplopia on extreme secondary (upwards) gaze and 2 patients had residual significant diplopia with upward gaze. CT morphologic assessment (8 patients) demonstrated: a) zone of bony injury was posterior to the equator of the globe; b) minimal to no extra-conal fat exists to protect the IR muscle; c) a trend toward increased length in the injured IR muscle.

CONCLUSIONS

With surgical intervention, improvement of diplopia (complete or near-complete resolution) occurred in 16/18 (89%) of patients presenting with symptomatic trapdoor orbital floor fractures. CT-based assessment demonstrated the vulnerability of the inferior rectus muscle with close proximity to the orbital floor and lack of periorbital fat for protection. Alteration of the length of the IR muscle may impact the force-length relationship and play a role in the outcomes. Early surgical intervention for symptomatic trapdoor fractures is recommended.