The descending limb of the force-sarcomere length relation of the frog revisited

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.

Sarcomere length non-uniformities dictate force production along the descending limb of the force-length relation

The force-length relation is one of the most defining features of muscle contraction, and yet a topic of debate in the literature. The sliding filament theory predicts that the force produced by muscle fibres is proportional to the degree of overlap between myosin and actin filaments, producing a linear descending limb of the active force-length relation. However, several studies have shown forces that are larger than predicted, especially at long sarcomere lengths (SLs). Studies have been conducted with muscle fibres, preparations containing thousands of sarcomeres that make measurements of individual SL challenging. The aim of this study was to evaluate force production and sarcomere dynamics in isolated myofibrils and single sarcomeres from the rabbit psoas muscle to enhance our understanding of the theoretically predicted force-length relation. Contractions at varying SLs along the plateau (SL = 2.25-2.39 µm) and the descending limb (SL > 2.39 µm) of the force-length relation were induced in sarcomeres and myofibrils, and different modes of force measurements were used. Our results show that when forces are measured in single sarcomeres, the experimental force-length relation follows theoretical predictions. When forces are measured in myofibrils with large SL dispersions, there is an extension of the plateau and forces elevated above the predicted levels along the descending limb. We also found an increase in SL non-uniformity and slowed rates of force production at long lengths in myofibrils but not in single sarcomere preparations. We conclude that the deviation of the descending limb of the force-length relation is correlated with the degree of SL non-uniformity and slowed force development.

The sarcomere force-length relationship in an intact muscle-tendon unit

The periodic striation pattern in skeletal muscle reflects the length of the basic contractile unit: the sarcomere. More than half a century ago, Gordon, Huxley and Julian provided strong support for the 'sliding filament' theory through experiments with single muscle fibres. The sarcomere force-length (FL) relationship has since been extrapolated to whole muscles in an attempt to unravel in vivo muscle function. However, these extrapolations were frequently associated with non-trivial assumptions, such as muscle length changes corresponding linearly to SL changes. Here, we determined the in situ sarcomere FL relationship in a whole muscle preparation by simultaneously measuring muscle force and individual SLs in an intact muscle-tendon unit (MTU) using state-of-the-art multi-photon excitation microscopy. We found that despite great SL non-uniformity, the mean value of SLs measured from a minute volume of the mid-belly, equivalent to about 5×10-6% of the total muscle volume, agrees well with the theoretically predicted FL relationship, but only if the precise contractile filament lengths are known, and if passive forces from parallel elastic components and activation-associated sarcomere shortening are considered properly. As SLs are not uniformly distributed across the whole muscle and changes in SL with muscle length are location dependent, our results may not be valid for the proximal or distal parts of the muscle. The approach described here, and our findings, may encourage future studies to determine the role of SL non-uniformity in influencing sarcomere FL properties in different muscles and for different locations within single muscles.

Towards the Exploitation of Physical Compliance in Segmented and Electrically Actuated Robotic Legs: A Review Focused on Elastic Mechanisms

Physical compliance has been increasingly used in robotic legs, due to its advantages in terms of the mechanical regulation of leg mechanics and energetics and the passive response to abrupt external disturbances during locomotion. This article presents a review of the exploitation of physical compliance in robotic legs. Particular attention has been paid to the segmented, electrically actuated robotic legs, such that a comparable analysis can be provided. The utilization of physical compliance is divided into three main categories, depending on the setting locations and configurations, namely, (1) joint series compliance, (2) joint parallel compliance, and (3) leg distal compliance. With an overview of the representative work related to each category, the corresponding working principles and implementation processes of various physical compliances are explained. After that, we analyze in detail some of the structural characteristics and performance influences of the existing designs, including the realization method, compliance profile, damping design, and quantitative changes in terms of mechanics and energetics. In parallel, the design challenges and possible future works associated with physical compliance in robotic legs are also identified and proposed. This article is expected to provide useful paradigmatic implementations and design guidance for physical compliance for researchers in the construction of novel physically compliant robotic legs.

How myofilament strain and strain rate lead the dance of the cardiac cycle

Movement of the myocardium can modify organ-level cardiac function and its molecular (crossbridge) mechanisms. This motion, which is defined by myocardial strain and strain rate (muscle shortening, lengthening, and the speed of these movements), occurs throughout the cardiac cycle, including during isovolumic periods. This review highlights how the left ventricular myocardium moves throughout the cardiac cycle, how muscle mechanics experiments provide insight into the regulation of forces used to move blood in and out of the left ventricle, and its impact on (and regulation by) crossbridge and sarcomere kinetics. We specifically highlight how muscle mechanics experiments explain how myocardial relaxation is accelerated by lengthening (strain rate) during late systole and isovolumic relaxation, a lengthening which has been measured in human hearts. Advancing and refining both in vivo measurement and ex vivo protocols with physiologic strain and strain rates could reveal important insights into molecular (crossbridge) kinetics. These advances could provide an improvement in both diagnosis and precise treatment of cardiac dysfunction.

Different Segments within Vertebrate Muscles Can Operate on Different Regions of Their Force-Length Relationships

To relate in vivo behavior of fascicle segments within a muscle to their in vitro force-length relationships, we examined the strain behavior of paired segments within each of three vertebrate muscles. After determining in vivo muscle activity patterns and length changes of in-series segments within the semimembranosus muscle (SM) in the American Toad (Bufo americanus) during hopping and within the sternohyoid (SH) muscle in the rat (Rattus rattus) during swallowing, and of spatially separated fascicles within the medial gastrocnemius (MG) muscle in the rat during trotting, we measured their corresponding in vitro (toad) or in situ (rat) force-length relationships (FLRs). For all three muscles, in vivo strain heterogeneity lasted for about 36-57% of the behavior cycle, during which one segment or fascicle shortened while the other segment or fascicle simultaneously lengthened. In the toad SM, the proximal segment shortened from the descending limb across the plateau of its FLR from 1.12 to 0.91 of its optimal length (Lo), while the distal segment lengthened (by 0.04 ± 0.04 Lo) before shortening down the ascending limb from 0.94 to 0.83 Lo. In the rat SH muscle, the proximal segment tended to shorten on its ascending limb from 0.90 to 0.85 Lo while the distal segment tended to lengthen across Lo (0.96-1.12 Lo). In the rat MG muscle, in vivo strains of proximal fascicles ranged from 0.72 to 1.02 Lo, while the distal fascicles ranged from 0.88 to 1.11 Lo. Even though the timing of muscle activation patterns were similar between segments, the heterogeneous strain patterns of fascicle segments measured in vivo coincided with different operating ranges across their FLRs simultaneously, implying differences in force-velocity behavior as well. The three vertebrate skeletal muscles represent a diversity of fiber architectures and functions and suggest that patterns of in vivo contractile strain and the operating range over the FLR in one muscle region does not necessarily represent other regions within the same muscle.

Downsizing the molecular spring of the giant protein titin reveals that skeletal muscle titin determines passive stiffness and drives longitudinal hypertrophy

Titin, the largest protein known, forms an elastic myofilament in the striated muscle sarcomere. To establish titin’s contribution to skeletal muscle passive stiffness, relative to that of the extracellular matrix, a mouse model was created in which titin’s molecular spring region was shortened by deleting 47 exons, the Ttn^Δ112-158 model. RNA sequencing and super-resolution microscopy predicts a much stiffer titin molecule. Mechanical studies with this novel mouse model support that titin is the main determinant of skeletal muscle passive stiffness. Unexpectedly, the in vivo sarcomere length working range was shifted to shorter lengths in Ttn^Δ112-158 mice, due to a ~ 30% increase in the number of sarcomeres in series (longitudinal hypertrophy). The expected effect of this shift on active force generation was minimized through a shortening of thin filaments that was discovered in Ttn^Δ112-158 mice. Thus, skeletal muscle titin is the dominant determinant of physiological passive stiffness and drives longitudinal hypertrophy.

Editorial note: This article has been through an editorial process in which the authors decide how to respond to the issues raised during peer review. The Reviewing Editor's assessment is that all the issues have been addressed (see decision letter).

Skeletal muscle contractile properties in a novel murine model for limb girdle muscular dystrophy 2i

Limb-girdle muscular dystrophy (LGMD) 2i results from mutations in fukutin-related protein and aberrant α-dystroglycan glycosylation. Although this significantly compromises muscle function and ambulation, the comprehensive characteristics of contractile dysfunction are unknown. Therefore, we quantified the in situ contractile properties of the medial gastrocnemius in young adult P448L mice, an affected muscle of a novel model of LGMD2i. Normalized maximal twitch force, tetanic force, and power were significantly smaller in P448L mice, compared with sex-matched, wild-type mice. These differences were consistent with the replacement of contractile fibers by passive tissue. The shape of the active force-length relationships were similar in both groups, regardless of sex, consistent with an intact sarcomeric structure in P448L mice. Passive force-length curves normalized to maximal isometric force were steeper in P448L mice, and passive elements contribute disproportionately more to total contractile force in P448L mice. Sex differences were mostly noted in the force-velocity curves, as normalized values for maximal and optimal velocities were significantly slower in P448L males, compared with wild-type, but not in P448L females. This suggests that the dystrophic phenotype, which may include possible changes in cross-bridge kinetics and fiber-type proportions, progresses more quickly in P448L males. These results together indicate that active force and power generation are compromised in both sexes of P448L mice, while passive forces increase. More importantly, the results identified several functional markers of disease pathophysiology that could aid in developing and assessment of novel therapeutics for LGMD2i and possibly other dystroglycanopathies as well. NEW & NOTEWORTHY Comprehensive assessments of muscle contractile function have, until now, never been performed in an animal model for any dystroglycanopathy. This study suggests that skeletal muscle contractile properties are significantly compromised in a recently developed model for limb-girdle muscular dystrophy 2i, the P448L mouse. It further identifies novel pathological markers of muscle function that are suitable for developing therapeutics and for better understanding of disease pathogenesis.

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.

A design concept of parallel elasticity extracted from biological muscles for engineered actuators

Series elastic actuation that takes inspiration from biological muscle-tendon units has been extensively studied and used to address the challenges (e.g. energy efficiency, robustness) existing in purely stiff robots. However, there also exists another form of passive property in biological actuation, parallel elasticity within muscles themselves, and our knowledge of it is limited: for example, there is still no general design strategy for the elasticity profile. When we look at nature, on the other hand, there seems a universal agreement in biological systems: experimental evidence has suggested that a concave-upward elasticity behaviour is exhibited within the muscles of animals. Seeking to draw possible design clues for elasticity in parallel with actuators, we use a simplified joint model to investigate the mechanisms behind this biologically universal preference of muscles. Actuation of the model is identified from general biological joints and further reduced with a specific focus on muscle elasticity aspects, for the sake of easy implementation. By examining various elasticity scenarios, one without elasticity and three with elasticity of different profiles, we find that parallel elasticity generally exerts contradictory influences on energy efficiency and disturbance rejection, due to the mechanical impedance shift thus caused. The trade-off analysis between them also reveals that concave parallel elasticity is able to achieve a more advantageous balance than linear and convex ones. It is expected that the results could contribute to our further understanding of muscle elasticity and provide a theoretical guideline on how to properly design parallel elasticity behaviours for engineering systems such as artificial actuators and robotic joints.

Length-dependent Ca2+ activation in skeletal muscle fibers from mammalians

We tested the hypotheses that 1) a decrease in activation of skeletal muscles at short sarcomere lengths (SLs) is caused by an inhibition of Ca(2+) release from the sarcoplasmic reticulum (SR), and 2) the decrease in Ca(2+) would be caused by an inhibition of action potential conduction from the periphery to the core of the fibers. Intact, single fibers dissected from the flexor digitorum brevis from mice were activated at different SLs, and intracellular Ca(2+) was imaged with confocal microscopy. Force decreased at SLs shorter than 2.1 μm, while Ca(2+) concentration decreased at SLs below 1.9 μm. The concentration of Ca(2+) at short SL was lower at the core than at the peripheries of the fiber. When the external concentration of Na(+) was decreased in the experimental media, impairing action potential conduction, Ca(2+) gradients were observed in all SLs. When caffeine was used in the experimental media, the gradients of Ca(2+) were abolished. We concluded that there is an inhibition of Ca(2+) release from the sarcoplasmic reticulum (SR) at short SLs, which results from a decreased conduction of action potential from the periphery to the core of the fibers.

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.

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.

Whole muscle length-tension relationships are accurately modeled as scaled sarcomeres in rabbit hindlimb muscles

An a priori model of the whole active muscle length-tension relationship was constructed utilizing only myofilament length and serial sarcomere number for rabbit tibialis anterior (TA), extensor digitorum longus (EDL), and extensor digitorum II (EDII) muscles. Passive tension was modeled with a two-element Hill-type model. Experimental length-tension relations were then measured for each of these muscles and compared to predictions. The model was able to accurately capture the active-tension characteristics of experimentally-measured data for all muscles (ICC=0.88 ± 0.03). Despite their varied architecture, no differences in predicted versus experimental correlations were observed among muscles. In addition, the model demonstrated that excursion, quantified by full-width-at-half-maximum (FWHM) of the active length-tension relationship, scaled linearly (slope=0.68) with normalized muscle fiber length. Experimental and theoretical FWHM values agreed well with an intraclass correlation coefficient of 0.99 (p<0.001). In contrast to active tension, the passive tension model deviated from experimentally-measured values and thus, was not an accurate predictor of passive tension (ICC=0.70 ± 0.07). These data demonstrate that modeling muscle as a scaled sarcomere provides accurate active functional but not passive functional predictions for rabbit TA, EDL, and EDII muscles and call into question the need for more complex modeling assumptions often proposed.

Differential splicing of the large sarcomeric protein nebulin during skeletal muscle development

We studied differential splicing of nebulin, a giant filamentous F-actin binding protein (M(r) approximately 700-800kDa) that is found in skeletal muscle. Nebulin spans the thin filament length, its C-terminus is anchored in the Z-disc, and its N-terminal region is located toward the thin filament pointed end. Various lines of evidence indicate that nebulin plays important roles in thin filament and Z-disc structure in skeletal muscle. In the present work we studied nebulin in a range of muscle types during postnatal development and performed transcript studies with a mouse nebulin exon microarray, developed by us, whose results were confirmed by RT-PCR. We also performed protein studies with high-resolution SDS-agarose gels and Western blots, and structural studies with electron microscopy. We found during postnatal development of the soleus muscle major changes in splicing in both the super-repeat region and the Z-disc region of nebulin; interestingly, these changes were absent in other muscle types. Three novel Z-disc exons, previously described in the mouse gene, were upregulated during postnatal development of soleus muscle and this was correlated with a significant increase in Z-disc width. These findings support the view that nebulin plays an important role in Z-disc width regulation. In summary, we discovered changes in both the super-repeat region and the Z-disc region of nebulin, that these changes are muscle-type specific, and that they correlate with differences in sarcomere structure.

Titin-isoform dependence of titin-actin interaction and its regulation by S100A1/Ca2+ in skinned myocardium

Titin, also known as connectin, is a large filamentous protein that greatly contributes to passive myocardial stiffness. In vitro evidence suggests that one of titin's spring elements, the PEVK, interacts with actin and that this adds a viscous component to passive stiffness. Differential splicing of titin gives rise to the stiff N2B and more compliant N2BA isoforms. Here we studied the titin-isoform dependence of titin-actin interaction and studied the bovine left atrium (BLA) that expresses mainly N2BA titin, and the bovine left ventricle (BLV) that expresses a mixture of both N2B and N2BA isforms. For comparison we also studied mouse left ventricular (MLV) myocardium which expresses predominately N2B titin. Using the actin-severing protein gelsolin, we obtained evidence that titin-actin interaction contributes significantly to passive myocardial stiffness in all tissue types, but most in MLV, least in BLA, and an intermediate level in BLV. We also studied whether titin-actin interaction is regulated by S100A1/calcium and found that calcium alone or S100A1 alone did not alter passive stiffness, but that combined they significantly lowered stiffness. We propose that titin-actin interaction is a “viscous break” that is on during diastole and off during systole.

The mechanical behavior of individual sarcomeres of myofibrils isolated from rabbit psoas muscle

The goal of this study was to develop a system to experiment with sarcomeres mechanically isolated from skeletal muscles. Single myofibrils from rabbit psoas were transferred into a temperature-controlled (22 degrees C or 15 degrees C) experimental chamber, and sarcomeres were isolated using precalibrated glass microneedles that were pierced externally, adjacent to the Z-lines. The force produced during activation was measured by tracking the displacement of the microneedles, and the sarcomere and half-sarcomere changes were measured by continuously tracking the Z-lines and A-bands position during the experiments. Sarcomeres produced a stress (force/cross-sectional area) of 112.75 +/- 4.96 nN/microm(2) (15 degrees C) and 128.47 +/- 5.58 nN/microm(2) (22 degrees C) at lengths between 2.0 microm and 2.4 microm. The descending limb was fitted with linear regression for length between 2.4 microm and 3.5 microm, which provided an abscissa extrapolating to 3.87 microm. The force-length relation was remarkably similar to a theoretical curve based on the degree of filament overlap. During sarcomere activation, we tracked the distance between the center of the A-band and the Z-lines. At lengths below 1.6 microm, movements of A-band were not detected. A-band movements increased with length to achieve a maximum displacement of 59.40 +/- 10.1 nm from the center at 2.0 microm-2.4 microm. A-band displacement decreased linearly in sarcomere lengths between 2.6 microm and 3.6 microm. A technique for monitoring force and length in single sarcomeres isolated from myofibrils represents a reliable technique to evaluate contractile mechanisms at the most basic, intact level of muscle organization, opening the possibility to clarify long-standing issues in the field of muscle contraction.

A multisegmental cross-bridge kinetics model of the myofibril

Striated muscle is a mechanical system that develops force and generates power in serving vital activities in the body. Striated muscle is a complex biological system; a single mammalian muscle fibre contains up to hundred or even more myofibrils in parallel connected via an inter-myofibril filament network. In one single myofibril thousands of sarcomeres are lined up as a series of linear motors. We recently demonstrated that half-sarcomeres (hS) in a single myofibril operate non-uniformly. We outline a mathematical framework based on cross-bridge kinetics for the simulation of the force response and length change of individual hS in a myofibril. The model describes the muscle myofibril in contraction experiments under various conditions. The myofibril is modeled as a multisegmental mechanical system of hS models, which have active and viscoelastic properties. In the first approach, a two-state cross-bridge formalism relates the hS force to the chemical kinetics of ATP hydrolysis, as first described by Huxley [1957. Muscle structure and theories of contraction. Prog. Biophys. Mol. Biol. 7, 255-318]. Two possible types of biological variability are introduced and modeled. Numerical simulations of a myofibril composed of four to eight hS show a non-uniform hS length distribution and complex internal dynamics upon activation. We demonstrate that the steady-state approximation holds only in restricted time zones during activation. Simulations of myofibril contraction experiments that reproduce the classic steady-state force-length and force-velocity relationships, strictly constrained or "clamped" in either end-held isometric or isotonic contraction conditions, reveal a small but conspicuous effect of hS dynamics on force.

Controlled intermittent shortening contractions of a muscle–tendon complex: muscle fibre damage and effects on force transmission from a single head of rat EDL

This study was performed to examine effects of prolonged (3 h) intermittent shortening (amplitude 2 mm) contractions (muscles were excited maximally) of head III of rat extensor digitorum longus muscle (EDL III) on indices of muscle damage and on force transmission within the intact anterior crural compartment. Three hours after the EDL III exercise, muscle fibre damage, as assessed by immunohistochemical staining of structural proteins (i.e. dystrophin, desmin, titin, laminin-2), was found in EDL, tibialis anterior (TA) and extensor hallucis longus (EHL) muscles. The damaged muscle fibres were not uniformly distributed throughout the muscle cross-sections, but were located predominantly near the interface of TA and EDL muscles as well as near intra- and extramuscular neurovascular tracts. In addition, changes were observed in desmin, muscle ankyrin repeat protein 1, and muscle LIM protein gene expression: significantly (P<0.01) higher (1.3, 45.5 and 2.3-fold, respectively) transcript levels compared to the contralateral muscles. Post-EDL III exercise, length-distal force characteristics of EDL III were altered significantly (P<0.05): at high EDL III lengths, active forces decreased and the length range between active slack length and optimum length increased. For all EDL III lengths tested, proximal passive and active force of EDL decreased. The slope of the EDL III length-TA+EHL force curve decreased, which indicates a decrease of the degree of intermuscular interaction between EDL III and TA+EHL. It is concluded that prolonged intermittent shortening contractions of a single head of multi-tendoned EDL muscle results in structural damage to muscle fibres as well as altered force transmission within the compartment. A possible role of myofascial force transmission is discussed.

Myofascial force transmission between a single muscle head and adjacent tissues: length effects of head III of rat EDL

Force transmission from muscle fibers via the connective tissue network (i.e., myofascial force transmission) is an important determinant of muscle function. This study investigates the role of myofascial pathways for force transmission from multitendoned extensor digitorum longus (EDL) muscle within an intact anterior crural compartment. Effects of length changes exclusively of head III of rat EDL muscle (EDL III) on myofascial force transmission were assessed. EDL III was lengthened at the distal tendon. For different lengths of EDL III, isometric forces were measured at the distal tendon of EDL III, as well as at the proximal tendon of whole EDL and at the distal tendons of tibialis anterior and extensor hallucis longus (TA+EHL) muscles. Lengthening of EDL III caused high changes in force exerted at the distal tendon of EDL III (from 0 to 1.03 +/- 0.07 N). In contrast, only minor changes were found in force exerted at the proximal EDL tendon (from 2.37 +/- 0.09 to 2.53 +/- 0.10 N). Increasing the length of EDL III decreased TA+EHL force significantly (by 7%, i.e., from 5.62 +/- 0.27 to 5.22 +/- 0.32 N). These results show that force is transmitted between EDL III and adjacent tissues via myofascial pathways. Optimal force exerted at the distal tendon of EDL III (1.03 +/- 0.07 N) was more than twice the force expected on the basis of the physiological cross-sectional area of EDL III muscle fibers (0.42 N). Therefore, a substantial fraction of this force must originate from sources other than EDL III. It is concluded that myofascial pathways play an important role in force transmission from multitendoned muscles.

The Relative Position of EDL Muscle Affects the Length of Sarcomeres Within Muscle Fibers: Experimental Results and Finite-Element Modeling

Background : Effects of extramuscular connective tissues on muscle force (experimentally measured) and lengths of sarcomeres (modeled) were investigated in rat. It was hypothesized that changes of muscle-relative position affect the distribution of lengths of sarcomeres within muscle fibers. Method of approach: The position of extensor digitorum longus muscle (EDL) relative to intact extramuscular connective tissues of the anterior crural compartment was manipulated without changing its muscle-tendon complex length. Results: Significant effects of EDL muscle relative position on proximal and distal EDL forces were found, indicating changes of extramuscular myofascial force transmission. EDL isometric force exerted at its proximal and distal tendons differed significantly. Finite-element modeling showed that the distribution of lengths of sarcomeres is altered by changes of muscle-relative position. Conclusions: It is concluded that forces exerted on a muscle via extramuscular myofascial pathways augment distributions of lengths of sarcomeres within that muscle.

Sarcomere length-dependence of activity-dependent twitch potentiation in mouse skeletal muscle

BACKGROUND

It has been reported that potentiation of a skeletal muscle twitch response is proportional to muscle length with a negative slope during staircase, and a positive slope during posttetanic potentiation. This study was done to directly compare staircase and posttetanic responses with measurement of sarcomere length to compare their length-dependence.

METHODS

Mouse extensor digitorum longus (EDL) muscles were dissected to small bundles of fibers, which permit measurement of sarcomere length (SL), by laser diffraction. In vitro fixed-end contractions of EDL fiber bundles were elicited at 22 degrees C and 35 degrees C at sarcomere lengths ranging from 2.35 microm to 3.85 microm. Twitch contractions were assessed before and after 1.5 s of 75 Hz stimulation at 22 degrees C or during 10 s of 10 Hz stimulation at 22 degrees C or 35 degrees C.

RESULTS

Staircase potentiation was greater at 35 degrees C than 22 degrees C, and the relative magnitude of the twitch contraction (Pt*/Pt) was proportional to sarcomere length with a negative slope, over the range 2.3 microm - 3.7 microm. Linear regression yielded the following: Pt*/Pt = -0.59 x SL+3.27 (r2 = 0.74); Pt*/Pt = -0.39 x SL+2.34 (r2 = 0.48); and Pt*/Pt = -0.50 x SL+2.45 (r2 = 0.80) for staircase at 35 degrees C, and 22 degrees C and posttetanic response respectively. Posttetanic depression rather than potentiation was present at long SL. This indicates that there may be two processes operating in these muscles to modulate the force: one that enhances and a second that depresses the force. Either or both of these processes may have a length-dependence of its mechanism.

CONCLUSION

There is no evidence that posttetanic potentiation is fundamentally different from staircase in these muscles.

Length dependence of staircase potentiation: interactions with caffeine and dantrolene sodium

In skeletal muscle, there is a length dependence of staircase potentiation for which the mechanism is unclear. In this study we tested the hypothesis that abolition of this length dependence by caffeine is effected by a mechanism independent of enhanced Ca2+ release. To test this hypothesis we have used caffeine, which abolishes length dependence of potentiation, and dantrolene sodium, which inhibits Ca2+ release. In situ isometric twitch contractions of rat gastrocnemius muscle before and after 20 s of repetitive stimulation at 5 Hz were analyzed at optimal length (Lo), Lo - 10%, and Lo + 10%. Potentiation was observed to be length dependent, with an increase in developed tension (DT) of 78 ± 12, 51 ± 5, and 34 ± 9% (mean ± SEM), at Lo - 10%, Lo, and Lo + 10%, respectively. Caffeine diminished the length dependence of activation and suppressed the length dependence of staircase potentiation, giving increases in DT of 65±13, 53 ± 11, and 45 ± 12% for Lo - 10%, Lo, and Lo + 10%, respectively. Dantrolene administered after caffeine did not reverse this effect. Dantrolene alone depressed the potentiation response, but did not affect the length dependence of staircase potentiation, with increases in DT of 58 ± 17, 26 ± 8, and 18 ± 7%, respectively. This study confirms that there is a length dependence of staircase potentiation in mammalian skeletal muscle which is suppressed by caffeine. Since dantrolene did not alter this suppression of the length dependence of potentiation by caffeine, it is apparently not directly modulated by Ca2+ availability in the myoplasm.

Length dependence of active force production in skeletal muscle

The sliding filament and cross-bridge theories of muscle contraction provide discrete predictions of the tetanic force-length relationship of skeletal muscle that have been tested experimentally. The active force generated by a maximally activated single fiber (with sarcomere length control) is maximal when the filament overlap is optimized and is proportionally decreased when overlap is diminished. The force-length relationship is a static property of skeletal muscle and, therefore, it does not predict the consequences of dynamic contractions. Changes in sarcomere length during muscle contraction result in modulation of the active force that is not necessarily predicted by the cross-bridge theory. The results of in vivo studies of the force-length relationship suggest that muscles that operate on the ascending limb of the force-length relationship typically function in stretch-shortening cycle contractions, and muscles that operate on the descending limb typically function in shorten-stretch cycle contractions. The joint moments produced by a muscle depend on the moment arm and the sarcomere length of the muscle. Moment arm magnitude also affects the excursion (length change) of a muscle for a given change in joint angle, and the number of sarcomeres arranged in series within a muscle fiber determines the sarcomere length change associated with a given excursion.

PEVK extension of human soleus muscle titin revealed by immunolabeling with the anti-titin antibody 9D10

Titin is a giant protein that spans half of the striated muscle sarcomere. The I-band portion of titin extends as the sarcomere is stretched, developing what is known as passive force. This portion of the molecule is composed mainly of tandem immunoglobulin (Ig) segments, consisting of serially linked Ig-like domains, and a recently discovered unique sequence termed the PEVK segment. The tandem Ig and PEVK segments have been suggested to extend sequentially when sarcomeres are stretched, with PEVK extension dominating at moderate to high degrees of sarcomere stretch (M. Gautel and D. Goulding, 1996, FEBS Lett. 385, 11-14; W. Linke et al., 1996, J. Mol. Biol. 261, 62-71; K. Trombitás et al., 1998). Previously we observed that the anti-titin antibody 9D10 labels a region in the I-band that increases in width as sarcomeres are stretched. Here we tested whether 9D10 labels the PEVK segment. The 9D10-labeled region of human soleus fibers was followed by immunoelectron microscopy as sarcomeres were stretched. It was found that 9D10 labeled a region in the I-band that was approximately 100 nm wide at a sarcomere length of 2.4 micrometer and approximately 550 nm wide at a sarcomere length of 4.0 micrometer. Results were compared with those obtained with sequence-specific antibodies that were used to mark the boundaries of the PEVK segment. Findings indicate that 9D10 labels the PEVK segment from close to its N-terminal end to its C-terminal end. Consistent with this conclusion are the results on cardiac myocytes that express a much shorter PEVK segment than skeletal muscle and where 9D10 labels a region that is much less wide than in skeletal muscle. The anti-titin antibody 9D10 is a useful tool for investigating the extensible behavior of the PEVK segment in both skeletal and cardiac muscles.

Titin extensibility in situ: entropic elasticity of permanently folded and permanently unfolded molecular segments

Titin (also known as connectin) is a giant protein that spans half of the striated muscle sarcomere. In the I-band titin extends as the sarcomere is stretched, developing what is known as passive force. The I-band region of titin contains tandem Ig segments (consisting of serially linked immunoglobulin-like domains) with the unique PEVK segment in between (Labeit, S., and B. Kolmerer. 1995. Science. 270:293-296). Although the tandem Ig and PEVK segments have been proposed to behave as stiff and compliant springs, respectively, precise experimental testing of the hypothesis is still needed. Here, sequence-specific antibodies were used to mark the ends of the tandem Ig and PEVK segments. By following the extension of the segments as a function of sarcomere length (SL), their respective contributions to titin's elastic behavior were established. In slack sarcomeres (approximately 2.0 micron) the tandem Ig and PEVK segments were contracted. Upon stretching sarcomeres from approximately 2.0 to 2.7 micron, the "contracted" tandem Ig segments straightened while their individual Ig domains remained folded. When sarcomeres were stretched beyond approximately 2.7 micron, the tandem Ig segments did not further extend, instead PEVK extension was now dominant. Modeling tandem Ig and PEVK segments as entropic springs with different bending rigidities (Kellermayer, M., S. Smith, H. Granzier, and C. Bustamante. 1997. Science. 276:1112-1116) indicated that in the physiological SL range (a) the Ig-like domains of the tandem Ig segments remain folded and (b) the PEVK segment behaves as a permanently unfolded polypeptide. Our model provides a molecular basis for the sequential extension of titin's different segments. Initially, the tandem Ig segments extend at low forces due to their high bending rigidity. Subsequently, extension of the PEVK segment occurs only upon reaching sufficiently high external forces due to its low bending rigidity. The serial linking of tandem Ig and PEVK segments with different bending rigidities provides a unique passive force-SL relation that is not achievable with a single elastic segment.

Influence of muscle morphometry and moment arms on the moment-generating capacity of human neck muscles

STUDY DESIGN

The function of neck muscles was quantified by incorporating experimentally measured morphometric parameters into a three-dimensional biomechanical model.

OBJECTIVE

To analyze how muscle morphometry and moment arms influence moment-generating capacity of human neck muscles in physiologic ranges of motion.

SUMMARY OF BACKGROUND DATA

Previous biomechanical analyses of the head-neck system have used simplified representations of the musculoskeletal anatomy. The force- and moment-generating properties of individual neck muscles have not been reported.

METHODS

A computer graphics model was developed that incorporates detailed neck muscle morphometric data into a model of cervical musculoskeletal anatomy and intervertebral kinematics. Moment arms and force-generating capacity of neck muscles were calculated for a range of head positions.

RESULTS

With the head in the upright neutral position, the muscles with the largest moment arms and moment-generating capacities are sternocleidomastoid in flexion and lateral bending, semispinalis capitis and splenius capitis in extension, and trapezius in axial rotation. The moment arms of certain neck muscles (e.g., rectus capitis posterior major in axial rotation) change considerably in the physiologic range of motion. Most neck muscles maintain at least 80% of their peak force-generating capacity throughout the range of motion; however, the force-generating capacities of muscles with large moment arms and/or short fascicles (e.g., splenius capitis) vary substantially with head posture.

CONCLUSION

These results quantify the contributions of individual neck muscles to moment-generating capacity and demonstrate that variations in force-generating capacity and moment arm throughout the range of motion can alter muscle moment-generating capacities.

Length changes of the cat soleus muscle under frequency-modulated distributed stimulation of efferents in isotony

The length changes of the cat soleus muscle have been examined in isotony within closed cycles of the stimulation rate change. Successive stimuli were applied in a cycle to five filaments of the preliminary dissected L7-S1 ventral roots (method of distributed stimulation), maximal rate did not exceed 80-90/s (16-18/s per single filament). At the beginning of a slow linear increase in the rate a muscle began shortening rather quickly, the rate changes without muscle reaction consisted of 5.91 +/- 0.28/s (mean +/- S.E.M.). A substantially linear movement was observed during increase of the input rate up to 40-50/s (i.e. 8-10/s per filament), a further rate increment could evoke a somewhat slowing of the shortening velocity with a distinctive infection of the rate-length curve. During a significant part of the rate decrease phase no movement was seen, the rate range with the absence of muscle lengthening was 29.93 +/- 1.57/s. After such a pronounced period of length fixation, a muscle began to elongate, the steady-state velocity at this part of the movement trajectory was invariably higher as compared with shortening velocity at the leading edge of the cycle. The striking feature of a powerful length clamping seen in active muscle at the phase of rate decrease preceded by previous rate increment allows us to suppose that this strongly non-linear behaviour of muscle might be a main reason for the existence of powerful dynamic components in efferent activity every time when muscle should shorten against external load in a ramp-and-hold fashion. We used the following experimental paradigm to check the assumption. Stimulation began with regular rate of 15/s; then, after transition from isometry to isotony and cessation of movement transients, the rate was raised linearly; after reaching a peak value of 50-90/s, it decreased linearly or exponentially, being afterwards fixed at several different levels between the maximal and initial values of the rate. It was demonstrated that such pattern of stimulation could be effective for a linear transition between two equilibrium lengths, provided that corresponding parameters in modulation signal were chosen in an optimal way. Duration and amplitude of the leading edge of the dynamic component seemed to completely define amplitude and velocity of the ramp phase of movement, parameters of decay to the final steady rate were, on the other hand, important for efficacy of the length clamping at hold phase. It was concluded that hysteresis effects of muscle contraction seemed to be an extremely important nonlinear property of muscle dynamics in producing any transition movements between two steady-states. Thus, oversimplified muscle models, like the spring model based on the isometric length-tension dependencies, seem to be incorrect. Possible mechanisms for the muscle hysteresis and its role in motor control are discussed.

Muscle hysteresis and movement control: A theoretical study

In this study we have tried to elaborate necessary theoretical approaches for the adequate analysis of the central motor commands to a mammalian muscle in the equilibrium states and during transition movements between these states. At present, the equilibrium point hypothesis has obtained a wide distribution in this field. The muscle is considered in the framework of the theory as an executive element of the reflex circuits originating in the muscle proprioceptors and being closed at the level of spinal cord and the supraspinal motor centres. The main parameter defining the muscle state is supposed to be the threshold of the stretch reflex--the minimal length value at which muscle begins to resist to the externally applied force. We have attempted to show that the theory has an essential shortcoming because it does not take into account such important non-linearity in the muscle behaviour as hysteresis. In the framework of the equilibrium point hypothesis, the muscle behaviour within the stretch reflex system does not depend on movement direction. The stretch and unloading reflexes are supposed to have the same length tension dependencies when the muscle is stretching or contracting with a rather slow velocity. However, powerful hysteresis of the stretch reflex system requires taking into account the direction of the current movement, the after-effects of previous movement led to a principal uncertainty in the muscle steady-state. We would like to stress that any process of active muscle shortening should be controlled by dynamic components in efferent inflow. At the same time, the resulting steady-state develops by using effective hysteresis mechanism for its maintenance. The following hypothesis was proposed to explain the length clamping mechanisms in shortening transition movements. A significant decrement of the arrived efferent activity at the phase of the length fixation can evoke an internal elongation of the contractile elements within the muscle and corresponding hysteresis-like enhancement of the contractile effectiveness. Hence, instead of considering the quasi-static and dynamic components of movement commands as in the equilibrium point hypothesis, it is preferable to adopt a model of the shared coding of both the final position and movement velocity. The dynamic component of the efferent discharge seems to be required for a complete definition of the final steady-state, but maintenance of the state is closely associated with energetically advantageous hysteresis mechanisms. It was concluded that the dynamic phase of efferent activity should play an extremely important role in the central coding of the real movements produced, in particular, by contraction of agonists in the absence of antagonist activation.

Length-dependent potentiation and myosin light chain phosphorylation in rat gastrocnemius muscle

Changes in muscle length affect the degree of staircase potentiation in skeletal muscle, but the mechanism by which this occurs is unknown. In this study, we tested the hypothesis that length-dependent change in staircase is modulated by phosphorylation of the myosin regulatory light chains (RLC), since this is believed to be the main mechanism of potentiation. In situ isometric contractile responses of rat gastrocnemius muscle during 10 s of repetitive stimulation at 10 Hz were analyzed at optimal length (Lo), Lo - 10%, and Lo + 10%. The degree of enhancement of developed tension during 10 s of repetitive stimulation was observed to be length dependent, with increases of 118.5 +/- 7.8, 63.1 +/- 3.9, and 45.6 +/- 4.1% (means +/- SE) at Lo - 10%, Lo, and Lo + 10%, respectively. Staircase was accompanied by increases in the average rate of force development of 105.6 +/- 7.7, 55.6 +/- 4.1, and 37.2 +/- 4.4% for Lo - 10%, Lo, and Lo + 10%, respectively. RLC phosphorylation after 10 s of 10-Hz stimulation was higher than under resting conditions but not different among Lo - 10% (40 +/- 3.5%), Lo (35 +/- 3.5%), and Lo + 10% (41 +/- 3.5%). This study shows that there is a length dependence of staircase potentiation in mammalian skeletal muscle that may not be directly modulated by RLC phosphorylation. Interaction of RLC phosphorylation with length-dependent changes in Ca2+ release and intermyofilament spacing may explain these observations.

Force-length properties in stable skeletal muscle fibers--theoretical considerations

Differences in the force-length (F-L) properties between sarcomeres and fibers have been associated with the supposed unstable nature of the sarcomere F-L relation on the descending limb (i.e. at sarcomere lengths greater than optimal length). Recently, it has been suggested that sarcomere behavior in a fiber is stable during contractions on the descending limb of the F-L relation; therefore, a factor other than sarcomere instability must be responsible for the observed differences in the F-L relations of sarcomeres and fibers. The purpose of this study was to determine theoretically the F-L relation of a muscle fiber when sarcomeres were at a stable, steady-state length. Three models of muscle fibers are presented; each model contains sarcomeres with different mechanical properties which have been observed experimentally. Results of these theoretical considerations demonstrate that sarcomeres with the classic F-L properties as measured by Gordon et al. (J. Physiol. 184, 170-192, 1966) cannot predict the F-L relation exhibited by fibers. The addition of cross-bridge stiffness properties to the classic sarcomere F-L relation still does not explain the differences between the sarcomere and fiber F-L relations. However, if history dependent sarcomere properties are used, the fiber F-L relation exhibits an elongated plateau and greater forces on the descending limb compared to the classic sarcomere F-L relation; and the fiber F-L relation corresponds qualitatively to experimental findings.

Passive tension in cardiac muscle: contribution of collagen, titin, microtubules, and intermediate filaments

The passive tension-sarcomere length relation of rat cardiac muscle was investigated by studying passive (or not activated) single myocytes and trabeculae. The contribution of collagen, titin, microtubules, and intermediate filaments to tension and stiffness was investigated by measuring (1) the effects of KCl/KI extraction on both trabeculae and single myocytes, (2) the effect of trypsin digestion on single myocytes, and (3) the effect of colchicine on single myocytes. It was found that over the working range of sarcomeres in the heart (lengths approximately 1.9-2.2 microns), collagen and titin are the most important contributors to passive tension with titin dominating at the shorter end of the working range and collagen at longer lengths. Microtubules made a modest contribution to passive tension in some cells, but on average their contribution was not significant. Finally, intermediate filaments contributed about 10% to passive tension of trabeculae at sarcomere lengths from approximately 1.9 to 2.1 microns, and their contribution dropped to only a few percent at longer lengths. At physiological sarcomere lengths of the heart, cardiac titin developed much higher tensions (> 20-fold) than did skeletal muscle titin at comparable lengths. This might be related to the finding that cardiac titin has a molecular mass of 2.5 MDa, 0.3-0.5 MDa smaller than titin of mammalian skeletal muscle, which is predicted to result in a much shorter extensible titin segment in the I-band of cardiac muscle. Passive stress plotted versus the strain of the extensible titin segment showed that the stress-strain relationships are similar in cardiac and skeletal muscle. The difference in passive stress between cardiac and skeletal muscle at the sarcomere level predominantly resulted from much higher strains of the I-segment of cardiac titin at a given sarcomere length. By expressing a smaller titin isoform, without changing the properties of the molecule itself, cardiac muscle is able to develop significant levels of passive tension at physiological sarcomere lengths.

Non-uniformity of sarcomere lengths can explain the 'catch-like' effect of arthropod muscle

The 'catch-like' effect, a hysteresis phenomenon in arthropod skeletal muscle contraction thought to be related to the catch of molluscan smooth muscle, was investigated in the closer muscle of the crab Eriphia spinifrons. Several parameters were varied to determine their influence on the catch-like effect. These parameters were (1) the frequency of repetitive stimulation of the slow excitatory neuron, (2) additional stimulation of the inhibitory neuron, (3) the amount of stretch applied to the muscle and (4) the stiffness of the mechano-electrical transducer. The results show that the catch-like effect is not related to the catch of molluscan smooth muscle but rather to the 'residual force enhancement' or 'creep' phenomenon described for vertebrate muscle. A hypothesis for residual force enhancement implies that the increase in force is caused by non-uniformity of sarcomere lengths along the muscle fibre. Based on this hypothesis and the actual force-length relationship of the crab muscle studied, calculations were carried out to determine, if the observed catch-like effect can be explained by such a model. The calculations corroborate the experimental evidence. The catch-like effect of arthropod muscles can thus be explained by the same mechanism responsible for residual force enhancement and creep in vertebrate muscle. A physiological relevance of the catch-like effect in arthropod muscle is inferred.

The effect of lattice spacing change on cross-bridge kinetics in rabbit psoas fibers

The effect of compression on the elementary steps of the cross-bridge cycle was investigated with the sinusoidal analysis technique and ATP hydrolysis rate measurement. The lattice spacing of rabbit psoas muscle fibers was osmotically compressed with a macromolecule, dextran T-500 (0-16%). The effects of MgATP, MgADP, Pi on exponential processes (B), (C), (D), and isometric tension were studied at different dextran concentrations. The experiments were performed at the saturating Ca concentration (pCa 4.5-4.8), 200 mM ionic strength, pH 7.0, and 20 degrees C. Our results show that the fiber width decreased linearly with an increase in the dextran concentration, and the width measurement was perfectly correlated with the lattice spacing measurement using equatorial x-ray diffraction studies. We find that the nucleotide binding steps, the ATP-isomerization step, and the cross-bridge detachment step were minimally affected by the compression. Our results indicate that the rate constant of the reverse power stroke step (k-4) decreases with mild compression (0-6.3% dextran), presumably because of the stabilization of the attached cross-bridges in the AM*DP state. We also found that the rate constant of the power stroke step (k4) decreases with higher compression (> 6.3% dextran), presumably because of increased difficulty in performing the power stroke reaction. Our results further show that the association constant (K5) of phosphate to cross-bridges is not changed with compression. The ATP hydrolysis rate declined almost linearly with an increase in the dextran concentration. This observation indicates that the rate limiting step is also affected by the lattice spacing change so that the associated rate constant (k6) becomes progressively less with compression.

The effect of lattice spacing change on cross-bridge kinetics in chemically skinned rabbit psoas muscle fibers. I. Proportionality between the lattice spacing and the fiber width

Chemically skinned rabbit psoas muscle fibers/bundles were osmotically compressed with a macromolecule dextran T-500 (0-16%, g/100 ml) at 20 degrees C, 200 mM ionic strength, and pH 7.0. The lattice spacing of psoas bundles was measured by equatorial x-ray diffraction studies during relaxation and after rigor induction, and the results were compared with the fiber width measurements by optical microscopy. The purpose of the present study is to determine whether fiber width is a reliable measure of the lattice spacing, and to determine the available spacing for myosin cross-bridges between the thick and thin filaments. We observed that both the lattice spacing and the fiber width decreased with an increase in the dextran concentration during relaxation or after rigor induction, and that the spacing and the fiber width were proportionately related. We further observed that, in the absence of dextran, the lattice spacing (and the fiber width) shrank on a relax-to-rigor transition, whereas in the presence of 16% dextran, the spacing expanded on a relax-to-rigor transition. The cross-over of these plots occurred at the 4-7% dextran concentration. During Ca activation, the fiber width shrank in the absence of dextran, and it slightly expanded in the presence of 14.4% dextran. The degree of expansion was not as large as in the relax-to-rigor transition, and the cross-over occurred at about 11% dextran concentration. We also carried out experiments with dextran T-40 and T-10 to determine the upper limit of the molecular weight that enters the lattice space. We found that the upper limit is about 20 kD.

Effect of small release on force during sarcomere-isometric tetani in frog muscle fibers

We investigated the effect of small shortening imposed on frog muscle fibers during sarcomere-isometric tetani. Sarcomere length was initially kept constant, then slightly shortened (1%-5% of initial length) and clamped again for the remainder of the tetanus. Force level after the shortening was higher than the force level preceding the release. The size of the increase was larger than that predicted by the descending limb of the linear force-length relation. The difference between measured and predicted force levels increased with sarcomere length. At a sarcomere length of 3.2 microns, the force level after the shortening was higher by 50% than the force level expected from the linear descending limb. Dispersion of sarcomere-length within the sampled region was measured by two independent methods: striation imaging and analysis of the intensity profile of the first diffraction order. Sarcomere-length inhomogeneity in the sampled region was too small (standard deviation from the average sarcomere-length was +/- 0.03 microns) to account for the size of the increase in force. We studied the dependence of increase in tetanic force level after small sarcomere-length release on the size, velocity and timing of the release, as well as on initial sarcomere-length. Release size was the major determinant of the amount of increase in force. Release of 20 nm per half sarcomere was sufficient to produce an almost full force increase. Larger releases increased the force only moderately. Over the range studied, release velocity and timing had little or no effect.

A comparison of isometric force, maximum power and isometric heat rate as a function of sarcomere length in mouse skeletal muscle

The isometric force, maximum power and isometric heat rate have been measured at different sarcomere lengths (SL) between 1.40 and 3.63 microns in two types of mouse muscle, soleus and omohyoideus, at 25 degrees C. The SL force relationship is different in the two muscles. At a SL above optimum filament overlap, 2.44 microns in omohyoideus muscles, maximum power declined while isometric force remained high. In soleus muscles this occurred above a SL of 2.33 microns. In parallel experiments, the isometric heat rate declined linearly with increasing SL above 2.33 microns in soleus muscles, while isometric force remained closer to its maximum. At short SL, between 2.33-1.75 microns in soleus and 2.44-2.15 microns in omohyoideus, maximum power remained at or near its maximum value as did heat rate (soleus) while isometric force fell. In both muscles at SL greater than optimum for force development maximum power output (unlike force) is proportional to filament overlap. The variation in heat rate over this SL range can be described as the sum of constant rate and a rate proportional to filament overlap. These observations are compatible with the idea that maximum power and heat rate are less affected by non-uniformities in SL than is force.

Four aspects of creep phenomena in striated muscle

Four aspects of the slow creep of tension and sarcomere lengths observed during fixed-end tetani are studied with computer simulations, using the instantaneous steady-state (adiabatic) approximation. (1) Most aspects of fixed-end creep phenomena can be simulated in the presence of the passive forces which correctly produce initially shortened end sarcomeres. However, the very large maximum tensions observed with fibres of low resting force for sarcomere lengths greater than 3.0 microns cannot be simulated within the adiabatic approximation. (2) Random variations in the passive tension-length curve between different sarcomeres can predict the reported incidence of contracting sarcomeres in the middle of the fibre, while avoiding significant tension creep when a central segment is length-clamped. They can also reverse the velocity of these sarcomeres during creep in fibres with high resting tension, as observed by Altringham and Bottinelli (1985). At sarcomere lengths of greater than or equal to 3.4 microns we find that spatial variations in passive tension strength also contribute to tension creep. (3) Crossbridge fluctuations in active tension have been estimated from the sliding-filament model, and do not contribute significantly to tension creep. (4) The need for inter-sarcomere stiffness or other mechanisms to produce an additional slow rise in tension at long times, and to smooth the sarcomere length distribution, is assessed.

Tension as a function of sarcomere length and velocity of shortening in single skeletal muscle fibres of the frog

1. Simple measurements of muscle tension at fixed fibre or segment length produce a range of length-tension relationships, depending primarily on the duration of the interval between stimulation onset and tension measurement, in contradiction with the simple predictions of current models. This has been explained by non-uniformity in sarcomere lengths, leading to internal motion and, in turn, to increasing tension because the force-velocity relationship has a much greater slope for slow lengthening than for slow shortening. 2. Previous attempts to reduce the effect of internal motion have been focused on decreasing the initial extent of non-uniformity and measuring tension early in a contraction, when non-uniformities are at a minimum. An alternative approach that has not been attempted previously is to reduce the non-linearity of the force-velocity relationship by avoiding the discontinuity in slope at zero velocity. This is accomplished by imposing overall fibre shortening at velocities sufficient to ensure that all sarcomeres are shortening. 3. When the tension maintained during shortening was measured and plotted against sarcomere length for each release velocity used, linear length-tension relationships resulted that extrapolated to a common sarcomere length intercept. This was true whether the release was applied early in the tetanus or near the end of the 'creep phase' of tension rise. These observations were duplicated by computer simulation using a multisarcomere model of a muscle fibre. 4. These results provide strong support for the view that cross-bridges function as independent force generators and for the explanation of the creep phase of fibre or segment isometric tension as being due to internal motion. The results also imply that the force-velocity relationship scales with sarcomere length without changing shape. 5. Using this novel method for obtaining length-tension relationships, the sarcomere length at which active tension fell to zero was found, by extrapolation, to be 3.65 microns in semitendinosus fibres and 3.53 microns in tibialis anterior fibres from the frog (Rana temporaria).

Effect of thin filament length on the force-sarcomere length relation of skeletal muscle

We studied a slow- and a fast-twitch muscle fiber type of the perch that have different thin filament lengths. The force-sarcomere length relations were measured, and it was tested whether their descending limbs were predicted by the cross-bridge theory. To determine the predicted relations, filament lengths were measured by electron microscopy. Measurements were corrected for shrinkage with the use of I-band and H-zone periodicities. Thick filament lengths of the two fiber types were found to be similar (1.63 +/- 0.06 and 1.64 +/- 0.10 microns for slow- and fast-twitch fibers, respectively), whereas the thin filament lengths were clearly different: 1.24 +/- 0.10 microns (n = 86) for the slow-twitch type and 0.94 +/- 0.04 microns (n = 94) for the fast type. The descending limbs of the two fiber types are therefore predicted to be shifted along the sarcomere length axis by approximately 0.6 microns. Sarcomere length was measured on-line by laser diffraction in a single region in the center of the fibers. The passive force-sarcomere strain relation increased much more steeply in the slow-twitch fibers. The descending limb of the active force-sarcomere length relation of fast twitch fibers was linear (r = 0.92), but was found at sarcomere lengths approximately 0.1 micron greater than predicted. The descending limb of the slow-twitch fibers was also linear (r = 0.87) but was now found at sarcomere lengths approximately 0.05 microns less than predicted. The difference in position of the descending limbs of the two fiber types amounted to 0.5 microns, approximately 0.1 micron less than predicted. The difference between measured and predicted descending limbs was statistically insignificant.