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

Reconsidering assumptions in the analysis of muscle fibre cross-sectional area

Cross-sectional area (CSA) is a fundamental variable in characterizing muscle mechanical properties. Typically, the CSA of a single muscle fibre is assessed by measuring either one or two diameters, and assuming the cross-section is either circular or elliptical in shape. However, fibre cross-sections have irregular shapes. The accuracy and precision of CSAs determined using circular and elliptical shape assumptions are unclear for mammalian skinned muscle fibres. Second harmonic generation imaging of skinned rabbit soleus fibres revealed that the circular assumption overstated real CSA by 5.3±25.9% whereas the elliptical assumption overstated real CSA by 2.8±6.9%. A preferred rotational alignment can bias the circular assumption, as real CSA was overstated by 22.1±24.8% when using the larger fibre diameter and understated by 11.4±13% when using the smaller fibre diameter. With 73% lower variable error and reduced bias, the elliptical assumption is superior to the circular assumption when assessing the CSA of skinned mammalian fibres.

A three filament mechanistic model of musculotendon force and impedance

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

Relationships Between Modifiable Risk Factors of Hamstring Strain Injury

ABSTRACT

Ripley, NJ, Comfort, P, and McMahon, JJ. Relationships between modifiable risk factors of hamstring strain injury. J Strength Cond Res 38(3): 510-516, 2024-The aims of this study were to determine whether any relationship exists between eccentric hamstring strength and isokinetic strength imbalances and bicep femoris long head (BF LH ) architecture. Eighteen physically active men (age 24.7 ± 4.3 years, height 181.9 ± 7.2 cm, mass 84.9 ± 12.9 kg) had resting BF LH muscle architecture assessed using ultrasound, with images taken at the midmuscle belly. Measures of isokinetic strength of the knee extensors and flexors involved subjects performing 3 maximal effort repetitions of concentric knee extension and eccentric knee flexion at 60°·s -1 . Good-excellent relative reliability (intraclass correlation coefficient ≥0.86) and low variability (coefficient of variation <10%) were observed for all variables. Relative BF LH fascicle length (FL) demonstrated significant moderate-to-nearly-perfect associations with isokinetic measures identified as hamstring strain injury risk factors ( p < 0.05, r = 0.38-0.92), whereas absolute BF LH FL was not significantly or meaningfully associated with isokinetic measures ( p = 0.07-0.961, r = 0.01-0.30). Relative BF LH FL should be considered when assessing resting BF LH muscle architecture because it is potentially a more appropriate measure of injury risk because of its greater association with strength measures. However, absolute BF LH FL may have a greater usefulness during growth, maturation, and individual proportions.

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.

Impact of stretch on sarcomere length variability in isolated fully relaxed rat cardiac myocytes

The contractility of cardiac muscle is greatly affected by preload via the Frank-Starling mechanism (FSM). It is based on preload-dependent activation of sarcomeres-the elementary contractile units in muscle cells. Recent findings show a natural variability in sarcomere length (SL) in resting cardiomyocytes that, moreover, is altered in an actively contracting myocyte. SL variability may contribute to the FSM, but it remains unresolved whether the change in the SL variability is regulated by activation process per se or simply by changes in cell stretch, i.e., average SL. To separate the roles of activation and SL, we characterized SL variability in isolated, fully relaxed rat ventricular cardiomyocytes (n = 12) subjected to a longitudinal stretch with the carbon fiber (CF) technique. Each cell was tested in three states: without CF attachment (control, no preload), with CF attachment without stretch, and with CF attachment and ~ 10% stretch of initial SL. The cells were imaged by transmitted light microscopy to retrieve and analyze individual SL and SL variability off-line by multiple quantitative measures such as coefficient of variation or median absolute deviation. We found that CF attachment without stretch did not affect the extent of SL variability nor average SL. In stretched myocytes, the averaged SL significantly increased, while the SL variability remained unchanged. This result clearly indicates that the non-uniformity of individual SL is not sensitive to the average SL itself in fully relaxed myocytes. We conclude that SL variability per se does not contribute to the FSM in the heart.

Impact of stretch on sarcomere length variability in isolated fully relaxed rat cardiac myocytes

The contractility of cardiac muscle is greatly affected by preload via the Frank-Starling Mechanism (FSM). It is based on the preload-dependent activation of sarcomeres - the elementary contractile units in muscle cells. Recent findings show a natural variability in sarcomere length (SL) in resting cardiomyocytes that, moreover, is altered in an actively contracting myocyte. SL variability may contribute to the FSM but it remains unresolved whether the change in the SL variability is regulated by activation process per se or simply by changes in cell stretch, i.e. average SL. To separate the roles of activation and SL, we characterized SL variability in isolated fully relaxed rat ventricular cardiomyocytes ( n  = 12) subjected to a longitudinal stretch with the carbon fiber (CF) technique. Each cell was tested in three states: without CF attachment (control, no preload), with CF attachment without stretch, and with CF attachment and ~ 10% stretch of initial SL. The cells were imaged by transmitted light microscopy to retrieve and analyze individual SL and SL variability off-line by multiple quantitative measures like coefficient of variation or median absolute deviation. We found that CF attachment without stretch did not affect the extent of SL variability and averaged SL. In stretched myocytes, the averaged SL significantly increased while the SL variability remained unchanged. This result clearly indicates that the non-uniformity of individual SL is not sensitive to the average SL itself in fully relaxed myocytes. We conclude that SL variability per se does not contribute to the FSM in the heart.

Characterizing residual and passive force enhancements in cardiac myofibrils

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

Cardiomyocyte sarcomere length variability: Membrane fluorescence versus second harmonic generation myosin imaging

Sarcomere length (SL) and its variation along the myofibril strongly regulate integrated coordinated myocyte contraction. It is therefore important to obtain individual SL properties. Optical imaging by confocal fluorescence (for example, using ANEPPS) or transmitted light microscopy is often used for this purpose. However, this allows for the visualization of structures related to Z-disks only. In contrast, second-harmonic generation (SHG) microscopy visualizes A-band sarcomeric structures directly. Here, we compared averaged SL and its variability in isolated relaxed rat cardiomyocytes by imaging with ANEPPS and SHG. We found that SL variability, evaluated by several absolute and relative measures, is two times smaller using SHG vs. ANEPPS, while both optical methods give the same average (median) SL. We conclude that optical methods with similar optical spatial resolution provide valid estimations of average SL, but the use of SHG microscopy for visualization of sarcomeric A-bands may be the "gold standard" for evaluation of SL variability due to the absence of optical interference between the sarcomere center and non-sarcomeric structures. This contrasts with sarcomere edges where t-tubules may not consistently colocalize to Z-disks. The use of SHG microscopy instead of fluorescent imaging can be a prospective tool to map sarcomere variability both in vitro and in vivo conditions and to reveal its role in the functional behavior of living myocardium.

Numerical instability of Hill-type muscle models

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

What Can We Learn from Single Sarcomere and Myofibril Preparations?

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

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

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

Sarcomere length measurement reliability in single myofibrils

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

Evidence for Muscle Cell-Based Mechanisms of Enhanced Performance in Stretch-Shortening Cycle in Skeletal Muscle

Force attained during concentric contraction (active shortening) is transiently enhanced following eccentric contraction (active stretch) in skeletal muscle. This phenomenon is called stretch-shortening cycle (SSC) effect. Since many human movements contain combinations of eccentric and concentric contractions, a better understanding of the mechanisms underlying the SSC effect would be useful for improving physical performance, optimizing human movement efficiency, and providing an understanding of fundamental mechanism of muscle force control. Currently, the most common mechanisms proposed for the SSC effect are (i) stretch-reflex activation and (ii) storage of energy in tendons. However, abundant SSC effects have been observed in single fiber preparations where stretch-reflex activation is eliminated and storage of energy in tendons is minimal at best. Therefore, it seems prudent to hypothesize that factor(s) other than stretch-reflex activation and energy storage in tendons contribute to the SSC effect. In this brief review, we focus on possible candidate mechanisms for the SSC effect, that is, pre-activation, cross-bridge kinetics, and residual force enhancement (RFE) obtained in experimental preparations that exclude/control the influence of stretch-reflex activation and energy storage in tendons. Recent evidence supports the contribution of these factors to the mechanism of SSCs, and suggests that the extent of their contribution varies depending on the contractile conditions. Evidence for and against alternative mechanisms are introduced and discussed, and unresolved problems are mentioned for inspiring future studies in this field of research.

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

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

Residual and passive force enhancement in skinned cardiac fibre bundles

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

The influence of training-induced sarcomerogenesis on the history dependence of force

The increase or decrease in isometric force following active muscle lengthening or shortening, relative to a reference isometric contraction at the same muscle length and level of activation, are referred to as residual force enhancement (rFE) and residual force depression (rFD), respectively. The purpose of these experiments was to investigate the trainability of rFE and rFD on the basis of serial sarcomere number (SSN) alterations to history-dependent force properties. Maximal rFE/rFD measures from the soleus and extensor digitorum longus (EDL) of rats were compared after 4 weeks of uphill or downhill running with a no-running control. SSN adapted to the training: soleus SSN was greater with downhill compared with uphill running, while EDL demonstrated a trend towards more SSN for downhill compared with no running. In contrast, rFE and rFD did not differ across training groups for either muscle. As such, it appears that training-induced SSN adaptations do not modify rFE or rFD at the whole-muscle level.

Sarcomere Lengths Become More Uniform Over Time in Intact Muscle-Tendon Unit During Isometric Contractions

The seemingly uniform striation pattern of skeletal muscles, quantified in terms of sarcomere lengths (SLs), is inherently non-uniform across all hierarchical levels. The SL non-uniformity theory has been used to explain the force creep in isometric contractions, force depression following shortening of activated muscle, and residual force enhancement following lengthening of activated muscle. Our understanding of sarcomere contraction dynamics has been derived primarily from in vitro experiments using regular bright-field light microscopy or laser diffraction techniques to measure striation/diffraction patterns in isolated muscle fibers or myofibrils. However, the collagenous extracellular matrices present around the muscle fibers, as well as the complex architecture in the whole muscles may lead to different contraction dynamics of sarcomeres than seen in the in vitro studies. Here, we used multi-photon excitation microscopy to visualize in situ individual sarcomeres in intact muscle tendon units (MTUs) of mouse tibialis anterior (TA), and quantified the temporal changes of SL distribution as a function of SLs in relaxed and maximally activated muscles for quasi-steady state, fixed-end isometric conditions. The corresponding muscle forces were simultaneously measured using a force transducer. We found that SL non-uniformity, quantified by the coefficient of variation (CV) of SLs, decreased at a rate of 1.9–3.1%/s in the activated muscles, but remained constant in the relaxed muscles. The force loss during the quasi-steady state likely did not play a role in the decrease of SL non-uniformity, as similar force losses were found in the activated and relaxed muscles, but the CV of SLs in the relaxed muscles underwent negligible change over time. We conclude that sarcomeres in the mid-belly of maximally contracting whole muscles constantly re-organize their lengths into a more uniform pattern over time. The molecular mechanisms accounting for SL non-uniformity appear to differ in active and passive muscles, and need further elucidation, as do the functional implications of the SL non-uniformity.

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.

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

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

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

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

Passive force enhancement in striated muscle

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

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.

Modifiability of the history dependence of force through chronic eccentric and concentric biased resistance training

The increase and decrease in steady-state isometric force following active muscle lengthening and shortening are referred to as residual force enhancement (RFE) and force depression (FD), respectively. The RFE and FD states are associated with decreased (activation reduction; AR) and increased (activation increase; AI) neuromuscular activity, respectively. Although the mechanisms have been discussed over the last 60 years, no studies have systematically investigated the modifiability of RFE and FD with training. The purpose of the present study was to determine whether RFE and FD could be modulated through eccentric and concentric biased resistance training. Fifteen healthy young adult men (age: 24 ± 2 yr, weight: 77 ± 8 kg, height: 178 ± 5 cm) underwent 4 wk of isokinetic dorsiflexion training, in which one leg was trained eccentrically (-25°/s) and the other concentrically (+25°/s) over a 50° ankle excursion. Maximal and submaximal (40% maximum voluntary contraction) steady-state isometric torque and EMG values following active lengthening and shortening were compared to purely isometric values at the same joint angles and torque levels. Residual torque enhancement (rTE) decreased by ~36% after eccentric training ( P < 0.05) and increased by ~89% after concentric training ( P < 0.05), whereas residual torque depression (rTD), AR, AI, and optimal angles for torque production were not significantly altered by resistance training ( P ≥ 0.05). It appears that rTE, but not rTD, for the human ankle dorsiflexors is differentially modifiable through contraction type-dependent resistance training. NEW & NOTEWORTHY The history dependence of force production is a property of muscle unexplained by current cross bridge and sliding filament theories. Whether a muscle is actively lengthened (residual force enhancement; RFE) or shortened (force depression) to a given length, the isometric force should be equal to a purely isometric contraction-but it is not! In this study we show that eccentric training decreased RFE, whereas concentric training increased RFE and converted all nonresponders (i.e., not exhibiting RFE) into responders.

Single sarcomere contraction dynamics in a whole muscle

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

The multiple roles of titin in muscle contraction and force production

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

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

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

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

PURPOSE

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

METHODS

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

RESULTS

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

CONCLUSION

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

Why are muscles strong, and why do they require little energy in eccentric action?

It is well acknowledged that muscles that are elongated while activated (i.e., eccentric muscle action) are stronger and require less energy (per unit of force) than muscles that are shortening (i.e., concentric contraction) or that remain at a constant length (i.e., isometric contraction). Although the cross-bridge theory of muscle contraction provides a good explanation for the increase in force in active muscle lengthening, it does not explain the residual increase in force following active lengthening (residual force enhancement), or except with additional assumptions, the reduced metabolic requirement of muscle during and following active stretch. Aside from the cross-bridge theory, 2 other primary explanations for the mechanical properties of actively stretched muscles have emerged: (1) the so-called sarcomere length nonuniformity theory and (2) the engagement of a passive structural element theory. In this article, these theories are discussed, and it is shown that the last of these-the engagement of a passive structural element in eccentric muscle action-offers a simple and complete explanation for many hitherto unexplained observations in actively lengthening muscle. Although by no means fully proven, the theory has great appeal for its simplicity and beauty, and even if over time it is shown to be wrong, it nevertheless forms a useful framework for direct hypothesis testing.

Does partial titin degradation affect sarcomere length nonuniformities and force in active and passive myofibrils?

The aim of this study was to determine the role of titin in preventing the development of sarcomere length nonuniformities following activation and after active and passive stretch by determining the effect of partial titin degradation on sarcomere length nonuniformities and force in passive and active myofibrils. Selective partial titin degradation was performed using a low dose of trypsin. Myofibrils were set at a sarcomere length of 2.4 µm and then passively stretched to sarcomere lengths of 3.4 and 4.4 µm. In the active condition, myofibrils were set at a sarcomere length of 2.8 µm, activated, and actively stretched by 1 µm/sarcomere. The extent of sarcomere length nonuniformities was calculated for each sarcomere as the absolute difference between sarcomere length and the mean sarcomere length of the myofibril. Our main finding is that partial titin degradation does not increase sarcomere length nonuniformities after passive stretch and activation compared with when titin is intact but increases the extent of sarcomere length nonuniformities after active stretch. Furthermore, when titin was partially degraded, active and passive stresses were substantially reduced. These results suggest that titin plays a crucial role in actively stretched myofibrils and is likely involved in active and passive force production.

In Vivo Sarcomere Lengths Become More Non-uniform upon Activation in Intact Whole Muscle

The sarcomere force-length relationship has been extensively used to predict muscle force potential. The common practice is to measure the mean sarcomere length (SL) in a relaxed muscle at a single location and at a given length, and this mean SL is assumed to represent the SLs at other locations across the muscle. However, in a previous study, we found that SLs are highly non-uniform across an intact passive muscle. Moreover, SL non-uniformity increases during activation in single myofibril experiments. Myofibrils lack some structural proteins that comprise an intact muscle, and therefore, the increased SL dispersion upon activation seen in myofibrils may not occur in intact whole muscle. The objectives of the current study were (i) to measure the distribution of SLs in an activated intact muscle; and (ii) to assess the feasibility of using the mean SL measured at a specific location of the muscle to predict muscle force. Using state-of-the-art multi-photon microscopy and a miniature tendon force transducer, in vivo sarcomeres in the mouse tibialis anterior were imaged simultaneously with muscle force during isometric tetanic contractions. We found that in vivo SL dispersion increased substantially during activation and reached average differences of ~1.0 μm. These differences in SL are associated with theoretical force differences of 70-100% of the maximal isometric force. Furthermore, SLs measured at a single location in the passive muscle were poor predictors of active force potential. Although mean SLs in the activated muscle were better predictors of force potential, predicted forces still differed by as much as 35% from the experimentally measured maximal isometric forces.

Skeletal muscle mechanics: questions, problems and possible solutions

Skeletal muscle mechanics have been studied ever since people have shown an interest in human movement. However, our understanding of muscle contraction and muscle mechanical properties has changed fundamentally with the discovery of the sliding filament theory in 1954 and associated cross-bridge theory in 1957. Nevertheless, experimental evidence suggests that our knowledge of the mechanisms of contraction is far from complete, and muscle properties and muscle function in human movement remain largely unknown.In this manuscript, I am trying to identify some of the crucial challenges we are faced with in muscle mechanics, offer possible solutions to questions, and identify problems that might be worthwhile exploring in the future. Since it is impossible to tackle all (worthwhile) problems in a single manuscript, I identified three problems that are controversial, important, and close to my heart. They may be identified as follows: (i) mechanisms of muscle contraction, (ii) in vivo whole muscle mechanics and properties, and (iii) force-sharing among synergistic muscles. These topics are fundamental to our understanding of human movement and movement control, and they contain a series of unknowns and challenges to be explored in the future.It is my hope that this paper may serve as an inspiration for some, may challenge current beliefs in selected areas, tackle important problems in the area of muscle mechanics, physiology and movement control, and may guide and focus some of the thinking of future muscle mechanics research.

In vivo Sarcomere Lengths and Sarcomere Elongations Are Not Uniform across an Intact Muscle

Sarcomere lengths have been a crucial outcome measure for understanding and explaining basic muscle properties and muscle function. Sarcomere lengths for a given muscle are typically measured at a single spot, often in the mid-belly of the muscle, and at a given muscle length. It is then assumed implicitly that the sarcomere length measured at this single spot represents the sarcomere lengths at other locations within the muscle, and force-length, force-velocity, and power-velocity properties of muscles are often implied based on these single sarcomere length measurements. Although, intuitively appealing, this assumption is yet to be supported by systematic evidence. The objective of this study was to measure sarcomere lengths at defined locations along and across an intact muscle, at different muscle lengths. Using second harmonic generation (SHG) imaging technique, sarcomere patterns in passive mouse tibialis anterior (TA) were imaged in a non-contact manner at five selected locations (“proximal,” “distal,” “middle,” “medial,” and “lateral” TA sites) and at three different lengths encompassing the anatomical range of motion of the TA. We showed that sarcomere lengths varied substantially within small regions of the muscle and also for different sites across the entire TA. Also, sarcomere elongations with muscle lengthening were non-uniform across the muscle, with the highest sarcomere stretches occurring near the myotendinous junction. We conclude that muscle mechanics derived from sarcomere length measured from a small region of a muscle may not well-represent the sarcomere length and associated functional properties of the entire muscle.