Sarcomere Length Non-uniformities Research Articles

Is Drosophila indirect flight muscle a good model to investigate residual force enhancement with minimal sarcomere length non-uniformities?

Is Drosophila indirect flight muscle a good model to investigate residual force enhancement with minimal sarcomere length non-uniformities?

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 3.6µm. 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.

An increase in force after stretch of diaphragm fibers and myofibrils is accompanied by an increase in sarcomere length nonuniformities and Ca2+ sensitivity.

When muscle fibers from limb muscles are stretched while activated, the force increases to a steady-state level that is higher than that produced during isometric contractions at a corresponding sarcomere length, a phenomenon known as residual force enhancement (RFE). The mechanisms responsible for the RFE are an increased stiffness of titin molecules that may lead to an increased Ca2+ sensitivity of the contractile apparatus, and the development of sarcomere length nonuniformities. RFE is not observed in cardiac myofibrils, which makes this phenomenon specific to certain preparations. The aim of this study was to investigate whether the RFE is present in the diaphragm, and its potential association with an increased Ca2+ sensitivity and the development of sarcomere length nonuniformities. We used two preparations: single intact fibers and myofibrils isolated from the diaphragm of mice. We investigated RFE in a variety of lengths across the force-length relationship. RFE was observed in both preparations at all lengths investigated and was larger with increasing magnitudes of stretch. RFE was accompanied by an increased Ca2+ sensitivity as shown by a change in the force-pCa2+ curve, and increased sarcomere length nonuniformities. Therefore, RFE is a phenomenon commonly observed in skeletal muscles, with mechanisms that are similar across preparations.

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.

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.

On sarcomere length stability during isometric contractions before and after active stretching.

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 muscle 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 whereas 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 with 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 with the corresponding isometric reference contraction, it appears unlikely that either SL instability or SL non-uniformity contribute to the residual force enhancement property of skeletal muscle.

Single sarcomere contraction dynamics in a whole muscle

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

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.

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.

Increased Non-Uniformity in In Vivo Sarcomere Length during a Tetanic Contraction

IntroductionThe maximal, steady-state, isometric force produced by a muscle depends on its sarcomere length (SL). In previous studies in single myofibrils, it was found that sarcomere length non-uniformities increased during activation and force production. However, single myofibrils lack much of the structural proteins that provide stability to entire muscles, thus the observed SL non-uniformities in myofibrils might not occur in whole muscles. This study was aimed at investigating the change in SL distribution during tetanic contractions in an intact muscles of live mice.MethodsMice were anaesthetized using isoflurane. The proximal femur and foot of the left lower limb were clamped. The skin over the left tibialis anterior (TA) muscle was opened and stretched to form a bath for a saline solution that allowed for imaging using a water-immersion objective. The TA was supra-maximally stimulated using a nerve cuff electrode on the sciatic nerve using 0.1ms square wave pulses at 60Hz for 1s. SL were measured using second harmonic generation microscopy for the fully stretched TA. Measurements were made for the passive and activated TA over an area of 160x3 µm2 in the mid-belly of the muscle.ResultsSLs for the passive muscle were 2.53±0.06µm (mean±sd). During contraction, sarcomeres shortened by ∼12% to 2.24±0.12µm. The coefficient of variation of the SLs doubled from 2.4% at rest to 5.2% during tetanic contractions. The range of SLs increased from the passive (2.36-2.71µm) to the active state (1.85-2.62µm).ConclusionSL non-uniformity doubled during muscle activation and differed by more than 0.7 µm. The functional implications of these massive SL non-uniformities need to be explored, and the common practice of representing muscles with a single SL value needs to be reconsidered.

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

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

Sarcomere Length and Passive Sarcomere Lengthening are Location-Dependent in Live Mouse Tibialis Anterior Muscle

Introduction The force produced by muscles depends on sarcomere length (SL). Typically, the SL measured at a single site is taken as representing the SLs of the entire muscle. However, there is little evidence to support that notion. The purpose of this study was to investigate the distribution of in vivo SL along a muscle and to measure sarcomere elongations resulting from passive muscle lengthening. Methods C57BL/6 mice (n=3) were anaesthetized using isoflurane. The skin over the left lower limb was surgically opened to expose the tibialis anterior (TA) muscle. The left knee and the left foot were pinned in a custom-made water chamber to allow imaging of SL using a water-immersion objective. The anisotropic bands (A-band) of the TA were imaged at three anatomical locations (proximal, middle, and distal) by second harmonic generation microscopy with the ankle being fully dorsiflexed (60° relative to tibia) and fully plantarflexed (180°). Results Locally, SL distributions were relatively uniform with a coefficient of variation ranging from 4.2 - 6.6%. However, sarcomere lengths were highly non-uniform along the TA. When fully dorsiflexed, SLs were 2.08±0.09, 2.25±0.08 and 2.16±0.04 µm (mean ± standard deviation) at the proximal, middle and distal sites, respectively. Going to full plantarflexion, the mean sarcomere elongations were also non-uniform. The distal muscle showed the greatest sarcomere elongations (25.1±3.0%), followed by the mid-section (8.6±2.63%) and proximal section (5.6±5.2%). Conclusion We conclude from this study that SLs in mouse TA are location-dependent and that passive elongation of the TA causes further SL non-uniformities along the muscle. Further research is required for active muscles under dynamic conditions to determine to what degree SL varies within a muscle for these conditions.

Eccentric contraction: unraveling mechanisms of force enhancement and energy conservation.

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

Residual force depression in single sarcomeres is abolished by MgADP-induced activation.

The mechanisms behind the shortening-induced force depression commonly observed in skeletal muscles remain unclear, but have been associated with sarcomere length non-uniformity and/or crossbridge inhibition. The purpose of this study was twofold: (i) to evaluate if force depression is present in isolated single sarcomeres, a preparation that eliminates sarcomere length non-uniformities and (ii) to evaluate if force depression is inhibited when single sarcomeres are activated with MgADP, which biases crossbridges into a strongly-bound state. Single sarcomeres (n = 16) were isolated from rabbit psoas myofibrils using two micro-needles (one compliant, one rigid), piercing the sarcomere externally adjacent to the Z-lines. The sarcomeres were contracted isometrically and subsequently shortened, in both Ca2+- and MgADP-activating solutions. Shortening in Ca2+-activated samples resulted in a 27.44 ± 9.04% force depression when compared to isometric contractions produced at similar final sarcomere lengths (P < 0.001). There was no force depression in MgADP-activated sarcomeres (force depression = −1.79 ± 9.69%, P = 0.435). These results suggest that force depression is a sarcomeric property, and that is associated with an inhibition of myosin-actin interactions.

Shortening-Induced Force Depression in Single Sarcomeres is Abolished by MgADP-Activation

The mechanisms behind the shortening-induced force depression (FD) commonly observed in skeletal muscles remain unclear, but have been associated with sarcomere length non-uniformity and/or cross-bridge inhibition. The purpose of this study was twofold: (i) to evaluate if FD is present in isolated single sarcomeres, a preparation that eliminates sarcomere length non-uniformities and (ii) to evaluate if FD is inhibited when single sarcomeres are activated with MgADP, which biases cross-bridges into a strongly-bound state. Single sarcomeres (n=16) were isolated from rabbit psoas myofibrils using two micro-needles (one compliant, one rigid), piercing the sarcomere externally adjacent to the Z-lines. The sarcomeres were contracted isometrically and subsequently shortened, in both Ca2+- and MgADP-activating solutions. Shortening in Ca2+-activated samples resulted in a 27.44% ± 9.04% force depression when compared to isometric contractions produced at similar final sarcomere lengths (P > 0.001). There was no FD in MgADP-activated sarcomeres (FD = −1.79% ± 9.69%, P = 0.435). These results suggest that FD is a sarcomeric property, and that is associated with an inhibition of myosin-actin interactions.

An Examination of Sarcomere Length Non-Uniformities in Actively Stretched Muscle Myofibrils

Residual force enhancement (RFE) is a characteristic of skeletal muscle describing the increase in force exhibited following an active stretch on the descending limb of the force-length relationship, compared to the force of an isometric contraction at the final length. It has previously been argued that RFE is a result of instable sarcomeres on the descending limb, causing longer, weaker sarcomeres to lengthen to a greater extent than shorter, stronger sarcomeres, when a myofibril is actively stretched. If this were the mechanism of RFE, then sarcomeres should become more non-uniform in length after an active stretch. The purpose of this study was to investigate length non-uniformities between sarcomeres within a myofibril in isometric contractions pre- and post-active stretch. We hypothesized that sarcomere lengths would be less uniform in the post-stretch condition. Rabbit psoas muscle myofibrils were stretched passively to an average sarcomere length of 3.2 μm. The myofibrils were then activated. Five seconds after full activation, myofibrils were rapidly shortened to an average sarcomere length of 2.4 μm, held at that length for ten seconds and then stretched back to 3.2 μm. Individual sarcomere lengths were then determined during the initial isometric contraction and again following the active stretch. Standard deviations of sarcomere lengths were compared to analyze non-uniformity. Preliminary results gave normalized sarcomere length standard deviations of 5.7 % and 10.2 % for the initial isometric contraction and following active stretch respectively (103 % RFE). This supports the hypothesis that sarcomere lengths might be less uniform after active stretch; however, further testing will increase the sample size to 20. This will allow for a more general idea of the development of sarcomere length non-uniformities following active stretch and might provide additional insight into the mechanism of RFE.

Residual force enhancement: the neglected property of striated muscle contraction

As pointed out by Dr Edman in his thoughtful review (Edman, 2012), residual force enhancement in striated muscles has been observed consistently over the past half-century, its properties have been well described, and its lack of explanation within the framework of the cross-bridge theory has been acknowledged. However, and this is the topic of Dr Edman's review, the primary mechanism producing force enhancement remains a matter of scientific debate. On the one hand, there is the classic explanation of the development of non-uniformities that develop upon muscle stretch; on the other hand, there is the idea of the ‘engagement’ of a passive structural element upon activation that produces the enhanced force following active muscle stretching. In his review, Dr Edman favours the idea that residual force enhancement is primarily a consequence of (half-) sarcomere length non-uniformities (e.g. [residual force enhancement]…‘is ultimately based on non-uniform sarcomere behaviour with the result that populations of sarcomeres, or half-sarcomeres, actually acquire a greater amount of filament overlap than expected from the overall sarcomere length recorded after stretch’; Edman, 2012). Here, we would like to make the argument that ‘the role of a passive structural element’, the second idea mentioned above, should not be dismissed prematurely. First, Dr Edman mentions the advantages of single fibre preparations over myofibril preparations, and all the points he makes are perfectly valid. However, the great advantage of myofibrils over single fibre preparations is that single myofibrils consist of serially arranged sarcomeres. Therefore, the forces measured at the ends of a myofibril reflect directly the force in each sarcomere. Furthermore, the instantaneous lengths of each and all sarcomeres of a myofibril can easily be quantified. In contrast, in a single fibre, sarcomeres are connected partly in parallel and partly in series forming a highly redundant network of force transmission and individual sarcomere lengths cannot be measured, thus making any inferences to sarcomere dynamics highly suspect. Regarding the involvement of a passive structural element in force enhancement, Dr Edman makes several statements that we do not agree with. For example, he states that: ‘It seems quite clear, however, that the phenomenon “force enhancement after stretch” is entirely limited to the active period of the fibre. It disappears completely as the fibre relaxes after the stimulation period.’ (Edman, 2012). This statement ignores the well-described passive force enhancement observed following active stretches of muscles (e.g. Herzog & Leonard, 2002), fibres (e.g. Lee et al. 2007) and myofibrils (e.g. Joumaa et al. 2007, 2008) which persists long after muscle stimulation has ceased. Dr Edman also mentions that: ‘Another strong indication that strain of elastic elements does not by itself determine the measured force is given by the fact that the force recorded during stretch is quite independent of the amplitude of the stretch ramp.’ (Edman, 2012). Again, we disagree; there is ample evidence that the forces during stretch increase with increasing stretch magnitudes, and that the forces at the end-length following stretches of different magnitudes are well correlated with the residual force enhancement (e.g. Bullimore et al. 2007). The sarcomere length non-uniformity theory, favoured in Dr Edman's review, also provides testable predictions. Arguably the most important of these is that a muscle cannot produce enhanced force that exceeds the maximal isometric force at optimal length (Edman et al. 1982). However, there are numerous studies showing peak force enhancements well in excess of 10% above the plateau forces (Lee & Herzog, 2008), and most importantly, force enhancement in single sarcomeres has been shown to exceed 35% on average, with peak values exceeding 50%, above the plateau of the force–length relationship (Leonard et al. 2010). These values cannot be attributed to random fluctuations or artifacts. In summary, we agree with Dr Edman that the mechanisms underlying residual force enhancement remain unknown. However, inferring single sarcomere mechanics from fibre experiments appears impossible. Myofibrils offer an elegant preparation to measure the mechanics of isolated sarcomeres directly and accurately, and have revealed enhanced forces exceeding 50% of the maximal isometric forces in single sarcomeres (Leonard et al. 2010). These results cannot be explained with increased myofilament overlap due to (half-) sarcomere length non-uniformities, but are consistent with the idea of the ‘engagement’ of a passive structural element upon activation. In agreement with Dr Edman, we speculate that titin might play a crucial role in this ‘passive’ force regulation (Herzog et al. 2012).

Force enhancement following stretch in a single sarcomere

It has been accepted for half a century that, for a given level of activation, the steady-state isometric force of a muscle sarcomere depends exclusively on the amount of overlap between the contractile filaments actin and myosin, or equivalently sarcomere length (Gordon AM et al., J Physiol 184: 170-192, 1966). Moreover, according to the generally accepted paradigm of muscle contraction, the cross-bridge theory (Huxley AF, Prog Biophys Biophys Chem 7: 255-318, 1957), this steady-state isometric sarcomere force is independent of the muscle's contractile history (Huxley AF, Prog Biophys Biophys Chem 7: 255-318, 1957; Walcott S and Herzog W, Math Biosci 216: 172-186, 2008); i.e., it is independent of whether a muscle is held at a constant length before and during the contraction or whether the muscle is shortened or lengthened to the same constant length. This, however, is not the case, as muscles and single fibers that are stretched show greatly increased steady-state isometric forces compared with preparations that are held at a constant length (Abbott BC and Aubert XM, J Physiol 117: 77-86, 1952; De Ruiter CJ et al., J Physiol 526.3: 671-681, 2000; Edman KAP et al., J Physiol 281: 139-155, 1978; Edman KAP et al., J Gen Physiol 80: 769-784, 1982; Edman KAP and Tsuchiya T, J Physiol 490.1: 191-205, 1996). This so-called "residual force enhancement" (Edman KAP et al., J Gen Physiol 80: 769-784, 1982) offers a perplexing puzzle for muscle physiologists. Many theories have been advanced to address the discrepancy between prediction and observation with the most popular and accepted being the sarcomere length nonuniformity theory (Morgan DL, Biophys J 57: 209-221, 1990), which explains the residual force enhancement with the development of large nonuniformities in sarcomere lengths during muscle stretching. Here, we performed experiments in mechanically isolated sarcomeres and observed that the residual force enhancement following active stretching is preserved. Since our preparation utilizes a single sarcomere, a redistribution of the length of neighboring sarcomeres to produce the higher force following stretch is, by design, precluded. Furthermore, the enhanced forces in the single sarcomeres always exceed the isometric forces on the plateau of the force-length relationship, thereby eliminating the possibility that our result might have been obtained because of a redistribution of half-sarcomere lengths. Since force enhancement in single myofibrils has been associated with actin-titin interactions (Kulke M et al., Circ Res 89: 874-881, 2001; Li Q et al., Biophys J 69: 1508-1518, 1995) and calcium binding to titin (Joumaa V et al., Am J Physiol Cell Physiol 294: C74-C78, 2008; Labeit D et al., Proc Natl Acad Sci USA 100: 13716-13721, 2003), titin may regulate the sarcomeric force enhancement observed here.