Sensitivity of muscle force response of a two-state cross-bridge model to variations in model parameters.

Muscle models based on the cross-bridge theory (Huxley-type models) are frequently used to calculate muscle forces for different contractile conditions. Dynamic and nonlinear characteristics of muscle forces produced during isometric, concentric, and eccentric contractions can be represented to a limited extent by using cross-bridge models. Cross-bridge models use various parameters to simulate force responses. However, there remains uncertainty as to the effect of changes in model parameters on force responses in Huxley-type models. In this study, we aimed to analyze the sensitivity of force response to changes in model parameters in Huxley-type models. A two-state Huxley model was used to determine the cross-bridge attachment distributions and forces for shortening and lengthening contractions. Sensitivity of muscle force to changes in attachment rate, detachment rate, and cross-bridge binding distance was examined within a range of ±20% of the nominal value using Monte Carlo simulations. Changes in the detachment rate influenced the predicted muscle forces the most for lengthening contractions, while changes in attachment rate and binding distance affected forces the most for shortening contractions. These results show once more the asymmetry between shortening and lengthening contractions and the difficulty in using a single cross-bridge model to predict forces during shortening and elongation accurately.

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.

Effect of Vastus Medialis Loss on Rabbit Patellofemoral Joint Contact Pressure Distribution.

Vastus medialis (VM) weakness is thought to alter patellar tracking, thereby changing the loading of the patellofemoral joint (PFJ), resulting in patellofemoral pain. However, it is challenging to measure VM force and weakness in human studies, nor is it possible to measure the associated mechanical changes in the PFJ. To obtain fundamental insight into VM weakness and its effects on PFJ mechanics, the authors determined PFJ loading in the presence of experimentally simulated VM weakness. Skeletally mature New Zealand White rabbits were used (n = 6), and the vastus lateralis, VM, and rectus femoris were stimulated individually through 3 custom-built nerve cuff electrodes. Muscle torque and PFJ pressure distribution were measured while activating all muscles simultaneously, or when the vastus lateralis and rectus femoris were activated, while VM was not, to simulate a quadriceps muscle strength imbalance. For a given muscular joint torque, peak pressures were greater and joint contact areas were smaller when simulating VM weakness compared with the condition where all muscles were activated simultaneously. The results in the rabbit model support that VM weakness results in altered PFJ loading, which may cause patellofemoral pain, often associated with a strength imbalance of the knee extensor muscle group.

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.

Differences in titin segmental elongation between passive and active stretch in skeletal muscle.

Since the 1950s, muscle contraction has been explained using a two-filament system in which actin and myosin exclusively dictate active force in muscle sarcomeres. Decades later, a third filament called titin was discovered. This titin filament has recently been identified as an important regulator of active force, but has yet to be incorporated into contemporary theories of muscle contraction. When sarcomeres are actively stretched, a substantial and rapid increase in force occurs, which has been suggested to arise in part from titin-actin binding that is absent in passively stretched sarcomeres. However, there is currently no direct evidence for such binding within muscle sarcomeres. Therefore, we aimed to determine whether titin binds to actin in actively but not in passively stretched sarcomeres by observing length changes of proximal and distal titin segments in the presence and absence of calcium. We labeled I-band titin with fluorescent F146 antibody in rabbit psoas myofibrils and tracked segmental elongations during passive (no calcium) and active (high calcium) stretch. Without calcium, proximal and distal segments of titin elongated as expected based on their free spring properties. In contrast, active stretch differed statistically from passive stretch, demonstrating that calcium activation increases titin segment stiffness, but not in an actin-dependent manner. The consistent elongation of the proximal segment was contrary to what was expected if titin's proximal segment was attached to actin. This rapid calcium-dependent change in titin stiffness likely contributes to active muscle force regulation in addition to actin and myosin.

Titin force enhancement following active stretch of skinned skeletal muscle fibres.

In actively stretched skeletal muscle sarcomeres, titin-based force is enhanced, increasing the stiffness of active sarcomeres. Titin force enhancement in sarcomeres is vastly reduced in mdm, a genetic mutation with a deletion in titin. Whether loss of titin force enhancement is associated with compensatory mechanisms at higher structural levels of organization, such as single fibres or entire muscles, is unclear. The aim of this study was to determine whether mechanical deficiencies in titin force enhancement are also observed at the fibre level, and whether mechanisms compensate for the loss of titin force enhancement. Single skinned fibres from control and mutant mice were stretched actively and passively beyond filament overlap to observe titin-based force. Mutant fibres generated lower contractile stress (force divided by cross-sectional area) than control fibres. Titin force enhancement was observed in control fibres stretched beyond filament overlap, but was overshadowed in mutant fibres by an abundance of collagen and high variability in mechanics. However, titin force enhancement could be measured in all control fibres and most mutant fibres following short stretches, accounting for ∼25% of the total stress following active stretch. Our results show that the partial loss of titin force enhancement in myofibrils is not preserved in all mutant fibres and this mutation likely affects fibres differentially within a muscle. An increase in collagen helps to reestablish total force at long sarcomere lengths with the loss in titin force enhancement in some mutant fibres, increasing the overall strength of mutant fibres.

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.

Muscle strategies for leg extensions on a "Reformer" apparatus.

Considering the kinematics of leg extensions performed on a Reformer apparatus, one would expect high activation of hip and knee extensor muscle groups. However, because of the bi-articular nature of some lower limb muscles, and the possibility to vary the direction of force application on the Reformer bar, muscles can be coordinated theoretically in a variety of ways and still achieve the desired outcome. Hence, the aim of this study was to determine the knee and hip moments during leg extensions performed on the Reformer apparatus and to estimate the forces in individual muscles crossing these joints using static optimization. Fifteen subjects performed leg extensions exercises on the Reformer apparatus using an individually chosen resistance. To our big surprise, we found that subjects performed the exercise using two conceptually different strategies (i) the first group used simultaneous hip and knee extension moments, (ii) while the second group used simultaneous hip flexion and knee extension moments to perform the exercise. These different strategies were achieved by changing the direction of the resultant force applied by the subject's feet on the Reformer bar. While leg extensions on the Reformer apparatus have been thought to strengthen the hip and knee extensors muscles, our results demonstrate that patients can perform the exercise in a different and unexpected way. In order to control the hip and knee moments and achieve the desired outcome of the exercise, the direction of force application on the Reformer bar must be controlled carefully.

Titin force is enhanced in actively stretched skeletal muscle.

The sliding filament theory of muscle contraction is widely accepted as the means by which muscles generate force during activation. Within the constraints of this theory, isometric, steady-state force produced during muscle activation is proportional to the amount of filament overlap. Previous studies from our laboratory demonstrated enhanced titin-based force in myofibrils that were actively stretched to lengths which exceeded filament overlap. This observation cannot be explained by the sliding filament theory. The aim of the present study was to further investigate the enhanced state of titin during active stretch. Specifically, we confirm that this enhanced state of force is observed in a mouse model and quantify the contribution of calcium to this force. Titin-based force was increased by up to four times that of passive force during active stretch of isolated myofibrils. Enhanced titin-based force has now been demonstrated in two distinct animal models, suggesting that modulation of titin-based force during active stretch is an inherent property of skeletal muscle. Our results also demonstrated that 15% of the enhanced state of titin can be attributed to direct calcium effects on the protein, presumably a stiffening of the protein upon calcium binding to the E-rich region of the PEVK segment and selected Ig domain segments. We suggest that the remaining unexplained 85% of this extra force results from titin binding to the thin filament. With this enhanced force confirmed in the mouse model, future studies will aim to elucidate the proposed titin-thin filament interaction in actively stretched sarcomeres.

Extracellular matrix integrity affects the mechanical behaviour of in-situ chondrocytes under compression.

Cartilage lesions change the microenvironment of cells and may accelerate cartilage degradation through catabolic responses from chondrocytes. In this study, we investigated the effects of structural integrity of the extracellular matrix (ECM) on chondrocytes by comparing the mechanics of cells surrounded by an intact ECM with cells close to a cartilage lesion using experimental and numerical methods. Experimentally, 15% nominal compression was applied to bovine cartilage tissues using a light-transmissible compression system. Target cells in the intact ECM and near lesions were imaged by dual-photon microscopy. Changes in cell morphology (N(cell)=32 for both ECM conditions) were quantified. A two-scale (tissue level and cell level) Finite Element (FE) model was also developed. A 15% nominal compression was applied to a non-linear, biphasic tissue model with the corresponding cell level models studied at different radial locations from the centre of the sample in the transient phase and at steady state. We studied the Green-Lagrange strains in the tissue and cells. Experimental and theoretical results indicated that cells near lesions deform less axially than chondrocytes in the intact ECM at steady state. However, cells near lesions experienced large tensile strains in the principal height direction, which are likely associated with non-uniform tissue radial bulging. Previous experiments showed that tensile strains of high magnitude cause an up-regulation of digestive enzyme gene expressions. Therefore, we propose that cartilage degradation near tissue lesions may be due to the large tensile strains in the principal height direction applied to cells, thus leading to an up-regulation of catabolic factors.

Functional and morphological adaptations to aging in knee extensor muscles of physically active men.

It is not known if a physically active lifestyle, without systematic training, is sufficient to combat age-related muscle and strength loss. Therefore, the purpose of this study was to evaluate if the maintenance of a physically active lifestyle prevents muscle impairments due to aging. To address this issue, we evaluated 33 healthy men with similar physical activity levels (IPAQ = 2) across a large range of ages. Functional (torque-angle and torque-velocity relations) and morphological (vastus lateralis muscle architecture) properties of the knee extensor muscles were assessed and compared between three age groups: young adults (30 ± 6 y), middle-aged subjects (50 ± 7 y) and elderly subjects (69 ± 5 y). Isometric peak torques were significantly lower (30% to 36%) in elderly group subjects compared with the young adults. Concentric peak torques were significantly lower in the middle aged (18% to 32%) and elderly group (40% to 53%) compared with the young adults. Vastus lateralis thickness and fascicles lengths were significantly smaller in the elderly group subjects (15.8 ± 3.9 mm; 99.1 ± 25.8 mm) compared with the young adults (19.8 ± 3.6 mm; 152.1 ± 42.0 mm). These findings suggest that a physically active lifestyle, without systematic training, is not sufficient to avoid loss of strength and muscle mass with aging.

Are titin properties reflected in single myofibrils?

Titin is a structural protein in muscle that spans the half sarcomere from Z-band to M-line. Although there are selected studies on titin's mechanical properties from tests on isolated molecules or titin fragments, little is known about its behavior within the structural confines of a sarcomere. Here, we tested the hypothesis that titin properties might be reflected well in single myofibrils. Single myofibrils from rabbit psoas were prepared for measurement of passive stretch-shortening cycles at lengths where passive titin forces occur. Three repeat stretch-shortening cycles with magnitudes between 1.0 and 3.0µm/sarcomere were performed at a speed of 0.1µm/s·sarcomere and repeated after a ten minute rest at zero force. These tests were performed in a relaxation solution (passive) and an activation solution (active) where cross-bridge attachment was inhibited with 2,3 butanedionemonoxime. Myofibrils behaved viscoelastically producing an increased efficiency with repeat stretch-shortening cycles, but a decreased efficiency with increasing stretch magnitudes. Furthermore, we observed a first distinct inflection point in the force-elongation curve at an average sarcomere length of 3.5µm that was associated with an average force of 68±5nN/mm. This inflection point was thought to reflect the onset of Ig domain unfolding and was missing after a ten minute rest at zero force, suggesting a lack of spontaneous Ig domain refolding. These passive myofibrillar properties observed here are consistent with those observed in isolated titin molecules, suggesting that the mechanics of titin are well preserved in isolated myofibrils, and thus, can be studied readily in myofibrils, rather than in the extremely difficult and labile single titin preparations.

Changes in patellofemoral joint contact pressures caused by vastus medialis muscle weakness.

BACKGROUND: Patellofemoral joint pain is a common knee disorder, but its underlying causes remain unknown. One proposed mechanism is an imbalance in force in the knee extensor muscles. Specifically, the vastus medialis and vastus lateralis are thought to play a crucial role in proper patellar tracking, and weakness in vastus medialis is thought to lead to a lateral shift in the patella causing increased contact pressures and pain. The purpose of this study was to create an animal model of vastus medialis weakness and to test the effect of this weakness on patellofemoral contact pressures. METHODS: Experiments were performed using New Zealand white rabbits (mass 4.9-7.7 kg, n=12). Loading of the patellofemoral joint was produced by femoral nerve stimulation of the knee extensor muscles. Knee extensor imbalance was produced by vastus medialis ablation. Fuji pressure sensitive film was used to record contact area, shape and pressures for maximal and sub-maximal, matched-force contractions at knee angles of 30°, 60°, and 90°. FINDINGS: Patellofemoral peak pressures, average pressures, contact areas and contact shapes were the same across all loading conditions for matched-force contractions before and after elimination of vastus medialis. INTERPRETATION: We conclude that vastus medialis weakness does not cause changes in patellofemoral contact pressures. Since the muscular and knee joint geometry in rabbits and humans is similar, we question the idea of vastus medialis weakness as a cause of patellar mal-tracking and patellofemoral joint pain.

Predictions of co-contraction depend critically on degrees-of-freedom in the musculoskeletal model.

In biomechanics, the calculation of individual muscle forces during movements is based on a model of the musculoskeletal system and a method for extracting a unique set of muscle forces. To obtain a unique set of muscle forces, non-linear, static optimisation is commonly used. However, the optimal solution is dependent on the musculoskeletal geometry, and single joints may be represented using one, two or three degrees-of-freedom. Frequently, a system with multiple degrees-of-freedom is replaced with a system that contains a subset of all the possible degrees-of-freedom. For example, the cat ankle joint is typically modelled as a planar joint with its primary degree-of-freedom (plantar-dorsiflexion), whereas, the actual joint has three rotational degrees-of-freedom. Typically, such simplifications are justified by the idea that the reduced case is contained as a specific solution of the more general case. However, here we demonstrate that the force-sharing solution space of a general, three degrees-of-freedom musculoskeletal system does not necessarily contain the solutions from the corresponding one or two degrees-of-freedom systems. Therefore, solutions of a reduced system, in general, are not sub-set solutions of the actual three degrees-of-freedom system, but are independent solutions that are often incompatible with solutions of the actual system. This result shows that representing a three degrees-of-freedom system as a one or two degrees-of-freedom system gives force-sharing solutions that cannot be extrapolated to the actual system, and vice-versa. These results imply that general solutions cannot be extracted from models with fewer degrees-of-freedom than the actual system. They further emphasise the need for precise geometric representation of the musculoskeletal system, if general force-sharing rules are to be derived.

Multi-functionality of the cat medical gastrocnemius during locomotion.

The functional role of biarticular muscles was investigated based on direct force measurement in the cat medial gastrocnemius (MG) and analysis of hindlimb kinematics and kinetics for the stance phase of level, uphill, and downhill walking. Four primary functional roles of biarticular muscles have been proposed in the past. These functional roles have typically been discussed independently of each other, and biarticular muscles have rarely been assigned more than one functional roles for different phases of the work cycle. The purpose of this study was to elucidate the functional role of the biarticular cat MG during locomotion. It was found that MG forces were primarily associated with the moment requirements at the ankle for most of the stance phase, but also helped to satisfy the moments at the knee in the initial phase of stance. In the second half of stance, MG transferred mechanical energy from the knee to the ankle from the knee to the ankle, while simultaneously producing a substantial amount of mechanical work. Based on these results, we hypothesize that MG's primary function is that of an ankle extensor. However, because of the coupling of the ankle extensor moment with a knee flexor moment in the initial, and a knee extensor moment in the final phase of stance, MG satisfies two joint moments in early stance, and transfers mechanical energy from the knee to the ankle in late stance. We conclude that cat MG has multiple functional roles during the stance phase of locomotion, and speculate that such multi-functionality also exists in other bi- and multi-articular muscles.