Motoshi Kaya

Nonlinear Elasticity and an 8-nm Working Stroke of Single Myosin Molecules in Myofilaments

Measuring Single Myosins at Work In the past 15 years, the molecular mechanism of muscle contraction has been investigated at the single-molecule level; however, results have varied between laboratories because of the nonprocessive properties of skeletal myosin. Now, Kaya and Higuchi (p. 686) have measured the nonlinear elasticity and working stroke size of single skeletal myosins by combining optical trapping and fluorescence imaging with subnanometer accuracy. The data suggest that it is important to relate myosins internal structural changes to physiological force generation and filament sliding. Single-molecule measurements refine our understanding of how muscle myosin works. Using optical trapping and fluorescence imaging techniques, we measured the step size and stiffness of single skeletal myosins interacting with actin filaments and arranged on myosin-rod cofilaments that approximate myosin mechanics during muscle contraction. Stiffness is dramatically lower for negatively compared to positively strained myosins, consistent with buckling of myosin’s subfragment 2 rod domain. Low stiffness minimizes drag of negatively strained myosins during contraction at loaded conditions. Myosins elastic portion is stretched during active force generation, reducing apparent step size with increasing load, even though the working stroke is approximately constant at about 8 nanometers. Taking account of the nonlinear nature of myosin elasticity is essential to relate myosin’s internal structural changes to physiological force generation and filament sliding.

Coordination of medial gastrocnemius and soleus forces during cat locomotion

SUMMARY We studied force-sharing behavior between the cat medial gastrocnemius (MG) and soleus (SOL) muscles by direct measurement of the muscle forces and electromyographic activities (EMGs), muscle lengths, speeds of contraction, joint kinematics and kinetics, for a variety of locomotor conditions. Previous studies suggested that the modulation of MG force and activation is associated with movement demands, while SOL force and activation remain nearly constant. However, no systematic, quantitative analysis has been done to evaluate the degree of (possible) modulation of SOL force and activation across a range of vastly different locomotor conditions. In the present study, we investigated the effects of speed and intensity of locomotion on the modulation of SOL force and EMG activity, based on quantitative, statistical analyses. We also investigated the hypothesis that MG forces are primarily associated with MG activation for changing movement demands, while SOL forces are primarily associated with the contractile conditions, rather than activation. Seven cats were trained to walk, trot and gallop at different speeds on a motor-driven treadmill, and to walk up and down different slopes on a walkway. Statistical analysis suggested that SOL activation (EMG activity) significantly increased with increasing speeds and intensities of locomotion, while SOL forces remained constant in these situations. MG forces and EMG activities, however, both increased with increasing speeds and intensities of locomotion. We conclude from these results that SOL is not maximally activated at slow walking, as suggested in the literature, and that its force remains nearly constant for a range of locomotor conditions despite changes in EMG activity. Therefore, SOL forces appear to be affected substantially by the changing contractile conditions associated with changing movement demands. In contrast, MG peak forces correlated well with EMG activities, suggesting that MG forces are primarily associated with activation while its contractile conditions play a minor role for the movement conditions tested here.

Stiffness, working stroke, and force of single-myosin molecules in skeletal muscle: elucidation of these mechanical properties via nonlinear elasticity evaluation

In muscles, the arrays of skeletal myosin molecules interact with actin filaments and continuously generate force at various contraction speeds. Therefore, it is crucial for myosin molecules to generate force collectively and minimize the interference between individual myosin molecules. Knowledge of the elasticity of myosin molecules is crucial for understanding the molecular mechanisms of muscle contractions because elasticity directly affects the working and drag (resistance) force generation when myosin molecules are positively or negatively strained. The working stroke distance is also an important mechanical property necessary for elucidation of the thermodynamic efficiency of muscle contractions at the molecular level. In this review, we focus on these mechanical properties obtained from single-fiber and single-molecule studies and discuss recent findings associated with these mechanical properties. We also discuss the potential molecular mechanisms associated with reduction of the drag effect caused by negatively strained myosin molecules.

Estimation of cat medial gastrocnemius fascicle lengths during dynamic contractions

In typical muscle models, it is often assumed that the contractile element (fascicle) length depends exclusively on the instantaneous muscle-tendon length and the instantaneous muscle force. In order to test whether the instantaneous fascicle length during dynamic contractions can be predicted from muscle-tendon length and force, fascicle lengths, muscle-tendon lengths, and muscle forces were directly measured in cat medial gastrocnemii during isometric and dynamic contractions. Two theoretical muscle models were developed: model A was based on force-time data obtained during the activation phase and model D on force-time data obtained during the deactivation phase of isometric contractions. To test the models, instantaneous fascicle lengths were predicted from muscle-tendon lengths and forces during dynamic contractions that simulated cat locomotion for speeds ranging from 0.4 to 1.6m/s. The theoretically predicted fascicle lengths were compared with the experimentally measured fascicle lengths. It was found that fascicle lengths were not uniquely associated with muscle-tendon lengths and forces; that is, for a given muscle-tendon length and force, fascicle lengths varied depending on the contractile history. Consequently, models A and D differed in fascicle length predictions; model D (maximum average error=8.5%) was considerably better than model A (maximum average error=22.3%). We conclude from this study that it is not possible to predict the exact fascicle lengths from muscle-tendon lengths and forces alone, however, adequate predictions seem possible based on such a model. The relationship between fascicle length and muscle force and muscle-tendon length is complex and highly non-linear, thus, it appears unlikely that accurate fascicle length predictions can be made without some reference contractions in which fascicle length, muscle-tendon length, and force are measured simultaneously.

Premature deactivation of soleus during the propulsive phase of cat jumping

It has been shown that cat soleus (SOL) forces remain nearly constant despite increases in electromyography (EMG) activity for increasing speeds of locomotion, while medial gastrocnemius (MG) forces and EMG activity increase in parallel. Furthermore, during jumping, average cat SOL forces decrease, while average EMG activity increases dramatically compared with walking conditions. Finally, during rapid paw-shake movements, SOL forces and EMG activities are nearly zero. Based on these results, we hypothesized that the SOL is deactivated, despite ankle extensor requirements, if the contractile conditions limit SOL force potential severely. The purposes of this study were to (i) investigate SOL EMG activity and force as a function of its contractile conditions during jumping, (ii) test whether SOL EMG activity is associated with SOL contractile conditions, and (iii) determine the functional implications of SOL EMG activity during jumping. It was found that the SOL was prematurely deactivated in two distinct phases during the propulsive phase of jumping, in which shortening speeds approached or even exceeded the maximal speed of muscle shortening. We concluded that the SOL was prematurely deactivated to save energy because its mechanical work output approached zero, and speculated that the first phase of deactivation might be caused by a decrease in group Ia firing associated with active shortening and the second by a pre-programmed response inherent to the central pattern generator.

Coordinated force generation of skeletal myosins in myofilaments through motor coupling

In contrast to processive molecular motors, skeletal myosins form a large motor ensemble for contraction of muscles against high loads. Despite numerous information on the molecular properties of skeletal myosin, its ensemble effects on collective force generation have not been rigorously clarified. Here we show 4 nm stepwise actin displacements generated by synthetic myofilaments beyond a load of 30 pN, implying that steps cannot be driven exclusively by single myosins, but potentially by coordinated force generations among multiple myosins. The simulation model shows that stepwise actin displacements are primarily caused by coordinated force generation among myosin molecules. Moreover, the probability of coordinated force generation can be enhanced against high loads by utilizing three factors: strain-dependent kinetics between force-generating states; multiple power stroke steps; and high ATP concentrations. Compared with other molecular motors, our findings reveal how the properties of skeletal myosin are tuned to perform cooperative force generation for efficient muscle contraction.

In vivo muscle force and muscle power during near-maximal frog jumps

Frogs’ outstanding jumping ability has been associated with a high power output from the leg extensor muscles. Two main theories have emerged to explain the high power output of the frog leg extensor muscles, either (i) the contractile conditions of all leg extensor muscles are optimized in terms of muscle length and speed of shortening, or (ii) maximal power is achieved through a dynamic catch mechanism that uncouples fibre shortening from the corresponding muscle-tendon unit shortening. As in vivo instantaneous power generation in frog hind limb muscles during jumping has never been measured directly, it is hard to distinguish between the two theories. In this study, we determined the instantaneous variable power output of the plantaris longus (PL) of Lithobates pipiens (also known as Rana pipiens), by directly measuring the in vivo force, length change, and speed of muscle and fibre shortening in near maximal jumps. Fifteen near maximal jumps (> 50cm in horizontal distance) were analyzed. High instantaneous peak power in PL (536 ± 47 W/kg) was achieved by optimizing the contractile conditions in terms of the force-length but not the force-velocity relationship, and by a dynamic catch mechanism that decouples fascicle shortening from muscle-tendon unit shortening. We also found that the extra-muscular free tendon likely amplifies the peak power output of the PL by modulating fascicle shortening length and shortening velocity for optimum power output, but not by releasing stored energy through recoiling as the tendon only started recoiling after peak PL power had been achieved.

PREDICTION OF MUSCLE FORCES USING STATIC OPTIMIZATION FOR DIFFERENT CONTRACTILE CONDITIONS

In this study, we introduced a novel cost function for the prediction of individual muscle forces for a one degree-of-freedom musculoskeletal system. Unlike previous models, the new approach incorporates the instantaneous contractile conditions represented by the force-length and force-velocity relationships and accounts for physiological properties such as fiber type distribution and physiological cross-sectional area (PCSA) in the cost function. Using this cost function, it is possible to predict experimentally observed features of force-sharing among synergistic muscles that cannot be predicted using the classical approaches. Specifically, the new approach allows for predictions of force-sharing loops of agonistic muscles in one degree-of-freedom systems and for simultaneous increases in force in one muscle and decreases in a corresponding agonist. We concluded that the incorporation of the contractile conditions in the weighting of cost functions provides a natural way to incorporate observed force-sharing features in synergistic muscles that have eluded satisfactory description.

Evaluation of muscle force predictions using optimization theory

Prediction of muscle forces using optimization based models of muscle coordination is an active research area in biomechanics. Theoretical calculation of individual muscle forces depends on solving the redundancy problem. In a musculoskeletal model, redundancy arises since the number of muscles in the model exceeds the number of degrees-of-freedom present. One of the widely used methods to solve this problem is to formulate a physiologically sound cost function and optimize this function subject to mechanical equality and inequality constraint equations. In this study, force predictions obtained from different optimization-based models were compared with those obtained from experimentally measured individual muscle forces recorded during a variety of movement conditions. Advantages and limitations of the tested models were discussed.

Non-Linear Elasticity of Skeletal Myosins is Essential for Collective Force Generation in Muscle

Muscle contraction occurs through the rotation of the myosin heads pulling actin filaments past myosin filaments. In order to achieve contractions efficiently, it is crucial for myosins to generate force collectively and to minimize the interference between motors. In the previous studies, it was suggested that the elasticity of myosin is linear so that myosins generate the large drag force opposing to muscle contraction if negatively strained. However, none of the previous studies has investigated the elasticity of single myosin explicitly in the negative strain region. Therefore, we investigated the elasticity of single skeletal myosins in both the positive and negative strain directions. In the absence of ATP, single myosins embedded in synthetic myosin-rod filaments were tightly bound to actin filaments and were stretched and shortened repeatedly by oscillating the two trapped beads on the both ends of acting filament manipulated by optical tweezers. The elasticity of myosins was characterized by obtaining the force-displacement curves, where forces on myosin heads were estimated by measuring the displacement of two beads, and displacements of myosin heads were obtained by tracking the position of quantum dots attached to the actin filament. We found that the elasticity is non-linear, in which stiffness is high (∼2.8 pN/nm) and low (∼0.02 pN/nm) in the positive and negative strain regions. The non-linear elasticity ensures high force generation with a small stretching of the elastic portion, and minimizing the drag force of negatively-strained myosins. Furthermore, the estimates of the actin sliding distance by the non-linear elasticity model were more consistent with experimental results observed in 20μM ATP than those by the linear elasticity model. Therefore, the non-linear elasticity might be an essential mechanical property of single myosin designed for the collective force generation in muscle.