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

Abstract

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.

Fig. 1

Nonlinear elasticity of single skeletal myosin molecules. a The elasticity of single skeletal myosin molecules is characterized by the force–displacement relationships obtained from the combination of optical tweezers and single-molecule fluorescent techniques [30]. The stiffness (slope of the curve) is higher in the positive displacement (strain) region and dramatically lower in the negative strain region. Below −80 nm of displacement, the stiffness increases as well. Taken together with the fact that the length of S2 is approximately 40 nm, the higher stiffness (approximately 2.9 pN/nm) observed in the positive strain region and below −80 nm likely represents the elasticity of S1, while S2 is fully stretched and becomes much stiffer (approximately 100 pN/nm), as depicted in the top illustration. In the negative strain region between 0 and −80 nm, the lower stiffness (approximately 0.02 pN/nm) represents the bending stiffness of S2, which is bent and buckled as shown in the top illustration. b The stiffness values are calculated as the slope of the curve in Fig. 1a and plotted as a function of the loads. The stiffness values increase continuously from −2 to 4 pN and are comparable to those reported in previous single-molecule studies. Except for the stiffness obtained in [40], the values in other studies [56, 57] are consistent with our stiffness curve, implying that the variation in stiffness may be explained by the nonlinear elasticity of myosin molecules. Note that data from Fig. 2b in [57] were used here, and the other data are the mean values from those studies [40, 56]

Fig. 2

Deflection of the myosin S2 rod under horizontal compressive loads. a The schematic diagram of the regular elastica model (left) and the elastica model (right) modified by adding the angle of shear deformations, γ. b The deflections of the S2 rod are estimated by the elastica model (left) and the modified elastica model (right). One end is fixed at the horizontal position of X = −40 nm, while the other, free end is subject to the horizontal compressive load (F). c The force–displacement relationships in the experiment (gray circles), the elastica model (blue line) and the modified elastica model (red line). In the elastica model, the displacements are calculated as the change in the horizontal displacement from its original position of X = 0, as denoted by $\mathrm{\Delta }X$ in Fig. 2a. The shaded region indicates the difference in curves between the experiment and the modified elastica model below the horizontal displacement of −40 nm. d A schematic diagram of the potential elasticity at the S2 rod-myosin filament junction. This elasticity, depicted by a spring, may contribute to the structural constraint that prevents the excessive rotation of the S2 rod toward the negative strain side, resulting in the discrepancy in the force–displacement relationships between the experiment and the elastica model below −40 nm

Fig. 3

Mechanical model of working stroke size. a The step size, the amount of stretching in the elastic portion, and the working stroke size are plotted as a function of load. The observed step sizes (circles) obtained from the optical trap assay decrease with increasing loads [30], while the amount of stretching in the elastic portion of the myosin head (triangles) estimated from the elasticity measurement in the positive strain side of Fig. 1a increases. The working stroke sizes (diamonds), defined as the sum of the step size and the amount of stretching, appear to be consistently approximately 8 nm at any load, suggesting that the working stroke size is 8 nm and that there is a structural limit for myosin conformational changes. b A schematic diagram of the working stroke size, along with the step size and the stretched amount of the elastic portion. At no load (the mid panel), the working stroke of the myosin head (W) is purely translated to the sliding movement of actin, which corresponds to the observed step size (W = S _F=0). When a load is applied (the bottom panel), the stretching of the elastic portion of the myosin head (E) partially cancels the working stroke size such that the working stroke size is reduced by E, and the remnant distance is translated to the actin sliding (W − E = S _F>0)