Coordinated force generation of skeletal myosins in myofilaments through motor coupling

Figure 1. Force generation of myosin-rod cofilaments measured by optical tweezers. (a) Schematic of the optical tweezer assay on a synthetic myosin-rod cofilament interacting with an actin filament. A bead coated with streptavidin is attached to a biotinylated actin filament and held above a myosin-rod cofilament. Scattered images of beads diagonally illuminated by a red laser are projected onto a quadrant photodiode sensor. Inset: measured bead displacements with detected steps (black) reveal stepwise displacements that are frequently generated within 1 ms (red arrowheads). (b–d) Time courses of bead displacement at 1 mM, 100 μM and 10 μM ATP in b–d, respectively. (e–g) Stepwise displacements of actin filaments in response to low loads (bottom panels) and high loads (top panels) at 1 mM, 100 μM and 10 μM ATP in e–g, respectively. The black solid lines represent steps detected by the step-finding algorithm40.

Figure 2. Step size and dwell time of myosin-rod cofilaments. (a–c) Histograms of step sizes experimentally observed at 1 mM ATP for low loads (mean of 4.4 pN) in a, moderate loads (mean of 15.4 pN) in b and high loads (mean of 29.3 pN) in c. Also see Supplementary Fig. 2 for other ATP concentrations. (e–g) Histograms of step sizes obtained from the simulation model at 1 mM ATP for low loads (mean of 4.1 pN) in e, moderate loads (mean of 15.3 pN) in f and high loads (mean of 30.1 pN) in g. Also see Supplementary Fig. 2 for other ATP concentrations. (d,h) Cumulative probability distributions of the dwell time fitted to a double exponential function for experimental data in d and simulation data in h. The time constants calculated from double exponential fits were used to calculate mean dwell times as shown in Fig. 3g–i. Arrowheads indicate the peak points of single or double Gaussian functions. Step sizes at the peak were used as the mean step size in Fig. 3a–c.

Figure 3. Step properties as a function of load at different ATP concentrations. (a–c) Mean forward and backward step sizes as a function of load obtained from experiments and the simulation model at 1 mM (experiment: n=181 and 84 for forward and backward steps, respectively, from 3 beads; simulation: n=649 and 220 for forward and backward steps, respectively, from 12 trials) in a, 100 μM in (n=863 and 205 for forward and backward steps, respectively, from 3 beads; simulation: n=668 and 239 for forward and backward steps, respectively, from 8 trials) in b and 10 μM ATP (n=335 and 89 for forward and backward steps, respectively, from 4 beads; simulation: n=368 and 114 for forward and backward steps, respectively, from 24 trials) in c. (d–f) Mean dwell times obtained from experiments and the simulation model at 1 mM, 100 μM and 10 μM ATP in d–f, respectively. The abscissas of the fitting functions provided estimates of the stall forces: 36, 54 and 74 pN at 1 mM, 100 μM and 10 μM ATP, respectively, in experiment; 37, 47 and 85 pN at 1 mM, 100 μM and 10 μM ATP, respectively, in simulation. (g–i) Stepping ratio calculated from experiments and the simulation model at 1 mM, 100 μM and 10 μM ATP…

Figure 4. Characteristics of step curves during the rising phase of actin displacement. (a,b) Ensemble-averaged displacement of actin filaments at 1 mM ATP for low loads (mean of 2.7 pN, n=42 for experiment; mean of 2.5 pN, n=2,455 for simulation) in a and high loads (mean of 23.1 pN, n=179 for experiment; mean of 18 pN, n=487 for simulation) in b. (c,d) Ensemble-averaged displacement of actin filaments at 10 μM ATP for low loads (mean of 4.3 pN, n=51 for experiment; mean of 2.7 pN, n=404 for simulation) in c and high loads (mean of 28.6 pN, n=169 for experiment; mean of 22.7 pN, n=545 for simulation) in d. The black lines are single exponential curves (d=ds{1−exp[−t/τ]}+d0) fitted to experimental data starting from one sampling point after the onset point (t=50 μs). The fitting curves extended to t=0 pass close to the origin for 1 mM ATP (d0=−0.6 or 0.4 nm, ds=8.7 or 5.3 nm and τ=120 or 180 μs for low and high loads, respectively), suggesting that the entire rising phase of actin displacement can be approximated by a single exponential event, owing to the nearly coordinated executions of power strokes among multiple myosin molecules (Supplementary Fig. 6a,b). As indicated by the red…

Figure 5. Simulation model for actin–myosin interaction. (a) Kinetic scheme for myosin and actin interaction cycles starting from ATP binding to myosin (AM). A, M, T, D and P are actin, myosin, ATP, ADP and Pi, respectively. Two steps of power stroke execution are accompanied at the transitions towards AMD* and AMD states. See details in the Methods section. (b) Schematic of 17 myosin molecules interacting with an actin filament connected to the spring, whose stiffness is equivalent to the trap stiffness of 0.16 pN nm−1 used in the experiments. (c) Free energy profiles of detached (MDP) and attached states (AMD* and AMD) calculated from the nonlinear elasticity of the myosin head as a function of the strain in the myosin head, x. The black dashed line represents the total free energy of ATP hydrolysis, ΔEATP (Methods). The difference in free energy minima between MDP and AMD* or AMD* and AMD are given as or ΔEAMD, respectively (Methods and Table 1). (d) Strain-dependent rate constants between four force-generating states (k4, k5 and k6) given by the Boltzmann factor. Also see details in the Methods section. (e) The mean population of each state for power stroke myosin within ±200 μs of the…

Figure 6. Simulation results for actin–myosin interaction. (a–c) Time-course data for the displacement of a single actin filament (left column) at 1 mM, 100 μM and 10 μM ATP in a–c, respectively. Stepwise displacements of actin filaments computed by simulation for low loads (right column). Random noise was added to the original computed steps (different coloured lines) to detect steps (black solid line) by using the step-finding algorithm40. The inset in a shows a zoomed-in plot of the box region, which shows a single step (black) generated by contiguous power strokes (green). (d) Time course of a single actin step (top) and corresponding strains of myosins bound to actin filaments (bottom) within ±200 μs of the onset of the step, as indicated by the green vertical line. In this example, four myosins, #1–#4, engage with an actin filament during step generation. Myosins #1 and #2 execute multiple power strokes, as highlighted by the red arrowheads, whereas myosins #3 and #4 have already completed power strokes. Thus, they remain bound to actin as a ‘stretched’ or ‘drag’ motor, respectively. Red or purple shaded regions indicate whether an average strain at t>0 is positive (stretched) or…

Figure 7. Load-dependent modulation of coordinated-power stroke stretched and drag motors. (a–c) The mean numbers of coordinated-power stroke, stretched and drag myosin motors as a function of loads obtained from the simulation model at 1 mM, 100 μM and 10 μM ATP in a–c, respectively. (d–f) Mean force per coordinated-power stroke, stretched and drag myosin motors as a function of the loads at 1 mM, 100 μM and 10 μM ATP in d–f, respectively. (g–i) Sum of forces generated by coordinated-power stroke, stretched and drag myosin motors at 1 mM, 100 μM and 10 μM ATP in g–i, respectively. Diagonal dashed lines represent the force level, which is equivalent to an applied load. The sum of these force curves perfectly aligns to this line. (j,k) Duty ratio at 1 mM, 100 μM and 10 μM ATP as a function of load calculated by two methods: a ratio of attachment time to cyclic time in j and a ratio of total number of power stroke, stretched and drag motors to 17 motors counted during 200 μs from the onset of detectable steps in k. (l) Mechanical work and efficiency at 1 mM, 100 μM and 10 μM ATP as a function of load. All mean values are plotted with error bars representing s.e.m., but most error bars are…