A myosin II nanomachine mimicking the striated muscle

Fig. 1. Assessing the number of HMMs available for actin interaction from rigor rupture events. a Schematics of the protocol: (1) formation of rigor bonds between the HMM array (blue) by the optical fibre (grey) and the actin filament (red) attached to the trapped bead (dark grey) via gelsolin (yellow); (2) optical fibre moved away from the actin filament in the direction (z) orthogonal to the actin–myosin interface. b Records of the nanopositioner movement (black, ΔZ velocity 25 nm s−1) and force with different [HMM] (colours refer to different concentrations as indicated in c; green: 25 µg ml−1; violet: 38 µg ml−1; red: 50 µg ml−1; blue: 100 µg ml−1). The small vertical bars indicate the rupture events (force drop <2.5 pN, complete in <50 ms and not rapidly reversed), the last of which corresponds to complete detachment of the actin filament. c Relation between the number of ruptures per interaction and [HMM] (mean ± SD, n = 14)

Fig. 2. Mechanical output of the myosin-II nanomachine in 2 mM ATP. a Schematic representation of three snapshots during the phases of the interaction between the actin filament and the motors numbered as in b. Components of the system coloured as in Fig. 1a. b Recording of the relative sliding (red trace) and force (blue trace) during the interaction. Phase 1, following the formation of the first bonds between the actin filament and myosin motors, the force rises in position feedback to the maximum isometric value (F0 ~ 17 pN). Phases 2–6, shortening response to a staircase of stepwise reductions in force (4 pN) separated by 1 s imposed in force feedback. c Another experiment in which in phase 1 in position feedback isometric force rises to F0 (~21 pN) with some force fluctuations and in frames 2–7 the staircase in force feedback is made by 5-pN steps separated by 1 s (3–5) and 0.5 s (6, 7). In phase 8, after a total active sliding of 2.7 µm, the control is switched back to position feedback, and the force redevelops up to the original F0. Phases 9–11, force response to a series of rapid lengthenings and shortenings of ~500 nm superimposed on F0. In both b, c, black lines are…

Fig. 3. Rate of force development. Upper row: time course of initial force development (a, Frame 1 from Fig. 2b) and force redevelopment following a large release (b, Frame 8 from Fig. 2c). The different trace thickness in a and b is due to different acquisition rates (500 and 5000 points s−1, respectively). Dashed lines are single exponential fits. Lower row: Model simulation of initial force development (c) and force redevelopment following a large release (d), using 16 available myosin heads and a series compliance of 3.7 nm pN−1. Dashed lines are single exponential fits. τ, calculated from fits to experimental traces as in a and b (0.15 ± 0.09 s, mean ± SEM, n = 34), is not significantly different from that calculated from fits to simulated traces in c and d (0.11 ± 0.06 s, mean ± SEM, n = 34) (see related Supplementary Fig. 5)

Fig. 4. Model simulation of the mechanical output of the machine. a Kinetic scheme, with three states of the myosin head (blue): D, detached; A1 and A2, attached to one monomer of the actin filament (brown). The scheme includes the possibility that during shortening the attached head in the A2 state slips to the next actin monomer farther from the centre of the sarcomere (red). The probability of a second slipping to the pink monomer is limited to 1/10 of that of the first slipping. Details on the strain dependence of the rate functions and how they are constrained by fitting skeletal muscle performance are in Supplementary Fig. 6. The corresponding equations are listed in Supplementary Table 1. The effect of trap compliance on the nanomachine performance is detailed in Supplementary Fig. 7. b F–V relation calculated for a number of available heads, N = 16 (continuous line) and experimental relation from Fig. 2e (open circles and dashed line). c Corresponding P–F relations. d Dependence on N of the three parameters featuring the machine performance, as indicated in the ordinate of each plot. The dashed lines are the respective experimental values. e Relation between number of attached…

Fig. 5. Model predictions of the energetic parameters. Dependence on N of the various parameters is calculated at the maximum power (Pmax). a Rate of ATP hydrolysis per myosin head, φPmax. b Efficiency, ε. c Power per myosin head, Pmax,h