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Mechanism of muscle contraction based on stochastic properties of single actomyosin motors observed in vitro

View Article: PubMed Central - PubMed

ABSTRACT

We have previously measured the process of displacement generation by a single head of muscle myosin (S1) using scanning probe nanometry. Given that the myosin head was rigidly attached to a fairly large scanning probe, it was assumed to stably interact with an underlying actin filament without diffusing away as would be the case in muscle. The myosin head has been shown to step back and forth stochastically along an actin filament with actin monomer repeats of 5.5 nm and to produce a net movement in the forward direction. The myosin head underwent 5 forward steps to produce a maximum displacement of 30 nm per ATP at low load (<1 pN). Here, we measured the steps over a wide range of forces up to 4 pN. The size of the steps (∼5.5 nm) did not change as the load increased whereas the number of steps per displacement and the stepping rate both decreased. The rate of the 5.5-nm steps at various force levels produced a force-velocity curve of individual actomyosin motors. The force-velocity curve from the individual myosin heads was comparable to that reported in muscle, suggesting that the fundamental mechanical properties in muscle are basically due to the intrinsic stochastic nature of individual actomyosin motors. In order to explain multiple stochastic steps, we propose a model arguing that the thermally-driven step of a myosin head is biased in the forward direction by a potential slope along the actin helical pitch resulting from steric compatibility between the binding sites of actin and a myosin head. Furthermore, computer simulations show that multiple cooperating heads undergoing stochastic steps generate a long (>60 nm) sliding distance per ATP between actin and myosin filaments, i.e., the movement is loosely coupled to the ATPase cycle as observed in muscle.

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Computer simulation of multiple head cooperative activity undergoing stochastic steps. We simulated cooperative action of myosin heads under a periodic and asymmetric potential as shown in Fig. 11B by numerically solving the Langevin equation, 0=−ρdxi/dt−dU(xi,t)/dx+F(t)−Ai,where xi is the position of i-th myosin head; ρ is a drag coefficient; F(t) is the random force obeying a Gaussian white noise characterized by the ensemble average, <F(t)>=0 and <F(t)F(s)>=2 kBTδ(t−s); Ai is the interaction force between the neighboring heads described as κ(xi−xi−1)−κ(xi+1−xi), where κ is the spring constant connecting the heads. The potential slope along the actin helical pitch (Fig. 10B) was simplified to be a straight saw-tooth shaped potential. Instead, the drag coefficient was set to be larger than it is in solution so that the velocity of the heads was equal to the maximum velocity in Fig. 7. Other parameters were chosen such that 1) the spring constant (κ) connecting the head was 0.1 pN/nm, which is approximately one tenth as large as that of a rigor crossbridge; 2) the ratio of potential rise to decline was 1 to 6 and the depth of the potential at the bottom was 2 kBT; 3) the pitch of the potential and the average intervals of myosin heads were 36 nm and 43 nm, respectively; 4) the number of heads interacting with the actin filament was 11 (∼20% overlap between actin and myosin filaments); 5) the rotation angle of the actin filament was 90°; and 6) the rate constant (k+) that the heads rebind to actin after the rewinding of the actin filament was 100 s−1head−1. The potential slope was assumed to be smaller than that estimated in the present experiment (see Fig. 10). The strain exerted on the neck domain would be much smaller during free shortening at zero load in muscle because the head is tethered to the myosin filament via a flexible α-helix (S2), while the head is directly attached at its tail end to the probe in the present measurement system. Thus, the potential slope depending on the strain would be smaller. (A) A typical time course of the movement of an actin filament. (B) Histogram of the sliding distance of actin filaments per ATP. The average sliding distance of actin filaments was 58.4 nm per ATP.
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f12-1_1: Computer simulation of multiple head cooperative activity undergoing stochastic steps. We simulated cooperative action of myosin heads under a periodic and asymmetric potential as shown in Fig. 11B by numerically solving the Langevin equation, 0=−ρdxi/dt−dU(xi,t)/dx+F(t)−Ai,where xi is the position of i-th myosin head; ρ is a drag coefficient; F(t) is the random force obeying a Gaussian white noise characterized by the ensemble average, <F(t)>=0 and <F(t)F(s)>=2 kBTδ(t−s); Ai is the interaction force between the neighboring heads described as κ(xi−xi−1)−κ(xi+1−xi), where κ is the spring constant connecting the heads. The potential slope along the actin helical pitch (Fig. 10B) was simplified to be a straight saw-tooth shaped potential. Instead, the drag coefficient was set to be larger than it is in solution so that the velocity of the heads was equal to the maximum velocity in Fig. 7. Other parameters were chosen such that 1) the spring constant (κ) connecting the head was 0.1 pN/nm, which is approximately one tenth as large as that of a rigor crossbridge; 2) the ratio of potential rise to decline was 1 to 6 and the depth of the potential at the bottom was 2 kBT; 3) the pitch of the potential and the average intervals of myosin heads were 36 nm and 43 nm, respectively; 4) the number of heads interacting with the actin filament was 11 (∼20% overlap between actin and myosin filaments); 5) the rotation angle of the actin filament was 90°; and 6) the rate constant (k+) that the heads rebind to actin after the rewinding of the actin filament was 100 s−1head−1. The potential slope was assumed to be smaller than that estimated in the present experiment (see Fig. 10). The strain exerted on the neck domain would be much smaller during free shortening at zero load in muscle because the head is tethered to the myosin filament via a flexible α-helix (S2), while the head is directly attached at its tail end to the probe in the present measurement system. Thus, the potential slope depending on the strain would be smaller. (A) A typical time course of the movement of an actin filament. (B) Histogram of the sliding distance of actin filaments per ATP. The average sliding distance of actin filaments was 58.4 nm per ATP.

Mentions: In order to test this model quantitatively, we performed computer simulations of cooperative action of multiple myosin heads undergoing biased Brownian motion along the actin helical pitches. The long (>60 nm) sliding distance per ATP could be successfully simulated by the present model (Fig. 12).


Mechanism of muscle contraction based on stochastic properties of single actomyosin motors observed in vitro
Computer simulation of multiple head cooperative activity undergoing stochastic steps. We simulated cooperative action of myosin heads under a periodic and asymmetric potential as shown in Fig. 11B by numerically solving the Langevin equation, 0=−ρdxi/dt−dU(xi,t)/dx+F(t)−Ai,where xi is the position of i-th myosin head; ρ is a drag coefficient; F(t) is the random force obeying a Gaussian white noise characterized by the ensemble average, <F(t)>=0 and <F(t)F(s)>=2 kBTδ(t−s); Ai is the interaction force between the neighboring heads described as κ(xi−xi−1)−κ(xi+1−xi), where κ is the spring constant connecting the heads. The potential slope along the actin helical pitch (Fig. 10B) was simplified to be a straight saw-tooth shaped potential. Instead, the drag coefficient was set to be larger than it is in solution so that the velocity of the heads was equal to the maximum velocity in Fig. 7. Other parameters were chosen such that 1) the spring constant (κ) connecting the head was 0.1 pN/nm, which is approximately one tenth as large as that of a rigor crossbridge; 2) the ratio of potential rise to decline was 1 to 6 and the depth of the potential at the bottom was 2 kBT; 3) the pitch of the potential and the average intervals of myosin heads were 36 nm and 43 nm, respectively; 4) the number of heads interacting with the actin filament was 11 (∼20% overlap between actin and myosin filaments); 5) the rotation angle of the actin filament was 90°; and 6) the rate constant (k+) that the heads rebind to actin after the rewinding of the actin filament was 100 s−1head−1. The potential slope was assumed to be smaller than that estimated in the present experiment (see Fig. 10). The strain exerted on the neck domain would be much smaller during free shortening at zero load in muscle because the head is tethered to the myosin filament via a flexible α-helix (S2), while the head is directly attached at its tail end to the probe in the present measurement system. Thus, the potential slope depending on the strain would be smaller. (A) A typical time course of the movement of an actin filament. (B) Histogram of the sliding distance of actin filaments per ATP. The average sliding distance of actin filaments was 58.4 nm per ATP.
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Related In: Results  -  Collection

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f12-1_1: Computer simulation of multiple head cooperative activity undergoing stochastic steps. We simulated cooperative action of myosin heads under a periodic and asymmetric potential as shown in Fig. 11B by numerically solving the Langevin equation, 0=−ρdxi/dt−dU(xi,t)/dx+F(t)−Ai,where xi is the position of i-th myosin head; ρ is a drag coefficient; F(t) is the random force obeying a Gaussian white noise characterized by the ensemble average, <F(t)>=0 and <F(t)F(s)>=2 kBTδ(t−s); Ai is the interaction force between the neighboring heads described as κ(xi−xi−1)−κ(xi+1−xi), where κ is the spring constant connecting the heads. The potential slope along the actin helical pitch (Fig. 10B) was simplified to be a straight saw-tooth shaped potential. Instead, the drag coefficient was set to be larger than it is in solution so that the velocity of the heads was equal to the maximum velocity in Fig. 7. Other parameters were chosen such that 1) the spring constant (κ) connecting the head was 0.1 pN/nm, which is approximately one tenth as large as that of a rigor crossbridge; 2) the ratio of potential rise to decline was 1 to 6 and the depth of the potential at the bottom was 2 kBT; 3) the pitch of the potential and the average intervals of myosin heads were 36 nm and 43 nm, respectively; 4) the number of heads interacting with the actin filament was 11 (∼20% overlap between actin and myosin filaments); 5) the rotation angle of the actin filament was 90°; and 6) the rate constant (k+) that the heads rebind to actin after the rewinding of the actin filament was 100 s−1head−1. The potential slope was assumed to be smaller than that estimated in the present experiment (see Fig. 10). The strain exerted on the neck domain would be much smaller during free shortening at zero load in muscle because the head is tethered to the myosin filament via a flexible α-helix (S2), while the head is directly attached at its tail end to the probe in the present measurement system. Thus, the potential slope depending on the strain would be smaller. (A) A typical time course of the movement of an actin filament. (B) Histogram of the sliding distance of actin filaments per ATP. The average sliding distance of actin filaments was 58.4 nm per ATP.
Mentions: In order to test this model quantitatively, we performed computer simulations of cooperative action of multiple myosin heads undergoing biased Brownian motion along the actin helical pitches. The long (>60 nm) sliding distance per ATP could be successfully simulated by the present model (Fig. 12).

View Article: PubMed Central - PubMed

ABSTRACT

We have previously measured the process of displacement generation by a single head of muscle myosin (S1) using scanning probe nanometry. Given that the myosin head was rigidly attached to a fairly large scanning probe, it was assumed to stably interact with an underlying actin filament without diffusing away as would be the case in muscle. The myosin head has been shown to step back and forth stochastically along an actin filament with actin monomer repeats of 5.5 nm and to produce a net movement in the forward direction. The myosin head underwent 5 forward steps to produce a maximum displacement of 30 nm per ATP at low load (&lt;1 pN). Here, we measured the steps over a wide range of forces up to 4 pN. The size of the steps (&sim;5.5 nm) did not change as the load increased whereas the number of steps per displacement and the stepping rate both decreased. The rate of the 5.5-nm steps at various force levels produced a force-velocity curve of individual actomyosin motors. The force-velocity curve from the individual myosin heads was comparable to that reported in muscle, suggesting that the fundamental mechanical properties in muscle are basically due to the intrinsic stochastic nature of individual actomyosin motors. In order to explain multiple stochastic steps, we propose a model arguing that the thermally-driven step of a myosin head is biased in the forward direction by a potential slope along the actin helical pitch resulting from steric compatibility between the binding sites of actin and a myosin head. Furthermore, computer simulations show that multiple cooperating heads undergoing stochastic steps generate a long (&gt;60 nm) sliding distance per ATP between actin and myosin filaments, i.e., the movement is loosely coupled to the ATPase cycle as observed in muscle.

No MeSH data available.


Related in: MedlinePlus