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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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Cooperative action of multiple heads undergoing stochastic steps. (A) Schematic diagrams of actin and myosin filaments in skeletal muscle78. The actin filament has a helical structure with a half pitch of 36 nm. The myosin filament also has a helical structure with a pitch of 43 nm and a subunit repeat of 14.3 nm. Myosin heads on a myosin filament project toward an actin filament at 43 nm intervals. In skeletal muscle, the actin and myosin filaments are arranged in a hexagonal lattice and one actin is surrounded by three myosin filaments. Therefore, the number of myosin molecules project toward one actin filament 0.7 µm long (length when fully overlapped with myosin filaments) is approximately 50. When the actin filament is rotated 90°64, the relative position between the actin helical pitches and the myosin heads shifts by approximately 3 actin monomers. The actin slopes along the actin helical pitches are represented by a color gradient. (B) Qualitative explanation of the cooperative action of myosin heads on a thick filament. The myosin filament is equivalently represented by a row of myosin heads connected with springs at intervals of 43 nm. The actin filament is represented by straight, periodic, saw-tooth shape potentials along the half helical pitches as shown in Fig. 10. Cooperative action of the myosin heads causes a long (>60 nm) sliding distance of an actin filament per ATP (see text for detail).
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f11-1_1: Cooperative action of multiple heads undergoing stochastic steps. (A) Schematic diagrams of actin and myosin filaments in skeletal muscle78. The actin filament has a helical structure with a half pitch of 36 nm. The myosin filament also has a helical structure with a pitch of 43 nm and a subunit repeat of 14.3 nm. Myosin heads on a myosin filament project toward an actin filament at 43 nm intervals. In skeletal muscle, the actin and myosin filaments are arranged in a hexagonal lattice and one actin is surrounded by three myosin filaments. Therefore, the number of myosin molecules project toward one actin filament 0.7 µm long (length when fully overlapped with myosin filaments) is approximately 50. When the actin filament is rotated 90°64, the relative position between the actin helical pitches and the myosin heads shifts by approximately 3 actin monomers. The actin slopes along the actin helical pitches are represented by a color gradient. (B) Qualitative explanation of the cooperative action of myosin heads on a thick filament. The myosin filament is equivalently represented by a row of myosin heads connected with springs at intervals of 43 nm. The actin filament is represented by straight, periodic, saw-tooth shape potentials along the half helical pitches as shown in Fig. 10. Cooperative action of the myosin heads causes a long (>60 nm) sliding distance of an actin filament per ATP (see text for detail).

Mentions: We assume that multiple myosin heads are bound to ADP and Pi during most of the ATPase cycle; are tethered to a myosin filament via elastic elements (neck domain and S2); and move along the actin helical pitches due to the potential slope generated by the steric compatibility (Fig. 11A). At some point in time, one of these heads releases Pi to form a rigor complex with actin (Fig. 11B Top). It has been demonstrated that the actin filament is rotated during sliding in vitro60–62 and during force generation in muscle63,64. Since the actin filament is rotated by approximately 90° in muscle64, we assume that the actin filament is rotated by 90° due to the formation of a rigor complex. The energy for rotating one end of the actin filament 1 µm long by 90°, whose other end is fixed to the z-line, is estimated to be 16–32 kBT based on its torsional rigidity (2.6–6.7×10−26 Nm2)65, which is similar to the free energy (20 kBT) driven by the hydrolysis of one ATP molecule. Then, an ATP molecule binds to the rigor head to dissociate it from actin and the actin filament rewinds to its original orientation because one end of the actin filament is fixed to the z-line (Fig. 11B Middle). The myosin heads with ADP-Pi bound that have interacted with actin, of which most should be near the bottom end of the potential slope, dissociate from the actin and then gradually interact with new actin monomers. Since the potential slope is shifted by about three actin monomers — corresponding to a 90° rotation of the actin filament — the heads previously located at the potential bottom can move the actin filament again according to the new potential slope (Fig. 11B Middle and Bottom).


Mechanism of muscle contraction based on stochastic properties of single actomyosin motors observed in vitro
Cooperative action of multiple heads undergoing stochastic steps. (A) Schematic diagrams of actin and myosin filaments in skeletal muscle78. The actin filament has a helical structure with a half pitch of 36 nm. The myosin filament also has a helical structure with a pitch of 43 nm and a subunit repeat of 14.3 nm. Myosin heads on a myosin filament project toward an actin filament at 43 nm intervals. In skeletal muscle, the actin and myosin filaments are arranged in a hexagonal lattice and one actin is surrounded by three myosin filaments. Therefore, the number of myosin molecules project toward one actin filament 0.7 µm long (length when fully overlapped with myosin filaments) is approximately 50. When the actin filament is rotated 90°64, the relative position between the actin helical pitches and the myosin heads shifts by approximately 3 actin monomers. The actin slopes along the actin helical pitches are represented by a color gradient. (B) Qualitative explanation of the cooperative action of myosin heads on a thick filament. The myosin filament is equivalently represented by a row of myosin heads connected with springs at intervals of 43 nm. The actin filament is represented by straight, periodic, saw-tooth shape potentials along the half helical pitches as shown in Fig. 10. Cooperative action of the myosin heads causes a long (>60 nm) sliding distance of an actin filament per ATP (see text for detail).
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Related In: Results  -  Collection

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f11-1_1: Cooperative action of multiple heads undergoing stochastic steps. (A) Schematic diagrams of actin and myosin filaments in skeletal muscle78. The actin filament has a helical structure with a half pitch of 36 nm. The myosin filament also has a helical structure with a pitch of 43 nm and a subunit repeat of 14.3 nm. Myosin heads on a myosin filament project toward an actin filament at 43 nm intervals. In skeletal muscle, the actin and myosin filaments are arranged in a hexagonal lattice and one actin is surrounded by three myosin filaments. Therefore, the number of myosin molecules project toward one actin filament 0.7 µm long (length when fully overlapped with myosin filaments) is approximately 50. When the actin filament is rotated 90°64, the relative position between the actin helical pitches and the myosin heads shifts by approximately 3 actin monomers. The actin slopes along the actin helical pitches are represented by a color gradient. (B) Qualitative explanation of the cooperative action of myosin heads on a thick filament. The myosin filament is equivalently represented by a row of myosin heads connected with springs at intervals of 43 nm. The actin filament is represented by straight, periodic, saw-tooth shape potentials along the half helical pitches as shown in Fig. 10. Cooperative action of the myosin heads causes a long (>60 nm) sliding distance of an actin filament per ATP (see text for detail).
Mentions: We assume that multiple myosin heads are bound to ADP and Pi during most of the ATPase cycle; are tethered to a myosin filament via elastic elements (neck domain and S2); and move along the actin helical pitches due to the potential slope generated by the steric compatibility (Fig. 11A). At some point in time, one of these heads releases Pi to form a rigor complex with actin (Fig. 11B Top). It has been demonstrated that the actin filament is rotated during sliding in vitro60–62 and during force generation in muscle63,64. Since the actin filament is rotated by approximately 90° in muscle64, we assume that the actin filament is rotated by 90° due to the formation of a rigor complex. The energy for rotating one end of the actin filament 1 µm long by 90°, whose other end is fixed to the z-line, is estimated to be 16–32 kBT based on its torsional rigidity (2.6–6.7×10−26 Nm2)65, which is similar to the free energy (20 kBT) driven by the hydrolysis of one ATP molecule. Then, an ATP molecule binds to the rigor head to dissociate it from actin and the actin filament rewinds to its original orientation because one end of the actin filament is fixed to the z-line (Fig. 11B Middle). The myosin heads with ADP-Pi bound that have interacted with actin, of which most should be near the bottom end of the potential slope, dissociate from the actin and then gradually interact with new actin monomers. Since the potential slope is shifted by about three actin monomers — corresponding to a 90° rotation of the actin filament — the heads previously located at the potential bottom can move the actin filament again according to the new potential slope (Fig. 11B Middle and Bottom).

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.

No MeSH data available.