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Fluctuation of actin sliding over myosin thick filaments in vitro

View Article: PubMed Central - PubMed

ABSTRACT

It is customarily thought that myosin motors act as independent force-generators in both isotonic unloaded shortening as well as isometric contraction of muscle. We tested this assumption regarding unloaded shortening, by analyzing the fluctuation of the actin sliding movement over long native thick filaments from molluscan smooth muscle in vitro. This analysis is based on the prediction that the effective diffusion coefficient of actin, a measure of the fluctuation, is proportional to the inverse of the number of myosin motors generating the sliding movement of an actin filament, hence proportional to the inverse of the actin length, when the actions of the motors are stochastic and statistically independent. Contrary to this prediction, we found the effective diffusion coefficient to be virtually independent of, and thus not proportional to, the inverse of the actin length. This result shows that the myosin motors are not independent force-generators when generating the continuous sliding movement of actin in vitro and that the sliding motion is a macroscopic manifestation of the cooperative actions of the microscopic ensemble motors.

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Effective diffusion coefficient (Dm, filled circles) and average sliding velocity (open squares) versus the actin length in a Monte Carlo simulation. The Dm values in the figure are the mean±SD (for N=10 different simulation runs). The filled curve represents β/(actin length) fitted to the Dm data by non-linear regression, where β=0.0173 μm3/s. If the Dm data were plotted against 1/(actin length) rather than the actin length, the plot could be fitted to a linear line passing through the origin, indicating that Dm approaches zero with the infinite increase in the actin length. The sliding velocity is virtually independent of the actin length above a certain length (>3 μm). Inset, a model of actin (A) sliding over an ensemble of myosin (M) units; x: the distance between a myosin unit and the myosin-binding site on actin; f(x): attachment rate; g1(x) and g2: detachment rates; h = 10 nm. Under the standard conditions in the present simulation, f(h)=43.33 s−1, g1(h) = 10 s−1 and g2= 836 s−1; the separation between the nearby two sites on actin=5.5 nm and that between the nearby two myosin units=42.9 nm.
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f1-1_45: Effective diffusion coefficient (Dm, filled circles) and average sliding velocity (open squares) versus the actin length in a Monte Carlo simulation. The Dm values in the figure are the mean±SD (for N=10 different simulation runs). The filled curve represents β/(actin length) fitted to the Dm data by non-linear regression, where β=0.0173 μm3/s. If the Dm data were plotted against 1/(actin length) rather than the actin length, the plot could be fitted to a linear line passing through the origin, indicating that Dm approaches zero with the infinite increase in the actin length. The sliding velocity is virtually independent of the actin length above a certain length (>3 μm). Inset, a model of actin (A) sliding over an ensemble of myosin (M) units; x: the distance between a myosin unit and the myosin-binding site on actin; f(x): attachment rate; g1(x) and g2: detachment rates; h = 10 nm. Under the standard conditions in the present simulation, f(h)=43.33 s−1, g1(h) = 10 s−1 and g2= 836 s−1; the separation between the nearby two sites on actin=5.5 nm and that between the nearby two myosin units=42.9 nm.

Mentions: The longer the actin filament, the larger the number of myosin heads involved in the interaction with the actin filament. Consequently, if the actions of individual myosin heads which cause an actin filament to slide are stochastic and statistically independent, then the fluctuation in the actin sliding displacements generated by the ensemble heads for a given time interval is smaller, owing to the attenuation of the actions of individual myosin heads by more myosin-actin interactions in longer actin filaments. Since the number of myosin heads driving an actin filament to slide is proportional to the actin length under the above ‘independent actions’ assumption, the effective diffusion coefficient is thus proportional to the inverse of the actin filament length7, as is the diffusion coefficient (D) of a filamentous particle undergoing a Brownian movement along its long axis to the inverse of the filament length22. The same 1/length dependence of the diffusion coefficient has also been found with microtubules in their Brownian movements generated by enzymatically inactive dynein and mutant ncd motors23–25. The 1/length dependence of Dm and D is a direct consequence of the mathematical statistics based on the premise that the actions of either protein motors or solvent molecules are stochastic and statistically independent4. To gain a better understanding of the 1/length dependence of Dm, we performed a computer simulation, although the 1/length dependence is model-independent as shown theoretically7. For the simulation, we use a simple model following Huxley’s 1957 model26. The simulation model considers the sliding of an actin filament generated by an ensemble of myosin motors. In the model, ‘spring’ myosin units are distributed in a relatively long array, and myosin-binding sites are discretely distributed on an actin filament of a given length (Fig. 1, inset). We herein consider, for the first time, the uniform distribution of myosin units. We assume that the actions of individual myosin heads, i.e., attachment and detachment of myosin units to and from actin, are stochastic and statistically independent. The attachment and detachment rates are assumed to depend on the distance between a myosin unit and the nearest binding site on actin as shown in Huxley’s 1957 model26 (Fig. 1, inset).


Fluctuation of actin sliding over myosin thick filaments in vitro
Effective diffusion coefficient (Dm, filled circles) and average sliding velocity (open squares) versus the actin length in a Monte Carlo simulation. The Dm values in the figure are the mean±SD (for N=10 different simulation runs). The filled curve represents β/(actin length) fitted to the Dm data by non-linear regression, where β=0.0173 μm3/s. If the Dm data were plotted against 1/(actin length) rather than the actin length, the plot could be fitted to a linear line passing through the origin, indicating that Dm approaches zero with the infinite increase in the actin length. The sliding velocity is virtually independent of the actin length above a certain length (>3 μm). Inset, a model of actin (A) sliding over an ensemble of myosin (M) units; x: the distance between a myosin unit and the myosin-binding site on actin; f(x): attachment rate; g1(x) and g2: detachment rates; h = 10 nm. Under the standard conditions in the present simulation, f(h)=43.33 s−1, g1(h) = 10 s−1 and g2= 836 s−1; the separation between the nearby two sites on actin=5.5 nm and that between the nearby two myosin units=42.9 nm.
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Related In: Results  -  Collection

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f1-1_45: Effective diffusion coefficient (Dm, filled circles) and average sliding velocity (open squares) versus the actin length in a Monte Carlo simulation. The Dm values in the figure are the mean±SD (for N=10 different simulation runs). The filled curve represents β/(actin length) fitted to the Dm data by non-linear regression, where β=0.0173 μm3/s. If the Dm data were plotted against 1/(actin length) rather than the actin length, the plot could be fitted to a linear line passing through the origin, indicating that Dm approaches zero with the infinite increase in the actin length. The sliding velocity is virtually independent of the actin length above a certain length (>3 μm). Inset, a model of actin (A) sliding over an ensemble of myosin (M) units; x: the distance between a myosin unit and the myosin-binding site on actin; f(x): attachment rate; g1(x) and g2: detachment rates; h = 10 nm. Under the standard conditions in the present simulation, f(h)=43.33 s−1, g1(h) = 10 s−1 and g2= 836 s−1; the separation between the nearby two sites on actin=5.5 nm and that between the nearby two myosin units=42.9 nm.
Mentions: The longer the actin filament, the larger the number of myosin heads involved in the interaction with the actin filament. Consequently, if the actions of individual myosin heads which cause an actin filament to slide are stochastic and statistically independent, then the fluctuation in the actin sliding displacements generated by the ensemble heads for a given time interval is smaller, owing to the attenuation of the actions of individual myosin heads by more myosin-actin interactions in longer actin filaments. Since the number of myosin heads driving an actin filament to slide is proportional to the actin length under the above ‘independent actions’ assumption, the effective diffusion coefficient is thus proportional to the inverse of the actin filament length7, as is the diffusion coefficient (D) of a filamentous particle undergoing a Brownian movement along its long axis to the inverse of the filament length22. The same 1/length dependence of the diffusion coefficient has also been found with microtubules in their Brownian movements generated by enzymatically inactive dynein and mutant ncd motors23–25. The 1/length dependence of Dm and D is a direct consequence of the mathematical statistics based on the premise that the actions of either protein motors or solvent molecules are stochastic and statistically independent4. To gain a better understanding of the 1/length dependence of Dm, we performed a computer simulation, although the 1/length dependence is model-independent as shown theoretically7. For the simulation, we use a simple model following Huxley’s 1957 model26. The simulation model considers the sliding of an actin filament generated by an ensemble of myosin motors. In the model, ‘spring’ myosin units are distributed in a relatively long array, and myosin-binding sites are discretely distributed on an actin filament of a given length (Fig. 1, inset). We herein consider, for the first time, the uniform distribution of myosin units. We assume that the actions of individual myosin heads, i.e., attachment and detachment of myosin units to and from actin, are stochastic and statistically independent. The attachment and detachment rates are assumed to depend on the distance between a myosin unit and the nearest binding site on actin as shown in Huxley’s 1957 model26 (Fig. 1, inset).

View Article: PubMed Central - PubMed

ABSTRACT

It is customarily thought that myosin motors act as independent force-generators in both isotonic unloaded shortening as well as isometric contraction of muscle. We tested this assumption regarding unloaded shortening, by analyzing the fluctuation of the actin sliding movement over long native thick filaments from molluscan smooth muscle in vitro. This analysis is based on the prediction that the effective diffusion coefficient of actin, a measure of the fluctuation, is proportional to the inverse of the number of myosin motors generating the sliding movement of an actin filament, hence proportional to the inverse of the actin length, when the actions of the motors are stochastic and statistically independent. Contrary to this prediction, we found the effective diffusion coefficient to be virtually independent of, and thus not proportional to, the inverse of the actin length. This result shows that the myosin motors are not independent force-generators when generating the continuous sliding movement of actin in vitro and that the sliding motion is a macroscopic manifestation of the cooperative actions of the microscopic ensemble motors.

No MeSH data available.


Related in: MedlinePlus