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Load-dependent sliding direction change of a myosin head on an actin molecule and its energetic aspects: Energy borrowing model of a cross-bridge cycle

View Article: PubMed Central - PubMed

ABSTRACT

A model of muscle contraction is proposed, assuming loose coupling between power strokes and ATP hydrolysis of a myosin head. The energy borrowing mechanism is introduced in a cross-bridge cycle that borrows energy from the environment to cover the necessary energy for enthalpy production during sliding movement. Important premises for modeling are as follows: 1) the interaction area where a myosin head slides is supposed to be on an actin molecule; 2) the actomyosin complex is assumed to generate force F(θ), which slides the myosin head M* in the interaction area; 3) the direction of the force F(θ) varies in proportion to the load P; 4) the energy supplied by ATP hydrolysis is used to retain the myosin head in the high-energy state M*, and is not used for enthalpy production; 5) the myosin head enters a hydration state and dehydration state repeatedly during the cross-bridge cycle. The dehydrated myosin head recovers its hydrated state by hydration in the surrounding medium; 6) the energy source for work and heat production liberated by the AM* complex is of external origin. On the basis of these premises, the model adequately explains the experimental results observed at various levels in muscular samples: 1) twist in actin filaments observed in shortening muscle fibers; 2) the load-velocity relationship in single muscle fiber; 3) energy balance among enthalpy production, the borrowed energy and the energy supplied by ATP hydrolysis during muscle contraction. Force F(θ) acting on the myosin head is depicted.

No MeSH data available.


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Illustrations of the sliding direction of a myosin head in the interaction area. (A) Definitions of parameters describing the sliding movement of a myosin head in the interaction area. The L-axis is parallel to the axis of the actin filament and the H-axis is perpendicular to the L-axis. The rhomboid OABC represents the interaction area. The myosin head is assumed to start its sliding movement at the original point O, and it slides in various directions depending on load P. Directions OD, OE and OC denote the sliding direction of the myosin head at Vmax (P=0), 1/2 Vmax and V=0 (P=Pmax), respectively. (B) Examples of sliding movements of a myosin head under heavy-load conditions (arrow Oa) and under light-load conditions below 1/2 Vmax (arrow Ob). Black arrow denotes the sliding trace of the myosin head in the interaction area. The green wavy arrow denotes Brownian movement of the myosin head around the long axis of the actin filament after dissociation of the myosin head from the actin molecule. The myosin head continues to slide in the interaction area under the given conditions, as shown by broken arrows.
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f4-5_11: Illustrations of the sliding direction of a myosin head in the interaction area. (A) Definitions of parameters describing the sliding movement of a myosin head in the interaction area. The L-axis is parallel to the axis of the actin filament and the H-axis is perpendicular to the L-axis. The rhomboid OABC represents the interaction area. The myosin head is assumed to start its sliding movement at the original point O, and it slides in various directions depending on load P. Directions OD, OE and OC denote the sliding direction of the myosin head at Vmax (P=0), 1/2 Vmax and V=0 (P=Pmax), respectively. (B) Examples of sliding movements of a myosin head under heavy-load conditions (arrow Oa) and under light-load conditions below 1/2 Vmax (arrow Ob). Black arrow denotes the sliding trace of the myosin head in the interaction area. The green wavy arrow denotes Brownian movement of the myosin head around the long axis of the actin filament after dissociation of the myosin head from the actin molecule. The myosin head continues to slide in the interaction area under the given conditions, as shown by broken arrows.

Mentions: Above, we introduced the interaction area on each actin molecule. Figure 4A shows the interaction area and its coordinates. The L- and H-axes are parallel and perpendicular to the axis of the actin filament, respectively. Angle α denotes the direction of the groove between the right-handed long-pitch strands of the actin filament on the radial projection; thus, α is constant. Force F(θ), the direction of which is the sliding direction of the myosin head, and load P+ρ are shown. The myosin head is assumed to start sliding in the interaction area at point O. In Equation (1) we assumed a linear relation between angle θ and the imposed load to simplify the model. The sliding direction of the myosin head in the interaction area is defined by angle α+β+θ, which is given counter-clockwise from the H-axis, where angle β denotes the effect of the internal load ρ on the sliding direction of the myosin head without the external load P, i.e., P=0, and is given as β=kρ. In the following discussion, the direction given by the angle α+β+θ is called direction θ owing to parameter θ. The direction θ of the myosin head sliding at maximum velocity Vmax is assumed to be given by α+β, because under this condition P=0 and θ=0. At half the maximum velocity 1/2Vmax, the sliding direction of the myosin head is assumed to be parallel to the axis of the actin filament; thus, direction θ is defined by α+β+θ=π/2. In the same way, direction θ under isometric contraction is defined by α+β+θ=π.


Load-dependent sliding direction change of a myosin head on an actin molecule and its energetic aspects: Energy borrowing model of a cross-bridge cycle
Illustrations of the sliding direction of a myosin head in the interaction area. (A) Definitions of parameters describing the sliding movement of a myosin head in the interaction area. The L-axis is parallel to the axis of the actin filament and the H-axis is perpendicular to the L-axis. The rhomboid OABC represents the interaction area. The myosin head is assumed to start its sliding movement at the original point O, and it slides in various directions depending on load P. Directions OD, OE and OC denote the sliding direction of the myosin head at Vmax (P=0), 1/2 Vmax and V=0 (P=Pmax), respectively. (B) Examples of sliding movements of a myosin head under heavy-load conditions (arrow Oa) and under light-load conditions below 1/2 Vmax (arrow Ob). Black arrow denotes the sliding trace of the myosin head in the interaction area. The green wavy arrow denotes Brownian movement of the myosin head around the long axis of the actin filament after dissociation of the myosin head from the actin molecule. The myosin head continues to slide in the interaction area under the given conditions, as shown by broken arrows.
© Copyright Policy
Related In: Results  -  Collection

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getmorefigures.php?uid=PMC5036636&req=5

f4-5_11: Illustrations of the sliding direction of a myosin head in the interaction area. (A) Definitions of parameters describing the sliding movement of a myosin head in the interaction area. The L-axis is parallel to the axis of the actin filament and the H-axis is perpendicular to the L-axis. The rhomboid OABC represents the interaction area. The myosin head is assumed to start its sliding movement at the original point O, and it slides in various directions depending on load P. Directions OD, OE and OC denote the sliding direction of the myosin head at Vmax (P=0), 1/2 Vmax and V=0 (P=Pmax), respectively. (B) Examples of sliding movements of a myosin head under heavy-load conditions (arrow Oa) and under light-load conditions below 1/2 Vmax (arrow Ob). Black arrow denotes the sliding trace of the myosin head in the interaction area. The green wavy arrow denotes Brownian movement of the myosin head around the long axis of the actin filament after dissociation of the myosin head from the actin molecule. The myosin head continues to slide in the interaction area under the given conditions, as shown by broken arrows.
Mentions: Above, we introduced the interaction area on each actin molecule. Figure 4A shows the interaction area and its coordinates. The L- and H-axes are parallel and perpendicular to the axis of the actin filament, respectively. Angle α denotes the direction of the groove between the right-handed long-pitch strands of the actin filament on the radial projection; thus, α is constant. Force F(θ), the direction of which is the sliding direction of the myosin head, and load P+ρ are shown. The myosin head is assumed to start sliding in the interaction area at point O. In Equation (1) we assumed a linear relation between angle θ and the imposed load to simplify the model. The sliding direction of the myosin head in the interaction area is defined by angle α+β+θ, which is given counter-clockwise from the H-axis, where angle β denotes the effect of the internal load ρ on the sliding direction of the myosin head without the external load P, i.e., P=0, and is given as β=kρ. In the following discussion, the direction given by the angle α+β+θ is called direction θ owing to parameter θ. The direction θ of the myosin head sliding at maximum velocity Vmax is assumed to be given by α+β, because under this condition P=0 and θ=0. At half the maximum velocity 1/2Vmax, the sliding direction of the myosin head is assumed to be parallel to the axis of the actin filament; thus, direction θ is defined by α+β+θ=π/2. In the same way, direction θ under isometric contraction is defined by α+β+θ=π.

View Article: PubMed Central - PubMed

ABSTRACT

A model of muscle contraction is proposed, assuming loose coupling between power strokes and ATP hydrolysis of a myosin head. The energy borrowing mechanism is introduced in a cross-bridge cycle that borrows energy from the environment to cover the necessary energy for enthalpy production during sliding movement. Important premises for modeling are as follows: 1) the interaction area where a myosin head slides is supposed to be on an actin molecule; 2) the actomyosin complex is assumed to generate force F(θ), which slides the myosin head M* in the interaction area; 3) the direction of the force F(θ) varies in proportion to the load P; 4) the energy supplied by ATP hydrolysis is used to retain the myosin head in the high-energy state M*, and is not used for enthalpy production; 5) the myosin head enters a hydration state and dehydration state repeatedly during the cross-bridge cycle. The dehydrated myosin head recovers its hydrated state by hydration in the surrounding medium; 6) the energy source for work and heat production liberated by the AM* complex is of external origin. On the basis of these premises, the model adequately explains the experimental results observed at various levels in muscular samples: 1) twist in actin filaments observed in shortening muscle fibers; 2) the load-velocity relationship in single muscle fiber; 3) energy balance among enthalpy production, the borrowed energy and the energy supplied by ATP hydrolysis during muscle contraction. Force F(θ) acting on the myosin head is depicted.

No MeSH data available.


Related in: MedlinePlus