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Kinetics of the Actin–Myosin Interaction

Jeffery W. Walker

10.1002/cphy.cp020106

Source: Supplement 6: Handbook of Physiology, The Cardiovascular System, The Heart

Originally published: 2002

Published online: January 2011

Full Article on Wiley Online Library



Abstract

The sections in this article are:

1 Crossbridges and Sliding Filaments
2 Regulation
3 Myosin and Actomyosin ATPase
3.1 Rates of Specific Steps
3.2 Energetics of Specific Steps
3.3 Cardiac versus Skeletal Actomyosin ATPase
4 The Crossbridge Cycle in Muscle
4.1 Energy Transduction and Muscle Mechanics
4.2 Transient Kinetics in Fibers Using Caged Compounds
4.3 Analysis of Specific Steps
4.4 Cardiac Muscle
5 In Vitro Motility
6 Atomic Structures of Actin and Myosin
6.1 Myosin S1
6.2 Actomyosin
6.3 Comparison of Structural Models to Other Models
7 Recent Progress
8 Regulation
8.1 The Steric Blocking Model
8.2 Kinetic Regulation
8.3 Dual Regulation of the Crossbridge Cycle
8.4 Phosphorylation and Protein Isoform Switching
9 Summary and Concluding Comments
Figure 1. Figure 1.

Muscle fiber ultrastructure. Fibers are comprised of bundles of myofibrils, each containing alternating dark bands (A‐bands) and light bands (I‐bands) when viewed in the light microscope. Illustrated in diagrams below the micrograph is the arrangement of proteins that underlie this banding pattern. The dark band corresponds to the thick myosin filament which has a bare zone or light stripe at its center. The light band corresponds to thin actin filaments which are anchored at the Z‐line in the center of the I‐band. The outer segments of the dark band represent the region of overlap between actin and myosin filaments where crossbridges are located and where productive actin‐myosin interactions occur. A sarcomere is the structure between two Z‐lines, and when the sarcomere shortens the distance between Z‐lines decreases.
Figure 2. Figure 2.

Time course of ATP hydrolysis catalyzed by myosin S1 and actomyosin S1 measured by formation of total Pi. Rapid mixing of ATP with myosin produces a Pi burst in the first few tenths of a second, followed by a slower rate of Pi formation (solid line). The burst is approximately equal in moles to the number of moles of myosin S1 present, and represents the first cycle of ATP hydrolysis bound to myosin S1. Further ATP hydrolysis (and Pi formation) requires product dissociation, which is very slow (t1/2 = 14 s) in the absence of actin. At intermediate actin concentrations, this second phase increases in rate but the overall time course remains distinctly biphasic. At very high actin concentration, the second phase approaches the rate of the initial (burst) phase making the burst less discernible.
Figure 3. Figure 3.

Transduction of chemical free energy into a mechanical process for a simple one step reaction. State A is a non‐force generating state so its basic free energy (GAchem) is independent of displacement. State B is a force generating state whose force is linearly related to displacement (F = κx) and whose mechanical free energy is parabolically related to displacement (GBmech = κx2/2). The dashed line indicates a pathway where all of the free energy is lost as heat and no work is done (as for isolated proteins in solution). The equilibrium constant for the A to B transition, KAB, would be large for the dashed pathway and the reaction would not be readily reversible. The A to B transition can be used to drive a vectorial mechanical process if A is converted to B at some displacement away from the free energy minimum of B (GBchem: where GBmech = 0). The heavy line indicates the pathway for an A to B transition where free energy is efficiently transformed into external work. If after the A to B transition the displacement toward x = 0 were prevented, then the equilibrium constant, KAB, would be small and the reaction would be readily reversible.
Figure 4. Figure 4.

A: A simplified chemical pathway for crossbridges undergoing attachment, force generation, and filament sliding in muscle. Two detached states, M.ATP and M.ADP.Pi, and two attached states, A.M.ADP.Pi and A.M.'ADP, from Scheme 13 are shown. B: Free energy diagram for the two detached x‐independent states, and the two attached x‐dependent states. The heavy line represents the pathway for crossbridges performing work as they move through the cross‐bridge cycle. Vertical steps indicate heat loss; movement along x indicates external work. During isometric contraction, movement along x is prevented so crossbridges become mechanically trapped near position II. These crossbridges would be readily reversible back to A.M.ADP.Pi, M.ADP.Pi and M.ATP (for instance in the presence of high Pi) because of the high free energy content of A.M.'ADP at position II. However, after A.M.'ADP reaches its free energy minimum due to filament sliding or because the proteins are not constrained within the filament (i.e. for ATPase in solution), the A.M.'ADP to A.M.ADP.Pi transition is much less readily reversed. Vectorial force generation and filament sliding require attachment of crossbridges away from their free energy minima. For example, mechanical free energy minima for A.M.ADP.Pi and A.M.'ADP must be displaced relative to one another in the direction appropriate for shortening.
Figure 5. Figure 5.

An idealized force‐velocity relationship (solid line) derived from the normalized Hill equation: V/Vmax = (1‐F/Fo)/(1+(F/Fo)(Fo/α)). This equation describes the observed inverse relationship between force (or load) and velocity with a characteristic curvature (Fo/α) for each fiber type. The left extreme of the curve is dominated by the action of positively strained crossbridges, the right side by detachment of negatively strained crossbridges, and the middle by dynamic mixtures of positively and negatively strained cycling bridges. A power‐load relationship (dashed line) derived from the idealized forced‐velocity data shows maximum power at 0.3Vmax. The power‐load curve and efficiency also depend upon the Fo/α factor for a given fiber type 49,112.
Figure 6. Figure 6.

Schematic representation of crossbridges in three states. I. Detached or weakly attached. In this state the crossbridge can assume many distinct orientations due to a flexible hinge where an elastic spring element attaches to the globular head. II. Strongly attached positively strained. This state would occur during isometric contraction after attachment, Pi release, and rotation of the crossbridge to stretch the spring. III. If the filaments are released the spring will recoil causing filament displacement. This state would occur if filaments were to slide beyond the mechanical equilibrium position to a position where the spring is compressed. This is a negatively strained crossbridge that impedes further sliding. Approximate locations of I–III on the free energy diagram are given in Figure 4B.
Figure 7. Figure 7.

Structure and photolysis half‐times for three caged compounds commonly used in skinned fiber studies. Approximate half‐times are listed for the rate‐limiting photochemical reactions under near physiological conditions, pH 7, 21°C. The version of caged Ca2+ illustrated is nitrophenyl EGTA 20.
Figure 8. Figure 8.

Close coupling between force generation and Pi release in skinned cardiac myocytes. A: Isometric force development after photochemical elevation of free Ca2+ within the filament lattice. The time course prior to “slack” shows that both the rate and extent of force development were altered by the presence of 10 mM added Pi (b) compared to no added Pi (a). Pi depressed the amplitude of the force response and accelerated the rate of approach to the final amplitude, consistent with Scheme 14. B: A complimentary experiment in which Pi was produced rapidly within isometric Ca2+‐activated myocytes. Increasing concentrations of photoreleased Pi, (a) 0.5 mM Pi, (b) 1 mM Pi and (c) 2.7 mM Pi, caused both a greater and more rapid depression of isometric force, consistent with Scheme 14. For comparison, Pi at 0.5 to 10 mM has no effect on the ATPase of isolated actomyosin. Data from 2 with permission.
Figure 9. Figure 9.

Elementary transitions in single myosin molecules. A: Experimental arrangement for optical trap measurements of unitary force and displacement by actomyosin. The actin filament is attached at each end to a bead (dark spheres). Each bead is controlled by a laser trap. The actin filament is lowered onto another bead (white sphere) coated with a low density of myosin molecules. From 23 with permission. B, C: Records of force and displacement produced by individual V1 and V1 cardiac myosin isoforms. The unitary force and displacements are similar for V1 and V3, but V3 events are prolonged. Verticle scale bars are 2 pN and 20 nm, respectively. D: Schematic of unitary events in cardiac myosin. In principle, myosins can differ by amplitude of unitary force or displacement on the y‐axis, by mean duration of attached strong binding states, or by duration of detached or weak binding states. Dotted lines illustrate time‐averaged force or displacement.

From 91 with permission
Figure 10. Figure 10.

Domains and clefts of myosin S1. A: Outlines of major domains are superimposed on a ribbon diagram taken from the crystal structure of chicken myosin S1 76,78. Also shown are the nucleotide cleft (vertical arrow) and actin site cleft (horizontal arrow). B: Schematic representation of myosin S1 including 20K (long helix), 25K, 50K, LC1, LC2, and an elastic element. In the nucleotide‐free state (left), the nucleotide site at the 25K–50K interface is open, but the actin interaction site at the 20K–50K interface is closed and S1 is tightly bound to actin. ATP binding in the nucleotide pocket results in large changes in the actin interaction site causing a greatly weakened interaction between myosin S1 and actin (right). Dissociation of Pi out of the actin site cleft permits the 20K–50K interface to close and strong bonds between S1 and actin to reform (bottom). An appropriate change in the angle of the 10 nm extended arm of the 20K domain, stabilized by light chains, could stretch an elastic element or displace the actin and myosin filaments relative to one another.


Figure 1.

Muscle fiber ultrastructure. Fibers are comprised of bundles of myofibrils, each containing alternating dark bands (A‐bands) and light bands (I‐bands) when viewed in the light microscope. Illustrated in diagrams below the micrograph is the arrangement of proteins that underlie this banding pattern. The dark band corresponds to the thick myosin filament which has a bare zone or light stripe at its center. The light band corresponds to thin actin filaments which are anchored at the Z‐line in the center of the I‐band. The outer segments of the dark band represent the region of overlap between actin and myosin filaments where crossbridges are located and where productive actin‐myosin interactions occur. A sarcomere is the structure between two Z‐lines, and when the sarcomere shortens the distance between Z‐lines decreases.



Figure 2.

Time course of ATP hydrolysis catalyzed by myosin S1 and actomyosin S1 measured by formation of total Pi. Rapid mixing of ATP with myosin produces a Pi burst in the first few tenths of a second, followed by a slower rate of Pi formation (solid line). The burst is approximately equal in moles to the number of moles of myosin S1 present, and represents the first cycle of ATP hydrolysis bound to myosin S1. Further ATP hydrolysis (and Pi formation) requires product dissociation, which is very slow (t1/2 = 14 s) in the absence of actin. At intermediate actin concentrations, this second phase increases in rate but the overall time course remains distinctly biphasic. At very high actin concentration, the second phase approaches the rate of the initial (burst) phase making the burst less discernible.



Figure 3.

Transduction of chemical free energy into a mechanical process for a simple one step reaction. State A is a non‐force generating state so its basic free energy (GAchem) is independent of displacement. State B is a force generating state whose force is linearly related to displacement (F = κx) and whose mechanical free energy is parabolically related to displacement (GBmech = κx2/2). The dashed line indicates a pathway where all of the free energy is lost as heat and no work is done (as for isolated proteins in solution). The equilibrium constant for the A to B transition, KAB, would be large for the dashed pathway and the reaction would not be readily reversible. The A to B transition can be used to drive a vectorial mechanical process if A is converted to B at some displacement away from the free energy minimum of B (GBchem: where GBmech = 0). The heavy line indicates the pathway for an A to B transition where free energy is efficiently transformed into external work. If after the A to B transition the displacement toward x = 0 were prevented, then the equilibrium constant, KAB, would be small and the reaction would be readily reversible.



Figure 4.

A: A simplified chemical pathway for crossbridges undergoing attachment, force generation, and filament sliding in muscle. Two detached states, M.ATP and M.ADP.Pi, and two attached states, A.M.ADP.Pi and A.M.'ADP, from Scheme 13 are shown. B: Free energy diagram for the two detached x‐independent states, and the two attached x‐dependent states. The heavy line represents the pathway for crossbridges performing work as they move through the cross‐bridge cycle. Vertical steps indicate heat loss; movement along x indicates external work. During isometric contraction, movement along x is prevented so crossbridges become mechanically trapped near position II. These crossbridges would be readily reversible back to A.M.ADP.Pi, M.ADP.Pi and M.ATP (for instance in the presence of high Pi) because of the high free energy content of A.M.'ADP at position II. However, after A.M.'ADP reaches its free energy minimum due to filament sliding or because the proteins are not constrained within the filament (i.e. for ATPase in solution), the A.M.'ADP to A.M.ADP.Pi transition is much less readily reversed. Vectorial force generation and filament sliding require attachment of crossbridges away from their free energy minima. For example, mechanical free energy minima for A.M.ADP.Pi and A.M.'ADP must be displaced relative to one another in the direction appropriate for shortening.



Figure 5.

An idealized force‐velocity relationship (solid line) derived from the normalized Hill equation: V/Vmax = (1‐F/Fo)/(1+(F/Fo)(Fo/α)). This equation describes the observed inverse relationship between force (or load) and velocity with a characteristic curvature (Fo/α) for each fiber type. The left extreme of the curve is dominated by the action of positively strained crossbridges, the right side by detachment of negatively strained crossbridges, and the middle by dynamic mixtures of positively and negatively strained cycling bridges. A power‐load relationship (dashed line) derived from the idealized forced‐velocity data shows maximum power at 0.3Vmax. The power‐load curve and efficiency also depend upon the Fo/α factor for a given fiber type 49,112.



Figure 6.

Schematic representation of crossbridges in three states. I. Detached or weakly attached. In this state the crossbridge can assume many distinct orientations due to a flexible hinge where an elastic spring element attaches to the globular head. II. Strongly attached positively strained. This state would occur during isometric contraction after attachment, Pi release, and rotation of the crossbridge to stretch the spring. III. If the filaments are released the spring will recoil causing filament displacement. This state would occur if filaments were to slide beyond the mechanical equilibrium position to a position where the spring is compressed. This is a negatively strained crossbridge that impedes further sliding. Approximate locations of I–III on the free energy diagram are given in Figure 4B.



Figure 7.

Structure and photolysis half‐times for three caged compounds commonly used in skinned fiber studies. Approximate half‐times are listed for the rate‐limiting photochemical reactions under near physiological conditions, pH 7, 21°C. The version of caged Ca2+ illustrated is nitrophenyl EGTA 20.



Figure 8.

Close coupling between force generation and Pi release in skinned cardiac myocytes. A: Isometric force development after photochemical elevation of free Ca2+ within the filament lattice. The time course prior to “slack” shows that both the rate and extent of force development were altered by the presence of 10 mM added Pi (b) compared to no added Pi (a). Pi depressed the amplitude of the force response and accelerated the rate of approach to the final amplitude, consistent with Scheme 14. B: A complimentary experiment in which Pi was produced rapidly within isometric Ca2+‐activated myocytes. Increasing concentrations of photoreleased Pi, (a) 0.5 mM Pi, (b) 1 mM Pi and (c) 2.7 mM Pi, caused both a greater and more rapid depression of isometric force, consistent with Scheme 14. For comparison, Pi at 0.5 to 10 mM has no effect on the ATPase of isolated actomyosin. Data from 2 with permission.



Figure 9.

Elementary transitions in single myosin molecules. A: Experimental arrangement for optical trap measurements of unitary force and displacement by actomyosin. The actin filament is attached at each end to a bead (dark spheres). Each bead is controlled by a laser trap. The actin filament is lowered onto another bead (white sphere) coated with a low density of myosin molecules. From 23 with permission. B, C: Records of force and displacement produced by individual V1 and V1 cardiac myosin isoforms. The unitary force and displacements are similar for V1 and V3, but V3 events are prolonged. Verticle scale bars are 2 pN and 20 nm, respectively. D: Schematic of unitary events in cardiac myosin. In principle, myosins can differ by amplitude of unitary force or displacement on the y‐axis, by mean duration of attached strong binding states, or by duration of detached or weak binding states. Dotted lines illustrate time‐averaged force or displacement.

From 91 with permission


Figure 10.

Domains and clefts of myosin S1. A: Outlines of major domains are superimposed on a ribbon diagram taken from the crystal structure of chicken myosin S1 76,78. Also shown are the nucleotide cleft (vertical arrow) and actin site cleft (horizontal arrow). B: Schematic representation of myosin S1 including 20K (long helix), 25K, 50K, LC1, LC2, and an elastic element. In the nucleotide‐free state (left), the nucleotide site at the 25K–50K interface is open, but the actin interaction site at the 20K–50K interface is closed and S1 is tightly bound to actin. ATP binding in the nucleotide pocket results in large changes in the actin interaction site causing a greatly weakened interaction between myosin S1 and actin (right). Dissociation of Pi out of the actin site cleft permits the 20K–50K interface to close and strong bonds between S1 and actin to reform (bottom). An appropriate change in the angle of the 10 nm extended arm of the 20K domain, stabilized by light chains, could stretch an elastic element or displace the actin and myosin filaments relative to one another.

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Article Title: Kinetics of the Actin–Myosin Interaction
 

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Jeffery W. Walker. Kinetics of the Actin–Myosin Interaction. Compr Physiol 2011, Supplement 6: Handbook of Physiology, The Cardiovascular System, The Heart: 240-263. First published in print 2002. doi: 10.1002/cphy.cp020106