Crossbridge Theory

Thick filaments contain the protein myosin, which is made up of a polypeptide chain with a globular head. These heads constitute the crossbridges that interact with the thin

Actin Myosin Cross Section Insect
Figure 18.2 Longitudinal section (top panel) and cross-section (lower panels) of a sarcomere showing its organization into bands. (Berne and Levy, 1993, p. 283, Fig. 17-3.)

filaments to form bonds that act in ratchet-like fashion to pull on the thin filaments. In addition, the myosin heads have the ability to dephosphorylate ATP as an energy source.

Thin filaments contain the three proteins actin, tropomyosin, and troponin. Each actin monomer is approximately spherical, with a radius of about 5.5 nm, and they aggregate into a double-stranded helix, with a complete twist about every 14 monomers. Because the coil is double-stranded, this structure repeats every 7 monomers, or about every 38 nm. Tropomyosin, a rod-shaped protein, forms the backbone of the double-stranded coil. The troponin consists of a number of smaller polypeptides, which include a binding site for calcium as well as a portion that blocks the crossbridge binding sites on the actin helix. When calcium is bound, the confirmation of the troponin-tropomyosin complex is altered just enough to expose the crossbridge binding sites. In Fig. 18.3 we show a scale drawing of the probable way in which the actin, tropomyosin, and myosin proteins fit together.

Contraction takes place when the crossbridges bind and generate a force causing the thin filaments to slide along the thick filaments. A schematic diagram of the cross-bridge reaction cycle is given in Fig. 18.4, with the accompanying physical arrangement shown in Fig. 18.5. Before binding and contraction, ATP is bound to the crossbridge heads of the myosin (M), and the concentration of calcium is low. When the calcium concentration increases, calcium ions bind to the troponin-tropomyosin complex, ex-

18.1

CROSSBRIDGE THEORY

Myosin Filament Ratchet Theory

Figure 18.3 A: Scale drawing of actin, myosin, and tropomyosin proteins. B: Scale drawing of the thick and thin filaments (labeled the A and I filaments here), showing the probable way in which the actin, myosin, and tropomyosin proteins fit together. Troponin, which is bound to tropomyosin, is not included in the diagram. (White and Thorson, 1975, Fig. 9, parts A and B (i).)

Figure 18.3 A: Scale drawing of actin, myosin, and tropomyosin proteins. B: Scale drawing of the thick and thin filaments (labeled the A and I filaments here), showing the probable way in which the actin, myosin, and tropomyosin proteins fit together. Troponin, which is bound to tropomyosin, is not included in the diagram. (White and Thorson, 1975, Fig. 9, parts A and B (i).)

posing the crossbridge binding sites on the actin filament (A). Where possible, a weak bond between actin and myosin is formed. Release of the phosphate changes the weak bond to a strong bond and changes the preferred configuration of the crossbridge from nearly perpendicular to a bent (foreshortened) position. While the crossbridge is in anything but this energetically preferred, bent state, there is an applied force that acts to pull the thin filament along the thick filament. The movement of the crossbridge to its newly preferred configuration is called the power stroke. Almost immediately upon reaching the preferred bent configuration, the crossbridge releases its ADP and binds another ATP molecule, causing dissociation from the actin binding site and return to its initial perpendicular and unbound position. ATP is then dephosphorylated, yielding ADP, phosphate, and the stored mechanical energy for the next cycle. Thus, during muscle contraction, each crossbridge cycles through sequential binding and unbinding to the actin filament.

As we will see in the following sections, to construct quantitative models of cross-bridge binding it is necessary to know how many actin binding sites are available to a single crossbridge. One possibility is that the crossbridge must be precisely oriented to the actin binding site, and thus, in each turn of the helix, only one binding site is available to each crossbridge. In other words, from the point of view of the crossbridge, the binding sites have an effective separation of about 38 nm. Because of the physical constraints on each crossbridge, this means that at any time, there is only a single

A + M•ADP • P high actin affinity actin dissociation and hydrolysis

low actin affinity

without ATP cycle stops here (rigor mortis)

actin binding

power stroke power stroke without ATP cycle stops here (rigor mortis)

Figure 18.4 Major reaction steps in the crossbridge cycle. M denotes myosin, and A denotes actin.

binding site available to each crossbridge. This is the assumption behind the Huxley model, which we consider in detail below.

However, from the distribution of actin binding sites and crossbridges shown in Fig. 18.3, it is plausible that this assumption is not correct. Perhaps, depending on the flexibility of the actin filament, each crossbridge has a number of potential binding sites. In our discussion we concentrate on models for the two extreme cases: first, where each crossbridge has only a single available binding site, and second, where each crossbridge has a continuous array of available binding sites. Intermediate models, in which the crossbridge has a small number of discrete binding sites available, are considerably more complex and are mentioned only briefly.

Because of the sarcomere structure, the tension a muscle develops depends on the muscle length. In Fig. 18.6 we show a curve of isometric tension as a function of sar-comere length. By isometric tension, we mean the tension developed by a muscle when it is held at a fixed length and repeatedly stimulated (i.e., with a high-frequency periodic stimulus). Under these conditions the muscle goes into tetanus, a state, caused by saturating concentrations of calcium in the sarcoplasm, in which the muscle is continually attempting to contract. Note that the muscle cannot actually contract, because it is held at constant length, although it must go through the chemistry cycle of the power stroke, since the development of tension requires that energy be consumed.

At short lengths, overlap of the thin filaments causes a drop in tension, but as this overlap decreases (as the length increases) the tension rises. However, when the length is large, there is less overlap between the thick and thin filaments, so fewer crossbridges

binding site actin myosin

ADP-P

Ca2+

f>ADP-P

crossbridge binding

ADP-

power stroke

ADP-P

ADP-P

Q-jATP

Ca2+

ADP-P

Figure 18.5 Position of crossbridge components during the major steps in the crossbridge cycle.

bind, and less tension develops. When there is no overlap between the thick and thin filaments, the muscle is unable to develop any tension.

Skeletal muscle tends to operate at lengths that correspond to the peak of the isometric length-tension curve, and thus in many experimental setups the tension the muscle develops does not depend significantly on the muscle length. However, the same is not true for cardiac muscle, which considerably complicates theoretical studies of this muscle type. For these reasons we restrict our attention to models based on data from skeletal muscle. Peskin (1975) presents a detailed description of some theoretical models of cardiac muscle.

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    How to bind model bridge?
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    Which section consists of both actin and myosin filaments?
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