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Muscle Length j rrrrrrrr rvvrrvr'! j

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Z Thick filaments Thin filaments 1 Disk Disk

FIGURE 9 The relationship between skeletal muscle length and isometric forces developed by the muscle. (A) The length-passive force curve represents the force exerted by the unstimulated muscle at each length. The length-total force curve represents the force exerted by the muscle during a tetanus at each length. The length-active force curve is obtained by subtracting the passive from the total force at each length. This represents the force developed by the crossbridges. The magnitude of the active force at each length depends mostly on the overlap of the thick and thin filaments at each muscle length. (B) The length at which maximum force occurs is the length at which there is optimal overlap (Lo). (C) As the muscle is stretched, some crossbridges cannot interact with the thin filaments, and active force falls.

previously) and the active force developed by cross-bridge cycling. Thus, a length-active force relationship can be obtained by subtracting the passive force from the total force at each length. By inspecting the length-active force curve, it is obvious that there is one length at which active force is maximal. This length is the optimal length (Lo). Going to either shorter or longer lengths results in less active force.

The length-force relationships can be explained on structural grounds. The length-passive force relationship is due to the elastic behavior of the cell membranes and of the connective tissue between the muscle cells. These structures resist the forces applied to a resting muscle. The length-active force relationship is due to the arrangements of the actin and myosin molecules within the sarcomere. As described previously, the core of the thick filament is made up of the tail regions of the myosin molecules, and the crossbridges are due to protrusion of a portion of the tail and of the globular heads of the myosin (see Fig. 2). Additionally, each thick filament is bilaterally symmetrical in the direction of protrusion of the crossbridges. There is a bare zone in the middle with no crossbridges. On each side of this zone, crossbridges extend outward and upward toward the thin filaments. At Lo, the thin and thick filaments overlap such that almost every myosin crossbridge is capable of interacting with an active site on the actin (Fig. 9B). This allows for maximum active force to be generated. Stretching the muscle lessens the overlap. Recall that the thin filaments are attached to the Z disks and that the Z disks are in turn attached to the cell membrane. Stretching the membrane results in the Z disks moving away from each other, dragging the thin filaments with them. This results in not every cross-bridge being able to reach an actin molecule (Fig. 9C). Thus, active force is reduced. If stretched to the point of no thick and thin filament overlap, no active force can be generated. At lengths shorter than Lo, the mechanisms responsible for the decreased force are less clear. A likely explanation is that, because cell volume must remain constant, the lateral distance between thick and thin filaments increases as the cell, and thus sarcomere, length shortens. This reduces the possibility of strong myosin crossbridge interactions with sites on actin.

In summary, the force of skeletal muscle contraction under isometric conditions is influenced by: (1) the number of cells in the muscle that are stimulated,

(2) the frequency at which they are stimulated, and

(3) the length of the muscle cells before stimulation.

Isotonic Contraction

Isotonic contractions can be recorded in vitro using a movable lever (Fig. 10A) instead of the force transducer o

Afterload st°pi pirot w I 1 J — Velocity meter

Muscle Stimulus

I Afterload

Afterload (force)

FIGURE 10 The relationship between the load against which a skeletal muscle must shorten (afterload) and the initial velocity of shortening. (A) A muscle is connected to a lever to which different weights (afterload) can be attached in such a way that the muscle does not bear the weight until it begins to contract. The initial muscle length before stimulation can be set by attaching a preload and holding the muscle at that length until shortening begins. (B) At any given initial muscle length, the velocity of shortening decreases as the afterload is increased. If the dashed line indicates values obtained with an initial length of Lo, either increasing (solid line) or decreasing (dotted line) the initial length will change the velocity at any given afterload, except for the velocity at zero afterload (Vmax). This velocity, Vmax, depends primarily on the isoform of myosin present in the muscle.

Afterload (force)

FIGURE 10 The relationship between the load against which a skeletal muscle must shorten (afterload) and the initial velocity of shortening. (A) A muscle is connected to a lever to which different weights (afterload) can be attached in such a way that the muscle does not bear the weight until it begins to contract. The initial muscle length before stimulation can be set by attaching a preload and holding the muscle at that length until shortening begins. (B) At any given initial muscle length, the velocity of shortening decreases as the afterload is increased. If the dashed line indicates values obtained with an initial length of Lo, either increasing (solid line) or decreasing (dotted line) the initial length will change the velocity at any given afterload, except for the velocity at zero afterload (Vmax). This velocity, Vmax, depends primarily on the isoform of myosin present in the muscle.

used to monitor isometric contractions. This lever is arranged so that changes in muscle length over time can be monitored and so that a weight can be added such that the muscle must bear the weight only after the muscle is fully activated. Such a weight is called an afterload. The experiment begins by setting the muscle to a given length with a preload. Then an afterload is added to the lever. The muscle is stimulated at a supramaximal pulse intensity at a tetanic frequency. If the muscle can develop force greater than that exerted by the afterload, the muscle will shorten and the initial velocity of shortening can be recorded. By using different afterloads—which really are equal to the forces that the muscle must develop in order to shorten—a force-velocity relationship is determined. If the experiment is repeated using different preloads to set different resting lengths, a family of force-velocity curves is generated (Fig. 10B). Note that all these curves have one point in common. If the curves are extrapolated back to zero afterload, a single velocity, the maximal velocity (Vmax), is obtained.

The force-velocity relationship can be explained partly by structure and partly by biochemical features of the muscle. For any particular muscle, the difference in velocity at any given afterload depends on the number of crossbridges taking part in the contraction; the more taking part, the higher the velocity, because each crossbridge will have to bear less of the load. As discussed above, the number of crossbridges taking part depends on the initial length of the muscle. Thus, the shortening velocity of an afterloaded muscle depends on muscle length. On the other hand, Vmax depends on the rapidity with which a single crossbridge can cycle unimpeded by any load. Theoretically, as long as one crossbridge is cycling under no load, the muscle will shorten at its maximal velocity. That is why Vmax is not affected by changes in initial muscle length. Vmax is determined by molecular properties of the contractile proteins (e.g., the ATPase activity of myosin).

Cardiac Muscle

As might be expected from their many structural and biochemical similarities, cardiac muscle exhibits many of the same mechanical characteristics as skeletal muscle; however, there are some important differences. Cardiac muscle cells, unlike skeletal muscle cells, are electrically coupled (see Chapter 11). Thus, once a stimulus pulse intensity is reached that effectively excites one cardiac muscle cell, the action potential spreads to all cells. Further increases in stimulus pulse intensity have little effect on contractile force. Also, unlike the situation seen in skeletal muscle, summation and tetanus do not occur in cardiac muscle. Action potential durations in cardiac muscle are almost as long as the contractile responses. Thus, the muscle relaxes before it is possible to stimulate it again because of the refractory period of the membrane (see Chapter 11). Also, the long duration of each action potential, through its associated rise in cytosolic calcium, allows for prolonged activation of the contractile proteins. This provides a longer time for crossbridge cycling to stretch the elastic structures of the muscle.

Cardiac muscle exhibits length-force and forcevelocity relationships similar to those of skeletal muscle (Fig. 11): (1) isometric force is a function of muscle length, (2) the velocity of contraction at any initial length is a function of the afterload, and (3) the velocity of contraction of an afterloaded muscle is a function of the initial length of the muscle. The explanations for these relationships in cardiac muscle are similar to those given for skeletal muscle. However, in cardiac muscle that normally functions in vivo at lengths less than Lo (see Chapter 13), the sensitivity of myofilament interaction to calcium may be modulated by more than the lateral distance between thick and thin filaments. Length effects on the affinity of troponin C for calcium also have been proposed.

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