## The relation between sarcomere length and isometric tension

The suggestion that contraction depends on the interaction of the actin and myosin filaments at the cross-bridges implies that the isometric tension should be proportional to the degree of overlap of the filaments. In order to test this idea it is necessary to measure the active increment of isometric tension at different known sarcomere lengths. The measurements have to be done on a single fibre and there are some technical difficulties because sarcomeres at the ends of a fibre may take up lengths different from those in the middle. A. F. Huxley and his colleagues overcame these difficulties by building an apparatus which used optical servomechanisms to maintain the sarcomere lengths in the middle of a fibre constant during a contraction.

Fig. 10.10 summarizes the results of these experiments. It is evident that the lengthâ€”tension diagram consists of a series of straight lines connected by a short curved region. There is a 'plateau' of constant tension at sarcomere lengths between 2.05 and 2.2 fxm. Above this range tension falls linearly with increasing length; the projected line through most of the points in this region reaches zero at 3.65 fxm. Below the plateau, tension falls gradually with decreasing length down to about 1.65 fxm, then much more steeply, reaching zero at about 1.3 fxm.

Does this curve fit the predictions of the sliding filament theory? We need to know the dimensions of the filaments (Fig. 10.11). Measurements by electron microscopy indicate that the myosin filaments are 1.6 fxm long and the actin filaments, including the Z line, are 2.05 fxm long. The middle region of the myosin filaments, which is bare of projections and therefore cannot form cross-bridges, is 0.15 to 0.2 fxm long and the thickness of the Z line is about 0.05 fxm.

Now let us see if the lengthâ€”tension diagram shown in Fig. 10.9 can be related to these dimensions, starting at long sarcomere lengths and working through to short ones. Above 3.65 |xm (stage 1 in Fig. 10.12) there should be no cross-bridges formed, and therefore no tension development. In fact there is some tension development up to about 3.8 |xm; this might well be due to some residual irregularities in the system. Between 3.65 ^m and 2.2 to 2.25 |xm (1 to 2) the number of cross-bridges increases linearly with decrease in length, and therefore the isometric tension should show a similar increase. It does. With further shortening (2 to 3) the number of cross-bridges remains constant and therefore there should be a plateau of constant tension in this region. There is. After stage 3 we might expect there to be some increase in the internal resistance to shortening since the actin filaments must now overlap, and after stage 4 the actin filaments from one half of the sarcomere might interfere with the cross-bridge formation in the other half of the sarcomere. We would expect both these effects to reduce the isometric tension, which does indeed fall at lengths below 2.0 |xm. At 1.65 |xm (stage 5) the myosin filaments will hit the Z line, and so there should be a considerable increase in the resistance to further shortening; there is a distinct kink in the curve at almost exactly this point, after which the tension falls much more sharply. The curve reaches zero tension at about 1.3 |xm, before stage 6 is reached.

It would be difficult to find a more precise test of the sliding filament theory than is given by this experiment, and the theory clearly passes the test with flying colours.

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