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 2. The [sarcomere] length-tension relation

The above section describes how passive and total (& hence active tension) varies as a function of the length of the muscle. Maximal active force is generated at lengths close to the resting length of the muscle. In the 1970's workers succeeded in dissecting out small bundles of viable muscle fibres that enabled them to set the length of the fibres, accurately measure the sarcomere length and record the passive and total force generated at each length. As you can probably imagine, this resulted in a similar length-tension relation, but this time the x-axis units will be in microns. You should recognise the graph as one used in the lectures:

 Figure 4 - The relation between sarcomere length (in microns) and active tension (passive and total omitted for clarity)

 Important! Tension measured as a function of sarcomere length Top

Having a measurement of sarcomere length with which to correlate with passive and total tension (& thereby the active tension), enabled workers to corroborate the sliding filament theory and estimate very accurately the length of the thick and thin filaments.

As part of your course you are required to be able to understand the structure of the sarcomere and to be able to interpret the graph in figure 4 in order to calculate the lengths of the thick and thin filaments.

To do this you may need to sketch out the sarcomere & consider where the actin and myosin filaments are within the sarcomere, before reading further.

To help you to understand the problem and how to solve it, I've provided additional graphs based on figure 4 but with cartoons of a stylized sarcomere superimposed on the graph. Remember two things here:

• The resting sarcomere is about 2.2 mm long
• If the sarcomere is over-stretched the number of cross bridges that can form is reduced linearly with increasing length.

 Figure 5 - Lack of filament overlap at longest lengths (when active force falls to zero)

It should be obvious from the cartoon that the actin filaments do not overlap the myosin filament - no cross bridges can form and so no contraction is possible. The arrow from the right hand z-disk is projected down to enable you to easily read off the sarcomere length at this point and also on down to illustrate on the graph that no active force is generated by muscle fibres at such extreme lengths.

 Maximal force at resting sarcomere length!!! Top

 What happens at short sarcomere lengths? Top

The remaining portion of the length-tension relation tells us that active force declines as the sarcomere becomes shorter than this 'optimum' length. Why?

The answer is not so easy to visualize. At moderately short lengths it seems that the ends of the actin filaments, which are 1 m m in length begin to meet in the middle of the sarcomere. In some text-books this is said to impare the proper association of myosin with the appropriate actin filament. Any cross bridges that form between the myosin filament and the wrong filament will result in wasted effort as the movement of the myosin head will not act to shorten the sarcomere. Thus, active stress falls away progressively as the sarcomere is made shorter and shorter. This is the interpretation I tend to favor.

At a point however the rate at which tension declines with ever decreasing sarcomere lengths changes abruptly. The next figure illustrates the probable cause for this.

 Figure 7 - Filament overlap and sarcomere appearance at the point of inflection

Although it is perhaps not completely obvious from the cartoon, one can imagine that at some point the myosin filament and the Z-disks that delimit the sarcomere will collide. The myosin filament is 1.6 m m in length. Look again at figure 7. The inflection occurs at almost exactly 1.6 m m! This was indeed the evidence that was used to suggest the length of the thick filament. It has since been measured directly using electron microscopy and these measurements also fix the length of the thick filament to be 1.6 m m.

There is still some active force generated at still shorter sarcomere lengths. How can this be?

There is a lot of energy being provided by all the myosin heads and this is able to deform and buckle the thick filament to some extent. There is a limit to this, however, and active force falls to zero when the sarcomere is about 1.2 m m in length. The stiffness of the thick filament is resisting any further shortening and none of the energy from the cross bridges is being done on the external load, the transducer.

 Figure 8 - The appearance of the sarcomere at the shortest length (where active force falls to zero)

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