Construction of a Length-Tension Diagram
Tips & hints1. The unit of length for the slider is 1% of the in vivo length of the muscle (i.e., the length of the muscle measured prior to dissecting it free from the frog and connecting it to the myograph).
2. For most of the ‘runs’ you do with this simulation, you’ll probably want to use small increases in muscle length, say 5%, between successive runs. (The default change in length when you do a mouse click with the cursor placed in the slider’s track is 5%.) However, once you’ve stretched the muscle to about 140% of its normal length, the Passive tension commences increasing very rapidly, and you’ll want to use 1% to 2% increments in muscle length between runs to avoid losing track of what’s happening. Note that in order to increment the length by 1%, you’ll have to click the slider’s up or down arrow twice, rather than once.
3. Just as would be the case if you were running this experiment in a wet lab setting (i.e., using living experimental animals and a physiograph or strip-chart recorder to record the data), the numerical data you need to complete the exercise will not be displayed for you on the computer screen. You’ll need to measure the length of line segments to get the data you need to complete the exercises and answer the questions at the conclusion of the experiment. Be sure to measure the 50 g scale line and record the measurement on your data sheet.
4. You’ll need to convert your measurements of Active and Passive tension into units of force. If you don’t recall how to do this conversion, click here for instructions.
Experimental Techniques
1. Use the slider to set the muscle’s length 50% of its normal in vivo value (i.e., move the slider at the top of its track and make sure the text field displays a value of 50). Click the “Go” button and note the change in the display. Use a ruler to measure the height of the short horizontal line segment above the x-axis ( = the Passive tension) and the length of the vertical line above that ( = the Active tension). Record your measurements on the data sheet (included below).
2. Increase the muscle’s length to 55% and repeat. Continue increasing the muscle’s length in, say, 5% increments and recording data after each run until you have a clear picture of the effect of muscle length on passive and active tension.
Questions and Exercises
1. Construct graphs of Passive, Active, and Total tension ( = Passive + Active) vs. muscle length. Be sure to convert your data into units of force before graphing. Note the appearance of each. What length yields maximum Total tension? Is the length that yields maximum Active tension the same, or different? Does the ‘shape’ of these three graphs correspond to your expectations based on what you know about the mechanism of striated muscle fiber contraction? Defend your answer.
2. Construct a graph of Active Tension vs. Passive Tension. What can you infer about skeletal muscle contraction from this graph?
3. Repeat #2, this time graphing the ratio of Active Tension to Passive Tension (i.e. Active Tension ¸ Passive Tension) vs. Passive Tension. Discuss the implications of this graph.
4. At what length should the gastrocnemius muscles’ efficiency (= work done/energy used) be the greatest – the length corresponding to maximal active tension, or the length corresponding to maximal total tension? Justify your answer.
5. Note the amount of Passive tension in the muscle at lengths producing maximal (or near-maximal) Active tension. In comparison with the Active tension generated at the same length, does the amount of Passive tension seem like a little, or a lot? Can you account for this on both a mechanistic basis and on an evolutionary (adaptive) basis? What do you conclude from this observation?
6. At what length would you expect that the gastrocnemius muscles’ efficiency (= work done ¸ energy used) would be the greatest: the length corresponding to maximal Active tension, or the length corresponding to maximal Total tension? Justify your answer.
Data Sheet For Length-Tension Diagram
Tracing Measurements (mm)
Calculated Tension
(N)
Muscle Length
(% of Normal)
Passive
Active
Passive
Active
Length of the 50 g scale line: _______________