A muscle has an optimal length for generating maximum tension

Two parts of a pull-up exercise are especially difficult. When your arms are fully extended, it is hard to start the pull-up; and when your chin has almost reached the bar, the last little bit is difficult. The structure of the sarcomere is the reason.

When a muscle changes length the sarcomeres also change length, and the spatial relationships between the actin and myosin filaments changes (Figure 47.12). If there is no actin–myosin overlap, cross-bridges cannot form and the sarcomere can't generate force. This is almost the situation when you are hanging from the pull-up bar. At the other extreme, when the muscle is fully contracted, the actin filaments are overlapping and the myosin filaments are bumping up against the Z lines, so additional force cannot be generated. With these considerations, you can ask how well a specific muscle—such as the frog jumping muscle—will function given a range of sarcomere lengths. In Investigating Life: What Is the Optimal Resting Position for the Jumping Muscle of the Frog?, we examine experiments done to identify the optimal sarcomere length for a forceful frog jump. As you review these experiments, think about how they apply to deciding on the best starting position for a sprint.

image
Figure 47.12 Force and Length The amount of force a sarcomere can generate depends on its resting length. When a muscle is stretched and its sarcomeres lengthened, there is less overlap between the actin and myosin filaments, and less force can be produced. When a muscle is fully contracted, the myosin filaments are bumping up against the Z lines of the sarcomeres, so further contraction is not possible.

1011

investigating life

What Is the Optimal Resting Position for the Jumping Muscle of the Frog?

experiment

Original Paper: Lutz, G. J. and L. C. Rome. 1994. Built for jumping: The design of the frog muscular system. Science 263: 370–372.

The force propelling a frog’s jump should be greatest when there is optimal overlap between the actin and myosin filaments and not when the muscle is stretched. The following experiment attempted to determine the resting sarcomere length that allows a frog to achieve a maximal jump.

image

work with the data

The resting position of the sarcomeres and the extent of their shortening during a jump maximize the force that the frog’s muscle can generate to power the jump. But in physical terms, power is a force applied over a specific time. Therefore the velocity of contraction (measured as muscle length/second [ML/s]) will influence the maximum power the muscle can generate, and the velocity of contraction depends on the load. If the load is too great, the contraction is isometric (velocity = 0). If the load is negligible, the velocity of contraction can be maximal. Figure A shows the relationship between force and velocity of contraction in a frog jumping muscle under different loads. The mean jump velocity is indicated. Figure B shows the change in muscle length (mm) during a jump (milliseconds).

QUESTIONS

Question 1

Power is work/time and work is force × displacement. Displacement/time = velocity. Therefore power = force × velocity. Using the data in Figure A, plot a curve that shows power as a function of contraction velocity for the frog muscle.

Question 2

What is the velocity of contraction of the frog jumping muscle in muscle lengths/sec? Use the data in Figure B.

The jump takes 50 ms (see Figure B), and the shortening in terms of muscle lengths is 7.5 mm/33.6 mm = 0.22 ML. So, velocity of muscle contraction in ML/sec = 0.22/.05 sec = 4.4.

Question 3

Is the speed and force of the frog muscle optimal for generating the most powerful jump?

The power generated by the jumping muscle is maximal at the observed mean jumping velocity.

A similar work with the data exercise may be assigned in LaunchPad.