Background

During isotonic contraction, skeletal muscle shortens against a load. The velocity of muscle shortening is related to the load applied and can be graphically represented by the Hill equation:

(F + a)(V + b) = (Fo + a)b Equation 1

Where F is the load, V is the velocity of shortening, Fo is the maximum force that can be developed by the muscle during an isometric contraction, and a and b are constants. This equation results in a hyperbolic curve. To make it more useful as a tool, this equation can be linearized to produce the following equation:

F = b [(Fo – F)/V] – a Equation 2

Now if we graph [(Fo – F)/V] and load we get a straight line with a slope of b and a y-intercept of –a. This is a useful form of the equation that allows us to use the power of regression to calculate the constants and to predict certain variables from measured parameters. More specifically, it allows us to calculate the velocity of muscle shortening when applying any load.


In animal systems, muscles provide locomotor capacity by attaching to the skeletal system and moving the bones in a lever fashion. There are three major classes of levers (1st class, 2nd class, and 3rd class) and most of the lever systems in animals are 3rd class with the muscle contraction closer to the fulcrum and on the same side as the load. However, other lever systems do exist in animal systems and the one we are going to focus on today is the 2nd class lever of the gastrocnemius muscle. 2nd class levers also have the load and muscle contraction on the same side of the fulcrum, but in this case the load is between the fulcrum and the lever.

We can now look at the animal’s velocity (the load) attributable to contraction of the gastrocnemius. To do this, we use rotational physics with the fulcrum as the pivot point and the load and muscle contractions as points rotating about the pivot. In a rotating body, all points along a line have the same angular speed (ω), however, not all points have the same tangential speed (νt). The relationship between tangential speed and angular speed is expressed as:

νt = r ω Equation 3

where r is the radius, or the distance from the fulcrum to the point of interest on the line. Tangential speed of the load, in turn, is the velocity that the animal moves forward due to contraction of the gastrocnemius and if we can determine the velocity of shortening (tangential speed of the muscle force) for the muscle with a given load and the length of bone between fulcrum, load, and muscle force application, then we can determine the speed that the load is propelled forward using the following formula:

νtL = rL νtM /rM Equation 4

Speed is not the only factor that is important to animals in lever systems, the power developed during contraction is also important. The strength a given muscle has to develop power using the boney levers is termed the mechanical advantage, which is simply the ratio of the load to the force of contraction; it can also be represented by the ratio of the lever arm to the load arm. Mechanical advantage and the maximum strength available in a muscle-bone lever are directly proportional. However, as the mechanical advantage is increased, the velocity of the lever system is decreased. Thus, there is a trade-off between speed and power in boney levers that can influence the evolution of particular skeletal features to maximize one or the other and we would expect speedy organisms to favor the velocity potential in levers while powerful animals would favor the mechanical advantage of levers.


Lab Activity

Introduction:

Today we are going to use the gastrocnemius muscle from a bullfrog (Rana catesbeina) to measure the force of contraction potential in a muscle and to measure the velocity of contraction given a particular load. From this data and some skeletal measurements we will be able to calculate the velocity potential for the frog from this particular muscle-lever system.

Materials:

·  Frog

·  Force transducer

·  Displacement transducer

·  Physiograph recorder (or PC)

·  Muscle stimulating electrodes

·  Stimulator

·  Ring stand and clamps

·  Femur clamp

·  Bone shears

·  Thread or Suture

·  Ruler

·  Amphibian Ringer’s solution

·  Weight pans with small weights.

·  Dissection kit and pan

·  Scale

Frog Dissection:

It will be necessary to isolate the gastrocnemius muscle still attached to the femur from a recently euthanized frog. You should obtain a frog from your instructor that has been correctly euthanized; it may still move slightly, but that is normal and does not mean that the frog is still alive. Dry the animal with a paper towel and weigh it. Using a scalpel, make an incision through the skin around the waist of the animal. Take a small pair of scissors and extend the incision from the waist down the ventral surface of each leg to the ankle. Carefully peal the skin off the animal from ventral to dorsal, completely removing the skin, but do not discard. Be sure to use The amphibian ringer’s solution liberally throughout this dissection to keep the muscles wet; never let the muscles dry out. Remove the muscles from the femur of one leg. Carefully, separate the gastrocnemius from the surrounding muscles and the tibia. Isolate the Achilles tendon from the calcaneus of the frog’s foot and tie it off tightly with the thread/suture (you are going to use this thread to attach the muscle to the transducers, so be sure it is securely fastened). You should now be able to cut the tendon distal to the thread and, using the bone shears, sever the femur about halfway along its length. You should now have an isolated gastrocnemius muscle still attached to the femur and anchored at the tendon with a piece of thread/suture. Place the cut end of the femur into the femur clamp and secure it tightly so that it does not slip. Ensure that the muscle is lubricated with ringer’s solution throughout the experiments; NEVER LET THE FROG MUSCLES DRY OUT!!

Experiment 1-Maximum Isometric Contraction:

1.  On the ringstand, place the following pieces of equipment, from top to bottom: Femur clamp, stimulating electrodes, force transducer.

  1. Ensure that the string from the gastrocnemius is attached to the force transducer and adjust the mounts so that there is minimal tension, but no slack in the line.
  2. Place the stimulating electrodes on the muscle and ensure there is good contact, but do not interfere with muscle contraction.

2.  Connect the force transducer to the physiograph and the electrodes to the stimulator.

3.  Calibrate the force transducer by hanging a known weight on it and recording the tracing on the physiograph. From the known weight and the tracing, you should be able to recognize the force of a contraction given a physiograph recording.

4.  Starting at 0.0V with a 10 ms pulse, stimulate the frog muscle and record the response. Increase the voltage in 0.25 V increments, recording a muscle twitch at each voltage, until a maximum contraction occurs (no increases in contraction force as the voltage is increase).

  1. Record the voltage at maximum contraction here ______V
  2. This is the voltage that elicits the maximum isometric contraction in this muscle and will be used in the ensuing experiment.

Experiment 2-Force and Velocity of Frog Gastrocnemius

1.  Using the setup from the previous experiment, replace the force transducer with the displacement transducer.

  1. Ensure the string from the gastrocnemius is attached to the displacement transducer and adjust the mounts so the muscle contraction can move the transducer arm a maximum distance without stretching the muscle when the weights are applied. Be sure the connection from the muscle to the transducer is vertical and there is no slack in the line.
  2. Place the weight pan on the other end of the transducer arm and be sure it does not touch the table.
  3. Ensure the stimulating electrodes are still in contact with the muscle and the muscle is moistened with ringer’s.

2.  Connect the displacement transducer to the physiograph and the electrodes to the stimulator.

3.  Measure the length of travel for the displacement arm and calibrate the physiograph.

  1. Start the physiograph and manually move the displacement arm through a full cycle.
  2. Use the measured length of the arm and the physiograph recording to determine the scale on the physiograph.
  3. Before proceeding, you should be able to determine the length of travel for the displacement arm given a tracing on the physiograph and you should be able to determine the time of travel.

4.  Using the voltage from the previous experiment and a 10 ms pulse duration, stimulate the muscle with the weight pan attached and record.

5.  From the recording you should be able to measure distance of travel/unit time (velocity of contraction) and using the weight of the pan, you can calculate force (g).

6.  Increase the weight on the muscle by ~ 10 g increments (in an afterloaded fashion, meaning no stretching of the muscle before contraction), recording a muscle contraction each time, until a maximum contraction is reached or until you are out of weights. The data should at least include the weight of the animal.

Experiment 3-Anatomical Measurements.

1.  Using the leg that is still on the animal and a ruler, measure the distance from the distal portion of the metacarpals to the articulation with the tibia & fibula.

2.  Repeat for the distance from the distal portion of the metacarpals and the insertion of the Achilles tendon.

Analysis of Data

1.  Using the data from experiment 1, graph the force of contraction (g) against the voltage (Volts) and use that graph to calculate the maximum isometric force of the muscle (Fo).

2.  Using the data from experiment 2, graph the velocity of contraction (V) against the force moved (g).

3.  Transform the data using equation 2 and graph again. Use a linear regression on this data and determine the slope (b) and y-intercept (-a) of the line.

4.  Using the weight of the animal and the above regression equation, determine the velocity of muscle contraction at that force/load (νtM). From that data and the measurement of the joint arrangement from the frog, calculate the velocity of the frog when the gastrocnemius contracts during locomotion.

  1. Is this actually the velocity of the frog when it moves? Why or why not?
  2. What would happen to the velocity of load movement if the calcaneus (the bone that the Achilles is attached to and that extends away from the ankle) were 4 times longer, but all other parameters stayed the same? What would that do to the mechanical advantage? What type of animals might have this arrangement?
  3. What type of attachment would you expect a horse or cheetah to have for this articulation? Why?


Experiment 1-Data Table:

Stimulation Voltage (Volts) / Force of Contraction (g)
0.00 V / Max Force=
0.25 V
0.50 V / Max Voltage=
0.75 V
1.00 V
1.25 V
1.50 V
1.75 V
2.00 V
2.25 V
2.50 V
2.75 V
3.00 V
3.25 V
3.50 V
3.75 V
4.00 V
4.25 V
4.50 V
4.75 V
5.00 V
5.25 V
5.50 V
5.75 V
6.00V


Experiment 2 & 3-Data Table

Distance Traveled (mm) / Time of Contraction (s) / Velocity (mm/s) / Weight (g) / Anatomical Measurements (mm)
Effort Arm:
Lever Arm:


Additional Reading:

Withers, P. C. 1992. Comparative Animal Physiology. Saunders College Publishing. New York.

Serway, R. A. and Faughn, J. S. 1995. College Physics, 4th Ed. Saunders College Publishing. New York.