During Isotonic Contraction, Skeletal Muscle Shortens Against a Load

Background

In physics, work (W) is defined as the application of a force over some distance (s) when an object is displaced. This relationship is represented by:

W = (F cos θ) sEquation 1

where F is the applied force modified by cos θ to encompass only that component of the force acting in the direction of the displacement. The combination of force and distance in this relationship results in the unit of work known as an N*m or the joule, which is a measure of the energy in a system. Energy can be found in many forms:

Kinetic Energy (KE) = the energy involved in motion

Potential Energy (PE) = the energy due to position

Chemical Energy (CE) = the energy available due to chemical states

Light Energy (LE) = the energy found in photons of light

Heat Energy (Heat) = the energy stored in the vibrations of atoms

There are other forms of energy, but these are the ones most applicable to biological systems.

The 1st law of thermodynamics indicates that energy can be transformed from one type to another, but it cannot be created or destroyed (in an isolated system). In general, this is called the conservation of energy and is used in biological systems to produce chemical reactions, locomotion, cellular production, and all of the other processes required for life. Biological systems can store energy (chemical/potential energy in the form of ATP, Adenosine Triphosphate) and use that storage form to drive any of the thousands of processes occurring in most organisms. Of course, the energy stored in ATP is itself generated from other chemical sources of energy and almost all of that can be traced back to the light energy absorbed by plants. Thus the sun constantly injects energy into the earth’s biological systems and that energy is then transformed into many forms to perform the work required for life.

The 2nd law of thermodynamics is also an important component in this arena. In generic physical terms, the 2nd law says that the universal entropy will tend to increase. This fairly simple statement has been the source of much misinterpretation over the years, especially when some scientists tried to equate entropy and disorder. However, the important point that the 2nd law of thermodynamics brings to biological systems is the idea that the transformation of energy from one state to another is never perfect and some energy is always converted to a lower ‘quality’ of energy. As biologists, we are not going to worry about the classification of energies according to physicists, because in living organisms the lowest form of energy (the ‘lost’ energy in any conversion) is always heat. Thus, whenever an organism uses some of the chemical energy stored in its system to do work (converting the energy to kinetic energy), a fraction of the total energy of the system is lost as heat. The fraction of the total energy that is lost as heat depends on the systems efficiency (e):

e = 1-Qc/QhEquation 2

where Qc is the energy lost as heat and Qh is the total energy available in the system.

Efficiency in biology is a complex concept because of the myriad of energy conversions that occur continuously in living organisms. Even the simplest of living things must transform energy thousands of times every minute to stay alive. In addition, the pathways for these conversions vary according to the particular needs of the organism and thus the end products are far from uniform. However, we can measure efficiency in biological systems by using something known as an energy budget. An energy budget measures the energy available (input) to an organism and the energy left (output) in an organism’s growth/waste and from that calculates the energy an organism uses and its efficiency of energy usage. For animal systems, that budget looks like:

C = P + U + F + M + WoutEquation 3

In this equation we can see that the energy available for the animal’s use is via what it consumes (C, the energy available in food and drink). The right side of the equation is the energy that wasn’t used or was used for some physiological need. These include: production (P, the energy used for tissue growth or reproduction), urination (U, the energy bound in the nitrogenous waste products of protein degradation), feces (F, the energy that was left over after digestion of consumables), metabolism (M, the energy associated with maintenance of a livable environment), and external work (Wout, the energy required for interaction with the external environment). To measure most of the energy available in many of these variables requires bomb calorimetry (C, U, F), growth measurements (P), and activity monitoring (Wout). However, one of these variables (M) is difficult to measure and has spawned an entire field of biology, respirometry.

Metabolism involves all of the processes in the body that are needed to keep an animal living. They can be as simple as protein replacement and membrane potential maintenance or as complex as the transmission of electrical signals through conduction systems. This is the energy that an animal requires just to maintain its current existence. The most direct method for measuring metabolism involves calorimetry where the investigator captures the heat energy emanating from the organism and measures it over time. Although an excellent method, it can be tedious and physically difficult when dealing with certain organisms; ever tried to keep an elephant in a really cold box and make sure it can’t get out? So, indirect measures of metabolism have been standard for many years and involve measuring other variables that are produced or consumed when energy is undergoing transformation in an organism. For the vast majority of animals on this planet, the proxy variables that can be directly related to energy conversion are oxygen (O2) and carbon dioxide (CO2). As chemicals like glucose are broken down to produce ATP, O2 is consumed in a known stochiometric relationship allowing us to calculate energy usage. In the same reaction, CO2 is formed and can be related to the energy produced by such processes. The rate of O2 used by an organism is called its oxygen consumption and is abbreviated as VO2. In a similar fashion, VCO2 is the abbreviation for CO2 production. Not all chemicals that are used to create biological energy have the same stoichiometry, thus the ratio of VCO2 to VO2 can be different. This ratio is known as the respiratory quotient (RQ) and varies between 1.0 for glucose/sugars and 0.7 for lipids (protein degradation results in an RQ of 0.84). Because most animals are metabolizing a mix of these compounds , it is often useful to measure the RQ in order to accurately assess the energy equivalent (Table 1), however using estimates of RQ are not uncommon as the differences in energy conversion are small.

Table 1

Lab Activity

Introduction

In this lab we are going to measure the metabolic rate, via respirometry, of various organisms and look at the changes that occurredas natural selection favored some organisms over others, driving the evolution of various physiological states. In addition, we will look at the metabolism of an organism as it undergoes strenuous activity and see how work affects measures of energy conversion.

Materials:

• Fish of various sizes
• 500 mL Erlenmeyer flask
• Oxygen electrode
• Balance
• Large container of declorinated, aerated water
• Aeration stone and air supply
• Zero-percent O2 calibration solution
• Physiograph recorder
• Magnetic stirrer and small stirring bar
• Parafilm or rubber stopper for flask
• A cloth or other dark structure to cover the flask

Optional (for Experiments 2 and 3)

• O2 gas analyzer
• Physiograph recorder
• Air pump
• Gas flow meter
• Respiratory chamber
• Drying column
• Drierite
• Lizard/turtle/snake
• Mouse
• A cloth or other dark structure to cover the chamber

Animal Handling:

These experiments are going to utilize live animals and you need to handle them with respect. None of the animals should die during this experiment unless mistreated, so be sure to give the animals the correct attention. All animals are capable of biting and some can deliver a very painful bite. The best way to keep from getting bitten is to handle the animals as little as possible and when you must handle them, do so correctly; try to stay away from the mouth end if possible and it’s a good idea to wear gloves (tough leather gloves, since no latex glove in existence can stop a determined set of teeth). If you do get bitten, don’t panic, you won’t die. Inform your instructor and get some first aid, the Band-Aid will help keep you from dripping blood all over your experiment.

Experiment 1-Standard Metabolic Rate of a Fish

1. The first trick is to weigh the fish; it’s not as tricky as it sounds.
2. Half-fill a small flask (big enough to hold the fish, but not much bigger) with declorinated water (not DI water) and place it on the balance.
3. Weigh the flask with and without the fish in it; the difference is the weight of the fish.
4. Keep the fish quiet in a flask of water until ready to use in the experiment, try not to stress the fish too much.
5. Now calibrate the O2 electrode using aerated water and the zero solution.
6. Connect the oxygen electrode to the physiograph
7. Place a beaker of aerated water on a magnetic stir plate and add the stir bar.
8. Introduce the electrode to the water ensuring that the measurement head of the electrode is completely submerged and the stir bar is on, but not hitting the electrode.
9. Record the voltage output from the electrode in air saturated water. To determine the concentration of O2 in the water you will need the solubility coefficient (ά).

[O2] = ά * PO2Equation 4

1. ά is temperature dependent (see Table 2) and in the units of μmoles/liter*kPa
2. [O2] has the units of μmoles/liter
3. PO2 is the partial pressure of O2 in kPa and is dependent on the water vapor pressure (Table 3)

Table 2-Solubility coefficient of water

Table 3-Water vapor pressure

1. Next introduce the electrode to the zero solution in the same fashion and record the voltage output.
2. You should now be able to construct a calibration curve for the electrode or calibrate the physiograph given the voltages and concentrations.

1. Rinse the electrode with DI water to remove all zero solution
2. Place the stir-bar in the Erlenmeyer flask with the fish and fill the flask to the very top with aerated water.
3. Keep the water aerated during this procedure.
4. Turn the stir bar on minimally. It should keep the flask mixing, but not create a dramatic current that stresses the fish.
5. Cover the flask with the cloth and allow the fish to get used to the flask for 10-15 minutes.
6. As quietly/calmly as possible; remove the air stone and add the O2 electrode. Cover the top of the flask with the Parafilm or stopper and ensure no gas can enter the flask; there should be NO air bubbles in the flask at this point, only water.
7. Keep the flask covered and try not to bump the table or make a lot of noise, fish stress very easily and stress can raise a fish’s metabolism very quickly.
8. Record the O2 electrode output for 30-60 minutes stopping if the O2 concentration in the water falls below ~60% of it’s initial value.
9. Return the fish to the stock tank and allow it to recover.

Analysis of Data:

1. From the recording of the experiment, measure the concentration of O2 at the beginning and end and the length of time that the experiment took place; this should allow you to calculate a VO2.
2. Consult with other groups in your lab and get their information with different sizes of fish, you will need weight and VO2 data for each fish
3. Graph the fish’s weight against the VO2.
4. What happens to VO2 as the size of the animal changes? Why?
5. Now calculate a mass-specific VO2 by dividing VO2/weight for each of the fish.
6. Again graph the data versus the weight of the animal
7. What happens to the mass-specific VO2 of the animal as size changes? What can you say about the efficiency of energy utilization?
8. Now make 2 more graphs, this time log the y-axis and the x-axis, how does this change the graphs?
9. Perform a regression analysis, what is the slope for the 2 lines?
10. What can you say about changes in metabolism with size?
11. Assuming an RQ of 0.85, how much energy is the fish using?

Note: The following experiments utilize equipment that may not be available, your instructor will inform you if you are going to perform these experiments)

Experiment 2-Standard Metabolic Rate of a Reptile

1. Obtain a reptile from your instructor; handle the animal with care and be sure to wear gloves.
2. Weigh the animal.
3. In this experiment you will be measuring metabolism via an open-system experiment. The formula for calculating VO2 in this situation is:

VO2 = [FiO2 – FeO2] * FlowEquation 5

where FiO2 and FeO2 are the fraction of oxygen entering and leaving the respiratory chamber, respectively, and flow is the rate of air flow through the chamber (note: this is a simplistic formula for metabolism that can get very complicated as other factors are taken into account. For our purposes, we are going to use this simplified form)

1. Place the animal in the respiratory chamber and cover it with the cloth. Be sure that the inflow and outflow from the chamber are not closed, so the animal can breathe normally. Allow the animal to get used to the chamber while you calibrate the machinery.
2. Now set up the rest of the system, such that the air supply pushes gas through the chamber then through the drying column and flow meter, respectively. The outflow from the flow meter should be sampled by the gas analyzer drawing from the outflow line with the air pump. Do not connect the respiratory chamber to the flow line at this point, instead creating a bypass loop (alternatively, you can put the chamber into the system, but keep the animal out of it until after calibration).
3. With atmospheric air flowing through the system at a constant flow rate (about 100 ml/min is a good place to start), allow the gas analyzer to come to equilibrium and calibrate the system. (Note: most gas analyzers only require a one-point calibration using atmospheric air. If, however, yours requires the use of a low-point gas, your instructor will have one available and you can do the same thing for the low end).
4. Measure the initial O2 concentration in the gas for a short while and then introduce the respiratory chamber with the animal into the flow stream. Allow the system to come to equilibrium (~1 h) and record the new O2 concentration.

Experiment 3-Basal Metabolic Rate of a Mammal

Repeat the above experiment using a mouse supplied by your instructor.

Analysis of Data:

1. Using equation 5 and the recordings from the mouse and reptile, calculate the VO2 for each of the animals. How do these data compare to that of the fish? To each other?
2. Calculate a mass-specific metabolism for each of these animals. Graph these new points on your fish graphs. How do these animals compare? Why?
3. What can you say about the efficiency of metabolism among the animals?
4. What factors might need to be accounted for if one wanted to measure metabolism more accurately in these last 2 experiments?
5. Assuming an RQ of 0.85, calculate the energy utilization for these animals and compare it to the fish.

Data Table:

Additional Reading:

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

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