Metabolic rate can be measured most directly as the rate of heat energy released from an animal's body, a procedure called calorimetry. Measuring heat released from an animal's body with any degree of precision requires very special and expensive instruments, so physiologists routinely measure a process that is correlated directly with heat production: rate of oxygen consumption. This indirect calorimeter has its basis in the knowledge that animals typically release energy for metabolism by aerobic respiration during oxidative phosphorylation.

It is obvious that a larger animal should have a higher rate of energy metabolism, all other conditions being equal, because there is more living substance in it to respire. Physiologists originally hypothesized that one of two logical relationships should govern rate of metabolism: If body mass, the amount of respiring tissue, alone governed metabolic rate, then metabolic rate should be described by the equation MR = aM, where MR = metabolic rate, M is body mass, and a is a proportionality constant characteristic of the group of animals being compared and the units of measurement employed. On the other hand, if metabolic rate were governed by the amount of surface area through which heat energy can escape from the animal's body, the equation should have the form MR = aM^b, where b has a value of 0.67 This appears to be related to SA/V relationships, as body size increases, mass increases as the cube (^3) of the dimensions, whereas surface area increases only as the square (^2) of the dimensions, all else being equal.

To their surprise, comparative physiologists discovered that although MR does increase in proportion to the body mass, the exponent b has a value between 1.0 and 0.667, closer to 0.75 in a wide range of animal (and even plant) types. Physiologists do not yet have an complete explanation for this peculiar relationship. One recent proposal by West et al. (1997) is that it is the geometry of branching systems such as the blood vessels in a vertebrate, or tracheal vessels in an insect, that limits the rate at which essential materials can be transported to the cells, and that this geometry of branching down to a set minimum vessel diameter--the diameter of a blood capillary or air capillary--scales to the 0.75 power of body dimensions. This scaling function governing the geometry of branching of the vessels then limits the metabolic rate that can be sustained in the whole body. (The larger the organisms, the more branching nodes there must be, because the initial vessels are correspondingly large.) Thus, surface area to volume ratios are again implicated in this relationship

In this laboratory we will measure metabolic rates, as rates of oxygen consumption, in insects (order Orthoptera) of widely differing body size, to see how their metabolic rates vary with size, and to derive a value for b in the formula above. In doing so you will learn the operation of a modern respirometer, the Micro-Oxymax. The Micro-Oxymax is an indirect calorimeter consisting of a closed system of known volume and pressure containing the organisms and sensors that monitors changes in the concentrations of oxygen and carbon dioxide in the air breathed by each animal over a known time interval. The oxygen detector consists of a fuel cell battery that consumes oxygen to produce an electrical current in direct proportion to the concentration of oxygen in the air. In this instrument, all calculations are done automatically during the experiment, and oxygen consumption values are provided as microlitres of oxygen/minute (mL/min). At the end of the experiment, you can use the data collected and stored on disk to perform the calculations needed to find the value of the exponent b in the equation above.

The animals

We will be using  the American Cockroach (periplaneta americanus) as our experimental organism. These creatures are indigenous to the American tropics where they can be found in moist shady areas outdoors, in yards, hollow trees, wood piles, and mulch. They are active and fast.  Males can be distinguished from females by the presence of longer wings, extending past the end of the abdomen. At the base of the wings are pheromone producing glands Male roaches produce seducin in these glands; females produce erectin. You can likely figure out how they are involved in mating. . A few days after mating the female can be seen with an ootheca (egg case) protruding almost all the way out of her body, The ootheca will be retracted and held to term, with the female giving birth to about 12 to 36 young nymphs. The young molt through several instars.  These instars will provide you with several discreet size classes as with all arthropods growth occurs only at the molt.

In order to compare metabolic rates for different animals under similar conditions, we must standardize the conditions of measurement as much as possible so that all animals are as close as possible to comparable physiological conditions. Therefore, the animals should all be at rest, neither moving about exploring their surroundings, nor grooming themselves. They should also be post-absorptive, that is, not digesting, absorbing, and assimilating foods, but existing on their stored fat reserves. They should all be at the same environmental and body temperature. Thus, all animals should be as near as possible to the lowest rate of metabolism consistent with minimal maintenance needs at the same specified temperature. This measurement, the Standard Metabolic Rate (SMR) must be calculated by extrapolating to zero from several active metabolic rates. This is beyond the scope of this lab so we will calculate average and resting metabolic rates. Even this is difficult as it is very hard to make an animal rest so as to measure its RMR. One generally has to wait for it to go to sleep, or otherwise come to rest, then collect metabolic measurements while it is quiescent. Therefore, we will start the experiment during the laboratory period, and allow the Micro-Oxymax to collect measurements for at least 24 hours. Measurements during this extended run should level out at a minimal rate at some time for each animal, provided it enters a resting state. These values will be considered to represent RMR for that animal. These data will be posted the next day and you can then put into a spreadsheet for analysis. You can also use paper, pencil, and calculator if you wish but this will, of course, cast some doubt on either your sanity or your tendencies toward masochistic machinations.

1. We will be using Periplaneta americanus Each team is assigned one or more sample flasks (animal chambers) and animals for each. However, everyone will use data from the class as a whole.
2. Your hypothesis will determine the experimental design. 
• If your hypothesis is that roaches in three different size classes will have different metabolic rates then you will require an n of at least 3 and you will need an anova and post hoc to address the hypothesis. You will, thus be limited to 3 discreet size classes if you want 3 replicates of each.  The oxymax can accommodate 10 sample flasks. so you will be limited to 3 replicates of 3 size classes. You can always run 3 additional size classes later if you choose. 
• If your hypothesis is that roaches like other animals will demonstrate a specific slope when the data is plotted on a log-log plot, you can use all ten flasks and use the goodness of fit (R squaired) as your statistical test.
• Think about these options and come to a consensus prior to setting up. You will need a value of 0.95 or greater to support the hypothesis that the the best fit line does indeed indicate correlation.
3. Carefully select roaches of the same size for each of your size classes.  You should avoid using very large old roaches as senescence affects metabolic rate. You might even want to avoid adults altogether, as sexual maturity certainly affects metabolic rate.  You also need to avoid freshly molted animals as they will be under considerable metabolic stress.  These nymphs can be identified by their color.
4. Tare your sample flask, and insert your animal, or animals. One adult size animal can go in a chamber, but several small nymphs should be pooled to approximate the weight of the larger adult and improve the precision of your measurements. Record the total weight of your insects to the nearest milligram. You can then calculate the average individual animal weight by dividing the total weight by the number of individuals in a chamber together. It is, therefore, very important that all the animals in a sample are as close to the same size as possible.
5. Recommendation: All of the flasks should have approximately the same total roach weight. Roaches in the same flask should have very close to the same weight.
6. After the weights are determined, insert a crumpled piece of damp paper towel for the animal to hide in, and carefully but firmly screw the flask onto its corresponding connector.
7. When all ten sample flasks are connected to the Micro-Oxymax, we will begin a setup procedure in which we enter the body weights of each subject, record the contents of each flask, and check the system for leaks.
8. When all parameters have been set in the computer, the experimental run will start and run for at least 24 hours. At the end of data collection period you should remove the organisms and clean up the glassware. As wet weights can vary in many organisms, using dry weight in the calculation of the weight specific metabolic rate can sometimes reduce the standard error. The easiest way to obtain dry weight is to place the flasks in the freezer until the roach is dead and then dry it at 105^o C for 24 hours. Be sure that the dry weight data is entered on the shared class Excel notebook. (WeightRate.exl).

1. Calculating SMR for each subject: The raw values for oxygen consumption are in ml/min. These are shown as negative values because oxygen was being consumed by the animal, so amounts were going down in the sample chamber air by the amounts indicated. You may disregard the minus signs in subsequent calculations, provided all values in your data set have the same negative sign.

2. For each experimental chamber, find a series of at least five samples in which the mean oxygen consumption rates and the standard deviation are lowest. This can be done by visually inspecting the data or you might try a more sophisticated moving boxcar average (3 to 5 samples). This mean will be our best estimate of SMR for that organism or group.

MR = aM^b   to   log MR = log a + b (logM)

With this transformation, the curve for the equation becomes a straight line, in which the slope of the line is specified as the value of b in the familiar y = mx+b equation for a straight line.  Remember to correct the values for both MR and mass when you have more than one roach in a jar.  You want the metabolic rate and mass for the average individual roach.

4. Calculating Mass-specific Metabolic Rates. -- To get another comparison of smaller versus larger animals, divide the mean rate ( mL min^-1) of each animal by its initial body mass in mg (mL min^-1mg^-1), and then multiply by 60 min hr^-1 to get all rates in units of mL O₂mg^-1hr^-1.  Again you want the mass-specific metabolic rate for the average individual roach to use in your graphs. Your measurements in these units now have the same numerical value as mL O₂ g^-1 hr^-1, and Liters O₂kg^-1hr^-1. You can therefore easily compare our measurements with those for various animals discussed in your textbook and other references.

If the data warrants it, a report would be a good idea. This laboratory exercise does not, however, require a formal lab report.  If you do not submit a formal report you should submit a series of graphs demonstrating the relationship between body mass and metabolic rate and paragraph discussing the significance of this relationship. .