1. Energetics of Mammals Brian Mulkern

2. Metabolism  Complete set of chemical reactions that occur in living cells.  Can be separated into two major sub categories refereed to as catabolism and anabolism.  Catabolism essentially acts as the part of the metabolic pathway responsible for the breakdown of molecules into smaller units and the release of energy.  Anabolism uses the energy gained from catabolism, where these larger molecules have been broken down and is used up in respiration.  Anabolism is a process that is usually powered by ATP and uses this energy to construct molecules.  The metabolic rate of an organism varies depending on a number of variables that are continually being investigated. As far as mammals are considered the resting metabolic rate can be predicted reasonably well on the basis of body weight.  Complete set of chemical reactions that occur in living cells.  Can be separated into two major sub categories refereed to as catabolism and anabolism.  Catabolism essentially acts as the part of the metabolic pathway responsible for the breakdown of molecules into smaller units and the release of energy.  Anabolism uses the energy gained from catabolism, where these larger molecules have been broken down and is used up in respiration.  Anabolism is a process that is usually powered by ATP and uses this energy to construct molecules.  The metabolic rate of an organism varies depending on a number of variables that are continually being investigated. As far as mammals are considered the resting metabolic rate can be predicted reasonably well on the basis of body weight.

3. Early Investigations in Body Weight vs. Metabolic Rate.  In 1883, a scientist by the name of Rubner performed a study where he examined the relationship between dogs metabolic rates in comparison to their body weight. His studies showed that his hypothesis for dogs was consistent that smaller dogs had a higher metabolic rate per Kg than ones of larger size.  Rubner determined that the metabolic rate was proportional to surface area or roughly to the 2/3 power of body weight.  In 1932, Klieber extended this study by examining the metabolic rates of mammals as well as birds.  In his experiments he was able to determine that the standard metabolic rate was more closely related to the 3/4 power of body weight than to Rubner’s 2/3.  Equation states M = 3W 0.75  (M) is the standard metabolism and (W) refers to the body weight of the animal in Kg.  In 1883, a scientist by the name of Rubner performed a study where he examined the relationship between dogs metabolic rates in comparison to their body weight. His studies showed that his hypothesis for dogs was consistent that smaller dogs had a higher metabolic rate per Kg than ones of larger size.  Rubner determined that the metabolic rate was proportional to surface area or roughly to the 2/3 power of body weight.  In 1932, Klieber extended this study by examining the metabolic rates of mammals as well as birds.  In his experiments he was able to determine that the standard metabolic rate was more closely related to the 3/4 power of body weight than to Rubner’s 2/3.  Equation states M = 3W 0.75  (M) is the standard metabolism and (W) refers to the body weight of the animal in Kg.

4. Additional Studies used for Experimental Design.  Zuntz developed a treadmill on which he measured the energy required to move a horizontal meter and the energy needed to move a meter on a vertical incline.  Slowtzoff who worked in the same lab made measurements on dogs of variable sizes and he determined that the cost of moving a horizontal meter was only approximately proportional to the 2/3 power of body weight. The cost of climbing 1m was nearly the same per Kg, regardless of animal weight.  Brody, Wilkie, and Hemmingsen all concluded that the maximum sustained metabolism was proportional to W 0.75.  Tucker reconsidered the energy costs of running 1 km in both birds and mammals and concluded that cost of running a distance of 1 km decreases with increasing speed.  Zuntz developed a treadmill on which he measured the energy required to move a horizontal meter and the energy needed to move a meter on a vertical incline.  Slowtzoff who worked in the same lab made measurements on dogs of variable sizes and he determined that the cost of moving a horizontal meter was only approximately proportional to the 2/3 power of body weight. The cost of climbing 1m was nearly the same per Kg, regardless of animal weight.  Brody, Wilkie, and Hemmingsen all concluded that the maximum sustained metabolism was proportional to W 0.75.  Tucker reconsidered the energy costs of running 1 km in both birds and mammals and concluded that cost of running a distance of 1 km decreases with increasing speed.

5. Experimental Design  Oxygen Consumption as well as rectal temperatures were monitored in mammals at both rest and on the treadmill at various speeds.  Air temperature remained constant between 22 and 27 degrees Celsius.  The relative humidity remained less than 50%.  Rodents were enclosed in sealed chambers and room air was forced through the chamber at rates between 335 - 1040 liters/hr  Dogs wore a mask that had room air pulled across at a constant rate between 2.76x10 3 and 1.2x10 4.  Oxygen Consumption as well as rectal temperatures were monitored in mammals at both rest and on the treadmill at various speeds.  Air temperature remained constant between 22 and 27 degrees Celsius.  The relative humidity remained less than 50%.  Rodents were enclosed in sealed chambers and room air was forced through the chamber at rates between 335 - 1040 liters/hr  Dogs wore a mask that had room air pulled across at a constant rate between 2.76x10 3 and 1.2x10 4.  Values were only obtained after the animal had reached a steady state of oxygen consumption that varied by less than 5% over a 30 minute interval.  Differences in oxygen consumption were measured by a Beckman model paramagnetic oxygen analyzer.  Rectal temperatures of the rodents was measured with thermocouples connected to a recording device.  The dogs rectal temperature was measured with a calibrated thermistor probe.

6. Results of Experiment  The steady state oxygen consumption for each animal increased nearly linearly with increasing speed.  The energetic cost of running can be determined by dividing the oxygen consumption by the velocity and the cost of running 1 km decreases with increasing speed.  On logarithmic coordinates the minimum cost of running Vs. body weight yields nearly a straight line. Expressed by the following equation M run = 8.46W -0.40.  The cost of running at any speed could be calculated by an animals weight if the y- intercept of the relationship between oxygen consumption and velocity could be predicted.  In the following study the average of the y-intercept was approximately 1.7 times the standard metabolism predicted in Klieber’s W 3/4 relationship.  The actual cost of running at any speed can be determined by taking the animals weight by adding its minimal cost of running times 1.7 times the predicted standard metabolism divided by the velocity traveled by the animal.  This equation would be M run = M run + 1.7M/V  The steady state oxygen consumption for each animal increased nearly linearly with increasing speed.  The energetic cost of running can be determined by dividing the oxygen consumption by the velocity and the cost of running 1 km decreases with increasing speed.  On logarithmic coordinates the minimum cost of running Vs. body weight yields nearly a straight line. Expressed by the following equation M run = 8.46W -0.40.  The cost of running at any speed could be calculated by an animals weight if the y- intercept of the relationship between oxygen consumption and velocity could be predicted.  In the following study the average of the y-intercept was approximately 1.7 times the standard metabolism predicted in Klieber’s W 3/4 relationship.  The actual cost of running at any speed can be determined by taking the animals weight by adding its minimal cost of running times 1.7 times the predicted standard metabolism divided by the velocity traveled by the animal.  This equation would be M run = M run + 1.7M/V

7. Alternative Perspective on Energetics of Running.  The amount of energy that is used when running a distance of a mile is almost the same whether it is run at maximum speed or at a leisure pace.  Although when considered on a per gram basis the cost of running is much higher in smaller animals.  When an animal is running the work is done by muscles and tendons used to both lift and accelerate the body and limbs. Some of the work required in running is recovered from muscle tendon springs and not at the cost of the metabolic system. The work rate does not parallel the metabolic rate in either size or speed.  Load carrying experiment have shown that the costs of supporting an extra Newton of load is the same as the weight specific cost of running.  In the following experiment it is believed that there is an inverse relationship between the rate of energy used when running and the time by which the foot places force on the ground with each stride.  The hypothesis states that the cost of supporting the animals weight and the time course that occurs in generating this force will determine the cost of running.  The amount of energy that is used when running a distance of a mile is almost the same whether it is run at maximum speed or at a leisure pace.  Although when considered on a per gram basis the cost of running is much higher in smaller animals.  When an animal is running the work is done by muscles and tendons used to both lift and accelerate the body and limbs. Some of the work required in running is recovered from muscle tendon springs and not at the cost of the metabolic system. The work rate does not parallel the metabolic rate in either size or speed.  Load carrying experiment have shown that the costs of supporting an extra Newton of load is the same as the weight specific cost of running.  In the following experiment it is believed that there is an inverse relationship between the rate of energy used when running and the time by which the foot places force on the ground with each stride.  The hypothesis states that the cost of supporting the animals weight and the time course that occurs in generating this force will determine the cost of running.

8. Three Basic Assumptions of the Experiment. I.Most of the force that is exerted by the muscle is used to oppose gravity. In an animal that is running it has been determined that the vertical force is ten times that of the horizontal force. This states that the average vertical force of a stride must be equal to that of the animals weight. II.The unit volume of the active muscles exerts the same force on the ground regardless of the animals speed or size. III.The muscles operate within similar ranges of the force - velocity relationship, irrespective of speed and size. I.Most of the force that is exerted by the muscle is used to oppose gravity. In an animal that is running it has been determined that the vertical force is ten times that of the horizontal force. This states that the average vertical force of a stride must be equal to that of the animals weight. II.The unit volume of the active muscles exerts the same force on the ground regardless of the animals speed or size. III.The muscles operate within similar ranges of the force - velocity relationship, irrespective of speed and size.

9. Hypothesis and Predictions.  The rate of energy consumption per Newton of body weight by the muscles of a running animal (E metab /W b ) is inversely proportional to the weight specific rate of force application, W b /T c divided by W b, where T c is the time for which the foot applies force to the ground during each stride.  Equation: E metab /W b = c * 1/ T c  C represents the cost coefficient.  It is predicted that animals with longer legs and step lengths will have a decreased transport cost.  The rate of energy consumption per Newton of body weight by the muscles of a running animal (E metab /W b ) is inversely proportional to the weight specific rate of force application, W b /T c divided by W b, where T c is the time for which the foot applies force to the ground during each stride.  Equation: E metab /W b = c * 1/ T c  C represents the cost coefficient.  It is predicted that animals with longer legs and step lengths will have a decreased transport cost.

10. Experimental Design  Steady state oxygen consumption as well as the average time off foot contact were measured of the range of aerobic running speeds.  Animals used were Kangaroo rats, ground squirrels, spring hares, dogs and ponies.  Oxygen consumption was measured while the animals ran at a constant rate on the treadmills while using an open flow system.  The extrapolated oxygen consumption was subtracted and set at zero speed from the measured value, assuming that the additional energy is used by the muscles during running.  The calculated rate of energy consumption was assumed to be 20.1 joules of energy being liberated for ml of oxygen that is consumed.  The time of contact for each limb with the ground was measured by high speed filming and with force platforms, represented by T c.  Steady state oxygen consumption as well as the average time off foot contact were measured of the range of aerobic running speeds.  Animals used were Kangaroo rats, ground squirrels, spring hares, dogs and ponies.  Oxygen consumption was measured while the animals ran at a constant rate on the treadmills while using an open flow system.  The extrapolated oxygen consumption was subtracted and set at zero speed from the measured value, assuming that the additional energy is used by the muscles during running.  The calculated rate of energy consumption was assumed to be 20.1 joules of energy being liberated for ml of oxygen that is consumed.  The time of contact for each limb with the ground was measured by high speed filming and with force platforms, represented by T c.

11. Results  The above equation was used to calculate the cost coefficient for each animal at each speed. As was predicted the coefficient was nearly constant across speed and about the same value for the different species.  Step length also showed only a slight increase over each animal’s aerobic speed range. Showing why the same amount of energy is consumed over the distance of a mile regardless of speed.  It was proven that the cost of transport decreased with increasing body.  The coefficient C is nearly constant over the range of body size with no indication of size dependency.  The above equation was used to calculate the cost coefficient for each animal at each speed. As was predicted the coefficient was nearly constant across speed and about the same value for the different species.  Step length also showed only a slight increase over each animal’s aerobic speed range. Showing why the same amount of energy is consumed over the distance of a mile regardless of speed.  It was proven that the cost of transport decreased with increasing body.  The coefficient C is nearly constant over the range of body size with no indication of size dependency.