# Describe the relationship between metabolic rate and body size

### » How does metabolic rate scale with size?

An explanation of the relationship between mass, metabolic rate and in to explain the relationship between metabolic rate and body mass for birds . of body size against which to scale various functions such as BMR. For Higher Biology, learn how metabolic rates are measured and the different ways in which oxygen The relationship between body mass and metabolic rate . proposed to explain this allometric relationship. The nutrient supply relationship between body size and metabolic rate, with a value of b typically close to.

Otherwise the protons cause the phosphorylation of adenosine diphosphate ADP to adenosine triphosphate ATP as they return across the inner membrane Jastroch et al. ATP is the fuel that powers animal tissues.

MMLE strives to predict the absolute value of the BMR of an animal rather than the exponent b or the constant a in the relationship aWb. The energy allocated to a tissue type is proportional to the number of mitochondria in the tissue. Thus MMLE tries to count the mitochondria in the tissues that compose an animal and then sum these counts for the entire animal.

It is a signature feature of MMLE theory that the vertebrate body is represented as a combination of masses instead of a single mass.

There are at least two masses: The heart, kidneys, liver and brain are the principal non-skeletal muscle tissues. Being a surface, the non-skeletal muscle surface can be mathematically described as the square of a length multiplied by an appropriate constant.

Any length could be used as long as the constant is adjusted to make the relationship exact.

## Metabolic rate

For MMLE theory the selected length is one that is related to propulsion dynamics. Go is the non-skeletal muscle constant. Gr is the resting metabolic rate constant. Gm, Go and Gr are universal constants that should apply to all vertebrates. The fundamental propulsion frequency, f, should be the same function of the characteristic length, l, for all vertebrates that are dynamically similar.

The mitochondrion capability coefficient, e, is a constant whose value should be approximately identical for all vertebrates in the same phylogenetic group with the same body temperature.

The characteristic length, l, and the sturdiness factor, s, have unique values for each individual animal. Go is defined so that m is dimensionless with a value of 1.

Gm and k were defined so that k is non-dimensional with a value of 1. Substituting this expression for f in Eq.

### Metabolic rate (article) | Khan Academy

Strouhal similarity obtains when inertial forces are proportional to oscillatory forces. Reynolds similarity obtains when inertial forces are proportional to viscous forces.

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Bats are the only animals examined in the present paper for which viscous drag, and hence Reynolds similarity, might be important. Strouhal similarity does apply to bats. This sort of dependence of the frequency on the characteristic length was not observed.

It should be noted, however, that the characteristic length for viscous drag and that for vortex growth and shedding could be different body dimensions.

### BBC Bitesize - Higher Biology - Metabolic rate - Revision 1

Two animals are geometrically similar if one can be made identical to the other by multiplying all its linear dimensions by the same factor Alexander, Properties of geometric similarity include surface area, S, being proportional to the square of the characteristic length, l2, and simultaneously volume, V, being proportional to the cube of the characteristic length, l3. Since mass, W, is proportional to volume, mass is also proportional to l3.

The fundamental frequency constant, c, in Eq. Froude and Strouhal dynamic similarity are separately compatible with geometric similarity. Hereafter, when it is stated that geometric similarity applies it also means that either Froude or Strouhal dynamic similarity also applies.

The most extreme example we are aware of is that bees in flight increase their oxygen consumption and thus their energy consumption by about fold in comparison to resting conditions BNID Similarly, humans taking part in the strenuous Tour de France consume close to 10, kcal a day, about five times the normal resting value.

It is most common to refer to the resting metabolic rate, which operationally means the animal is not especially active but well fed. As the alert reader can imagine, it is not easy to ensure rest for all animals, think of an orca killer whale as one example.

The values themselves are often calculated from the energy consumption rate that is roughly equal to the energy production rate, or in other cases from the oxygen consumption.

A famous illustration representing this relationship is shown in Figure 1. The difference between Over the years, several models have been put forward to rationalize why the scaling is different from that expected based on surface area.

Most prominent are models that discuss the rate of energy supply in hierarchical networks, such as blood vessels in our body, which supply the oxygen required for energy production in respiration.

To give a sense of what this scaling would predict, in moving from a human of kg consuming W, i. But as can be appreciated in Figure 1, the curve that refers to unicellular organisms is displaced in comparison to the curves depicting mammals by about that amount.

Histograms of resting metabolic rates normalized to wet weight. Across many orders of magnitudes of body size and widely differing phylogenetic groups the rates are very similar at about 0.