# Metabolic rate and body mass relationship in chemical equations

Apr 1, This enabled calculation of an allometric equation of the form BMR = aMb. . Relationship between body mass (M, g) and basal metabolic rate. Metabolism is the sum of all of the chemical reactions that are involved in catabolism reactions use), then the body stores the excess energy by building fat . of the sympathetic nervous system; increases heart rate and heart contractility. METABOLIC RATE AND BODY MASS IN WILD WATERFOWL Our results suggest the waterfowl equation provides a more appropriate estimate of RMR.

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 (article) | Khan Academy

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.

## Metabolic rate

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

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.

## Kleiber's law

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 sturdiness factor is best understood by looking at Fig.

The data in Fig. This was purportedly the reason large creatures lived longer than small ones — that is, as they got bigger they lost less energy per unit volume through the surface, as radiated heat. There were many exceptions, and the concept of metabolic rate itself was poorly defined and difficult to measure.

It seemed to concern more than rate of heat generation and loss. Concepts of efficiency in the use of energy by the metabolism[ edit ] This limit to blood flow considerations is problematic when claims are made that the theoretical models also are relevant to things without blood flow, like bacteria and coral. Attempts to understand the metabolic rate of a multi-cellular organism field metabolic rate, that includes the activity of the organism are couched in terms of the product between average basal metabolic rate, and number of cells.

Too much blood would be required. This intimates that as proposed and popularly handled, the equation does not have the relevance to biology claimed, and is based upon assumptions that are not part of the equation, like fractality. This term is a ratio of the efficiency of redox coupling between the biomass battery W, and the sources of chemical energy available to it, measured against loss to heat.

### Kleiber's law - Wikipedia

ME is therefore a ratio of amperes of anabolism to amperes of catabolism. Efficiencies like these are not found in nature unless thermogenesis is included as part of metabolic rate.

This removes the WBE version of Kleiber's law, which the metabolic theory of ecology rests on, from any biological relevance whatsoever.

The efficiency that is purported to be modeled is actually assumed. In plants, according to a paper in in Nature, the exponent of mass is close to 1.

The key problem is the nature of metabolic energy and the extent of what is considered metabolism. The problem is most clearly noticeable in the unit term for metabolic rate, i. Calories are a measure of heat energy. This leads to the idea that thermogenesis is part of metabolism, Kleiber's original treatment, and rules out that metabolism is all about chemical energy, not heat energy.

The picture is further obfuscated when the idea of respiratory metabolism is introduced to refine and limit the definition of metabolism such that oxygen consumption and synthesis of ATP are its ultimate factors.

Furthermore, glycogenesis is excluded from metabolic consideration on this model since glycogenesis is not included in the respiratory chain, and is itself a reduction reaction not strictly dependent upon the proximity of certain molecules and atoms delivered by capillaries and vibrating from Brownian motion. Energy is required for glycogenesis, and the blood does not deliver energy, just the ingredients for endergonic reactions.

The energy comes from redox coupling, what ME is all about. Metabolic rate becomes the rate at which a biomass recharges so that its degeneration is prevented, and its organization is perpetuated.

ME is here understood as a ratio of the rate of reduction reactions necessary for the maintenance, growth, replication and behavior of the biomass, to the rate of availability of energy captured and expended by that biomass. ME is a statement of redox coupling efficiency.

ME excludes thermogenesis as part of metabolism, consequently.