FEB 21, 2014 12:00 AM PST

Scientists Gain Greater Understanding of Kleiber's Law

Kleiber's law is a well-known formula in the biological field. It simply states that the metabolism of a living being equals its mass raised to the 3/4 power. Max Kleiber, a Swiss biologist, formed this theory in the 1930s after observing this pattern throughout nature.

In essence, the law points out that as living things increase in size, their life spans and metabolic processes also increase at a predictable rate. Since that time, scientists have used the law in many different ways-from predicting the energy needs of animals to correctly scaling up human dosages of medicines based on testing with mice-but the explanation of why this law works has proven elusive.

As animals get larger, their metabolisms can't increase at the same rate as their volume, because of the heat that would be generated. As an animal processes its food to create energy, heat is generated in the process, and must be dissipated. For animals with body surface areas that are disproportionately smaller than their mass, such as tigers, surface cooling alone cannot handle the heat load (with surface area alone, the factor in Kleiber's Law would be mass raised to the 2/3 power). Since flaming tigers are not seen in the wild, and Kleiber's Law has been well established by many observations, there has to be at least one other factor at work.

Researchers at Maryland University and the University of Padua in Italy believe they have the answer. By studying the shapes of both plants and animals with an evolutionary perspective, the team discovered a factor that explained the differential-the speed at at which nutrients flow through the systems. In the case of animals, that's accomplished via blood flow. The research team found a correlation in the rate of mass to blood velocity, with the velocity of blood flow in an animal equaling its mass raised to the 1/12 power.

By contrasting a plant system (in this case, trees) to animals, the team applied the logic of evolution. The tree, being stationary, simply has to produce energy via converting sunlight. It assumes the necessary branching shape to maximize this effect. Gardeners are familiar with a similar phenomenon on a smaller time scale with certain plants that adjust leaf positions to sunlight patterns, an effect known as heliotropism.

By contrast, tigers burn more fuel through their daily motions, and their systems had to adapt accordingly to maintain energy efficiency. Thus tigers and other animals have pumps (hearts) to pass nutrients through their systems at whatever speed is required to regulate their metabolism proportionately to their mass, in accordance with Kleiber's Law. Trees do not require such a pump, and therefore their correlation with Kleiber's Law is more straightforward.

Indeed, the team discovered that the mass and metabolic rates of trees conform to Kleiber's Law straightaway-and when the blood flow variable was incorporated, so did the mass and metabolic rates of animals.
Sometimes, a simple answer to a problem eludes us when it's right in front of us the entire time, and scientists are no different than the rest of us in that regard.
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