Physicists Find Simple Solution To Great-And-Small Mystery

Physicists have devised a simple mathematical explanation for a centuries-old mystery about why many biological processes change in curiously disproportional but precisely predictable ways depending on the mass of an organism's body. In the May 13 issue of the journal Nature, a team of physicists will reveal a general theorem capable of explaining the phenomenon, known as allometric quarter-power scaling.

"The pulse rate of a mouse weighing 30 grams may be 600 beats per minute, whereas the heart of a 5 ton elephant beats only about 30 times per minute, which is an example of how pulse rate in mammals scales inversely as the quarter power of the animal's mass," says Jayanth Banavar, professor of physics at Penn State and an author of the Nature paper. "Many other biological properties vary in animals and plants as powers of the mass derivable from the number 4," he adds.

"Because life exists in three dimensions, you might logically expect the characteristic scaling relationship to be derivable from the number 3 instead of the number 4," says Banavar, whose curiosity about the mystery was sparked by another research team's recent publication of a general mathematical model to explain allometric quarter-power scaling based on the geometry and dynamics of plant and animal circulation systems. "That model was exciting, but its detailed assumptions were quite complicated and too specific to be found everywhere, plus it still left us wondering why this scaling relationship based on the number 4 is so curiously pervasive throughout nature," Banavar says.

As physicists accustomed to the quest for simple and elegant mathematical theorems, Banavar and his colleagues set out to develop a simple theorem of allometric quarter-power scaling. In addition to Banavar, the research team includes Amos Maritan, of the International School for Advanced Studies in Italy, and Andrea Rinaldo, of the University of Padova in Italy and the Massachusetts Institute of Technolo

Contact: Barbara K. Kennedy
Penn State

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