2009 APS March Meeting
Volume 54, Number 1
Monday–Friday, March 16–20, 2009;
Pittsburgh, Pennsylvania
Session Z8: Statistical Physics in Biology
11:15 AM–2:15 PM,
Friday, March 20, 2009
Room: 414/415
Sponsoring
Unit:
DBP
Chair: Marek Cieplak, Johns Hopkins University
Abstract ID: BAPS.2009.MAR.Z8.1
Abstract: Z8.00001 : Allometric Scaling in Biology
11:15 AM–11:51 AM
Preview Abstract
Abstract
Author:
Jayanth Banavar
(Penn State)
The unity of life is expressed not only in the universal basis of
inheritance and energetics at the molecular level, but also in
the pervasive
scaling of traits with body size at the whole-organism level.
More than 75
years ago, Kleiber and Brody and Proctor independently showed
that the
metabolic rates, B, of mammals and birds scale as the
three-quarter power of
their mass, M. Subsequent studies showed that most biological
rates and
times scale as $M^{-1/4}$ and $M^{1/4}$ respectively, and
that these so called quarter-power scaling relations hold for a
variety of
organisms, from unicellular prokaryotes and eukaryotes to trees
and mammals.
The wide applicability of Kleiber's law, across the 22 orders of
magnitude
of body mass from minute bacteria to giant whales and sequoias,
raises the
hope that there is some simple general explanation that underlies
the
incredible diversity of form and function. We will present a general
theoretical framework for understanding the relationship between
metabolic
rate, B, and body mass, M. We show how the pervasive quarter-power
biological scaling relations arise naturally from optimal
directed resource
supply systems. This framework robustly predicts that: 1) whole
organism
power and resource supply rate, B, scale as $M^{3/4}$; 2) most
other rates, such as heart rate and maximal population growth
rate scale as $M^{-1/4}$; 3) most biological times, such as blood
circulation
time and lifespan, scale as $M^{1/4}$; and 4) the average velocity
of flow through the network, $\bar {v}$, such as the speed of blood
and oxygen delivery, scales as $M^{1/12}$. Our framework is valid
even when there is no underlying network. Our theory is
applicable to
unicellular organisms as well as to large animals and plants.
This work was
carried out in collaboration with Amos Maritan along with Jim
Brown, John
Damuth, Melanie Moses, Andrea Rinaldo, and Geoff West.
To cite this abstract, use the following reference: http://meetings.aps.org/link/BAPS.2009.MAR.Z8.1