Biomedical Engineering Reference
In-Depth Information
Figure 1
. A logarithmic plot of metabolic rate as a function of mass. The entire range is
shown, covering 27 orders of magnitude, from a cytochrome oxidase molecule and respiratory
complex through a mitochondrion and single cell in vitro (red dots) up to whole mammals
(blue dots). The solid red and blue lines through the corresponding dots represent
M
3/4
fits.
The dashed line is the predicted linear extrapolation from the mass for the smallest mammals
to an isolated mammalian cell. This figure is reproduced with permission from West et al.
(2002) (13).
(Figure 2) (1). Typically,
E
has a value in the range of 0.6-0.7 eV, reflecting a
common biochemistry underlying most of life (1,18). Ontogenetic growth rates,
heart rates, and even rates of conflict between beetles also scale with a similar
Boltzmann factor (18). Lifespan (1), time to first reproduction (5), and the in-
trinsic rate of increase for a population (17,18) all scale as an inverse Boltzmann
factor.
What is remarkable is that body size (as expressed in quarter-power al-
lometric scaling) and temperature (as expressed by the Boltzmann factor) ex-
plain the dominant variation among biological rates: for example, correcting
metabolic rate for mass and temperature reduces the variation from fifteen or-
ders of magnitude variation to approximately one (1). Therefore, these two vari-
ables, along with just two numbers,
E
and 1/4, provide a surprisingly robust
baseline for biological phenomena.
An intriguing consequence of these laws is the emergence of approximately
invariant quantities, something physicists recognize as signatures of fundamen-
tal underlying constraints. For example, lifespan increases as
M
1/4
e
E/kT
(Figure 3),
