Biomedical Engineering Reference
In-Depth Information
calculable. These idealizations provide a baseline for quantitatively analyzing,
understanding, and assessing real biological systems, which are viewed as per-
turbations or variations from the idealized norms. This idea is motivated by the
existence of the many scaling laws that reveal the remarkable similarity among
organisms of vastly different sizes, temperatures, and structures despite the ex-
traordinary complexity and diversity of life. Living organisms span a mass range
of over 21 orders of magnitude from the smallest mycoplasma (10
-13
g) to the
largest mammals and plants (10
8
g). Overall, the life process covers almost 30
orders of magnitude from gene structure and the terminal oxidase molecules of
the respiratory complex up to ecosystems. This vast range exceeds that of the
earth's mass relative to the galaxy's, which is
only
18 orders of magnitude, and is
comparable to an electron relative to a cat. By focusing on metabolic rate, which
we assume places fundamental constraints on all organisms, we gain a foothold
for studying this immense diversity. For our idealized organisms, fundamental
properties of resource-distribution networks are the paramount evolutionary
traits, and the aforementioned perturbations and variations from some average
idealized norm in real biological systems are presumed to be due to local envi-
ronmental niches or external conditions that select for many other, often unre-
lated traits. Comparing organisms over large ranges in body size and
temperature effectively averages over environments and diminishes the impor-
tance of evolutionary innovation in response to specific environmental condi-
tions. Consequently, a coarse-grained quantitative, predictive description
becomes conceptually feasible, so that a generalized theory can apply over many
orders of magnitude.
Allometric scaling relates biological parameters to body mass,
M
. The best-
known of these is for basal metabolic rate, which was first shown by Kleiber
(21) and Brody (22) to scale as
M
3/4
for mammals and birds. (For a recent and
extensive compilation and analyses of metabolic rate data for mammals, see
Savage et al. (3).) This observation was extended by Hemmingsen (23) to ecto-
therms and unicellular organisms and later by other researchers to many other
taxa, including plants (12,24,25). More recently, it was extended to the respira-
tory complex within mitochondria down to the terminal oxidase molecules (the
universal respiratory machinery responsible for the production of ATP, the basic
currency of aerobic metabolism), thereby covering an astonishing 27 orders of
magnitude (Figure 1) (13). A synthesis of the enormous amount of data encoded
in allometric scaling was summarized in the early 1980s in four topics that con-
vincingly showed the predominance of quarter-power scaling across all scales
and almost all forms of life (2,26-28).
After body size, the biggest determinant of biological rates and times is
body temperature (29,30). Basal metabolic rate for hibernating mammals, birds
in torpor, amphibians, reptiles, plants, and unicellular organisms have all been
shown to scale as a Boltzmann factor,
e
-
E/kT
, where
E
is the activation energy for
biochemical reactions,
k
is Boltzmann's constant, and
T
is absolute temperature
