The secret of life is not to be found in the molecular nuts and bolts in
living organisms. Instead, it may be in how organisms use energy. This
mini-series will hint at what lies in store, which gives concrete meanings to
renewable living energy and sustainability. A selection of the articles in the
series will be circulated.
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The mouse to elephant line
Naturalists have long observed
that many living processes vary with the size of organisms. Bigger animals
live at a more plodding pace, have slower heartbeats, longer lives, and grow
more slowly. But the variation is far from random.
It was Max Kleiber, a Swiss agricultural chemist who
first expressed this observation quantitatively in a paper published in 1932
on “Body size and metabolism”. He showed that the basal (resting) metabolic
rate of mammals, from mouse upwards to elephant, varies with body weight according
a simple mathematical equation, that came to be known as the ‘allometric scaling
B = B0Ma
Where both a and B0
A graph of log B against log M, gave a
straight line with slope a, and intercept, log B0.
The constant a was later assigned a value of ¾ in a book published
in 1961, The Fire of Life, which was translated into many languages
and widely used in university courses. This ‘mouse-to-elephant’ line became
one of the best-known generalizations in bioenergetics, the study of energy
relationship in living organisms.
Figure 1. The mouse-to-elephant line
Since then, hundreds
of basal metabolic rates of both cold- and warm-blooded species have been
measured, and all appear to confirm Kleiber’s relationship, especially the
value of a, which is invariably ¾ or nearly so, over some 21 orders
of magnitude of body weight, from bacteria to blue whales and giant redwoods.
But no one had been
able to offer a convincing explanation for this remarkable phenomenon until
1997, when Geoffrey West, a theoretical physicist from Los Alamos National
Laboratory, teamed up with James Brown and Brian Enquist in the University of New Mexico, Albuquerque, to publish a paper in Science. In
the paper, they derived the scaling relationship from first principles, not
just for basal metabolic rate, but also for a range of other biological variables.
For example, while basal metabolic rates of entire organisms scale as M3/4;
rates of cellular metabolism, heartbeat, and maximal population growth scale
as M-1/4; and times of blood circulation, embryonic growth
and development, and life-span scale as M1/4.
A theory of everything?
The theory presented by West, Brown and
based on the simple fact that living organisms are maintained by transport
of materials through networks such as the blood vessels in vertebrates, the
trachea (transporting air) in insects, and the xylem and phloem (tubes transporting
water and nutrients) in plants. These branching structures are optimised for
their task, maximising the area across which they can take up and release
resources and minimising the energy needed to transport those resources through
the organism. Mathematically, such networks have fractal, self-similar
geometry, i.e., they have fractional dimensions between the usual 1,
2, or 3; and the same or similar structure over many scales, from less than
a micron to tens of metres.
Filling a three-dimensional
volume with a network that maximises surface area available for capturing
and releasing resources creates a four-dimensional geometric entity, and that
is essentially why biological variables scale as quarter powers of the body
It is interesting that
self-similar fractal networks give minimum energy dissipation. In my book,
The Rainbow Worm published in 1998 (see www.i-sis.org.uk),
I proposed that organic space-time is fractal because it optimises energy
transfer, based on thermodynamic arguments (see “Why are organisms so complex?”
this series). Maybe there is a deep relationship that deserves further investigation.
The researchers have since
used the theory to describe a range of biological phenomenon across, such
as biomass production and variation in life-history of trees. Different plant
life histories, with very different rates of growth and timings of sexual
maturity, simply represent different ways of following the same law for optimum
use of energy.
For example, in a study of more than 2 000 trees belonging
to 45 species in a tropical dry forest over a period of 20 years, vastly different
increases in diameter occurred. But, there was a trade-off in wood density,
so that the faster growing trees had less dense wood. When the different tree
diameters were adjusted for wood density, all the graphs of different
species collapsed to a single line. And, despite the wide variation, production
scaled as M3/4, the same as in animals.
That means plants have
managed to evolve a great diversity of species of different sizes that can
co-exist, simply by varying their strategy of growing at different rates,
laying down wood of different densities and maturing at different sizes.
A universal metabolism
In yet another coup, the researchers
teamed up with James Gillooly, who joined the University of New
Mexico in 2000, and showed
that all living organisms basically share the same resting metabolic
rate when body size and temperatureare taken into account.
Metabolism lies at
the basis of all living activities. It is how the organism extracts energy
from sunlight (in the case of green plants) or from food or nutrients to build
up their bodies, to grow and develop and to do all the other things that constitute
So, when metabolic
rates are adjusted for body mass and plotted against temperature, the model
predicts that the data from any organism would yield a similar straight line
with a universal slope.
The researchers found that metabolic rates,
expressed per unit body weight, and plotted against temperature, resulted
in very similar straight lines across the whole range of species. Data from
250 species, including copepods, sycamores, bananas, peas and fish were plotted,
and each species closely resembled all the others, revealing a universal metabolic
rate, said Geoffrey West.
Actually, they did not all have exactly
the same resting metabolic rate, but the maximum difference separating any
of the groups, is only about 20-fold. This is smaller than the variation in
metabolic rate that can occur between exercise and rest in a single organism.
Many biologists are excited
about these generalizations. Understanding the basic physical principles that
govern metabolic rates for all organisms could help track the turnover of
nutrients, such as carbon, in entire ecosystems, and how ecosystems sustain