Fwd: Living energies mini-series - Biology s Theory of Everything

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23 Jan 2004 17:10:29 -0000

Living energies mini-series - Biology s Theory of Everything

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The Institute of Science in Society

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ISIS Director m.w.ho

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Biology’s Theory of Everything?

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Biology is promising its own unifying theory that explains all life, and the key

is in how organisms use energy.Dr. Mae-Wan Ho investigates.

 

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 law’:

 

B = B0Ma

 

Where both a and B0 are constants.

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.

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.

 

 

 

 

Figure 1. The mouse-to-elephant line

 

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 Enquist is 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 weight.

 

 

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 temperature

are 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 being alive.

 

 

So, when metabolic rates are adjusted for body mass and plotted against

temperature, the model predicts that the data from any organismwould yield a

similar straight line with a universal slope.

 

--\

----------

 

How metabolic rate scales as body weight and temperature

*********************************************

The idea is quite simple. Basal metabolic rate B is the sum of many different

biochemical reactions. The rate of each reaction depends on three major

variables: concentration of reactants, fluxes of reactants and kinetic energy of

the system. The first two variables are determined by the rates of supply of

substrates and removal of products, and are the parts that depend on body weight

M3/4. The last term contains the dominant temperature dependence, which is

governed by the Boltzmann factor, e-E/kT. E represents the average activation

energy for the biochemical reactions of metabolism. The combined effects of body

size and temperature on metabolic rate is therefore approximately,

 

 

B #8776; M3/4 e-E/kT

 

--\

----------

 

 

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 themselves.

 

 

Sources

*******

 

Smil V. Laying down the law. Nature 2000, 403, 597.

 

 

West GB, Brown JH and Enquist BJ. A general model for the origin of allometric

scaling laws in biology. Science 1997, 276, 122-6.

 

 

“All creatures great and small”, John Whitfield, Nature 2001, 413, 342-4.

 

 

Enquist BJ, West BG, Charnov EL and Brown JH. Allometric scaling of production

and life-history variation in vascular plants. Nature 1999, 401, 907-11.

 

 

“All fired up: A universal metabolic rate”, Kathryn Brown, Science 2001, 293,

2191.

 

 

Gilloly JF, Brown JH, West GB, Savage VM and Charnov EL. Effects of size and

temperature on metabolic rate. Science 2001, 293, 2248-51.

 

 

 

 

 

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