Supply and demandor demand and supply

West and Brown teamed up with the Los Alamos biochemist William Woodruff to report perhaps the most thought-provoking finding of all in 2002. They published data in the Proceedings ofthe National Academy ofSciences in which they extended their fractal model to the mitochondria. They showed that mitochondria, and even the thousands of miniscule respiratory complexes within individual mitochondria, could be plotted onto the same universal quarter-power scale. In other words, they said, the relationship between metabolic rate and body size extends from the level of individual respiratory complexes right up to the blue whale, spanning 'an astounding 27 orders of magnitude'. When I set out the proposal for this book, I had it in mind to discuss their paper. I had read it carefully enough to find the central argument compelling, but had not really come to grips with its implications. I've been struggling with them ever since— is it true that a straight line connects the metabolic rate of individual complexes within the mitochondria with the metabolic rate of a blue whale? And if it is true, what does it mean?

Because the metabolic rate is defined as the rate of oxygen consumption, which takes place mainly in the mitochondria, then ultimately the metabolic rate reflects the energetic turnover of the mitochondria themselves. The baseline rate of mitochondrial energy production is proportional to the size of the organism. According to West and his colleagues, the slope of this line is determined by the properties of the supply network connecting to the cells, then to the mitochondria, and finally, deep inside, to the respiratory complexes themselves. This means that the telescopic series of networks constrains the metabolic rate, and forces a particular metabolic rate on individual mitochondria. West and his colleagues do refer to the network as a constraint, what they call 'network hierarchy hegemony'.2 But if the supply networks do constrain the metabolic rate, then as animals become larger the metabolic rate of individual mitochondria is forced to slow down, regardless of whether this is good or not. The maximum power they can possibly attain must fall. Why? Because as animals get bigger, the scaling of the network constrains each capillary to feed a larger number of cells (or the model doesn't work at all). Metabolic rate is obliged to fall in harness with capillary density. As West and colleagues admit, this is a constraint of larger size, not an opportunity, and has nothing to do with efficiency.

If this is true, then one of West's colloquial arguments must be wrong. He argues: 'As organisms grow in size, they become more efficient. That is why

2 In fact they make a specific prediction based on this. The presence of a network obliges individual mitochondria to operate more slowly than they would if they were relieved from the constraints of the network. When grown in culture, cells have a lavish supply of nutrients delivered to them directly from the surrounding medium: there is no network, so cells can't be constrained by it. If unconstrained, the metabolic rate should rise. On this basis, West, Woodruff, and Brown calculate that cultured mammalian cells should become more meta-bolically active in culture, and they predict that cells should contain approximately 5000 mitochondria after several generations in culture, each with about 3000 respiratory complexes. These numbers seem wrong. Mammalian cells tend to adapt to culture by losing mitochondria, becoming instead dependent on fermentation to provide energy, giving off the waste product lactate. Accumulation of lactate is known to impede the growth of mammalian cell cultures. As to the number of respiratory complexes in a single mitochondrion, most estimates are in the order of 30 000, not 3000. Far from 'agreeing with observation', West, Woodruff, and Brown's estimate appears to be an order of magnitude out.

nature has evolved large animals. It's a much better way of utilising energy.' If West's fractal argument is correct, then the truth must actually be the reverse. As animals become larger, their constituent cells are forced by the supply network to use less energy. Large animals must find a way of surviving with less power, at least in relation to their mass. This is not efficiency so much as rationing. If the network really does constrain metabolic rate, this adds up to another reason why the evolution of large size, and with it complexity, is so improbable.

So are organisms constrained by their network? The network is certainly important, and may well be fractal in its behaviour, but there are good reasons to question whether the network constrains the metabolic rate. In fact, the contrary may be true: there are certainly some instances in which the demand controls the network. The balance between supply and demand might seem more relevant to economists, but in this instance it makes the difference between an evolutionary trajectory towards greater complexity, and a world perpetually stuck in a bacterial rut, in which true complexity is unlikely to evolve. If cells and organisms become more efficient as they become bigger, then there really are rewards for larger size, an incentive to get bigger. And if size and complexity really do go hand in hand, then any rewards for larger size are equally rewards for greater complexity. There are good reasons for organisms to become larger and more complex in evolution. But if larger size is only rewarded by enforced frugality, the tight-fisted welcome of a miser, then why does life tend to get larger and more complex? Large size is already penalized by the requirement for more genes and better organization, but if the fractal model is right, size is also penalized by an everlasting vow of poverty—what's in it for giants?

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