Power, Sex, Suicide: Mitochondria and the Meaning of Life (31 page)

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
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?

There are various reasons to question whether the fractal model is really true, but one of the most important is the validity of the exponent itself—the slope of the line connecting the metabolic rate to the mass. The great merit of the fractal model is that it derives the relationship between metabolic rate and mass from first principles. By considering only the fractal geometry of branching supply networks in three-dimensional bodies, the model predicts that the metabolic rate of animals, plants, fungi, algae, and single celled organisms should all be proportional to their mass to the power of ¾, or mass
^0.75
. On the other hand, if the steady accumulation of empirical data shows that the exponent is
not
0.75, then the fractal model has a problem. It comes up with an answer that is found empirically not to be true. The empirical failings of a theory may inculcate a fantastic new theory—the failings of the Newtonian universe ushered in relativity—but they also lead, of course, to the demise of the original model. In our
case here, fractal geometry can only explain the power laws of biology if the power laws really exist—if the exponent really is a constant, the value of 0.75 genuinely universal.

I mentioned that Alfred Heusner and others have for decades contested the validity of the 3/4 exponent, arguing that Max Rubner’s original 2/3 scaling was in fact more accurate. The matter came to a head in 2001 when the physicists Peter Dodds, Dan Rothman, and Joshua Weitz, then all at MIT in Cambridge, Massachusetts, re-examined ‘the 3/4 law’ of metabolism. They went back to the original data sets of Kleiber and Brody, as well as other seminal publications, to examine how robust the data really were.

As so often happens in science, the apparently solid foundations of a field turned to rubble on closer inspection. Although Kleiber’s and Brody’s data did indeed support an exponent of 3/4 (or in fact, of 0.73 and 0.72, respectively) their data sets were quite small, Kleiber’s containing only 13 mammals. Later data sets, comprising several hundred species, generally failed to support the 3/4 exponent when re-analysed. Birds, for example, scale with an exponent close to 2/3, as do small mammals. Curiously, larger mammals seem to deviate upwards towards a higher exponent. This is in fact the basis of the 3/4 exponent. If a single straight line is drawn through the entire data set, spanning five or six orders of magnitude, then the slope is indeed approximately 3/4. But drawing a single line already makes an assumption that there
is
a universal scaling law. What if there is not? Then two separate lines, each with a different slope, better approximate the data, so large mammals are simply different from small mammals, for whatever reason.
³

This may seem a little messy, but are there any strong empirical reasons to favour a nice crisp universal constant? Hardly. When plotted out reptiles have a steeper slope of about 0.88. Marsupials have a lower slope of 0.60. The frequently cited 1960 data set of A. M. Hemmingsen, which included single-celled organisms (making the 3/4 rule look truly universal) turned out to be a mirage, reforming itself around whichever group of organisms were selected, with slopes varying between 0.60 and 0.75. Dodds, Rothman, and Weitz concurred an earlier re-evaluation, that ‘a 3/4 power scaling rule… for unicellular organisms generally is not at all persuasive.’ They also found that aquatic invertebrates and algae scale with slopes of between 0.30 and 1.0. In short, a single universal constant cannot be supported within any individual phyla, and can only be perceived if we draw a single line through all phyla, incorporating many orders of magnitude. In this case, even though individual phyla don’t support the universal constant, the slope of the line is about 0.75.

West and his collaborators argue that it is precisely this higher level of magnification that reveals the universal importance of fractal supply networks—the non-conformity of individual phyla is just irrelevant ‘noise’, like Galileo’s air resistance. They may be right, but one must at least entertain the possibility that the ‘universal’ scaling law is a statistical artefact produced by drawing a single straight line through different groups, none of which conforms individually to the overall ‘rule’. We might still favour a universal law if there was a good theoretical basis for believing it to exist—but it seems the fractal model is also questionable on theoretical grounds.

There are some circumstances when it is clear that supply networks do constrain function. For example, the network of microtubules within individual cells are highly efficient at distributing molecules on a small scale, but probably set an upper limit to the size of the cell, beyond which a dedicated cardiovascular system is required to meet demand. Similarly, the system of blind-ending hollow tubes, known as trachea, which deliver oxygen to the individual cells of insects, impose quite a low limit to the maximum size that insects can attain, for which we can be eternally grateful. Interestingly, the high concentration of oxygen in the air during the Carboniferous period may have raised the bar, facilitating the evolution of dragonflies as big as seagulls, which I discussed in
Oxygen
. The supply system can also influence the lower limits to size. For example, the cardiovascular system of shrews almost certainly nears the lower size limit of mammals: if the aorta gets much smaller, the energy of the pulse is dissipated, and the drag caused by blood viscosity overcomes smooth flow.

Within such limits, does the supply network limit the rate of delivery of oxygen and nutrients, as specified by the fractal model? Not really. The trouble is that the fractal model links the
resting
metabolic rate with body size. The resting metabolic rate is defined as oxygen consumption at rest, while sitting quietly, well fed but not actively digesting a meal (the ‘post-absorptive state’). It is therefore quite an artificial term—we don’t spend much time resting in this state, still less do animals living in the wild. At rest, our metabolism cannot be limited by the delivery of oxygen and nutrients. If it was, we would not be able to break into a run, or indeed sustain any activity beyond sitting quietly. We wouldn’t even have the reserves of stamina required to digest our food. In contrast, though, the
maximum
metabolic rate—defined as the limit of aerobic performance—is unquestionably limited by the rate of oxygen delivery. We are swiftly left gasping for breath, and accumulate lactic acid because our muscles must turn to fermentation to keep up with demand.

If the maximum metabolic rate also scaled with an exponent of 0.75, then the
fractal model would hold, as the fractal geometry would predict the maximal aerobic scope, which is to say the range of aerobic capacity between resting and maximum exertion. This might happen if the maximal and resting metabolic rates were connected in some way, such that (evolutionarily) one could not rise unless the other did. This is not implausible. There certainly
is
a connection between the resting and maximal metabolic rates: in general, the higher the maximal metabolic rate, the higher the resting metabolic rate. For many years, the ‘aerobic scope’ (the increase in oxygen consumption from resting to maximal metabolic rate) was said to be fixed at 5 to 10-fold; in other words, all animals consume around 10 times more oxygen when at full stretch than at rest. If true, then both the resting and the maximal metabolic rates would scale with size to the power of 0.75. The entire respiratory apparatus would function as an indivisible unit, the scaling of which could be predicted by fractal geometry.

So does the maximum metabolic rate scale with an exponent of 0.75? It’s hard to say for sure, as the scatter of data is confoundingly high. Some animals are more athletic than others, even within a species. Athletes have a greater aerobic scope than couch potatoes. While most of us can raise oxygen consumption 10-fold during exercise, some Olympic athletes have a 20-fold scope. Athletic dogs like greyhounds have a 30-fold scope, horses 50-fold; and the pronghorn antelope holds the mammalian record with a 65-fold scope. Athletic animals raise their aerobic scope by making specific adaptations to the respiratory and cardiovascular systems: relative to their body size, they have a greater lung volume, larger heart, more haemoglobin in red cells, a higher capillary density, and suchlike. These adaptations do not rule out the possibility that aerobic scope might be linked to size as well, but they do make it hard to disentangle size from the muddle of other factors.

Despite the scatter, there has long been a suspicion that the maximum metabolic rate
does
scale with size, albeit with an exponent that seemed greater than 0.75. Then in 1999, Charles Bishop, at the University of Wales in Bangor, developed a method of correcting for the athletic prowess of a species, to reveal the underlying influence of body size. Bishop noted that the average mammalian heart takes up about 1 per cent of body volume, while the average haemoglobin concentration is about 15 grams per 100 ml of blood. As we have seen, athletic mammals have larger hearts and a higher haemoglobin concentration. If these two factors are corrected against (to ‘normalize’ data to a standard), 95 per cent of the scatter is eliminated. Log maximum metabolic rate can then be plotted against log size to give a straight line. The slope of this line is 0.88—roughly, for every four steps in metabolic rate there are five steps in mass. Critically, this exponent of 0.88 is well above that for resting metabolic rate. What does that mean? It means that maximum metabolic rate and mass are closer to being directly proportional—we are closer to the expectation that
for every step in mass we have a similar step in metabolic rate. If we double the body mass—double the number of cells—then we very nearly double the maximum metabolic rate. The discrepancy is less than we find for the resting metabolic rate. This means that the aerobic scope rises with body size—the larger the animal, the greater the difference between resting and maximum metabolic rate; in other words, larger animals can in general draw on greater reserves of stamina and power.

This is all fascinating, but the most important point, for our purposes, is that the slope of 0.88 for maximal metabolic rate does not tally with the prediction (0.75) of the fractal model—and the difference is statistically highly significant. On this count, too, it seems that the fractal model does not correspond to the data.

So why does the maximal metabolic rate scale with a higher exponent? If doubling the number of cells doubles the metabolic rate, then each constituent cell consumes the same amount of food and oxygen as before. When the relationship is directly proportional, the exponent is 1. The closer an exponent is to 1, then the closer the animal is to retaining the same cellular metabolic power. In the case of maximum metabolic rate, this is vital. To understand why it is so important, let’s think about muscle power: clearly we want to get stronger as we get bigger, not weaker. What actually happens?