Power, Sex, Suicide: Mitochondria and the Meaning of Life (32 page)

The strength of any muscle depends on the number of fibres, just as the strength of a rope depends on the number of fibres. In both cases, the strength is proportional to the cross-sectional area; if you want to see how many fibres make up a rope, you had better cut the rope—it’s strength depends on the diameter of the rope, not its length. On the other hand, the weight of the rope depends on its length as well as its diameter. A rope that is 1 cm in diameter and 20 metres long is the same strength, but half the weight, as a rope that is 1 cm in diameter and 40 metres long. Muscle strength is the same: it depends on the cross-sectional area, and so rises with the square of the dimensions, whereas the weight of the animal rises with the cube. This means that even if every muscle cell were to operate with the same power, the strength of the muscle as a whole could at best increase with mass to the power of 2/3 (mass
^0.67
). This is why ants lift twigs hundreds of times their own weight, and grasshoppers leap high into the air, whereas we can barely lift our own weight, or leap much higher than our own height. We are weak in relation to our mass, even though the muscle cells themselves are not weaker.

When the Superman cartoons first appeared in 1937, some captions used the scaling of muscle strength with body mass to give ‘a scientific explanation of
Clark Kent’s amazing strength.’ On Superman’s home planet of Krypton, the cartoon said, the inhabitants’ physical structure was millions of years advanced of our own. Size and strength scaled on a one-to-one basis, which enabled Superman to perform feats equivalent, for his size, to those of an ant or a grasshopper. Ten years earlier, J. B. S. Haldane had demonstrated the fallacy of this idea, on earth or anywhere else: ‘An angel whose muscles developed no more power, weight for weight, than those of an eagle or a pigeon would require a breast projecting for about four feet to house the muscles engaged in working its wings, while to economise in weight, its legs would have to be reduced to mere stilts.’

For biological fitness, it’s plainly important to be strong in proportion to weight, as well as just having brute strength. Flight, and many gymnastic feats such as swinging from trees or climbing up rocks, all depend on the strength-to-weight ratio, not on brute strength alone. Numerous factors (including the lever-length and contraction speed) mean the forces generated by muscle can actually rise with weight. But all this is useless if the cells themselves grow weaker with size. This might sound nonsensical—why would they grow weaker? Well, they would grow weaker if they were limited by the supply of oxygen and nutrients, and this would happen if the muscle cells were constrained by a fractal network. Muscle would then have two disadvantages—the individual cell would be forced to become weaker, and at the same time the muscle as a whole would be obliged to bear greater weights. A double whammy. This is the last thing we would want: there is no way out of muscle having to bear greater weights with increasing size, but surely nature can prevent the muscle cells becoming weaker with size! Yes it can, but only because fractal geometry doesn’t apply.

If muscle cells don’t become weaker with larger size, their metabolic rate must be directly proportional to body mass: they should scale with an exponent of 1. For every step in mass there should be an equal step in metabolic rate, because if not the muscle cells can’t sustain the same power. We can predict, then, that the metabolic power of individual muscle cells should not decline with size, but rather scale with mass to an exponent of 1 or more; they should not lose their metabolic power. This is indeed what happens. Unlike organs such as the liver (wherein the activity falls sevenfold from rat to man, as we’ve seen) the power and metabolic rate of the skeletal muscle is similar in all mammals
regardless of their size
. To sustain this similar metabolic rate, the individual muscle cells must draw on a comparable capillary density, such that each capillary serves about the same number of cells in mice and elephants. Far from scaling as a fractal, the capillary network in skeletal muscles hardly changes as body size rises.

The distinction between skeletal muscle and other organs is an extreme case
of a general rule—the capillary density depends on the tissue
demand
, not on the limitations of a fractal supply network. If tissue demand rises, then the cells use up more oxygen. The tissue oxygen concentration falls and the cells become
hypoxic
—they don’t have enough oxygen. What happens then? Such hypoxic cells send distress signals, chemical messengers like vascular-endothelial growth factor. The details needn’t worry us, but the point is that these messengers induce the growth of new capillaries into the tissue. The process can be dangerous, as this is how tumours become infiltrated with blood vessels in cancer (the first step to metastasis, or the spreading of tumour outposts to other parts of the body). Other medical conditions involve the pathological growth of new blood vessels, such as macular degeneration of the retina, leading to one of the most common forms of adult blindness. But the growth of new vessels normally restores a physiological balance. If we start regular exercise, new capillaries start growing into the muscles to provide them with the extra oxygen they need. Likewise, when we acclimatize to high altitude in the mountains, the low atmospheric pressure of oxygen induces the growth of new capillaries. The brain may develop 50 per cent more capillaries over a few months, and lose them again on return to sea level. In all these cases—muscle, brain, and tumour—the capillary density depends on the tissue demand, and not on the fractal properties of the network. If a tissue needs more oxygen, it just asks for it—and the capillary network obliges by growing new feeder vessels.

One reason for capillary density to depend on tissue demand may be the toxicity of oxygen. Too much oxygen is dangerous, as we saw in the previous chapter, because it forms reactive free radicals. The best way to prevent such free radicals from forming is to keep tissue oxygen levels as low as possible. That this happens is nicely illustrated by the fact that tissue oxygen levels are maintained at a similar, surprisingly low level, across the entire animal kingdom, from aquatic invertebrates, such as crabs, to mammals. In all these cases, tissue oxygen levels average 3 or 4 kilopascals, which is to say about 3 to 4 per cent of atmospheric levels. If oxygen is consumed at a faster rate in energetic animals such as mammals, then it must be delivered faster: the through-flow, or
flux
, is faster, but the concentration of oxygen in the tissues need not, and does not, change. To sustain a faster flux, there must be a faster input, which is to say a stronger driving force. In the case of mammals, the driving force is provided by extra red blood cells and haemoglobin, which supply far more oxygen than is available in crabs. Physically active animals therefore have a high red blood cell and haemoglobin count.

Now here is the crux. The toxicity of oxygen means that tissue delivery is restricted, to keep the oxygen concentration as low as possible. This is similar in all animals, and instead a higher demand is met by a faster flux. The tissue flux
needs to keep up with maximum oxygen demand, and this sets the red blood cell count and haemoglobin levels for any species. However, different tissues have different oxygen demands. Because the haemoglobin content of blood is more or less fixed for any one species, it can’t change if some tissues need more or less oxygen than others. But what
can
change is the capillary density. A low oxygen demand can be met by a low capillary density, so restricting excess oxygen delivery. Conversely, a high tissue oxygen demand
needs
more capillaries. If tissue demand fluctuates, as in skeletal muscle, then the only way to keep tissue oxygen levels at a constant low level is to divert the blood flow away from the muscle capillary beds when at rest. Accordingly, skeletal muscle contributes very little to resting metabolic rate, because blood is diverted to organs like the liver instead. In contrast, skeletal muscle accounts for a large part of oxygen consumption during vigorous exercise, to the point that some organs are obliged to partially shut down their circulation.

The diversion of blood to and from the skeletal muscle capillary beds explains the higher scaling exponent of 0.88 for maximal metabolic rate: a larger proportion of the overall metabolic rate comes from the muscle cells, which scale with mass to the power of 1—in other words, each muscle cell has the same power, regardless of the size of the animal. The metabolic rate is therefore somewhere in between the resting value of mass
^2/3
or mass
^3/4
(whichever value is correct) and the value for muscle, of mass to the power of 1. It doesn’t quite reach an exponent of 1 because the organs still contribute to the metabolic rate, and their exponent is lower.

So the capillary density reflects tissue demand. Because the network as a whole adjusts to tissue demands, the capillary density
does
actually correlate with metabolic rate—tissues that don’t need a lot of oxygen are supplied with relatively few blood vessels. Interestingly, if tissue
demand
scales with body size—in other words, if the organs of larger animals don’t
need
to be supplied with as much food and oxygen as those of smaller animals—then the link between capillary network and demand would give an
impression
that the supply network scales with body size. This can only be an impression, because the network is always controlled by the demand, and not the other way around. It seems that West and colleagues may have confounded a correlation for causality.

The fact that resting metabolic rate scales with an exponent of less than 1 (it doesn’t matter what the precise value is) implies that the energetic demand of cells falls with size—larger organisms do not need to spend as great a proportion of their resources on the business of staying alive. What’s more, the fact
that an exponent of less than 1 applies to all eukaryotic organisms, from single cells to blue whales (again, it doesn’t matter if the exponent is not exactly the same in every case), implies that the energetic efficiencies are very pervasive. But that doesn’t mean that the advantage of size is the same in every case. To see why energy demand falls, and what evolutionary opportunities this might offer, we need to understand the components of the metabolic rate, and how they change with size.

In fact, regardless of the network, we have yet to show that greater size actually yields efficiencies rather than constraints—from the exponent alone, it can be almost impossible to tell. For example, the metabolic rate of bacteria falls with size. As we saw in the previous chapter, this is because they rely on the cell membrane to generate energy. Their metabolic power therefore scales with the surface area to volume ratio, i.e. mass
^2/3
. This is a constraint, and helps to explain why bacteria are almost invariably small. Eukaryotic cells are not subject to this constraint because their energy is generated by mitochondria inside the cell. The fact that eukaryotic cells are much larger implies that their size is not constrained in this way. In the case of large animals, unless we can show
why
energy demand falls with size, we can’t eliminate the possibility that scaling reflects a constraint rather than an opportunity.

We have noted that the large skeletal muscles contribute very little to the resting metabolic rate. This should alert us to the possibility that different organs contribute differently to the resting, and the maximal, metabolic rate. At rest, most oxygen consumption takes place in the bodily organs—the liver, the kidneys, the heart, and so on. The scale of their consumption depends on their size relative to the body as a whole (which may change with size), coupled to the metabolic rate of the cells that make up the organ (which depends on the demand). For example, the beating of the heart necessarily contributes to the resting metabolic rate of all animals. As animals get larger, their hearts beat more slowly. Because the proportion of the body filled by the heart remains roughly constant as size increases, but it beats more slowly, the contribution of the heart muscle to the overall metabolic rate must fall with size. Presumably something similar happens with other organs. The heart beats more slowly because it can
afford
to—and this must be because the oxygen demand of these other tissues has fallen. Conversely, if the tissue demand for oxygen rises, for example if we break into a run, then the heart must beat faster to provide it. The fact that the heart rate is slower in larger animals implies that there really are energetic efficiencies that can be gained from greater size.

Different organs and tissues respond differently to an increase in body size. A good example is bone. Like muscle, the strength of bone depends on the cross-sectional area, but unlike muscle the bone is metabolically almost inert. Both factors influence scaling. Imagine a 60-foot giant—ten times taller, ten times
wider, and ten times thicker than an ordinary man. This is an example from Haldane again, who cites the giants Pope and Pagan from
The Pilgrim’s Progress
—one of the few references that dates his essay, as I doubt that many science writers today would turn to Bunyan for an everyday analogy. Because bone strength depends on cross-sectional area, the giants’ bones are 100 times the strength of ours, but the weight they must bear is 1000 times greater. Each square inch of giant bone must withstand ten times the weight of our own. Because the human thigh bone breaks under about ten times the human weight, Pope and Pagan would break their thighs every time they took a step. Haldane supposes this is why they were sitting down in his illustration.

The scaling of bone strength to weight explains why large, heavy animals need to be a different shape to smaller, lighter ones. Such a relationship was first described by Galileo in his
Dialogues Concerning Two New Sciences
, a delightful title that could hardly be matched these days. Galileo observed that the bones of larger animals grew more quickly in breadth than in length, compared with the slender bones of small animals. Sir Julian Huxley put Galileo’s ideas on a firm mathematical footing in the 1930s. For a bone to retain the same strength relative to weight, its cross-sectional area must change at the same rate as body weight. Let’s restrain ourselves to doubling the dimensions of our giant. His volume, and therefore weight, increases eightfold (2
³
). To support this extra weight, his bones must grow eightfold in cross-sectional area. However, bones have length as well as cross-sectional area. If their cross-section is raised eightfold, and their length doubled, the skeleton is now sixteen (or 2
⁴
) times heavier. In other words, the skeleton takes up a greater proportion of body mass. Theoretically, the scaling exponent is 4/3, or 1.33, although in reality it is less than this (about 1.08) because bone strength is not constant. Nonetheless, as Galileo realized in 1637, bone mass imposes an insurmountable limit on the size of any animal that must support its own weight—the point at which bone mass catches up with total mass. Whales can surpass the size limit of terrestrial animals because they are supported by the density of water.