The Equations of Life

by Charles S. Cockell

  Thompson’s book is underpinned by the same logic that runs through much of this book. Physical laws, incontestable and unavoidable, operate in life. Organisms that transport themselves on legs must scale up in a certain way to counter the laws of gravity, as must trees. Hydrodynamics dictates the shape of a fish. A regular spiral in a snail will always conform to some sort of self-similar pattern along its length. Not surprisingly, if we go about measuring the shapes and forms of organisms, we find some repetitive and similar features. But there are, however, two things that Thompson does not do. He does not really try to articulate why his observations apply to life, and apart from his intriguing graphical shearing and rotating transformations, he does not suggest a realistic mechanism of how they might have come about.

  He does, throughout his book, explain that many of these relationships are caused by the environments in which things live. For example, he says that plant growth is a response to movement against gravity and to the forces experienced during growth. Although he never forcefully drives home the point that these relationships must emerge from the tight coupling of evolutionary processes and physical principles, his book provides the first serious attempt to demonstrate the mathematical regularity in life.

  The second question, on how all this happens, he leaves alone entirely, and this has caused some trouble. Why he never visited this question is uncertain, but we might equally ask why he was obliged to. His interest was in demonstrating how evolution leads to symmetry and predictable form. That was probably enough for one book. In the pre-DNA age of the 1910s, to have speculated on how these shapes came about would have taken the discourse into the territory of phantasm.

  Since then, however, his critics have suggested that this lacuna implies that he implicitly rejects natural selection. His mathematics-infused assessment of life apparently leaves no room for the process of Darwinian evolution and its exploration of wondrous forms. Some observers have even claimed that his book supports vitalism, the belief that life has some sort of force or substance, discrete from nonliving matter, as the component that animates it. Inanimate objects do not mysteriously transmutate into others, a rock into a metal bar, for example. So if Thompson believes that life is just mathematical relationships bundled into organic form and he does not invoke natural selection, he must be saying that there is something else in life, some vital force that allows for one form of life to transform into a different one.

  These critiques probably miss the point. Thompson’s analysis says nothing of the sort. He merely points out that life, however it works, whatever process is at the heart of evolution, results in forms with predictable shapes. He observes that life is not boundless, but tightly hemmed in by laws. These rules account for the conspicuous symmetry and patterns we find in life. They explain instances of convergent evolution, and they might also help explain the lack of certain features in the biosphere. Nevertheless, with modern molecular and genetic insights in biology, it is worth asking how these things might come about. With our new insights, we are much better placed to understand how physics can shape life.

  How does evolution achieve these feats of transformation? About a century ago, if you had asked this question, you would have been met by a standard Darwinian response. The information in life mutates, maybe by errors in reading the code or by some environmental assault, such as a damaging chemical. These small variations produce different offspring, some of which are better adapted to the environment than others. Those that are better adapted survive and reproduce, and those that are maladapted die. This incremental process of selection fashions life into new and exotic forms.

  This Darwinian synthesis, despite refinement and improvement in our understanding of its mechanism, remains fundamentally accurate. However, our understanding of the mechanisms has been augmented in considerable detail during the last few decades by a growing knowledge of the process of animal and plant development, called evolutionary developmental biology or, sometimes, evo-devo. For some reason, I find this fashionable abbreviation dreadful.

  By studying embryos and how genes switch on and off during development, biologists have shown that life is built up of simple modules, basic construction bricks that can be modified into a range of forms. The paradigmatic shift at the heart of this work was the realization that the code of life is not just a giant length of DNA read from one end to another with millions of bits produced and then self-assemble into life. Darwinism does not need changes in single units of this genetic code over vast tracts of time, an accumulation of small alterations that may seem improbable. Instead, genes are switched on and off, controlled by a whole battery of regulatory genes that can turn two very similar pieces of DNA into two ultimately different forms.

  The difference between you and a chimpanzee does not merely reside in the 4 percent difference in the DNA code between the both of you, but resides in how sections of the other 96 percent are read.

  Evolutionary developmental biology has revealed much more. Not only can life do clever things in the way it reads different parts of the same DNA code, but scientists also discovered that the instruction manual of life is structured into a grand hierarchy. Some genes cause differences that are small, but some genes control the whole pattern of development. None are as dramatic and impressive as the Homeobox (Hox) genes. Found ubiquitously in animals, from houseflies to humans, these Hox genes control limb development—the legs in a fly, the fins in a fish, and your hands and feet.

  The extraordinary ability to modify entire biological architectures with some simple gene changes goes some way to accounting for the versatility in many important pieces of a living thing, and one of the most self-evident in animals is the limbs. In his wonderful book about this field, Endless Form Most Beautiful, Sean Carroll explores how appendages are merely modifications of the number and shape of fixed modules (digits) on a common design. Produce three long and spindly digits, and you have the foot of a crane, but put them at the end of a wing, and they now anchor the airfoil of a swooping falcon. Bury them in a flat flipper, and a sea turtle can now cross an ocean; reduce the digits to two and put them in a hard casing, and you have the foot of a camel striding across the baked surface of the Arabian Desert. These developments come about by subtle modifications of the Hox genes; the number and timing of the expression of these genes modify the limbs that an animal ends up with.

  Evolutionary developmental biology’s contribution has been to link development with evolution, but it also provides the beginnings of a better explanation for how evolution works. Like a Transformer in a Hollywood movie, by building life from repeating modules—whether they be digits, vertebrae, or even the cells that make certain tissues—changes in these modules can effect radical reorganizations as organisms exploit and move into different environments. Whether the life is in water, land, or air, these modules can be reconfigured by mutation to generate the architecture of living things that can persist in places that may be poles apart.

  But what has all this to do with physics?

  In evolutionary developmental biology, we have the groundwork for harmony between evolution and the laws of physics. Consider our mole. To claim that the laws of physics drive moles in Europe and Australia to the same solution to the problem of optimizing P=F/A is to invite the question “But how?” How can a mole whose relatives are shrews and weasels look so starkly similar to a mole whose relatives are kangaroos and koalas? Isn’t that uncanny? And how could this resemblance occur with incremental changes? Once an animal is locked into looking like a shrew or a kangaroo, is there no turning back? How could two lineages bring about the changes needed to converge on a similar form?

  As the laws of physics work relentlessly on new forms that emerge from the old, the modular design of life makes possible transformations that do not require entirely new designs. The existing tool kit of limb units allows for front legs that are strengthened and wider, producing an animal design that is a tunneling mole with no alteration in the underlying basic units o
f life. Some of this variation may be possible merely by changing the expression of particular genes with no radical mutations, but the evolutionary study of development also shows us that there is the possibility for these more cardinal changes. Evolutionary developmental biology goes further, suggesting that organisms may not be so tightly bound by their prior development as was once assumed and that modular rearrangements can help circumvent the constraints of genetic heritage. Such flexibility might increase the opportunity that physics has to creep in and determine what evolution can and cannot do. Lacunae in the evolutionary experiment may not always be explained away by a simple developmental barrier, but instead might sometimes be genuinely less adaptive from the standpoint of physical principles.

  Within the evolutionary story of whole organisms, there are other mysteries about the shape-shifting behavior of life. Prominent among them is how an organism in one environment that has a certain set of dominant laws can diverge from its ancestors and make the transition into another, where a different set of rules comes to the fore without the animal ending up as a mushy evolutionary mess of jerry-built chaos?

  One transition is impressive by any standards—the invasion of land. This transition provides a particularly lucid example of a decided shift between two environments, water and continents, with different physical requirements. The science of evolutionary developmental biology provides a clearer picture of how organisms can make these strides from one set of physical conditions to another.

  Moving from a watery habitat to a new home on land presents life with some very profound changes in the physics of how one exists. There is room for intermediate transition stages. Muddy ponds and tidal regions on land offer something of a twilight zone of a water and land existence. In the water, some fish walk along the sea floor looking more like land animals. But the complete transition from water to land is nevertheless profound.

  As an animal moves to land, a noticeable difference is the enormous gravitational field that is no longer counteracted by its buoyancy in water. A full 9.8 m/s2 pulls down on an organism as it seeks to wrench its body from the water and make progress over a muddy foreshore, experiencing what astronauts feel, newly returned from a space station and needing to recline in a seat for a while lest they stumble under their own laborious weight. If this value for gravity still seems a little arcane, do 250 push-ups right now with one arm. Yes, that’s right—that’s the effort of pushing up against 9.8 m/s2.

  In the water, the overall forces that acted on the fish before it launched an expedition onto land were given by the expression:

  F = mg − ρVg

  The term mass multiplied by gravity (mg) expresses the weight of the organism pressing downward. Then there is the buoyancy of the fish, the upward force that offsets the downward force of its weight to allow it, with minimal effort, to glide through the ocean with a flip of its fins. That buoyancy is the term ρVg, made up of the density of the fluid (ρ) multiplied by the volume of water the fish displaced (V) and the gravitational acceleration, or g. You will have experienced how buoyancy relieves you somewhat of gravity as you wallow and float in a swimming pool or the ocean on a summer vacation. Now on land, ρVg has all but vanished; the buoyancy of an animal in the relatively thin atmosphere is irrelevant. All that is left is the downward force of gravity, mg, the weight of the poor, beleaguered creature. The animal must make up for losing ρVg by the sheer effort of pushing itself off the ground.

  Here we have a transition as difficult as any, between two places that impose a different concatenation of laws. Now we have a conundrum. How can the physics of these two worlds and this divergence in evolutionary trajectory be reconciled? How can this transition occur?

  The answer may lie in small mutations, or it may instead reside in dramatic changes. Evolutionary developmental biology has shown us that the modular design of life, in which whole segments of an organism, such as its limbs, may be modified using alterations to one or a few genetic units, is well suited to allow these transitions between environments that seem very dissimilar.

  In stunning experiments, researchers have explored how fish may have made the transition to early four-legged animals, the tetrapods. The Hox genes that control limb development are controlled by a set of regulatory genes that tell them when to switch on and off. These global control regions harbor strands of DNA, which mastermind the production of hormones that themselves influence the development of appendages in the developing embryo. The scientists found that particular genes, such as the CsB gene, could be transplanted from zebra fish into a mouse and could drive the development of limbs. They found that the gene oversaw further genetic expression in the autopod, the part of the limb that produces the digit and the essential parts of legs for walking on land. In inverse experiments, enhancer genes from mice can be transplanted into fish and will drive development of the fins.

  These impressive, if ghoulish, experiments show us that the genes that regulate fins and limbs are similar and very ancient. Deep in the history of evolution, the basic genes that evolved to control the general architecture of developing appendages in animals continue to regulate limb development, whether that is a fin or a leg.

  Now it would be apropos for the reader to exclaim surprise. How did an early animal know that the genes that control a fin would eventually be required to do the work of making limbs to walk on land? How is versatility in a genetic code locked into early animals that would one day be used to take on the challenge of very different physical environments from the ones in which they emerged? This so-called inherency, as it has sometimes been called—the curious apparent foresight that evolution seems to have for challenges yet to come—might seduce anyone into accidentally thinking there are grander minds at work.

  Remarkable though the feat of turning fins into limbs may seem, perhaps we should not be too amazed. We are not asking life to make the move from the oceans to living on the surface of a neutron star with gravitational forces many millions of times greater. No radical physics is being asked for here. Provided that the environment is not inimical to the modules from which a multicellular organism is made (not too hot, cold, acidic, and so on), then the basic chassis from which animals are constructed can be modified to suit the laws prevailing in many environments. Those genes that evolved to make a fin are now being asked to regulate in such a way as to make the bones separate into distinct digits and fashion them thicker to withstand a world in which the buoyancy term, ρVg, in the force equation is now irrelevant. That transition is difficult but not utterly alien. We are removing one term in an equation in which the weight of an organism (mg) becomes more pronounced, but it was nevertheless there from the beginning of evolution.

  As the first fish pulls itself onto land, those offspring with stronger bones and muscles will more effectively yank themselves off the ground and drag themselves along to find food and maybe some shelter from the midday sun.

  How fish made the transition between swimming and walking is still somewhat of a matter of debate. Intermediate forms of locomotion are seen in some mudskippers and tidal-flat-dwelling animals even today, including tail-flip jumping, an awkward way a fish can hurl itself into the air on its side by a good, sharp whack of its tail against the ground. The slightly more graceful, but primitive prone jumping is similar to tail-flipping, but here the fish uses its tail to throw itself upward and forward with its belly facing down so that it is right side up. It can at least see where it is going, and it does not land on its eyes. By contrast, some fish, such as the pink frogmouth, Chaunax pictus, walk across the sea floor very much like land animals do, a feat suggesting that fish learned to walk even before they emerged onto land.

  Ultimately, the fundamental physical alteration that was needed was the transition between fins and limbs that were sufficiently engineered to hold an animal up against gravity with the requisite flexibility to allow walking. Once that organism can move around on land with primitive limbs, alterations in animal size from this point on are a si
mple scaling between the mass of the organism that defines the weight, mg, it must hold up and the thickness of the bones and the strength of the muscles to hold them up. These are the scaling laws that Thompson so vividly observed.

  Nonetheless, in the history of animal life, among the many independent vertebrate invasions of land, only one lineage led to us. In this evolutionary detail, we have evidence that the transition between water and land is not trivial. There is no foregone inherent capacity in the early evolution of marine life to move onto land. The laws that operate in both environments are sufficiently different and the selection pressures so enormous that it seems this transition required several experiments to succeed.

  The notion that physical limits could prevent animals from making some transitions is not wild conjecture. Even on Earth, there are environments, from the boiling volcanic pools of Rotorua in New Zealand to the acidic rivers of the Rio Tinto in Spain, where animals cannot live. In these places, only microbes reign supreme. Places like these demonstrate that physical limits can be too extreme for animal evolution. Evolutionary inherency is impressive, but not limitless.

  Dealing with the physics of a disappearing buoyancy term in the equation that defines one’s movement on land is not the only challenge in clambering out of water. Apart from the difficulty of walking around, there are other problems, too. Under the glaring sun, water evaporates without mercy from the scaly surface of our new land denizen. The latent heat of vaporization, which is the energy you need to turn water from a liquid into a vapor, is high, 2257 kilojoules per kilogram, about ten times higher than for many other fluids, but nevertheless the sun’s energy is more than enough to drive off water, as you may have experienced drying off in the summer sun after a swim. Without drinking water, dehydration follows. A paradox for a creature that has chosen to leave the security of bountiful water is that it must now remain close to abundant water to prevent itself from desiccating. And the physics doesn’t end there. As water evaporates from the surface, it also carries off energy, thus cooling the animal. It had better beware, lest it get so cold that it cannot move.