The Equations of Life

by Charles S. Cockell

  It is easy to appreciate our reluctance to allow physics to creep into the variety and color of life. Not only does physics bring to many people a terrifying reductionism, a cold, calculated view of the safari of living things that abound on Earth, but it also weakens a historical view that life differs from inanimate matter.

  For many centuries, the idea that life is imbued with a vitalism, a force or substance that gives life its characteristic energy and unpredictability, was an essential way to build a barrier between the physical world and the domain of life. Without this barrier, living things and, dangerously therefore, people might well be relegated to a gray intersection with inanimate objects. It is this separation that has largely been responsible for the delay in understanding the evolutionary experiment in the context of physical principles. Throughout this book, we have explored how these principles variously restrict life at all levels of its hierarchy. The influence of physical principles on life should come as no shock. But if we briefly explore the history of the dichotomy between people’s historical view of life and their understanding of physics, we can better understand why it has taken so long for life to be understood as a process embedded firmly in the same unassailable laws as those governing inanimate matter.

  For centuries, the notion of spontaneous generation lay at the core of the difference between inanimate and animate matter. To move from the nonliving to the living, an elusive force must somehow transform material. In an age before peer review, science academies, and the general milieu of scientific discourse, no end of unusual and deeply strange recipes were on offer. Consider this one from Jan Baptista van Helmont, who in 1620 published a cookbook-like instruction for making mice:

  If you press a piece of underwear soiled with sweat together with some wheat in an open mouth jar, after about 21 days the odor changes and the ferment coming out of the underwear and penetrating through the husks of the wheat, changes the wheat into mice. But what is more remarkable is that mice of both sexes emerge, and these mice successfully reproduce with mice born naturally from parents. But what is even more remarkable is that the mice which came out of the wheat and underwear are not small mice, not even miniature adults or aborted mice, but adult mice emerge.

  Many people would try to refute spontaneous generation. Experiments with animals were easy. In the seventeenth century, Francesco Redi, an Italian doctor, showed that by covering meat with a gauze, it would no longer carry out its famed spontaneous transformation into maggots, yet the gauze should have allowed a vital force through. The next step, to demonstrate that flies were necessary to make maggots, came rather readily.

  However, microbes made life hard for the newly emerging scientific consensus. Just over sixty years after van Leeuwenhoek’s discovery of microbes, John Turberville Needham, a well-respected scientist of the eighteenth century, reported his mutton-gravy experiment. Transferring some of his gravy from his household fire into vials and then closing them with stoppers, he reported how the gravy, after it had been sealed from the outside world, later teemed with life. He surmised that spontaneous generation was proven. The organic matter of the gravy had been infused with a vegetative life force.

  We now know that it was likely that his gravy became contaminated with microbes. Lazzaro Spallanzani, better known for his pioneering studies on the regeneration of organs in frogs, repeated Needham’s broth experiments, but he was more careful. After placing wetted seeds into vials, he sealed them and then heated them to kill anything that might still be alive. In vials heated for short periods, large animalcules died quickly. We now think these organisms must have been amoebae. He noticed that smaller animalcules, which were probably bacteria, could tolerate heat for many minutes until even they no longer moved. He then showed that if he heated his vials for long enough, they could be turned into “an absolute desert.” He had demonstrated the concept of sterilization.

  Now you might think this pioneering set of experiments would finally put the spontaneous-generation lobby out of business, but not so. It was easy for proponents to argue that the failure of life to be generated was because the material in the vials lacked access to air. By sealing his vials, Spallanzani had denied the organic matter the very gases needed for the life force.

  With this historical backdrop, the now legendary Frenchman Louis Pasteur entered the stage. He had a mind of wonderful clarity for planning experiments. He would pioneer the process of pasteurization, in which the rapid and short-lived heating of milk could kill off microbes without changing the taste and so help preserve it. His response to this centuries-old question was an experiment of ingenious simplicity. He made swan-neck flasks, whose tapered ends elegantly curved to the side in a meandering S shape, denying the microbes the chance to drop directly into his broths, yet providing the liquid with oxygen. By the end of the nineteenth century, as well as destroying the last credibility of spontaneous generation, he had also demonstrated how to make a liquid sterile and keep it that way.

  Embodied within this history is a deep and passionate conviction that there is something different about life. Even after the remnants of spontaneous generation have long since been dispersed in the storm of scientific progress, there remains an enduring feeling that biology should never merely be reduced to something driven in shape and form by physical processes. To accept that humans emerged from apes was difficult enough to bear after the exceptionalism of our Solar System was dismissed by the Copernican revolution, but at least apes stand with us, in biology, not of the inanimate realm. Darwin’s evolutionary ideas could be explained by the hand of the Creator using evolution as a tool to achieve an ultimate end. Evolution was the mechanism behind Creation, but it was still special.

  The successful union of biology and physics has been hampered not only by a long history that seeks a comfortable, special home for life, but also by a difference in culture and approach within the subjects themselves. I remember when I joined a physics department as a person who had spent most of his professional life among life scientists. Something startling did stand out to me. Sit down with a biologist and talk about a collaboration, and the first thing they do is start at the top, maybe talking about a microbe. Then, depending on the question you ask, they will work down into lower hierarchies in search of the answer. This habit probably stems from the vast complexity of ecosystems and living things in general. Trying to explain a mole’s biology in terms of its constituent subatomic particles would seem a ridiculously futile task. Better to start with the mole and then try to answer questions at the next level down, its basic structure and what appendages it has. A biologist’s proclivities to work from the top down are understandable.

  Grab a cup of tea and start a discussion with a physicist, and you will often see the polar opposite. Their instinct is to start at the bottom and try to construct a simple model, perhaps manifested in an equation, of the process of interest. The proverbial spherical cow comes into view. This habit too is understandable. A field whose history has been to investigate the physical basis of the world around us and to express those features in mathematical relationships seeks to build, like a house, an edifice of knowledge from fundamental principles upward.

  Neither approach is wrong. In fact, both approaches seem eminently suited to their subject matter. Physicists seek to acquire definiteness by working up to levels of a hierarchy where the behavior of lumps of matter can be encapsulated within equations. Biologists seek certitude in the face of extraordinary diversity and complexity in the biosphere by working reductively downward into things that can be more easily teased apart. But in these two approaches, there seems to be evidence of two very different sets of material. The two fields seem quite antipodal. To better understand how these apparently diametrical cultures have emerged, we should briefly explore the material that both sets of scientists grapple with.

  If you rummage around at the bottom of the hierarchies of matter, its physics can become indiscernible. As Heisenberg revealed, small things are slippery customers. Meas
ure the position of a subatomic particle, and you do not know what momentum it has. Measure its momentum, and its position is obscure. This fundamental property of particles, the Heisenberg uncertainty principle, is a behavior of the quantum world, the world of the miniature. Particles of matter, particularly subatomic ones, are not discrete entities that exist in one particular location, like a table or a chair. Rather, at this infinitesimal scale, they have wavelike properties like light, and these properties give their position in any place as a probability, not an exact value. The quantum world harbors other strange properties that seem quite alien and unfamiliar to our usual experiences.

  But at the large scale, the variations in lots of different particles, say, the atoms of a gas, average out and we really can know something about objects, the scale of the universe familiar to you and me. Those uncertainties vanish in the sheer number of particles at this larger view. We can write down simple equations, like the ideal gas law, which allows us to predict the relationship between the pressure, volume, and temperature of a gas:

  PV = nRT

  where the pressure (P) and volume (V) of a gas is related to the number of moles of the gas (n), its temperature (T), and the universal gas constant (R).

  The equation gives us certainty, whatever the uncertainties that swirl around the individual atoms of that gas. The idea is that physics has indiscernibility at the smallest scale, but it becomes less so when we look at things at the higher levels of a hierarchy. This is one reason why physicists (except those whose job is to understand the quantum world) often seek to describe phenomena by moving up the hierarchy to a vista where equations can capture the general behavior of matter.

  Now compare this approach to how biologists look at living things. At the small scale, the structure of living things seems much simpler than the zoo of life we observe at the large scale all around us. In the machinery of the cell, there is predictability: molecules fold up according to principles of thermodynamics, binding occurs between base pairs in the genetic code in apparently predictable ways driven by simple chemical considerations, and energetic pathways that are ancient can be explained by thermodynamics. It all seems so far removed, so much more containable, than the diversity and endless forms we see in the world of whole organisms. At this larger scale, biology seems unpredictable. A vast collection of evolutionary creations makes up the biosphere and bedazzles the observer with its apparently limitless variety, a consequence of the creations’ different histories and contingent details.

  With this in mind, is it not surprising that biologists seek to escape this deluge of information by going after more tractable principles that operate at a level or two down in the structure of life? We might reasonably conclude that biology is predictable at the small scale, but it becomes whimsical and unpredictable at the scale of whole creatures. In contrast, physics is indiscernible at the small scale, but more predictable when Heisenberg’s uncertainties and the oddity of quantum behavior seem to take back stage at the macroscopic scale. Biology is irretrievably the opposite of physics.

  Although there is merit in this view, for me there is an equally compelling alternative, a perspective that emphasizes the unity between both fields and the similarity in the material that is their subject of study.

  At the small scale, just like physics, biology does in fact have its uncertainties. Although the genetic code and the proteins that usher forth from its translation appear to be more predictable, less contingent than once was thought, biology is in one important respect less discernible at the small scale. The genetic code, faithfully reproducing information, generation after generation, is subject to change, to mutations.

  Ionizing radiation, including natural background radiation, is one source of these changes. UV radiation from the Sun can do its bit to damage DNA. The energy it imparts to the code can cause adenine bases to bind together to form twins, known as pyrimidine dimers. When the genetic replication machinery meets these stuck-together bases, it misreads and introduces an error.

  Chemicals too can damage DNA, including the mutation-causing carcinogens in cigarettes. Even more surprising is that no radiation or malign chemistry is needed to make mutations in DNA. They can occur quite spontaneously. Some bases (adenine and guanine) can fall apart, so to speak, dropping out of the double helix. Come replication time, those holes in the code cause an error in the new strand of DNA.

  All of this shows us that unsurprisingly, DNA, like all machines, is not perfect. As it is exposed to the vagaries of the environment, natural chemical processes, and its imperfect replication, errors in its code are introduced. As we cannot predict exactly where in the code these mutations will occur (although we can define the susceptibility of certain molecules to damage of different kinds), there is an inherent unpredictability at the atomic and molecular level in how the code will alter over time. Most of these uncertainties are not quite the same as the uncertainties I have been speaking about in the quantum world. They are rather capricious changes caused by the imperfections of a genetic machine operating in a natural environment full of unexpected interferences from chemicals, radiation, or its own inherent weaknesses.

  However, uncertainties familiar to physicists and biologists might well sometimes be one and the same, bringing the two fields into complete congruence. It was Per-Olov Löwdin, a Swedish scientist, who proposed that some mutations in DNA might be caused by quantum effects.

  The binding of the base pairs down the center of the DNA double helix depends on bonding between the hydrogen (a proton) on one base and the oxygen or nitrogen atoms on its neighbor on the opposing DNA strand. These hydrogen bonds keep the two opposing strands of the DNA double helix together. They are the same bonds that come apart when the cell unzips the DNA down the middle to replicate the molecule during cell division or to translate it into protein.

  Now sometimes that proton involved in a hydrogen bond, for example, on an adenine, can swap partners and leap across to the thymine partner on the other strand of the DNA. This proton swapping is rather problematic because now, with a proton relocated to a new molecule, the DNA replication machinery can become confused. When it meets the modified adenine, rather than attaching a thymine to it in the newly synthesized DNA strand as it should do, it may instead erroneously bind a cytosine. Now a mutation has been introduced; the code has been corrupted.

  What was intriguing about Löwdin’s suggestion was the mechanism for how this might occur. Getting a proton to jump across the middle of the DNA double helix from one base to another is no easy matter. Like driving your car over a hill on your way to the supermarket, you need to put in some energy. You need to step on the gas to get your car over to the other side. So too in chemistry. The proton must jump over a metaphorical hill that represents the energy needed to make that chemical change occur. It needs some energy to do this. But imagine that some generous neighbor has made a convenient tunnel through your local hill. Now, instead of using fuel to get over the hill, you drive effortlessly through the tunnel to the other side.

  In the odd and strange quantum world in which subatomic particles reside, precisely this quantum shortcut can occur. Rather than have to jump an energy-intensive hill, our peripatetic proton can quantum-tunnel from one base to another, more effortlessly making the transition. Löwdin theorized that quantum effects might lie at the heart of some mutations. His notion has been subjected to many efforts to model it and it remains something of a curiosity. Even if quantum tunneling does occur, is it common or even important? Nevertheless, I raise the question because it shows that at the small scale, some of the uncertainties in biology and physics may come from a common quantum source. Indeed, the entire field of quantum biology is built on investigating the physical uncertainties that unify the behavior of the smallest components of all matter, whether the matter is a gas or a goose.

  Just like the case in physics, as we zoom out from all those unpredictable mutations, the picture differs and we can find common themes at the higher levels of o
rganization too. At the large scale, all those capricious mutations, like the myriad of positions and motions of atoms in a container of gas, average out. We end up with an organism that conforms to large-scale laws regardless of what may have happened at the atomic or molecular level. A mole is subject to P = F/A, and its cylindrical, pointy-faced shape, designed for optimizing the force it can apply to burrow and scrape its way through the soil, leads to convergent evolution. No matter how many unpredictable mutations have occurred in whatever bases in the genetic code of different moles, unless the changes are lethal, they do not obviate the requirement for those moles at the large scale to conform predictably to the laws that dominate their subterranean lifestyle.

  In both evolutionary biology and physics, the material with which they work has uncertainty at the atomic scale, which smooths out at the larger scale to make systems of matter that take on forms grossly predictable. The two fields are thus unified.

  I must, however, concede that there is one distinction that does exist between biology and physics, between living things and inanimate matter. One crucial difference between life and nonlife is how all those uncertainties at the atomic and molecular scale change things at the grander scale. As Jacques Monod so eloquently pointed out, at the small scale, variations in most matter are often the source of its eventual deterioration and destruction. A small defect in a crystal might cause it to crumble away. An atomic displacement in a metal might be the source of a weakness, ultimately the birthplace of its structural failure, as bridge builders are only too aware. Crystals can develop a defect, but they have a problem. There is generally no way to reliably continue that defect into later generations of crystals so that we can find out whether, under certain circumstances, it might actually provide a way for the structure of that crystal to persist for longer than another crystal that has no defect. Because the inanimate object does not reproduce, there is no easy way for us to scatter small bits of that crystal into far-flung environments that have different physical and chemical conditions to see in which of those myriad places the defect provides an advantage that would then be passed on to later crystals while many of the rest of them just crumble into dust.