The Equations of Life

by Charles S. Cockell

  When it is added to water, something astonishing happens. The tails of the different molecules line up to face each other while the heads point outward into the water. A two-layered structure of these molecules spontaneously forms, in which the tails, now huddled together in the middle, can avoid the water, as is their wont, while the heads, pointing into the fluid, can satisfy their attraction to the substance.

  This lipid membrane has not yet finished its tricks. It will not form an endless sheet, flapping aimlessly in the water. Just as a raindrop forms a sphere to minimize its energy, to minimize the surface-tension forces, this sheet of lipids will also curve in on itself and form a sphere. Spontaneously, and with no direction, the membrane becomes a sphere with a liquid interior. A cellular compartment has materialized. In the alignment of the lipids and their propensity to form a ball, the physical principles of ionic interactions between molecules and their tendency to minimize their energy drive these long molecular chains inevitably toward a cellular bag.

  About four billion years ago, such spontaneously forming vesicles, microscopic spheres, would have encapsulated molecules that could replicate. Now ensconced in a chamber, the products of these molecular reactions would be concentrated. They would have accumulated inside the early cell, reaching concentrations that could allow a variety of reactions. Slowly, steadily, the metabolic complexity we observe in a modern-day cell emerged. The first molecules enclosed in these so-called protocells may have been active forms of ribonucleic acid (RNA), the sister molecule to DNA, a pioneering form of genetic code.

  Once a cell had been born, evolution now did its work, not merely on lone pieces of genetic information floating around in a pond, but also on these early bundles of life. The cell itself now became the unit on which environmental conditions operated to drive evolution.

  But, you might say, surely this is all speculation?

  In the 1980s, David Deamer, at the University of California Santa Cruz, set out to find out whether simple chemicals, extracted from an ancient meteorite, could make membranes. Was the formation of a cellular structure—the answer to the physical problem of dilution—a chance event or something that was also physically inevitable? He chose meteorites, rocks that have blazed across the sky in the last leg of their journey from space and landed on Earth. Some are the most primitive materials in our Solar System. Among the family of these rocks are carbonaceous chondrites, black rocks known to contain carbon compounds. One such is the Murchison meteorite that fell in Victoria, Australia, in 1969. Long since a source of fascination for astrobiologists interested in finding out where the building blocks of life came from, these rocks, fabricated in the churning and swirling material of the early Solar System, were found to contain amino acids, the chemical units that make up proteins. But they also contain many more riches.

  Deamer extracted some simple molecules similar to lipids. These carboxylic acids, like the lipids, have a charged head and a hydrophobic tail, but they are less intricate and generally shorter than the lipids used in modern cells. Deamer collected these molecules from the meteorite and added them to water. Spontaneously, the molecules gathered and formed vesicles.

  Deamer had shown that membranes can spontaneously form, their shapes amenable to physical prediction and study. Not only that, but the molecules that make these cellular compartments were strewn through our Solar System in carbon-rich rocks. The ancient material fabricated from the swirling gases that orbited and condensed around the early Sun formed within them the very molecules to make cells.

  Provided that the gases and other material in our own Solar System are not a freak accident, a one-in-a-million concoction, then we might expect the molecules of cellularity to form in any primordial cloud, ready to deliver their cargo of protocell material to the surface of any planet with a waiting abundance of liquid water.

  Deamer’s meteoritic haul of carbon compounds is not the only place to find these molecules. Experiments have shown a whole range of ways in which you can make them. Even on early Earth itself before life arose, chemical reactions may have produced membranes. Pyruvic acid, a simple organic molecule, will make membrane material when heated and pressurized. Apparently, these early cell ingredients were plentiful on the planet.

  Although these ingenious and relatively straightforward experiments show how cell membranes can be formed, the exact place where this happened on the early Earth is a matter of contention.

  Deep in the oceans, at the ridges that spread and split apart between tectonic plates, are hydrothermal vents. These chimneys of minerals are formed from fluids rich in dissolved metals and other chemical goodies that precipitate into towering mounds of rock as the fluid comes into contact with the cold ocean waters. Within these monoliths, searing water, still liquid at several hundred degrees Celsius because of the high pressures, gushes forth through pores and larger holes in the minerals, driving chemistry in these extreme conditions.

  Some scientists think that within these sorts of environments, life’s early chemistry began, taking advantage of the changing concentration of chemicals within the rocky pores. Eventually, when the first metabolic processes occurring on these mineral-rich surfaces were ready, they would have peeled off within the membranous coating to take flight into the wider world.

  Some people eschew hydrothermal vents and contend that life began on the seashore, in the to-and-froing of tides washing in new molecules to concentrate in ephemeral pools or rocky outcrops. Others think that impact craters are a more likely place for life to begin, the intense heat as a space rock slams into the ground generating gradients of warmth and water circulation ideal for life. Perhaps Darwin’s “warm little pond” literally manifested in a pool at the edge of some volcano on land was life’s birthplace.

  Whether the first self-replicating molecules and the cells that eventually enclosed them needed somewhere special to emerge or whether this process could have been happening in many places is a question to be resolved. But Deamer’s experiments suggest that compartmentalization of chemistry into cellular structures is not a contingent result of a historical quirk, but is highly likely anywhere schizophrenic molecules with a combined love and hatred for water find themselves collected.

  A mere bag of membranes and some enclosed molecules will not achieve much. As those cells emerged, in parallel with developing a genetic code, metabolic pathways to run those cells must have been forged. Within these cellular compartments, the pathways of life, the production lines of the building blocks of life, could become more complex, leading to the bewildering number of roads to the synthesis of the different components of life that characterize a typical cell. With our cellular membrane in place, we might now ask ourselves whether these earliest metabolic pathways were themselves strange chance events or whether there are predictable physical principles in these as well.

  Take a cursory glance at a map of the cell’s metabolic pathway on the internet, and all you will see is a vast number of arcs and lines linking the hundreds of products and intermediates of chemical roadways. These pathways produce everything, including amino acids that make proteins, complex sugars, the bricks of the genetic code, and various molecules that are the broken-down products of your food. Surely, these convoluted pathways are something different from their enclosing cell? In this labyrinthine mat of strands, surely contingency, more capricious historical events now have their chance?

  Yet within this riot of complexity, there is astonishing minimalism. Some of the most ancient metabolic pathways found in cells, such as the reverse citric acid cycle, which produces the basic starting materials for many other pathways, use chemical compounds that could have been available on early Earth. The simplicity of these pathways, the chemicals involved in them, and the pathways’ energetics suggest to many people that these reactions too could be universal. Their ubiquity across life appears to be more than just an accident fixed into the first cells.

  Even greater store is given to these conclusions by the study of other parts
of this patchwork of pathways, some of which also bear the imprint of universality. The glycolysis pathway, which breaks down the sugar glucose in the cell, and gluconeogenesis, the reverse pathway for making it, are ancient and very conserved routes for making and breaking sugars, essential for cellular construction and gathering energy. By testing thousands of alternative possible molecules and pathways, scientists at the University of Edinburgh showed that the routes used in life produce the highest flux of compounds of all possible alternatives.

  These independent investigations show us that the metabolic transformations that emerged in the earliest cells on Earth were not mere flukes, but were the result of physical rules, although the information within them and the way they are structured may contain the imprint of their biological heritage. Nor do these sorts of conclusions support the idea that the pathways are accidents, fixed into living things early on and impervious to change afterward. Indeed, quite the contrary, it seems that they are quite flexible and that some pathways can turn into others with just a few mutations that alter the chemicals they use. If life wanted to escape the strictures of many of its existing routes to build itself, then it apparently could.

  Instead, many metabolic processes in the cell are optimized in ways that have profound implications, suggesting that if life arose elsewhere in the universe, it too might land on the same, or very similar, networks and that we could a priori predict what those networks might look like.

  For over three billion years before animal life, the microbes, these single-celled organisms with their attendant metabolic pathways, ruled the Earth alone. Yet on the outside, in their shapes, physical processes were slowly but ineluctably crafting them, just as they would eventually sculpt the moles and other complex life.

  Talk to someone about a microbe, and the listener might, understandably, want to suppress a soporific yawn. Almost anyone unfamiliar with microbes thinks they are not much to look at. Yet within their microscopic domain, they show a farrago of fantastic shapes. Spheres, rods, spirals, filaments, and even bean-, star-, and square-shaped microbes abound in the world.

  When the first cells moved out into the world from their birthplace, they too were shaped by laws, and their slavery to physics was a harbinger of how animals, although more complex, would later also be molded by inescapable rules. One first indefatigable effect of the environment on these new ambassadors of life was to keep them small. Most cells, whatever their shape, are minuscule. And they stay that way. But why?

  There are many causes for a cell’s diminutive size. A large bag is likely to collapse under gravity. The smaller the cell, the less likely gravitational forces will distort it and cause its contents to settle out. In this observation, we find gravity at play.

  Cells have to contend with other challenges as well. They need to take in food and nutrients and expel any waste. Consider a spherical cell. The surface area is given by 4πr2, where r is the radius of cell. However, its volume is 4πr3/3, so as we increase the radius, the volume increases by a cube power compared with its surface area, which is squared. As a cell gets larger, the volume gets larger quicker than its surface area does. In other words, for every unit volume of its interior, there is less and less surface area to provide a means for nutrients to enter and waste to exit. The smaller you are, the more surface area you have in relation to your internal volume to make those vital exchanges. Added to the woes of getting larger is the problem of diffusion inside the cell. The larger you are, the longer it takes for nutrients to slowly migrate through the cell, perhaps from one end to another. So it pays to be small.

  There may be other causes of smallness, but building a bag that does not collapse and ensuring the effective exchange of materials across the cell’s boundary are two prominent benefits. Both of these results have simple physical principles behind them. It brings up the question of the size of the smallest possible cell. It cannot be so small that the DNA and other vital machinery cannot fit in. That smallest theoretical size is about two hundred to three hundred microns, just enough to fit in some genetic material and its attendant proteins and to allow for a few metabolic pathways. The estimate actually fits well with the smallest bacteria found in the wild, including Pelagibacter ubique, a miniature bacterium with a width of only 0.12 to 0.20 micrometers and a length of about 0.9 micrometers.

  Being small counts, but it also brings some problems. What happens if you are running out of food and you want more surface area to mop up more of those nutrients lying around? One way is just to grow bigger, but as we have seen, the bigger a sphere you are, the bigger the problem with a declining surface area compared with your volume. The cell needs a way around this paradox, and it does this by not merely scaling up a ball, but instead by forming a rod-shaped body.

  Think of a cylindrical microbe with a radius of one micron (µm) and a length of five microns. Now if I double that length to ten microns, the ratio of the surface area to the volume will reduce from 2.4 to 2.2, an 8.3 percent drop. There is slightly less surface area to serve any given amount of the volume. In contrast, consider a spherical microbe that starts with the same surface area as our cylindrical microbe that is five microns long and then expands in radius to have the same surface area as our elongated cylindrical microbe. Its surface-area-to-volume ratio has decreased from 1.73 to 1.28, a 26 percent drop. An expanding sphere has much less surface area to serve any given amount of its internal volume, and the surface-area-to-volume ratio drops faster than it does in a growing cylindrical microbe. If you want to increase your surface area, it is better to become a longer cylinder than a bloated sphere.

  This is no mere physics fantasy. When we study microbes in the laboratory or in the wild, we often find that when microbes are starved, they become filamentous. Only some very basic math is needed to explain this shape-shifting behavior. Physics makes long microbes.

  That is not to say that microbes cannot grow large and that they are always forced into long, spindly shapes. When we talk of smallness, it is all relative, and although in our world all microbes seem small, in their domain some get big. The giant bacterium Epulopiscium fishelsoni lives in the gut of the surgeonfish and grows to an incredible 0.6 millimeters across, large enough to be seen with the naked eye. Surely, this little beast has contradicted everything we have just said about the need to be as small as possible? However, a closer look shows that it is not defying the laws of physics. It lives in a gut with a high nutrient content from the fish’s digested food, ensuring that even with the low surface-area-to-volume ratio, enough food gets into the cell. Throughout its membrane are folds, invaginations that hugely increase the effective surface area of the bacterium, a further modification that gets around the surface-area problem.

  Some shapes that evolution has sculpted are surprising and arresting. The curvaceous shapes of certain bacteria, a mystery for many years, may allow them to attach to surfaces to form films, holding on in environments where water flows over them. The physical principles at work on these microbes emerge from the behavior of liquids and how they exert a shear stress (σ). Through high shear stress, liquids tend to rip the microbes away from the surface. These forces are expressed in equations such as the shear-stress equation:

  σ = 6Qμ/h2w

  where the shear stress (σ) is calculated according to the flow rate (Q), the viscosity of the fluid around the microbe (μ), the width of the channel (w) where the microbe is located, and the height of the channel (h).

  Here, instead of nutrient needs, hydrodynamics comes face-to-face with life at the microscopic scale to shape and organize cells.

  Across a planet with a legion of different environments, other physical properties may become just as prominent as, or more prominent than, fluid flow. Many bacteria find themselves in syrupy liquids, even more sticky than water normally is at their small scale. In a dried-out pond filled with organic gloop in your backyard or in the interior of an animal’s gut, where the fluids are particularly viscous, there are many places where microbes are
denied the free-flowing liquid in a river or stream. In these places, being a spiral shape seems to make moving around easier, as the microbes propel their way through their gluey world. Here too, a simple law, the behavior of particles in thick, viscous fluids, takes control.

  Like moles and ladybugs, the single cells of the microbial domain are driven to convergent forms by simple physical laws, in some ways more easily distilled and discerned than those in more-complex multicellular creatures, but nevertheless just as uncompromising and predictable in the forms that they ultimately fashion.

  We have overlooked one little detail in all these amazing shapes. Those membranous lipids from which these microbes are made are intrinsically flexible. They tend to form a sphere or squashy, amorphous blobs. Life had to stumble across one other critical invention. Surrounding most microbial membranes is a cell wall. Made of a substance called peptidoglycan, the wall is like a chicken wire mesh of linked-up sugars and amino acids. This wall provides the shape and rigidity to the cell and allows the cells to adopt these multifarious forms.

  In the plethora of shapes we have toured, we find good explanations of how the cell wall emerged. The chicken wire coating may have given form to the first amorphous microbes. Unable to fix their shapes, they would have survived for sure, but they would have limped and bobbed aimlessly in their world. A cell that produced a substance that hardened its membrane could now be shaped by mutations and selection pressures to become spherical or filamentous or curved, enhancing its efficiency at attaching to surfaces, gathering food, or spiraling through goo. We can think of the cell wall as an adaptation that allowed life to be shaped by diverse physical principles, be they the laws of diffusion, hydrodynamics, or viscosity, to maximize its chances for survival and reproduction. For different microbial shapes, we can represent physical principles in equations and mathematically model how the principles influence the behavior and potential success of differently shaped microbes in their various environments.