How Big is Big and How Small is Small
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“Seeing” the universe, or at least “seeing” nature, is where all of science starts. We call something large or small because of the way we first see it with our eyes or feel it with our fingers. One could not rationally “prove” the existence of stars (except, maybe, our Sun, for we can feel the heat) if one did not first see them. Sight is essential for our inquiry into nature. By the end of this book we will be talking about the universe, of which we can only see 1% of 1%, and the particle universe, a trillion times smaller than the diameter of a human hair, but we will continue to use the language developed for our biological sensors. At all scales things will be called large, small, heavy, light, in motion, with energy and so forth because those are words associated with our everyday experience. Using accelerators and radio telescopes we will still talk about “seeing nature.”
So how is it that we actually see? What is that bit of ourselves that senses the stars, the moon, the mountains, mice and even the fleas on the hair of that rodent? The eye is an amazing organ that can sense and distinguish things smaller than a hair and as large as galaxies. The smallest thing we can see with the unaided eye is a bit less than 10−4 m across; that is, between a tenth and a few hundredths of a millimeter across. Which leads to the question of what sets the limit of the smallest thing you can see?
When your eyes are young you can hold an object a few centimeters from the lens of your eye and still focus upon it. Since your eye is also a few centimeters in diameter this means that the lens of the eye will project an image of the object on the retina at the back of your eye, which is just about the same size as the original object. So the limit of the detail that you can see is set by the size of the sensors or “pixels” of the retina. The retina is a complex network of light-sensing rod cells and color-sensing cone cells as well as a web of nerve cells that connect them. But in the end the size of the pixel is related to the size of a cell. The size of a cell is about 10−5 m, similar to the smallest thing you can see. Actually vision is much more complex than mere pixels because the brain uses all sorts of information to form our internal images. Motion and color are part of the equation. I may be able to see a single hair, but I am not so certain that I could recognize a hair if viewed end on.
What about the biggest thing you can see? In some sense, on a starry night you can see the whole universe. There is nothing between you and the most distant astronomical object, but you would not notice it. What is the most faint object that you can perceive? Here I am making the distinction between the faintest thing that fires a neuron in your retina and that which registers awareness in your brain and consciousness. The eye is amazingly sensitive; it is sensitive enough to see a single photon. The most sensitive cameras—those with charge coupled devices, which are used in the most deep-seeing telescopes—can do no better than that. But telescopes like the Hubble are patient. If a handful of photons arrive from a distant star both the eye and the telescope will sense them. If they all arrive in a brief moment the human brain will notice them. But if they are spread out across an hour our brains will be distracted and will not notice them. The telescope is patient and waits and stares at a single point in the sky.
So our eyes are sensitive enough to see even a galaxy beyond our own Milky Way. The naked eye can see the Andromeda galaxy, two million light years, or 2 × 1022 m away. Some people can even see the Triangulum galaxy, nearly three million light years away. But we cannot tell with just the naked eye that these are collections of stars, or ‘island universes” as Immanuel Kant described them in 1755. To the unaided eye they appear as single points of dim light. It takes the optics of the telescope to gather enough light and to spread out that image and separate the stars. The unaided eye can distinguish objects that are about 0.02° to 0.03° apart. One cell of the retina, as viewed from the eye’s lens, subtends about 0.02° to 0.03°. So the most distant object we can see, like the smallest, is determined by the size of a cell. We can see things that vary in size from just under 10−4 m to around 1022 m (maybe really more like ~1020 m), which is astonishing! So the range of vision is limited and determined by the size of a cell, which leaves us with the question, “What sets the size of a living cell?”
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Cells are the smallest things that “live,” and all living things are made of cells. What sets their size is the fact that they must somehow accomplish “life.” Life is not easy to simply define. But we do know what is alive when we see it. So instead of defining life, what we tend to do is list the attributes that all living things share. If you crack open an introductory biology textbook, someplace in Chapter 1 will be a list of the attributes of life, which will include: regulates itself, uses energy, grows, adapts to its environment, responds to stimuli and reproduces. There is one other attribute that I have never seen listed. If living things grow and reproduce continuously the Earth would become crowded—unless living things also must die. When living things die it is very different from what happens when inanimate objects stop functioning. You can “kill” a computer program or turn off your car, and then turn both of them on later without any detrimental effects. But when a living thing is turned off, it stays off. Why?
Living things stay dead because they decay and fall apart and they are too complex to reassemble. They stay dead because of their complexity. How complex and therefore how large will the smallest living thing be? Erwin Schrödinger (1887–1961) tried to address this problem in his public lectures at Trinity College in Dublin in 1944. Schrödinger was a physicist and tried to cast the problem in terms that he could deal with. He said that atoms are fickle things that tend to bounce around, but that life required something with a bit more stability. The only way to make something stable out of erratic atoms was to use enough atoms so that they are “statistically” stable; that is, so that the “average atom” is sitting still. Therefore, he reasoned, a cell needs to be made up of at least tens of thousands of atoms. Schrödinger did not really pin down the size of the smallest living thing, but he asked an important question and tried to answer it. How small can a living thing be?
We now know that molecules are intrinsically more stable than Schrödinger believed and that it would not require statistical stability to give persistence to biological molecules. What seems to set the lower limit on the size of living things is that being alive is a complex problem that requires machinery of some sophistication. Living things must be complex enough to do things like grow, reproduce and use energy, and must be stable enough to do it repeatedly. A fire-cracker can use a great deal of energy, but only once. It takes a much more complex device, like an engine, to do it repeatedly with control and regulation.
Thousands of atoms across is the size of some very important organic molecules essential to life. Proteins and DNA can contain millions of atoms, but are coiled up into bundles a thousand atoms in length. A virus can be a thousand atoms wide. But a virus by itself does not qualify as being a truly living thing because it cannot do those things that we listed for living things, or at least not by itself. A virus can reproduce, use energy, and so forth only after it invades a real living cell. It can then usurp the machinery of the fully functioning cell and subject the cell’s metabolic tools to its DNA or RNA control. A thousand atoms across is one ten millionth of a meter. It is big enough and complex enough to be biologically important, but it is not complex enough to be fully alive.
The smallest truly living things are prokaryotes, which are cells that do not contain internal structure. The dominant type of prokaryote is the bacteria and these measure about a micrometer, or a millionth of a meter, on a side. The famous bacterium, E. coli, is about two micrometers across. Bacteria are so common that it is estimated that there are about 5 × 1030 (five nonillion) bacteria on Earth. Even though they are so tiny, they still add up to tons of bacteria. They could cover the whole Earth in a layer 5 mm thick or could be gathered into a cube over 10 km on a side! Does this tell us more about the amount of bacteria on our planet, or about the vast surface area of the Eart
h?
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Bigger than bacteria are eukaryotes cells, which are cells with internal structure. All multicellular creatures, such as flatworms, fleas, humans and trees are made of eukaryote cells. Often when people talk about cells they are referring to only eukaryote cells, and we will use the word in this way from this point on.
A curious thing about cells is that they have a very limited range of sizes. Only a factor of two separates the largest and the smallest of cells, except for truly oddball cells. The ostrich egg is technically a single cell, and the largest cell of modern times, although some dinosaurs had bigger eggs. But eggs are really cells that have been stretched around a lot of stored food for the embryo. Some nerve cells (neurons) can also be of extreme dimensions. Humans have neurons that stretch from their toes to their spine and these can be over a meter long. Giraffe have neurons several meters long running the length of their necks. Squid have neurons a millimeter thick and several centimeters long. But when we are talking about these extreme lengths, we are talking about the dendrites of the nerve cells, which are really just curious appendages to these cells. The body of the cell itself still tends to be about ten micrometers across. The human red blood cell is often cited as a typical cell, at just under ten micrometers across. This is, as you will recall, about one tenth the thickness of a human hair, or about the thickness of common cooking foil. But why is it that essentially all cells, from the feathers of falcons to the root hairs of fir trees, are about the same size?
The primary factor that sets the size of cells is the mechanism for getting nutrients into, and waste out of, a cell. Nutrients are absorbed through the surface of the cell. If a cells grows and doubles its length it will also increase its surface area by a factor of four and its volume by a factor of eight. This is such an important point in the size of biological systems that it is worth repeating. If I have a square that is 1 m on a side and I double the length scales, all lengths will double. The length of a side has gone from 1 m to 2 m. The perimeter will increase from 4 m to 8 m, because it too is a length. But the area goes up by a factor of four, or “doubled times doubled,” from 1 m2 to 4 m2. In three dimensions, volume grows even faster than surface area. So as a cell grows, the volume of the cell grows faster, much faster, than the surface area (see Figure 2.1). Volume and surface are not “scaling.” This relationship between surface and volume will prove to be one of the most important concepts in setting the size of cells. Not only cells, but whole animals, the nucleus of an atom and the size of stars, are also determined by the surface-to-volume ratios.
Figure 2.1 The relationship between surface and volume. If you double the length of an object, the surface area increases by a factor of four and the volume increases by a factor of eight. This is true independent of the shape of the object.
In cells, when the length doubles the volume increases by a factor of eight. The amount of nutrients needed also increases by eight. But the surface area only increases by a factor of four. The surface is where nutrients are absorbed. It is the entrance point, and so the cell cannot easily increase the amount of food it takes in to satisfy the bulging appetite of the greater volume.
This problem of balancing surface to volume also affects macroscopic things like towns and cities. Cities need railways or expressways to balance their “surface”-to-“volume” ratio just like living things. Imagine a square town that is 1 km on a side and is home to 10,000 people. This square town has a boundary of 4 km, and radiating out of it are four roads—maybe a north, south, east and west road. Enough food and other supplies come in on these four roads to feed the population, and enough waste is trucked out to keep the community healthy. So this means that each road carries the food and waste for 2500 people, and the traffic level is perfectly acceptable.
Figure 2.2 As towns grow into cities the traffic for supplies must increase. The town (left) has 10,000 people and 4 roads and so 2500 people per supply road. The city (right) has 1,000,000 people and 40 roads and so 25,000 people per supply road.
Now imagine that this town has grown into a city and its population has grown by a factor of 100, but it has the same population density of 10,000 people per km2 (see Figure 2.2). The city is now 10 km on a side, it covers 100 km2 and it has a population of 1,000,000 people. It is still square, but now it has a boundary 40 km long and so it may have 40 roads upon which supplies are brought in and waste is removed. But each road now serves 25,000 people. There will be ten times as much traffic on the city supply roads as on the town’s supply roads! Also the original part of the city, the old town, which is presumably some place near the center of the city, needs to have all of its supplies and waste moved through the small streets of the surrounding neighborhoods. The solution? The city will build arterial roads, which are dedicated to carrying more traffic. When Baron Haussmann reshaped Paris in the middle of the nineteenth century he may have been motivated to build great avenues and boulevards to make the city more pleasant—as well as to control the mobs—but he also provided traffic pressure relief. Railroad corridors, great roads and highways allow a city to grow. But between the avenues and the boulevards, you could still have village-like streets; that is, unless you started to build taller buildings and had an even greater population density!
There is one other important factor that determines cell size; living things are supposed to control and regulate themselves. The mechanism for regulation is that proteins are produced in the cell’s nucleus and they diffuse out into the main body of the cell. When a cell doubles in length and the volume increases by a factor of eight, the nucleus needs to work eight times harder and produce eight times as many proteins to control all that volume. But it is even a bit more complex than that because the proteins move by diffusion and the time it takes something to diffuse goes as the square of the distance that it needs to travel. Thus by doubling the length of a cell, the nucleus needs to produce many many more proteins to regulate itself than otherwise!
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Now all of life is not just about cells. In fact, seeing cells as the basic constituent of living creatures is a relatively modern view. Life has traditionally been viewed in the form of multicellular organisms. These differ from unicellular creatures in that cells differentiate and take on specialized tasks, but still work together for common survival. The simplest multicellular organism is the sponge, where different cells specialize in such duties as digestion, fluid flow, structure and reproduction. But sponges lack a true body design.
Rotifers are a class of creatures that are a bit bigger than single cells. They can be as little as 100 µ m(10−4 m), or ten cells, long. They can be made up of as few as a thousand cells in total. These aqueous creatures are as long and as wide as an average human hair is thick.
At a slightly larger scale, a few ten thousandths of a meter in size, there are thousands, if not millions of species. The flatworm Monogenea can be as little as a half a millimeter (500µ m) across. The house dust mite is 400 µ m long and 300 µ m wide. All of these tiny creatures have real structure. Structure and specialization is another way of solving the problems of nutrient flow, regulation and doing what needs to be done to be alive. Remember, if a cell grows to be too big it essentially suffocates or starves because its volume, and so its demands for nutrients, grow faster than its surface area.
So why can a collection of cells that we call an organism do much better? It has to do with the fact that cells can specialize to do one task very well when they do not have to do all the tasks required to stay alive. For example, a cell in a lung can be thin and allow oxygen in if it does not have to also be thick and provide protection. Specialization of tasks is what allows railroads and highways to move enough goods to support a dense city population. But these are not the roads that people will shop, work and live along. Likewise, specialization is why a production line in a factory can be so efficient and produce more widgets per worker per hour than a solo artisan or craftsman in their isolated studio or workshop.
However
, specialization by itself does not solve the problem of living. Suppose I have a simple flea that is 2 mm on a side and is made up of ten million cells, 2% of them on the surface. This flea cannot get enough air through its skin alone, so if this were the only way it could breathe it would suffocate. But in multicellular organisms some cells can be rigid and offer structure. With rigid structure nature has devised a simple solution for breathing. The sides of an insect are perforated with trachea, small channels that allow air to get deep within an insect.
This solution is not unique to insects; plants also need to breathe. Plants do most of their work in their leaves, which clearly have a lot of surface area, but not enough. It has been estimated that an orange tree with 2,000 leaves has a surface area of about 200 m2. But the air passages within the leaves, the stomata, effectively increase the surface area by a factor of thirty to 60,000 m2 or 6 hectares (15 acres).
Larger than this are slugs, worms, snails and various insects. As the body forms grow in variety it becomes harder and harder to assign a single “length” to the whole species. As an example of the problem of quantifying the size of a species with a single number let us look at Littorina saxatilis, the smooth periwinkle. This is a snail that lives in the intertidal zone on the rocky coastline of the Atlantic. Although at first glance the periwinkle would appear to be a nearly spherical creature, defining its size is not so easy. In fact this is a problem that will plague and pursue us across the universe. What is the size of a periwinkle?