A mouse and an elephant live in fundamentally different physical worlds so far as their own spatial dimensions and their relation to the force of gravity are concerned — a fact evident enough in the way mice scurry around, darting this way and what, while the elephant carries its weight more slowly and deliberately. Or, to approach the matter from a very different direction: if you dropped a mouse from seven meters (twenty-three feet) above a meadow, it would likely right itself after landing and scamper away. If you dropped an elephant from that height, it would die from massive internal trauma. And if you simply left a beached blue whale where it lay, it might die from any of several different causes, one of which is being crushed under its own weight. All this has to do with the changing relation between the weight of an animal and the surface area of its body as its overall size changes.1
So when we talk about the diverse environments in which organisms live, one aspect of the diversity has to do with their varying experiences of the force of gravity in relation to the dimensional aspects of their lives. To be a different size is already to live in a different world.
Einstein, so it is said, was led to his theory of special relativity due in part to his having imagined what it would be like to “ride on a light beam”. Might we possibly discover equally strange things if we tried to imagine what it would be like to dwell within an individual living cell?
Unlike Einstein with his task, ours would be much simpler. It would not require bold new understandings in physics, but simply a willingness to imagine the changing play, at different dimensions, of well understood physical laws. And, fortunately, we have at least one scientific paper, written thirty years ago, that has already done much of the work of imagining the startlingly different conditions of life at the scale of the cell.
That 1990 paper was written by Guenter Albrecht-Buehler of the Northwestern University Medical School in Chicago. He began his professional life as a physicist before moving into cell biology. However, unlike what you might expect of a physicist, one of his larger concerns was rooted in the conviction that we cannot build up an understanding of organisms by starting from the molecular level. His paper, titled “In Defense of ‘Nonmolecular’ Cell Biology”, has not, in my judgment, received the attention it deserves. The present chapter represents my effort to summarize only that part of the paper dealing with the wildly unexpected consequences of differences of scale, and then to offer a few additional comments of my own.
Unless otherwise indicated, quotes in the following section are drawn from Albrecht-Buehler’s paper.
Warning: This chapter is a bundle of contradictions. In fact, that is more or less its point. The ways we think and speak about the submicroscopic world are almost guaranteed to be impossibly off the mark, and yet anyone who would point this out has no choice but to use the established, off-the-mark language, which is the only language we currently have available. So if you begin to notice a jarring dissonance between the intended meaning and the actual language of particular statements — and I hope you will — you can take it as a sure sign that you are getting the point of the chapter.
For example, you will hear me saying that “If you considered two isolated electrons to be point masses and placed them 1 meter apart …” You will likewise hear me talking about the “collisions” of “particles”, and you will listen to a prominent cell biologist remarking how the 5 billion proteins in a cell are “jammed shoulder to shoulder, [while] also charging past one another at insanely high speeds”. These references to “isolated electrons”, “point masses”, “collisions”, and “proteins charging past one another” all seem to demand that we imagine particular things acting in the manner of the familiar objects of our experience.
But, as I hope you will realize by the end of the piece, there are no things of that sort “down there”. What is down there is a very good question. And if you are asking it by the time you finish reading this, then the chapter will have accomplished its purpose.
Albrecht-Buehler begins his main discussion by remarking that the size of cells “is so dramatically much smaller than the macroscopic objects we are accustomed to judging, that it is fair to say they live in an utterly alien world”. The surface-to-volume ratio of a cell — a crucial consideration underlying the mouse–elephant comparison above — is 100,000 times greater for a typical cell-sized sphere than for an everyday-sized sphere with a diameter of 50 centimeters (about 20 inches). But the “alien” character we discover by imagining the life of a cell at its own dimensions goes far beyond the principle we learn by dropping mice and elephants to the ground. Nevertheless, that principle isn’t a bad place to start.
We see the natural tendency of such shaping forces in water when we observe tiny droplets of dew on a waxy leaf. Instead of spreading out over the leaf, the water draws itself into a roughly spherical shape. But if we instead had a ball of water 10 centimeters (4 inches) in diameter and could manage to place it on a flat surface, the water’s much greater weight would overwhelm its shaping forces, so that the liquid would flow out in all directions. Only in the tiny droplets that might remain here and there would we again see the spherical, dew-drop shape we are familiar with on leaves, grass blades, and so on.
The point to attend to, then, is that change of size can result in dramatic differences in the play of forces. Of course, our wine bottle’s reduction in size was not very great. Reflect now upon the fact that the volume of water in a typical cell is not 10 times, but rather 28,000 times smaller than the volume of a wine bottle. Albrecht-Buehler remarks of the non-flowing wine in the neck of the shrunken wine bottle that it appears to have become rigid, “like jelly”. Indeed, “wine can turn into jelly just by existing in smaller amounts”. Try to imagine the implications of that statement in light of a scale reduction by a factor of 28,000!
Albrecht-Buehler compares the effects of viscous drag upon two objects moving through water — a spherical cell, and a sphere with a 50-centimeter diameter. Both spheres are assumed to consist of the same protein matrix. He asks: if an initial movement of one diameter per second is imparted to both of them, how quickly would they come to a stop due to the resistance of the water? It turns out that the larger sphere will travel long enough to traverse many diameters. By contrast, the cell-sized sphere will stop within about a millionth of a second, during which it will have traveled about a millionth of a diameter — which is more or less to say that it stops immediately and doesn’t travel at all.
This might seem to suggest that if you or I lived at the size of a cell — or, worse, a molecule within a cell — and if we wanted to take a swim, we might just as well try swimming inside a large block of concrete. But this can’t really be the case, and only illustrates the difficulty of transporting ourselves in imagination to a different scale of existence. Objects like you and I — or pebbles and flowers, or the gears and levers of a machine — could not be scaled down to a sub-cellular level and still remain what they were in any meaningful sense. They would become objects of an entirely different character.
Further, molecules “live” at a radically reduced scale compared to the
cell, so in moving from the whole cell to the molecular level (what I will
call the “microworld”), we see the various lawful relations changing yet
again. In reality, molecules move through their cellular environs (as we
will see below) with remarkable speed. Moreover, despite the example
above, even cells move quite well in their viscous environment. So still
other factors must come into play.
The motion, which gained the name “Brownian”, was further characterized by later investigators. Their work confirmed three features of the movements: they were indeed random in the sense that all directions were “equally likely”; “further motion seemed totally unrelated to past motion”; and “the motion never stopped”. In addition, “small particle size and low viscosity of the surrounding fluid resulted in faster motion” (Encyclopedia Britannica editors).
In the early twentieth century the French physicist, Jean Baptiste Perrin, recorded the positions of three particles in water at 30-second intervals, as viewed through the microscope. His representation is shown in Figure 15.2.
Today Brownian movement is commonly visualized, however
as being due to random collisions (“random thermal fluctuations”) of a
liquid’s molecules with a very small suspended object. In this sense,
writes Albrecht-Buehler, the contents both within a cell and in its
external, watery environment are “jerking violently”. Moreover, these
effects outweigh those of gravity to such an extent that collisions with
just two to three molecules in a cell’s environment are enough to
counterbalance the gravitational weight of the cell, keeping it from
sinking in water. Given the countless trillions of such impacts coming
from all sides, “another way of formulating this result is to say that
gravity is an entirely irrelevant force in the violently chaotic world of
Here is one example of the use of chemical energy. A single muscle cell
contains hundreds of subunits (“sarcomeres”) whose dimensions are less
than 3 millionths of a meter. They contract by converting chemical energy
into mechanical energy. The force delivered by one sarcomere, as
Albrecht-Buehler remarks, is such that “it can lift 60 entire cells! In
other words, the cells submersed in violently jerking molasses of their
surrounding aqueous media have literally gigantic forces at their
The answer is that you would have to separate the electrons by approximately 200,000 light years.7 This amounts to more than 34 billion times 34 billion miles. This is too much to get one’s head around, so the take-home point is simply that the electrical force is inconceivably stronger than the gravitational force.
The remarkable thing is that, in most of our routine experience of the world around us, we would hardly suspect the ubiquitous presence of such monstrous forces relative to our experience of gravity. This has to do with the fact that, in the world we normally experience, the bearers of negative electrical forces, such as electrons, are more or less counterbalanced by bearers of positive electrical forces, such as protons.
The way in which charged particles naturally tend to distribute themselves gets very complex, but the upshot of it all is the following: while the electrical forces between cellular constituents are unthinkably more powerful than the gravitational forces, they don’t simply rip the cell to smithereens. Here, too, negative and positive charges tend to balance each other out, but the operative word is “tend”. The imbalances that do exist are enough to help account for a lot of what goes on.
Albrecht-Buehler puts the matter this way: in the molecular collectives of cells, “[charged] molecules do not notice each other until they come closer than about one-third of their diameter. Once they are that close, however, they are attracted or repelled with almost irresistible electrical forces”. And again: a single electron charge within the typical electric field spanning a nerve membrane “can balance the weight of an entire cell”. He goes on to mention that “cell surfaces contain thousands of electron charges”.
We might also consider, not just static electrical forces, but electrical currents. Michael Persinger, the late Laurentian University (Canada) neuroscientist who investigated bioelectric phenomena in both the brain and the earth’s atmosphere, was looking, not for great differences, but for close parallels between the two widely varying scales. And he found them. But even here the parallels show how differently we must think, for example, of the brain compared to our routine picturing of physiological processes.
For example, the electrical impulse traveling along the axon of a neuron, is driven by what might seem to be a trivial action potential of 0.09 volts. But this voltage applies across a 10 nanometer neuronal membrane, which means that it amounts to millions of volts per meter. This is on the order of the action potential of an atmospheric lightning bolt. And the density (amperes per square meter) of the current traveling along the neuronal path is, according to Persinger, “remarkably similar” to the density of the electric current flowing in a lightning bolt.
So the reality looks rather as if our brains are continually “lit up” by
countless cascading, lightning-like discharges — perhaps on the order of a
billion discharges per second
This can happen because the chemical addition of another subunit to a polymer of the cytoskeleton is an energetic process. “The force of the addition of only one [protein] subunit is ten times larger than the weight of a cell!” In theory, therefore, “adding one subunit to a polymer could lift ten cells by the thickness of the subunit”. This tells us a good deal about how cells can move. At the normal scale of our lives we see nothing like this ability of a tiny unit of matter to be chemically joined to others of its kind and thereby to shift material objects (cells) that happen to be billions of times more massive than that tiny unit. (A typical human cell has been estimated to contain several billion protein molecules, in addition to water, lipids, carbohydrates, and all its other contents.)
You will recall from our earlier discussion that a dew drop on a leaf is “pulled” into a sphere by its shaping forces. (See Figure 15.1.) Further, we heard that these forces, relative to the gravitational force that might break the droplet’s form and cause it to flow over the flat surface of the leaf, become vastly greater at very small scales. At the level of a cell, one of these shaping forces (surface tension) is “several thousand times larger than the weight of the cell, and we should expect the surface force to shape the cell as a perfect sphere”.
The question, therefore, is why a cell is not held rigidly in the shape of a sphere (Figures 15.3 and 15.4). Cells often have all sorts of non-spherical protrusions, and some kinds of cell readily flatten themselves against a surface and slide over it. In doing so, they are overcoming the hugely powerful shaping forces just mentioned. Part of the answer to this particular puzzle is, in Albrecht- Buehler’s words, that “the surface forces are no match for the strong polymerization forces”. Bundles of cytoskeletal filaments extending in a common direction have no difficulty re-shaping a cell and helping to bring it into movement.
How all these unfamiliar elements of the cellular world add up is not easy to picture. And it becomes even less easy when we look at some of the apparent dynamics of cellular life. “Imagine packing all the people in the world into the Great Salt Lake in Utah — all of us jammed shoulder to shoulder, yet also charging past one another at insanely high speeds. That gives you some idea of how densely crowded the 5 billion proteins in a typical cell are.”10
Those “insanely high speeds” in crowded places are thought to explain how, as a standard textbook puts it, “a typical enzyme will catalyze the reaction of about a thousand substrate molecules every second” — meaning that the enzyme must bind to a new substrate in a fraction of a millisecond. This happens despite the fact that there tend to be relatively few substrate molecules per cell. If, for example, there is only 1 substrate molecule for every 100,000 water molecules, “nevertheless, the active site [the place where catalysis occurs] on an enzyme molecule that binds this substrate will be bombarded by about 500,000 random collisions with the substrate molecule per second”. At the same time, “a large globular protein [like many enzymes] is constantly tumbling, rotating about its axis about a million times per second” (Alberts et al. 2002, pp. 77-8).
As if everything we have heard so far is not difficult enough to comprehend, the problem of imagining microworlds truthfully is greatly magnified by emerging technologies that generate seductive images. When biologists speak so casually of atoms and molecules as things, and when engineers then present us with “pictures” of them, we can hardly help taking the pictures as images of actual phenomena. And yet, the phenomena we are dealing with are not “down there”. They are “up here”, where we are experiencing our instruments.
What we derive from “down there” (at the atomic and molecular levels) is mostly mountains of data produced by our instruments. The pictures we look at are representations of that data. If we take these pictures at face value — if we unthinkingly accept them in the same way we accept the terms of our visual engagement with the familiar world — then we are projecting into the microworld phenomena that are not actually there.
This is a problem. If images like the one in Figure 15.5 truly represented anything like the physical objects around us, merely reduced to very small dimensions, and if billions of such objects (commonly, if nonsensically, referred to as “molecular machines”) were racing around inside the cell at “insanely high speeds”, tumbling around while rotating a million times per second, they would presumably achieve nothing but rampant destruction within the cell.
Figure 15.5, which is said to represent carbon atoms, is not in any normal sense a photograph of atoms, as the scientists and engineers who produce such images well know. There is no “thing” anywhere in the world that looks like this, except the picture itself. Responsible physicists do not talk about things at this level of observation at all. In this particular case we are looking at a kind of colored graph of a data set produced by an atomic force microscope. The spatial distribution of the artificial colors represents the relations between the highly refined measuring instrument, on one hand, and forces at an extremely small (atomic) scale, on the other. It is a picture of a distribution of forces. Forces are not things.
So what do we make of all the foregoing? It’s hard to say — and maybe that itself is the important point. It is clear enough that when we imagine the world of atoms and molecules in terms of our familiar experience, we are far from truth. If we want some sort of picture, it will hardly do to conjure images of nanorobots or sewing machines or pliers, merely reduced in size and spinning around a million times per second, or a brick beneath a skyscraper receiving an electrical charge and thereby raising the building off the ground, or molecules consisting of brightly colored baubles.
The one thing we can be sure of is that the cellular realm is not composed of anything like our familiar objects, just made smaller. The really foundational question is whether, and at what scale of observation, we are justified in talking about “things” at all, as opposed to forces or potentials.12 This question certainly bears on the common appeal by molecular biologists to machine and computer models. As Albrecht-Buehler has written:
To my knowledge, there is not even a clue as to how to build a liquid miniature computer that would function despite thermal fluctuations and other turbulences in the liquid that would disrupt the circuitry. (Albrecht-Buehler 1985)
There is, quite simply, nothing there that could remotely qualify as “circuitry” in the sense of “machine parts”.
One might have thought that the puzzling revelations from our indirect, instrument-mediated encounters with the microworld would have opened up a space for free inquiry as we considered the nature of perceptible, material appearance. (On this, see Chapter 11 “All Science Must Be Rooted in Experience”.) One might indeed have expected that — given a realm considered fundamental to our understanding, yet inaccessible to the direct activity of our senses — we might have warned ourselves about the temptation to project falsely imagined perceptual contents into what is in fact an experiential blank for us.
And, given the scientific commitment to empirical (experience-based) evidence, what are we to make of a microworld characterized almost solely in terms of thought-models, mathematical formulae, and theoretical constructs, with no sense experience to ground us? Such grounding — together with a desire to get beyond the unfettered flights of medieval cerebration — was a good part of the resolve of the pioneers of the Scientific Revolution.
Perhaps we should pick up again from where they started.
1. As the size of an animal decreases, its volume (and therefore its weight) decreases much more rapidly than its surface area. In other words, as any given object is reduced in size, its surface-to-volume (surface-to-weight) ratio rises. The increased surface-to-weight ratio of the mouse is why its rate of fall is reduced by air resistance more than the elephant’s rate of fall.
More significantly for the fate of the mouse and the elephant in our rather twisted thought experiment, the different surface-to-weight ratios mean that the weight of the mouse per square centimeter of its body surface striking the ground is minuscule compared to the weight overlying the elephant’s area of contact with the ground. So the crushing effect of the impact is much greater for the larger animal.
2. Among the interrelated shaping forces of a liquid such as water are internal cohesion and surface tension.
5. The word “collisions” suggests an activity of particles conceived in the manner of our everyday experience of tiny bits of matter. Thinking of water molecules in this way is not something any physicist today would want to defend.
6. It is worth remembering that the lives of large, multicellular organisms — ourselves, for example — are not centered upon the cellular and molecular level. As we walk, run, and otherwise pursue our lives on earth, our bodies must work against the pull of gravity. If we do not sufficiently perform that work — if we are bedridden or live a sedentary life-style — our bodies suffer ill effects.
We know further that the weightlessness endured by astronauts on long missions results in significant loss of bone mass, density, and strength (Keyak 2009). Likewise, lions raised in zoos, apart from the rigors and stresses of hunting and the need to patrol large territories, have a bone structure differing from lions raised in the wild (Holdrege 1998).
So Albrecht-Buehler’s assertion that “gravity is an entirely irrelevant force in the violently chaotic world of cells”, while it may be true when we are looking at the interplay of forces in the decontextualized cell, can hardly be true for cells in the context of our bodies. If someone experiences changes in bone mass and muscle strength while living in a gravity-free environment, this implies radical changes in cells, including the loss (death) of cells. The fact that, when a person stands upright on earth, the weight of a 150-pound body comes to bear upon the small surface area of two feet certainly makes gravity a “relevant force” for the tissues and cells on the bottoms of our feet. And much the same can be said about the distribution of weight and weight-bearing surfaces throughout our bodies.
Actually, the importance of a larger context was very much part of Albrecht-Buehler’s argument in his paper. He was claiming, quite rightly, that we cannot explain either cellular or organismic behavior by trying to ground our picture upon molecular-level analyses.
7. I have this answer courtesy of the physicist, George Burnett-Stuart.
11. Figure 15.5 credit: IBM Research–Zurich.
12. Some experimental techniques do give us a form of sense-perceptible report from the microworld. For example, the relatively small “green fluorescent protein” (GFP) can be fused to particular molecules of interest in a cell. When the cell is irradiated with blue or ultraviolet light, the protein fluoresces, revealing under a light microscope the distribution of the target molecules in a cellular location. Again, however, blobs of fluorescent light, while informative of location, do not give us pictures of molecular “objects” residing at that location.
When a student collects a quantity of DNA on a glass rod, she is not looking at DNA molecules, but rather at a white, sticky substance. Similarly, a prospector may be looking at a chunk of iron ore, but he is not examining iron atoms. To say that our instruments, by eliciting responses at an atomic scale, can trace significant structure at that scale, is not to answer in any meaningful experiential sense, “structure of what?” — not if by “what” we refer to objects possessing sense-perceptible, material descriptions.
As a hypothetical question: what would we “see” if, through some sort of inner work, we should develop in the future a cognitive (clairvoyant?) capacity to experience — bring to appearance — whatever can be found, say, at the quantum level? This is, of course, pure speculation. But my surmise is that we would discover an intricately structured play of “forces” of will. We would discover, that is, a field of potential that, when probed in appropriate ways, can be brought to manifestation as materially engaged force. The fact that our own wills (in a manner of which we are completely ignorant and unaware) can take form in the enfleshed mechanical forces of our bodies, while a very different matter, may nevertheless be suggestive in this regard.
Alberts, Bruce, Alexander Johnson, Julian Lewis et al. (2002). Molecular Biology of the Cell, 4th edition, pp. 75-6. New York: Garland Science.
Albrecht-Buehler, Guenter (1985). “Is Cytoplasm Intelligent Too?”, chapter 1 in Cell and Muscle Motility, edited by Jerry W. Shay, pp. 1-21. Boston: Springer.
Albrecht-Buehler, Guenter (1990). “In Defense of ‘Nonmolecular’ Cell Biology”, International Review of Cytology vol. 120, pp. 191-241. doi:10.1016/S0074-7696(08)61601-0
Callier, Viviane (2021). “A Newfound Source of Cellular Order in the Chemistry of Life”, Quanta Magazine (January 7). https://www.quantamagazine.org/molecular-condensates-in-cells-may-hold-keys-to-lifes-regulation-20210107/
Encyclopedia Britannica editors, “Brownian Motion”. https://www.britannica.com/science/Brownian-motion. Downloaded January 27, 2021.
Holdrege, Craig (1998). “Seeing the Animal Whole: The Example of the Horse and Lion.” In Goethe’s Way of Science, edited by David Seamon and Arthur Zajonc. Albany: SUNY Press, pp. 213-232.
Keyak, J. H., A. K. Koyama, A. LeBlanc, Y. Lu and T. F.Lang (2009). “Reduction in Proximal Femoral Strength Due to Long-Duration Spaceflight,” Bone vol. 44, no. 3, pp. 449-53. doi:10.1016/j.bone.2008.11.014
Persinger, Michael A. (2012a). “Brain Electromagnetic Activity and Lightning: Potentially Congruent Scale-Invariant Quantitative Properties”, Frontiers in Integrative Neuroscience vol. 6, article 19 (May). doi:10.3389/fnint.2012.00019
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Steve Talbott :: Puzzles of the Microworld