Fast Biology

Living cells are frenzied, crowded places. Numbers help us make sense of it.

This is the first piece in our new Editor’s Column, a series of essays written by the Asimov Press team.

Imagine the Minute Man

In the 1860s, a German polymath named Karl Ernst von Baer conducted a thought experiment. He imagined two people – the Minute Man and the Millenium Man – who each experienced time in a different way. The Minute Man experienced the world at such high speed that an entire lifetime passed by in just a few moments. The Millenium Man experienced the world slowly; a single lifetime stretched out over a thousand years.

If these two characters were plucked from their universes and dropped into our own, what might they make of it? 

Our world would feel incredibly slow to the Minute Man. A spinning jet turbine would appear frozen in place, and a speeding F1 car would move around a track with unbearable slowness. The Millennium Man’s experience would be the opposite; our world would feel impossibly quick. A child would seem to be born, grow up, love, work, and die in scarcely any time at all.

I first encountered Von Baer’s thought experiment in Richard Fisher’s book, The Long View. “We” — humanity — “have mastered one of these perspectives, but not the other,” Fisher writes. “It’s now fairly easy to step into the shoes of the Minute Man: through camera technology, we can slow down time in extraordinary fidelity.” But it’s more difficult, he continues, to put ourselves in the shoes of the Millenium Man, as our “minds struggle to perceive what it would be like to take in million-year chronologies.” 

I share Fisher’s views on the Millenium Man. When I close my eyes and imagine far-off futures, I struggle to conjure up any detailed mental images. But I don’t quite accept his view on the Minute Man. Do we really appreciate, let alone understand, what it means for something to be fast? 

Karl Ernst von Baer as a young man. Credit: Wellcome Images

I don’t think so. There is an inverse, linear relationship between the size of a thing and the speed at which it changes. Tiny things are easier to move. Cameras may allow us to “slow down” time, but they are limited by their resolution and are best-suited, often, to high speeds that occur at the macroscopic scale. In trying to study objects of increasingly small sizes, all the way down to a single cell, or even individual atoms within molecules, our best efforts are often stymied. At the nanoscale, one must contend with both small sizes and rapid movements, pushing the boundaries of both pixels and shutter speeds.

Within cells, there are enzymes that perform millions of chemical reactions each second. Protein ‘motors’ make energy-storing molecules by spinning around thousands of times a minute. Sugar molecules fly by at 250 miles per hour, nearly double the speed of a Cessna 172 airplane at cruising speed.¹ Every protein in the cell is hit by 10¹³ water molecules every second. 

When I first heard these numbers, I thought they were made up. After all, how is it even possible to measure such speeds? The world’s most powerful microscope cannot necessarily “see” a protein motor spinning, or watch a sugar molecule move through a cell.

While a PhD student, I jumped head-first into the world of biological speed. My goal was to collect some “fast” numbers in biology and understand the experiments that brought them to light. My search made me appreciate how remarkable it is that life functions at all, considering the chaotic conditions in which cells exist. It also gave me a new appreciation for biology, and the incredible exactitude that one must have to engineer it — let alone engineer it successfully.

Collecting the Numbers

We can easily measure some things in biology yet struggle to measure others. Thanks to decades of progress in molecular sequencing technologies, it is simple to read out the order of nucleotides in a DNA sequence, for example, or to quantify messenger RNAs as they are made by a cell. But measuring the physical speed of such molecules remains difficult.

Biologists often skirt around the “speed problem” by freezing molecules in place. Given the frenzied pace of the molecular world, it is not possible to “see” a protein’s structure simply by training a microscope at its surface. Instead, scientists extract the proteins from cells, freeze them, and then bombard them with x-rays or electrons. In this way, they are able to measure biological objects indirectly; a protein’s structure is pieced together by compositing images of diffracted x-rays, or by spotting the electrons that reflect into a detector.

It is all the more remarkable when scientists devise an experiment that allows direct observation of a rapid biological process. Brilliant scientists have quantified many of the smallest and fastest biological processes with incredible precision, without freezing anything. When I first read about their experiments, I felt a deep appreciation for both the speed of life and the cleverness of the human mind. Two of these experiments, in particular, left an indelible impression upon me.

The first has to do with ATP synthase, a barrel-shaped protein, made from three subunits, that makes the energy storage molecules of the cell. ATP synthase does this by combining ADP with a free-floating phosphate to form ATP. The barrel-shaped protein sits embedded in a membrane and performs this chemical reaction by harnessing the flow of protons down a concentration gradient. It spins around and around, each rotation yielding three molecules of ATP. Making ATP is, for these reasons, both a chemical and a mechanical process.

Unfortunately, it’s not possible to watch ATP synthase spin around with one’s eyes or even a powerful microscope. The protein is too small and moves too fast. The protein also can’t be frozen in place, because then it would stop spinning entirely. More than two decades ago, though, some researchers in Tsukuba, Japan figured out a way to get around this problem and watch ATP synthase as it spins. Their experiment stands out as among the most beautiful in the history of biology.

The Japanese scientists took an ATP synthase motor and fixed it on a flat surface. They then fused one of its three subunits to a tiny, gold bead. The bead was tethered to the protein via another protein, called actin, which acted as a molecular rope. 

As the ATP synthase spun around, it whipped the bead in a circle. The bead measured just 40 nanometers in diameter — fifty times smaller than the length of a single E. coli bacterium — but was large enough to be detected by a microscope. A camera captured an image of the rotating bead 8,000 times per second.

The scientists observed that ATP synthase spins around exactly 134 times each second, or 8,040 times each minute. That speed is significantly faster than the propeller on most piston airplanes, and about half the r.p.m. of a Boeing 737 jet engine.

Now, I can practically hear your objections through the page! “Wouldn’t the bead cause the ATP synthase motor to slow down? After all, it must add some drag!” 

Yes, a bead that is too large would slow down the turbine. But the Japanese team did another experiment to ensure that wasn’t the case. They ‘tethered’ many different beads, of varying sizes, to ATP synthase. Then they repeated their experiment, carefully taking images as the differently-sized beads were spun around. What they found was that, with a sufficiently small bead (such as the 40-nanometer one), it did not impede the motor’s movements whatsoever.

The ATP synthase “bead” experiment was part of a 2001 study published in the journal Nature.

And this number — 134 rotations per second — brings me to the second experiment. 

ATP is like a battery that the cell draws energy from to stay alive. The main way that cells “burn” this energy is by making proteins. Protein synthesis consumes about half of all ATP in a quickly-growing bacterial cell. At any given moment, thousands of messenger RNAs are being translated into proteins by ribosomes, which are protein-making machines that are, themselves, made from a mixture of proteins and RNA.²

Ribosomes move along a strand of mRNA, "read" each codon, and add the corresponding amino acid to a growing protein chain. The ribosome burns ATP at each step, and all of this happens several times a second. But again, how do we know? After all, ribosomes move so quickly and our eyes are not so good.

In 2008, researchers at UC Berkeley devised an ingenious solution. They "watched" individual ribosomes move along an mRNA, carefully monitoring their many starts and stops along the way, by tracking the distance between two plastic beads.

Here’s how they did it: First, the researchers chemically-synthesized a strand of mRNA and attached each of its ends to a little plastic bead. Each bead was then suspended in an optical tweezer, meaning that a laser beam was directed at them and the force resulting from the scattering of photons was enough to suspend each in place.

The mRNA molecule, suspended between these beads, had been specially crafted to have a loop, or hairpin, in the middle of its sequence. The beads were held in the optical tweezers with a force of exactly 20 piconewtons; just enough to hold the mRNA molecule in place, but not enough to unwind its hairpin.

Now here's the beautiful part: As the ribosome began to move along the mRNA strand, reading its individual codons and then popping amino acids into a protein, it exerted just enough force to unwind the hairpin. And as the hairpin came undone, the mRNA stretched out in length, the two beads became more distant from one another, and the increasing distance between the optical tweezers could be precisely measured.

It’s an astonishing experiment. By repeating it several times, the researchers found that ribosomes don’t glide along mRNA at a steady speed, but rather jump from one codon to the next in time steps of about 0.1 seconds. Some ribosomes even take brief pauses between each jump. We now know, through this experiment and others, that ribosomes build proteins at an average rate of 20 amino acids per second.³

Part of the beauty of science is that it builds upon itself, one experiment at a time. As scientists devise more experiments and take more measurements, they often make them available in papers, pre-prints, websites and blogs. Then other scientists sift through all these papers and compile all the numbers into an online database called BioNumbers. And now, at long last, we — humanity — have built a collection of useful numbers, a starting point, for biological numeracy. 

Back of the Envelope

Physicists often use order-of-magnitude calculations to do “sanity checks” on their thinking. At 5:29 a.m. on 16 July 1945, all the scientists from Los Alamos came out to watch the explosion of the first atomic bomb in the New Mexico desert. Enrico Fermi was standing about 10 miles away from the bomb, and decided to estimate how much energy was released in the blast:

“About forty seconds after the explosion the air blast reached me, I tried to estimate its strength by dropping from about six feet small pieces of paper before, during and after the passage of the blast wave. Since, at the time, there was no wind, I could observe very distinctly and actually measure the displacement of the pieces of paper that were in the process of falling while the blast was passing. The shift was about 2.5 metres, which, at the time, I estimated to correspond to a blast that would be produced by ten thousand tons of TNT.”

Fermi’s estimate was accurate to within an order of magnitude. In another, now famous, feat of estimation, the Greek astronomer, Eratosthenes, calculated the circumference of the Earth by measuring little more than the angles of shadows. He set up a pole in Alexandria and, on the summer solstice, measured the length and angle of its shadow. This measurement was taken at the same time that the sun shone straight down into a well in the Egyptian city of Syene, about 500 miles away. He then used these data to estimate the Earth’s circumference: 25,000 miles, a value that is shockingly close to truth (about 24,900 miles).

My point here is that biologists, too, can wield seemingly simple numbers to arrive at extraordinarily useful estimates. There is a surprising amount of low hanging fruit to be gathered just from knowing the numbers involved in cellular processes, and using those numbers to perform calculations and sanity checks.

Rather than vague descriptions of a molecular phenomenon, such as DNA goes to RNA goes to protein, researchers could strive for more precision, calculating how long it would take for, say, a gene of 3,000 nucleotides to be translated into a fully-folded protein.⁴ They could similarly estimate the theoretical fastest speed at which one cell could divide into two, using available numbers about the totality of atoms in a cell, the time required to copy a genome, and so forth. 

A recent study used order-of-magnitude estimates to correctly predict that ribosomes — the great, big complexes that make new proteins — are the fundamental bottleneck for one cell becoming two. The reason that E. coli doubles every twenty or thirty minutes, instead of every ten minutes, is because it can’t make enough ribosomes fast enough. If scientists wanted to engineer cells to divide faster, then, they should start with the ribosomes.

A back-of-the-envelope calculation on the division rate of a bacterial cell. Escherichia coli have about 5 million base pairs of DNA in their genome, and divide every 20 minutes. But each replisome can only copy DNA at a rate of 1,000 base pairs per second. These numbers suggest that E. coli must copy their genome using multiple replisomes — no experiments are required to figure that out! Credit: Rob Phillips and Ron Milo, Cell Biology by the Numbers.

The goal of such rough calculations is not to get the right answer, but to guide our thinking. They are a starting point for experiments, allowing one to evaluate what is possible with biology versus what ought to remain consigned to the realms of science fiction.

In my own work, I sometimes use numbers and calculations to more precisely hold an image of the cell in my mind. I can close my eyes and imagine (or, at least, try to imagine) what it might feel like to zoom into a bacterium, or to watch as proteins and polymerases latch onto its genome. They glide along in fits and starts, making RNA molecules at a rate of 45 nucleotides per second. Hundreds of proteins do this at the same time. The newly-made RNAs jostle and push their way through a densely crowded cell. Ribosomes latch onto these RNAs, one after another, in a Conga line, and begin to make protein after protein after protein, in parallel. A new protein emerges, fully-formed, every 30 seconds. Proteins shuttle in and out of the cell membrane, as ATP synthases whip around and make energy storage molecules 130 times each second. It is chaotic but flowing; expertly choreographed in an often-unintelligible way.

These mental, cellular scenes are based on extant data and emerge from calculations scribbled on the backs of envelopes and scraps of paper. They help to make my imagination more vivid and precise. For when our eyes and familiar tools are insufficient to capture the true complexity of biology, we must resort to physics and mathematics. It is through numeracy that we are able to see through the Minute Man’s eyes.

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Niko McCarty is a founding editor at Asimov Press. 

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Thanks to David Savage, Tony Kulesa, Daniel Goodwin and Yonatan Chemla for reading drafts of this essay.

Video credit: Martina Maritan, Scripps Research. “3D Whole Cell Model of a Mycoplasma Bacterium.”

Cite this essay: Niko McCarty. "Fast Biology." Asimov Press (2024). DOI: https://doi.org/10.62211/73yu-91ek

Correction: An earlier version of this article said that Fermi was standing 210 miles away from the atomic bomb explosion. He was standing about 10 miles away.

1. The instantaneous velocity of a molecule can be calculated as v = sqrt(kT/M), where k is the Boltzmann constant, T is temperature, and M is the mass of the particle. Smaller molecules move faster than big ones, and everything moves faster at higher temperatures. As a rule-of-thumb, a typical protein will move through a cell at about 10 meters per second or, barring collisions, move across a typical room in just one second. But cells are so densely crowded, and collisions so common, that this is not always their speed; merely an average.

2. Our bodies make about 70 kg of ATP every day. But at any given moment, only a few grams of ATP are available. The molecule is made — and destroyed — very quickly.

3. Recently developed methods can image single messenger RNAs, and track their movements in live cells, using microscopy. This paper is one example.

4. Transcription rates, or the conversion of DNA to RNA, varies from one organism to the next. But a good rule of thumb is 40 nucleotides per second. This implies that it would take at least 75 seconds for the RNA polymerase enzyme to transcribe a gene of 3,000 bases into a strand of messenger RNA. Translation rates also vary, but let’s say a ribosome adds 5 amino acids to a protein chain each second, corresponding to 15 nucleotides per second. It would then take about 200 seconds for one ribosome make one protein. Summed together, it would then take 275 seconds, or nearly 5 minutes, to convert our hypothetical gene into one protein.