Longer Than the Universe's Lifetime: Protein Folding

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Every protein in your body is born as a straight thread and takes on a single correct shape within fractions of a second. But if it tried to find that shape by trial and error, the entire age of the universe so far would not be enough. So the chain is not really searching — then what is it doing?

Inside your cells, right at this moment, there is a loom running without pause. This machine, called the ribosome, reads the genetic instruction letter by letter, and for every letter it reads, it dangles one bead from its tip. There are twenty kinds of bead: the amino acids. They are strung one after another, in a single file. What comes off the loom is a flexible, straight thread, hundreds of beads long, resembling nothing at all. At a rate of a few beads per second, thousands are produced every minute. And it has to be said that this thread, on its own, is good for nothing. As a straight thread, a protein is not an enzyme, not a transporter, not a channel. It is nothing.

Because a protein's job comes from its shape. Think of an enzyme: its task is to catch a particular molecule and either cut it or join it to something else. To do that, its surface must carry a pocket that fits that molecule, and only that molecule. The depth of the pocket, its width, the placement of the charges along its walls, the pattern of how it pushes water away or draws it in — all of it must be finely tuned. That pocket emerges when the thread bends and folds back on itself. Two amino acids sitting perhaps forty beads apart in the sequence end up side by side once folding is complete, forming the two walls of that pocket. Shape is function itself. The wrong shape is not a broken tool; it is no tool at all.

Here is the astonishing part: the thread finds this shape by itself. There is no external mold, no press stamping the thread into the required form, no separate instruction file saying "now bend here." The moment the thread leaves the loom and is released into a watery environment, it gathers itself up spontaneously and settles, almost every single time, into the same single three-dimensional structure. And it does this very quickly: for small proteins the job is over somewhere between a millionth of a second and a thousandth of a second; for large ones it takes at most a few seconds. The same sequence, today and tomorrow, in you and in a fish, always arrives at the same shape.

The experiment that proved this really is how it works was done in nineteen sixty-one. Christian Anfinsen was working on an enzyme called ribonuclease. This enzyme is one hundred twenty-four amino acids long, a small and sturdy protein, and its structure is additionally clamped together by four sulfur bridges. Anfinsen first tore the enzyme down. With urea he destroyed the delicate balance holding the structure, and with a reducing agent he cut the four bridges. What he had left in his hands was a slack, functionless, straight thread adrift in solution. The enzyme was dead — or rather, it had stopped being an enzyme.

Then Anfinsen removed those agents from the solution and waited. The thread pulled itself back together. The severed bridges were rebuilt, and ninety-four percent of the enzyme's activity came back. One detail here lifts the experiment out of being an ordinary story of recovery and turns it into decisive proof: the protein had eight sulfurs ready to form bridges, and there are one hundred and five different ways to pair those eight sulfurs into four couples. If the bridges had formed at random, the chance of hitting the correct pattern would have been around one percent. Yet the thread found the correct pattern almost every time.

The conclusion that emerged became one of the cornerstones of molecular biology: all the information that determines a protein's final shape is already contained in its amino acid sequence. Given the sequence, the shape appears on its own, as the chain settles in water into the most stable, lowest-energy arrangement available. For this work, Anfinsen shared the nineteen seventy-two Nobel Prize in Chemistry with Stanford Moore and William Stein.

It is also worth adding just how fragile the thing holding that shape up really is. There is no strong cement gripping a folded protein. There are hydrogen bonds, there are weak electrical attractions, there is the mutual finding of positive and negative charges — but the most decisive factor is the behavior of water. Some of the amino acids are oil-like; they shy away from any contact with water. Rather than keeping them outside, water presses them inward in order to preserve its own ordering. Seen from the outside, the protein becomes a shell on friendly terms with water, while inside it becomes a tightly packed oily core. Each one of these forces, taken individually, is comparable in size to the jostling the molecules suffer from ordinary heat. In other words, a protein stands up by the sum of a set of whispers, and most proteins are only a few whispers away from coming undone.

Anfinsen had closed the question of "why this shape." But at that very moment, without realizing it, he opened a far more unsettling one. If the shape is written in the sequence, how does the thread find that shape?

The person who turned this question into a calculation was the American molecular biologist Cyrus Levinthal. Levinthal belonged to the first generation to set computers running on biological questions; he was someone accustomed to thinking in numbers. At a scientific meeting he attended in nineteen sixty-nine, he asked the thing no one had been asking out loud: what is the thread actually doing while it finds the correct shape? The first answer that comes to mind is searching. It tries out various shapes and stays with whichever is most stable. Levinthal worked out what that answer would cost.

Along the backbone of a protein strand there are bonds that can rotate. At its own point of connection, every amino acid has two fundamental rotational freedoms — and that is before we count the twisting of the side chains. These rotations are not entirely free: atoms collide with one another, and certain angles are forbidden. But even if only a handful of distinct postures were available to each amino acid, those postures multiply as you move along the chain. For a medium-sized protein of one hundred fifty amino acids, Levinthal estimated the number of reachable shapes at roughly ten to the three hundredth power.

It is not easy to grasp what that number means, because nothing in everyday life corresponds to it. The total count of all the atoms in the observable universe is somewhere around ten to the eightieth power. So if you took every atom in the universe and treated it as a separate universe, and then took every atom in each of those universes and treated it as a universe again, and repeated the trick three times over, you still would not reach ten to the three hundredth power. That is the range of options standing in front of a single protein strand.

Now let us add time. For a bond to swing around and settle into a new posture takes place on the scale of the fastest molecular motions physicists know of: roughly ten to the minus thirteenth power seconds — a few trillionths of a second. Even if the protein worked at that maximum speed, never stopping, never hesitating, never trying the same shape twice, exhausting every option would take ten to the two hundred eighty-seventh power seconds. The universe is thirteen point eight billion years old; converted into seconds, that is roughly ten to the seventeenth power seconds — a one followed by seventeen zeros. Take the ratio, and for a single small protein to finish working through its list of shapes you would need ten to the two hundred seventieth power times the lifetime of the universe.

Set the sum up from the other end and the picture is unchanged. A protein finishes folding in fractions of a second. In that span, on the most generous estimate, the number of shapes it could try does not exceed a figure with eight zeros after it. This was precisely Levinthal's point: the ratio of the shapes a protein visits in its lifetime to the shapes available to it is indistinguishable from zero. The protein is not finishing the search; it is not even properly beginning it.

This went down in history as Levinthal's paradox, though the name is slightly misleading. There is no logical contradiction here. What there is, is a refutation. If the assumption of blind search were correct, proteins could not fold. Since proteins do fold, the assumption is wrong. That was Levinthal's own conclusion as well: folding is not a search, it is a route. The strand is not wandering among shapes; it is following a particular path. Levinthal took this idea so seriously that he went as far as to suggest that the shape a protein settles into need not be the most stable shape at all — it might simply be the shape that is reachable. That stood in tension with Anfinsen's conclusion, and it was the seed of a dispute that split the field in two for years.

What is more, as the experiments advanced, the paradox did not ease — it grew heavier. As measurement techniques sharpened, it became clear that proteins fold faster than anyone had supposed. Some small protein fragments finish the job on the scale of a microsecond, a millionth of a second. And at exactly this point the question outgrows the boundaries of biology and takes on a barer form: how does physics — which cannot see ahead, does not calculate, does not know the target — find the needle in an unimaginably vast haystack on its very first move?

It was not the numbers that were wrong. What was wrong was the picture in our heads.

The idea of a search quietly builds an image in the mind: a perfectly flat expanse, billions of equivalent points spread across it, and somewhere a single hole. Ken Dill likened this image to a gigantic golf course: wherever you place the ball, you get no clue at all about the hole, because the ground is at the same height everywhere. On a course like that, the only way to find the hole really is to try every point — and Levinthal's arithmetic holds flawlessly on such a course. The question is this: why should a protein's energy landscape be a golf course?

In nineteen eighty-seven, Joseph Bryngelson and Peter Wolynes approached that question from an unexpected direction. They adapted the statistical mechanics of disordered magnetic materials — systems known as spin glasses — to the protein chain. The decisive concept in this approach is conflict. The amino acids within a chain can enter into many different pairings with one another at the same time, and some of those pairings exclude each other: if one is formed, the other cannot be. In a randomly written chain, conflict is abundant; such a chain gets stuck among hundreds of competing, half-stable states and can never commit to any of them. What Bryngelson and Wolynes saw was that natural proteins are not random chains. Evolution had selected sequences in which conflict is minimized. In a chain like that, almost all of the correct contacts reinforce one another.

In nineteen ninety-two, Leopold, Montal and Onuchic captured what this property does to the landscape in a single word: a funnel. Not a flat playing field, but a broad funnel, sloping from its rim down toward the center, pitted and ridged along the way, with the correct structure sitting at the bottom. Here is the difference: in this landscape, the chain doesn't have to try anything at all. At every step, a slight energetic tilt nudges it downward, and each step taken downward sharply narrows the set of options that remain. A single contact formed correctly sweeps thousands of shapes off the table at once. A very small amount of guidance per step is enough to bring durations on the order of the lifetime of the universe down to microseconds. The protein isn't finding a needle in a haystack; everywhere in the haystack, the ground slopes toward the needle.

The broad outlines of real folding fit this picture. First comes a collapse on the order of a millionth of a second: the amino acids that behave like oil flee inward under the pressure of water, and the chain, its volume shrunk several fold, turns into a tangle that is still loose but now gathered together. This intermediate state is called the molten globule; the shape is roughly right, the details haven't settled into place yet. Then, at the bottom of the funnel, the fine tuning begins, and the atoms lock into their final positions.

That this picture is more than theory was shown in twenty eleven. David E. Shaw's team simulated twelve small, fast-folding proteins atom by atom on a special supercomputer called Anton, designed to compute nothing but molecular motion. Inside the computer, the chains folded on their own, unfolded, and folded again; the structures they arrived at matched the structures measured in the laboratory, and the times they took matched the times measured in the laboratory. What's more, the routes became visible: there is no single path, but a family of routes converging toward the bottom. Levinthal was right to speak of a path, but the path was not a single one.

Even so, it would be wrong to declare a clean ending here, because the "protein folding problem" is really three separate questions. How does sequence determine shape; how does folding happen this fast; and can we compute shape from sequence. The last question has been solved. In twenty twenty, at the international structure prediction contest held every two years, an artificial intelligence system called AlphaFold produced structures with an accuracy close to experimental measurement, opening up a field that had been blocked for decades in a single stroke. Half of the twenty twenty-four Nobel Prize in Chemistry went to Demis Hassabis and John Jumper for protein structure prediction, and the other half to David Baker for protein design. But these systems work by reading the statistical traces evolution has left in the sequences of related proteins. They tell you the destination; they don't tell you the journey. Knowing where a protein will settle is not the same as knowing how, and how quickly, it gets there. The second question, Levinthal's question, is the part that remains open.

The inside of a cell, moreover, doesn't resemble a test tube. The chain emerges from the ribosome not all at once but gradually, from one end to the other; folding begins before the sequence is even complete, which means the first half of the protein gives itself a shape without ever having seen the second half. The cell is so crowded that molecules sit right up against one another. For risky chains there are dedicated helper proteins; these enclose the newborn strand and insulate it from the outside world, opening up a sheltered room in which it can pull itself together.

Why that help is needed is explained by the dark side of the funnel. Some of the dimples along the funnel's rim are so deep that a chain falling into one cannot get out. Misfolded proteins glue their exposed oily surfaces to one another and build long, stiff fibers; the deposits that accumulate in the brain in Alzheimer's and Parkinson's disease are of this kind. In prion diseases the situation is even more unsettling: a misfolded shape imposes its own shape on neighboring molecules, which is to say the error copies itself. In these examples, the protein's natural shape isn't even the most stable of the shapes available to it; it is merely the shape the chain reaches sooner. That contrarian intuition of Levinthal's found its counterpart, fifty years later, in the biology of disease. And on top of that, a significant fraction of human proteins contain regions that never settle into a stable shape and stay loose; these do their jobs precisely because they remain undefined. One sequence corresponds to one shape is not a law, but a good rule of thumb.

Looking back, the thing that actually changed isn't the number. Levinthal's ten to the power of three hundred never got any smaller; it is still correct today. What changed is how we read that number. We had taken it for a calculation about time; in fact, it is a measure of what evolution was forced to do. A randomly written chain of amino acids doesn't fold, it clumps. The ability to fold isn't an intrinsic property of a chain; it is the privilege of special sequences, won through billions of years of selection, that have turned their landscape into a funnel. So the answer to the question "how is it this fast" is not a fast search. The answer is that there was never any search at all.

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