Scientist Stories: George Whitesides, The Most Cited Chemist in the World and Co-Founder of Genzyme

George Whitesides explores how life might have originated on the early Earth and how to understand living systems as dynamic networks. He describes experiments with simple chemical reactions that generate metabolic-like cycles without enzymes, and proposes that robustness, not optimization, may have driven early life. He uses control theory and analogies to flames to explain how abrupt state changes could separate non-living chemistry from living systems.
Chapters
Let me tell you a little bit about— just a brief sentence about what a university professor is. It's something that comes with being geriatric. But when I asked— when somebody called me up and said this was happening, they said, Is there any advantage to it? Do you get money? Does anything of that sort happen? They said no. I said, well, why worry? They said, well, the virtue of being a university professor is that you get to teach a course on any subject that you want, regardless of whether you know anything about it or not, to students regardless of whether they want to learn anything about it or not. And in that spirit, I'm going to tell you about the subject I'm going to tell you about. And then one other warning as an introduction. One of— all of us, I think, wander around from place to place and talk to people. And it sometimes can be pretty tedious. So I try to think of an interesting question to ask just to sort of keep things going in a lively way. And one of my questions in the last period of time has been to ask particularly physicists, what is an electron? And they look at me with, I just think, absolutely charming disdain. And say, "You're a chemist. You don't understand." And I said, "What do you mean?" And they say, "You can't ask that question. You can say, 'What does an electron do?' But you can't say, 'What an electron is?'" So I want you to put that in the back of the mind as we talk about what life is or does or where it came from, because that's the subject. So this is very different as a talk from what we've been talking about It's concerned with two subjects which are deeply interesting to me. The first is, how could life have originated? Where did it come from? This is more a cultural issue than it is a utilitarian issue. I don't know what I'd do with the information, but I'm really interested in the question. And then the second question is, we're talking about systems, and life in some sense is a system, and so how should I think mechanistically about a system? And chemistry has been historically very good about thinking at systems at equilibrium, minimum, which are, as we loosely say, dead, if anything. And pretty bad about thinking of dynamic systems that are networks. So what we've been interested in is asking just what would be the simplest questions that one could ask about a network and what can one learn about that. So let me give you some points of background to make the case that The origin of life is interesting. Obviously, one can never establish where it came from, only plausibility. But it's a remarkably difficult and interesting problem. The formation of Earth was about a little bit more than 4 billion years ago.
The end of the period of heavy bombardment was about 3.
And that's the period which was marked by what were called ocean evaporators, meaning that they were objects that fell on the planet.
And when they hit the ocean, you ask, what happened to all that energy?
And the answer was the ocean evaporated. And so for 10,000 or 100,000 years, the surface of the Earth was covered with superheated steam.
It doesn't sound like a great place to start, you know, making life.
So the question is, how did reactions occurring in those circumstances begin to put themselves together into the first things that we would call living. And one of the alarming things about this is that it seemed as if life was originating in this period. That is, it seemed to have happened very rapidly. Now, what does that mean? We don't know.
So these are the questions. And why are they interesting?
And they're not interesting so much for utilitarian reasons as they are for cultural reasons.
One is, of course, the question of how we started, we being us, the species.
The second is, are we alone?
And what that means is that if it really is the case that if you have a bunch of chemicals and a water planet and life is inevitable because it's pretty plausible where it came from, then, you know, the statistic is you hold your finger the size of a quarter point in any direction in the sky, that amount of area subsumes about a billion galaxies, and each galaxy is in the order of 10 billion stars.
And so there are lots of those stars with planets.
So life will be inevitable under those circumstances. There's a question of alive and not alive.
Are they different?
Are they somehow the same thing? Is life more than the name of a set of molecular processes?
That is, is there something else there?
And I'm going to spend some time talking about that. And then this issue of order from chaos and different forms of life, which I'm not going to talk about here.
But from a chemist's point of view, and I think even from a biologist's point of view, there's a really interesting question in this.
And that is that we know that a cell is a collection of molecules that have structure and are reacting.
And we know that molecules are not alive. And we know that reactions are not alive. But the collection of molecules and reactions is alive. So what happened? And that to me is one of the great questions in science right now, and the answer is we don't know. We just don't have a sense.
So the problem that we're going to talk about is this one. We know, I know, how to convert chicken into chicken soup. I do not know how to convert chicken soup into chicken.
And so how does that happen?
And here's the second part of the problem, and that is that you look at milk pouring into a cup, and this makes perfectly good sense.
If I reverse it, it really makes you nervous, or it should, like, make you nervous. One of the very few things that I know for sure is the second law of thermodynamics.
And this is sort of what happened.
How did it happen?
Well, obviously it doesn't violate the second law. We know that. But what does happen? And so there are sort of two views of life. We've heard a lot of this view that exponential growth in which information is coded in DNA and so on.
It's all terrific.
There's another view, which is if you look inside the box, you see this stuff.
And, you know, this is just one of these wall charts, and it's a bunch of reactions.
And the characteristic of this system is what's given here. And that is that every one of these reactions basically is coded, is catalyzed by a valve called an enzyme whose interactions with the rest of what's in there is modulated. So we think of enzymes as being catalysts. That's probably the least interesting thing they do. The most interesting thing that they do is that they provide the communication network by which one set of reactions talks to another set of reactions.
How does that work?
Now, I should just say by way of background that this is a very interesting area culturally and science in the sense that there are two communities working in it which get along very well but which absolutely do not see eye to eye.
And there's a group of people, and an example is my very good friend and colleague Jack Szostak, who say that there's so much of this that you can think of, similarities between the ribosome and everything else, that all you have to do is assume RNA and you're done. Just assume RNA and you're done. I mean, that's fine.
The problem is that I'm a chemist and I can't figure out how I can possibly assume RNA. So I say all of this is irrelevant. And what's really difficult is to go from HCN from space raining down to get to something that looks like a cell. And he says, "Well, that's all technical detail, and you chemists will take care of that." And I say, "This doesn't make any difference anyway." And so we proceed in orbit that way.
Now, I'm going to give you one orientational slide here about some of the technology.
I'm going to show you some technology. It's going to have the characteristic that you're not going to understand it.
I'm going to show it to you anyway because I don't want you to understand it because I can barely understand it, which is the point.
What is the language that we can use to think about it?
And you'll see what I mean in a moment.
But one of the arguments I want to make to you is that when you're looking at systems, it's always good to look at models.
And so we have something down here called a cell.
And what a cell does is to take nutrients and oxygen, glucose, stuff of that sort, It's run into this container, and out of this comes waste, CO2 and heat. And then what happens is things go on in there that make more cell.
That's what's really going on. That's what life does.
The argument I want to make to you is that there's actually an analogy between this thing, which burns glucose to make complex molecules and gives heat and waste, and a flame which burns methane to give not molecules but heat and light, but also waste.
So one can think about various analogies, which I'll come to as we go along in a moment.
But you may be offended to say a cell and a flame have something in common.
But both of them are actually— there are thermodynamic characteristics there that are worthwhile thinking about.
And so what we're going to do in a little bit of what I'm talking about is to model this in terms of what chemical engineers called a CSTR, otherwise known as a continuous stirred tank reactor, which is just something in which you take in reactants, you stir it, and out come products and waste. And what's the connection between this and this? It's contained. This is stirred, if you want to think of it that way, diffusively. This is stirred mechanically. But they both do chemistry, and something interesting happens.
Now, one of the things that we wished to do and has proved to be very difficult is to take a, quote, simple metabolic cycle in the cell, ideally one of the ones that has the characteristic that it's common to all of life as we know it, like the Krebs cycle, and simply see if we can model something like that de novo, not with enzymes, but just to ask, how could you put a system like this together? How might it have formed spontaneously?
Because one of the problems with life as we know it is that it all depends on enzymes, and there can't have been enzymes there at the very beginning.
There may have been other catalysts, but there can't have been enzymes at the beginning.
So look at this, and it's much too complicated.
I don't know how to deal with it. But one of the things that you find in many of these cycles are thioesters, and there are reasons to believe that thioesters could be something that could have been present in the early Earth. It was not an oxidizing environment. There was a lot of H2S because of volcanic activity, a lot of stuff of this sort.
So what we've done is—
let me show you first the reaction.
The reaction basically takes a thioester and an amine and does chemistry on it in such a fashion that you end up with 2 of these for every 1 of these that you start with.
I'll show you how that actually works in a moment.
But this is kind of chemistry that probably didn't— wasn't exactly the chemistry that happened at the beginning, but it has the characteristics of being like that chemistry. So how do you do it?
What's the technical detail here? Not terribly important. You make a little microreactor into which you can feed the reagents, whatever they might be.
It's thermostated.
You take the products that come out, run it into a sampler, do an assay, and read that out. And it just— these are microfluidic systems of the sort that we've been talking about.
Now, here's the chemistry.
And you look at this and you say, I can't understand that, which is perfectly all right. I couldn't understand it either at the beginning. And the characteristic of this that's interesting is that there are two ways of thinking about this problem. One of them is to write this down kinetically as a series of coupled differential equations. And you can do that. And you can simulate what's going on. And it provides, at least for me, almost no intuition about what's happening. And if you go to a real metabolic cycle and you try to couple the million reactions that are going on in the cell in a computer model, You might or might not ever be able to do it, but it's certainly going to tell you nothing about what life is. So there has to be some other way of thinking about the problem. And one of the things that I've been concerned with is trying to understand, is there an alternative way of thinking about this kind of thing that would be useful in what you guys do and also what we do?
And the answer is—
let me—
first, let me show you the answer. Chemically, what— if you design the system correctly, and this is designed, what you see is that the process by which you produce the reactants has a remarkable set of characteristics, some of them things that you see in life. For example, it's multistable depending upon the space velocity, which is how rapidly you run the reactants into that system.
That is, there's a stable state, a stable state, a stable state.
And now you reverse this system and you start going back up this way, it doesn't reverse. It goes to something different. So it's bistable in that sense.
It's oscillatory, so it shows a very well-defined oscillatory behavior.
Here's the bistability. The oscillatory behavior shows something which I will come to in a moment, which is it shows bifurcations at both ends. So it's oscillatory over a particular region of space velocities,. But when you get down to here, it stops.
And when it gets to here, it stops. And that's relevant to some of the things we're concerned with. Now, all of that detail is terrific, and, and I'm happy to explain any of it that anyone happens to be interested in.
But this is really the point of this slide. It turns out that a very useful way of thinking about this problem is not to do chemistry, but to do control theory. And what control theory does is basically to take a problem that's very complicated and it breaks it up into modules. And so in this particular case, it turns out that you need 3 modules. You need a module which allows you to have reactions that are autoamplifying.
And we've designed an autoamplifying reaction.
You have to have a trigger that sets off the autoamplification to control the trigger. You have something that generates the trigger and then something that destroys the trigger. And the relative rates of generation and destruction determine the concentration that's here, which determines how rapidly it autoamplifies.
You set things off.
And then wash-off is another part of this. So that those things like oscillations and multistability come out of something in which I can now look at this as a chemist And I can design this, and I can design this, and I can understand that, where I could not understand a collection of differential equations.
It turns out this is also a big deal in a lot of what goes on in complex processes in chemical engineering. And I think it's a trick that could be used very usefully in a lot of cell biology. And so I recommend it to you as something to think about. Now, one of the issues that we just touched on has to do with this subject here, that oscillations stop and oscillations stop there.
I'm going to return to that in a moment, but there's something here which is a little—
it's interesting and problematic. And that is that if you look at the range of reaction conditions in which you see this remarkable complex behavior, emergent behavior, it's very narrow. And life is actually pretty sturdy. Now, I don't know exactly what that means, but it does have the characteristic that it raises a question which I've begun to think about, which is the Darwinian question. We all know that Darwin was terrific, and Darwin had basically the idea that life emerged and was refined toward the fittest organism. And we tend to think now of fitness in terms of our view of We're a cheetah and we're going to chase a gazelle. Can we catch the gazelle or can the gazelle catch us? But if you think about the origin, it was a fantastically unfavorable place for life. So it may well have been that what Darwinian origins really refers to is not in fact optimization but robustness. That what one should consider is that living systems had the characteristic that they were, they were generated to survive the broadest range of conditions rather than anything else. And there's a very important observation, a very interesting observation that we've made here, which is that if you have one of these systems that has the characteristic that it, let's say, oscillates, you change the reactants, ceases to oscillate. This is the kind of thing that, you know, you could see a small perturbation leading to a change in the system. However, if you put in a bunch of reactions that are similar, like it with that one that's oscillating, even under conditions in which the one that doesn't oscillate has ceased to oscillate, the whole system will continue to oscillate. That is, they entrain one another. And by having a series of competing pathways that are similar, you get a stability that you cannot get out of a single optimized reaction. And why is that important? And you ask the question of why, for example, you might have a bunch of gene variants present. And a reason for having a bunch of gene variants is to make the system robust. Now, let me show you the second part of this talk, which you might say is even further from what you're interested in, but maybe not. You live in California after all, or some of you do. It has to do with forest fires.
And I said we're interested in flames because flames are prototypically dissipative systems.
In which multiple flames can talk to one another, all kinds of interesting things can happen with flames.
So we're going to model forest fires.
And, you know, one of the things we're doing is building an analog model of a forest fire.
Forest fires are actually very interesting because they have a characteristic which is called blowup. And in a blowup, you have a fire which is progressing. And this looks pretty hot, but it's just being a forest fire. But when it gets to a crown region, What happens is that all of a sudden it skips to the top. All sorts of stuff goes on.
And the fire starts behaving totally differently, moves very rapidly. And most of the damage in forest fires comes from blowups. And almost all the deaths come from blowups. So they're actually quite important.
But there are nonlinearities in the system. And there are also interesting issues that I'm going to come to in a moment that have to do with this issue of segregation between states and things of that kind.
And I'll show you what this is in a moment.
So back to this. This is the analogy that we're going to be pursuing now.
But here we're going to actually look at a flame. And here the interesting point to pay attention to is an idea that you don't hear so much in biology, but I think could be critically important. And that is folded bifurcations, bifurcations in general. But let's just talk about folded bifurcations.
We are accustomed to thinking that as you take something and you increase the— whatever it is you're looking at, there's a relation between this variable and this variable. And as you increase it, let's say global climate, you warm the climate, it gets—
you warm—
you increase CO2 levels, you get the climate hotter.
And so this would just go on. And the nice thing about this notion is that if it gets too hot, you lower the temperature, you lower the CO2, and it gets cooler again.
But actually, there are many systems that don't do that.
And what happens instead is something in which you go along this pathway, and then there's a jump to another state.
And the jump can be abrupt. And this is, again, a kind of behavior that you see pretty commonly in biology.
And there is a very, you know, straightforward method of thinking about this kind of thing. And this In this particular case, it's called a folded bifurcation in which you can go along here, but at this stage, it can't go further. It can't go backwards for various reasons. It hops. But if you get to this stage and you then go backwards this way, it doesn't go back to there. It goes back down here.
And it won't return until you get to there.
And for those of you who are interested in climate, this is the kind of thing that you'd look at here. We increase forcing in terms of population or CO2, the climate gets worse and worse and worse, and then all of a sudden, abruptly, it does that, not gradually. And those are interesting things to think about. Now, there's some technical issues here, which I'm going to pass by for the sake of argument. But let me show you the experimental system. What we do is simply to take a piece of basically filter paper, and on that, we put something that burns well, which is a piece of nitrocellulose. And what we find in this kind of system is that you can have two totally different flames for the same piece of nitrocellulose.
One is structured and one is turbulent. Two states.
And what we will do to induce a transition is just to put in a perturbation.
And let's see if I can— I'll show you a movie. I should show you a movie. If I can figure out how to do it here. It's on.
Oh, it's on. Okay, so it's doing itself. Thank you. So here it is burning its way this way. You see this. It gets close to this hump. It begins to do this. And then all of a sudden it blows up into this new state and progresses on from there. So that in this region it is burning stably at a small flame. It goes through the hump. Here it burns stably, but we're at a totally different level. So it's transitioned between a small state and a large state. And that all seems interesting. And what's a little eerie about it is if you go through exactly the same thing and you start with the extreme state, go through the hump, it will sometimes revert and do that.
So that's a transition.
The question is, how do you describe that? We can describe one half of that.
We can't at the moment describe the other half of it.
But what we're seeing here is something of this sort. That is, that we look at some parameter with the strip, and you get a stable state. But if you perturb it in here, it can hop to this.
If it gets to this point on whatever axis you're working with, it always hops to there.
And then when it comes back, you can perturb it, and it will go back at some point. But the behavior of this is just much more complicated than any simple relationship.
So I want to test your intuition. We're going to take this kind of system on a piece of paper, and we're going to put in nitrocellulose disks of this sort to act as models of pine trees.
And what we're going to do is, you know, obvious experiments. You pack them closer together Does it burn more rapidly or less rapidly?
And the closer together you pack them, the better they burn. That makes perfectly good sense.
But now here's the experiment.
I just want you to see what's going on. Let's see what happens if I do that.
Yeah. Here is how this kind of system behaves with the flame propagating just in the piece of filter paper. Here is the flame propagating in the filter paper with the trees, that is the nitrocellulose discs. And you can see the differences in behavior.
And I think it's interesting to ask how you think about that in a biological context because it obviously makes a difference.
Now, here's the examination. What we're going to do is to take a given packing of disks on a surface, and we're going to pack them in 3 ways. Either nest them all so that they can get close to one another, nest them in islands, or nest them in a scattered way.
And my question to you is, what's the difference in burning between the three? And I have to say my intuition was completely wrong. The answer is they all burn exactly the same. Okay, not what I'd expected. All right, so the two ideas that I've introduced here are, one, control theory as a way of breaking apart a complicated problem into simple problems. In which you don't have to understand the inner workings of each box in order to get a system in which you can understand what's going on. You just look empirically at what goes on inside the box.
And then if you can build up a system based on boxes, you can ask what happens inside each box. And the second is this notion of bifurcations. But I just want to make a few final points.
You know, we're talking about systems.—
I mean, this is systems biology and patient-specific medicine and all the rest of this kind of thing.
We need to be careful, I would argue, in the definition of system. And I happen to be a— I personally happen to be a public health guy as opposed to an end-of-life for-profit guy.
Forgive me, Roger. The issue here is, is the issue that we're concerned with the patient or the population or the patient and the population? You say, well, it's both. In a Kantian world, we're interested in the patient.
In a utilitarian world, we're interested in the population. Why not do both? The answer is it's a resource-limited environment, and it's a resource allocation problem, and how are we going to allocate resources? So do we treat lung cancer, or do we do social engineering to get people to stop smoking? And one of the wonderful things I learned from you is that we should apparently encourage people to smoke. Only if you plan to die of lung cancer, apparently.
So this is an interesting issue, precision medicine or public health. And there is something that I think— I was entranced by the talk about big data yesterday.
And that particular argument had the notion that, you know, build it and they will come. That is to say, get data and out of data will spontaneously emerge understanding.
And let me just give you a couple of examples of things to consider there. One is microeconomics.
If you want to find a system in which we have more detailed relevant information than any other one, it's probably economics. And the stock market. We know everything about every stock from time immemorial.
And the characteristic of that system is that we can predict nothing. I mean, you can't. What you can do—— to say something about economic performance, the performance of the economy, but about individual stocks you can say nothing. And the issue here I think is a clear analogy in this case that doesn't tell you anything, but it makes you think. Weather, we have an enormous amount of information about weather. In weather we can do good predictions at the 3-day level, we can do pretty good predictions oddly enough at the 1-year level, We do terrible predictions at the 3-week level.
What do you make of that? Well, okay.
And then war is the same kind of thing.
At the engagement level, you can often predict.
You can sometimes predict at the campaign level. We're doing very poorly predicting outcomes overall. So this question of understanding what we do with the flood of information that will come out of the healthcare system, does it have to be hypothesis-driven?
Can you simply do deep learning or whatever it is to have it come out?
I don't know the answer to that. And then one last issue down here, which is pinging versus passive observation. One of the things that you find in systems of this noisy sort is that you do much better in general if you ping, that is to say you send a signal in and you see how the thing that you're interested in reacts against the background of noise, rather than just waiting passively and observing what comes into it.
So think about that.
All of that is neither here nor there. And then a last thought, which has to do with this issue of life. There is a view of life which would say you start with reactions. The reactions aggregate somehow. They get better.
The system gets to be more complicated. And it's just a question of layering on layers of chemical complexity.
There's another issue which says that it becomes more complex and it's just a bunch of chemical reactions, and then there's a point where the ignition occurs and it becomes alive. I don't at the moment know which is the right answer, but I think we can at least define the question. And this leads to neat questions of this sort.
That is, are not alive and alive different?
Are they just variations in the same thing? Very relevant, I think, to issues like Will the web at some point become alive?
Could there be life completely different from ours?
That's the web question.
Planets, this is a different kind of thing.
And all of the rest of these kinds of things, this is how it could have happened.
It's one of two remaining Copernican revolutions. We've learned that we're not the center of the universe. It would be one of the revolutions I think that's coming is that we're not the only intelligent thing. The other one is maybe made of silicon or something else. And then the final one is that life may be common as pond scum across the galaxy, which sort of puts us in our place. And I think that's the— I'll skip this for the moment. So that's the end of the talk. And I thank you very much for the opportunity to come.
Let me start with one question. So the issue of predictability of systems, and you used economic systems, I think the difference from biological systems in my view is the time scale of evolution where you can accelerate evolution of financial systems because of the players who can react to changes. So in biological systems, maybe in tumors you have something similar, similar but not at that time scale.
Any comments on that?
I would agree with that. But the point that makes me, I guess, a little uneasy is that in economic systems, you have so much information. You can do the experiments so rapidly. You can see it all. And biology is just that much more difficult. So— but biology has a whole series of principles that have to do with the fact that biological systems are optimizing themselves for survival. And the question of predator-prey relations in economic systems is more complicated.
So speaking of difference between life and chemistry, I would say that potentially life has feedback, i.e., control, and storage memory of what's— so it can use that to optimize, and that would be the two different things.
And without memory, you're not going anywhere. But I agree with that. And the point about these oscillating reactions is they have memory. It's a different kind of memory. But the question is, where can memory have come from if we have a mechanism for storing information in DNA or RNA or perhaps something like that, but the chemistry required, the molecular chemistry required to make that machinery cannot, that I can see, obviously have arisen from the world that was the prebiotic world?
That really is the problem.
Any sort of memory. We'll take 2 questions and then we'll take a break and then resume later.
Sure, so I'm just inspired to respond to that one. So if we condense life to the fact that you need to have memory that propagates and diversifies and advances over time, and clearly a genome does that, right? But what's the machinery? Well, is it perhaps that we're lacking the intuition of the scale of the experiment, right? 10 billion stars or galaxies under my thumb, and there's 15 billion years since the start of the universe. And so, albeit unlikely that something came together to make some kind of linear polymer that could transmit energy, we had a lot of chips in the experiment and it happened on Earth once that we know. I mean, the fact that we don't have other linear polymers that actually encode life is interesting, but it can be fantastically unlikely and yet happen a billion times across the universe. So we lack the intuition to really, you know, to really say whether or not it's probable that something came together that could propagate information like that.
I completely agree with all of that. But having said it, there are two, I think, facts that are relevant. One is that it happened here very quickly. I mean, there were still giant meteors falling in the ocean when there were the first signs of life. So that doesn't mean that— you know, it probably occurred somewhere in the ocean where the environment was more stable. But it still was not so improbable on a scale of a few, you know, hundreds of millions of years and a few oceans.
But then, you know, the other— But on the flip side, we only have one frame of reference, right? So we can't say how unlikely— if we did the experiment again, would it happen again as quickly? Who knows?
We could be the one in all of the possible universes. In which case we are special. Or not.
But we're not. We're not. So yeah, I think it's kind of important to deconstruct this term memory because there is certainly molecular memory that's not life, but we won't deal with that from a reaction kinetics point of view. But one of the interesting things, it seems to me, is— and I think, George, you've thought about this a lot— is the issue of hydrophobicity. I mean, because really life is defined as the partitioning. I mean, it's very important to get this system isolation. And how that emerged in this aqueous environment I think is a kind of an important thing because once you had— once you're able to isolate a set of reactions from the surrounding environment, then there is an opportunity to see that thing progress along the kind of thermodynamic curves you you talk about, but how did you get there?
The argument there is that one of the components that people tend to leave out of this in thinking about the organic chemistry is the geochemistry. I think there's at least a plausible argument that said the first cell may have been a crack in the rock that just had a gooey glob on one end, so it was in fact compartmentalized, but there was enough stuff going in and out that you could do things, and the walls were lined with catalytically active iron sulfides and things of the sort that show up in the Krebs cycle. If you look particularly in the redox enzymes in some of these protocycles, you find that they have to just be organic stuff wrapped around colloids. So I mean, the frustration about this is you can see where everything could have come from, but not how it could have come together. At least I can see where everything can have come from. But not how it could have come together. And that's what makes the problem interesting.
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