Field of Science

In praise of contradiction

Scientists usually don't like contradictions. A contradiction in experimental results is like a canary in a coal mine. It sets off alarm bells and compels the experimentalist to double-check his or her setup. A contradiction in theoretical results can be equally bad if not worse. It could mean you made a simple arithmetical mistake. Contradiction could force you to go back to the drawing board and start afresh. Science is not the only human activity where contradictions are feared and disparaged. A politician or businessman who contradicts himself is not considered trustworthy. A consumer product which garners contradictory reviews raises suspicions about its true value. Contradictory trends in the stock market can put investors in a real bind.

Yet contradiction and paradoxes have a hallowed place in intellectual history. First of all, contradiction is highly instructive simply because it forces us to think further and deeper. It reveals a discrepancy in our understanding of the world which needs to be resolved and encourages scientists to perform additional experiments and decisive calculations to settle the matter. It is only when scientists observe contradictory results that the real fun of discovery begins. It’s the interesting paradoxes and the divergent conclusions that often point to a tantalizing reality which is begging to be teased apart by further investigation.

Let's consider that purest realm of human thought, mathematics. In mathematics, the concept of proof by contradiction or reductio ad absurdum has been highly treasured for millennia. It has provided some of the most important and beautiful proofs in the field, like the irrationality of the square root of two. In his marvelous book "A Mathematician's Apology", the great mathematician G H Hardy paid the ultimate tribute to this potent weapon:
"Reductio ad absurdum, which Euclid loved so much, is one of a mathematician's finest weapons. It is a far finer gambit than any chess gambit: a chess player may offer the sacrifice of a pawn or even a piece, but a mathematician offers the game."
However, the great ability of contradiction goes far beyond opening a window into abstract realms of thought. Twentieth-century physics demonstrated that contradiction and paradoxes constitute the centerpiece of reality itself. At the turn of the century, it was a discrepancy in results from blackbody radiation that sparked one of the greatest revolutions in intellectual history in the form of the quantum theory. Paradoxes such as the twin paradox are at the heart of the theory of relativity. But it was in the hands of Niels Bohr that contradiction was transformed into a subtler and lasting facet of reality which Bohr named 'complementarity'. Complementarity entailed the presence of seemingly opposite concepts whose co-existence was nonetheless critical for an understanding of reality. It was immortalized in one of the most enduring and bizarre paradoxes of all, wave-particle duality. Wave-particle duality taught us that contradiction is not only an important aspect of reality but an indispensable one. Photons of light and electrons behave as both waves and particles. The two qualities seem to be maddeningly at odds with each other. Yet both are absolutely essential to grasp the essence of physical reality. Bohr codified this deep understanding of nature with a characteristically pithy statement- "The opposite of a big truth is also a big truth". Erwin Schrödinger followed up on his own disdain for complementarity by highlighting an even more bizarre quantum phenomenon- entanglement- wherein particles that are completely separated from each other are nonetheless intimately connected; by doing this Schrödinger brought us the enduring image of a cat helplessly trapped in limbo between a state of life and death.

The creative tension created by seemingly contradictory phenomena and results has been fruitful in other disciplines. Darwin was troubled by the instances of altruism he observed in the wild; these seemed to be contradicting the ‘struggle for existence’ which he was describing. It took the twentieth century and theories of kin selection and reciprocal altruism to fit these seemingly paradoxical observations into the framework of modern evolutionary theory. The history of organic chemistry is studded by efforts to determine the molecular structures of complex natural products like penicillin and chlorophyll. In many of these cases, contradictory proposed structures like those for penicillin spurred intense efforts to discover the true structure. Clearly, contradiction is not only a vital feature of science but it is also a constant and valuable companion of the process of scientific discovery.

These glittering instances of essential contradiction in science would seem perfectly at home with the human experience. While contradiction in science can be disturbing and ultimately rewarding, many religions and philosophies have come to savor this feature of the world for a long time. The Chinese philosophy of Yin and Yang recognizes the role of opposing and contrary forces in sustaining human life. In India, the festival celebrating the beginning of the Hindu new year includes a ritual where every member of the family consumes a little piece of sweet jaggery (solidified sugarcane juice) wrapped in a bitter leaf of the Neem tree (which contains the insecticide azadirachtin). The sweet and bitter are supposed to exemplify the essential combination of happy and sad moments that are necessary for a complete life. Similar paradoxes are recognized in Western theology, for instance pertaining to the doctrines of the Trinity and the Incarnation.

The ultimate validation of contradiction however is not through its role in life or in scientific truth but through its role as an insoluble part of our very psyche. We all feel disturbed by contradiction, yet how many of us think we hold perfectly consistent and mutually exclusive beliefs in our own mind about all aspects of our life? You may love your son, yet his egregious behavior may lead you to sometimes (hopefully not often) wish he had not been born. We often speak of 'love-hate' relationships which exemplify opposing feelings toward a loved one. If we minutely observe our behavior at every moment, such observation would undoubtedly reveal numerous instances of contradictory thoughts and behavior. This discrepancy is not only an indelible part of our consciousness but we all realize that it actually enriches our life, makes it more complex, more unpredictable. It is what makes us human.

Why would contradictory thinking be an important part of our psyche? I am no neuroscientist, but I believe that our puzzlement about contradiction would be mitigated if we realize that we human beings perceive reality by building models of the world. It has always been debatable whether the reality we perceive is what is truly 'out there' (and this question may never be answered); what is now certain is that neural events in our brains enable us to build sensory models of the world. Some of the elements in the model are more fundamental and fixed while others are flexible and constantly updated. The world that we perceive is what is revealed to us through this kind of interactive modeling. These models are undoubtedly some of the most complex ever generated, and anyone who has built models of complex phenomena would recognize how difficult it is to achieve a perfectly logically consistent model. Model building also typically involves errors, of which some may accumulate and others may cancel. In addition models can always be flawed because they don't include all the relevant elements of reality. All these limitations lead to models in which a few facts can appear contradictory, but trying to make these facts consistent with each other could possibly lead to even worse and unacceptable problems with the other parts of the model. Simply put, we compromise and end up living with a model with a few contradictions in favor of a model with too many. Further research in neuroscience will undoubtedly shed light on the details of model building done by the brain, but what seems unsurprising is that these models contain some contradictory worldviews which nonetheless preserve their overall utility.

Yet there are those who would seek to condemn such contradictory thinking as an anomaly. In my opinion, one of the most prominent examples of such a viewpoint in the last few years has been the criticism of religious-minded scientists by several so-called 'New Atheists' like Richard Dawkins and Sam Harris. The New Atheists have made it their mission to banish what they see as artificial barriers created between science and religion for the sake of political correctness, practical expediency and plain fear of offending the other party. There is actually much truth to this viewpoint, but the New Atheists seem to take it beyond its strictly utilitarian value.

A case in point is Francis Collins, the current director of the NIH. Collins is famous as a first-rate scientist who is also an ardent Catholic. The problem with Collins is not that he is deeply religious but that he tends to blur the line between science and religion. A particularly disturbing instance is a now widely discussed set of slides from a presentation where he tries to somehow scientifically justify the existence and value of the Christian God. Collins's conversion to a deeply religious man when he apparently saw the Trinity juxtaposed on his view of a beautiful frozen waterfall during a hike is also strange, and at the very least displays a poor chain of causation and inadequate critical thinking.

But all this does not make Collins any less of an able administrator. He does not need to mix science with religion to justify his abilities as a science manager. To my knowledge there is not a single instance of his religious beliefs dictating his preference for NIH funding or policy. In practice if not in principle, Collins manages to admirably separate science from storytelling. But the New Atheists are still not satisfied. They rope in Collins among a number of prominent scientists who they think are 'schizophrenic' in conducting scientific experiments during the week and then suspending critical thinking on Sundays when they pray in church. They express incredulity that someone as intelligent as Francis Collins can so neatly compartmentalize his rational and 'irrational' brain and somehow sustain two completely opposite - contradictory - modes of thought.

For a long time I actually agreed with this viewpoint. Yet as we have seen before, such seemingly contradictory thinking seems to be a mainstay of the human psyche and human experience. There are hundreds of scientists like Collins who largely manage to separate their scientific and religious beliefs. Thinking about it a bit more, I realized that the New Atheists' insistence on banishing perfectly mutually exclusive streams of thinking seems to go against a hallowed principle that they themselves have emphasized to no end- a recognition of reality as it is. If the New Atheists and indeed all of us hold reality to be sacrosanct, then we need to realize that contradictory thinking and behavior are essential elements of this reality. As the history of science demonstrates, appreciating contradiction can even be essential in deciphering the workings of the physical world.

Now this certainly does not mean that we should actively encourage contradiction in our thinking. We also recognize the role of tragedy in the human experience, but few of us would strive to deliberately make our lives tragic. Contradictory thinking should be recognized, highlighted and swiftly dealt with, whether in science or life. But its value in shaping our experience should also be duly appreciated. Paradox seems to be a building block in the fabric of the world, whether in the mind of Francis Collins or in the nature of the universe. We should in fact celebrate the remarkable fact that the human mind can subsume opposing thoughts within its function and still operate within the realm of reason. Simply denying this and proclaiming that it should not be so would mean denying the very thing we are striving for- a deeper and more honest understanding of reality.

Will-o'-the-wisp around 5 sigma: the hunting of the Higgs

Mr. Hunter, we have rules that are not open to interpretation, personal intuition, gut feelings, hairs on the back of your neck, little devils or angels sitting on your shoulder.... - Capt. Ramsey ('Crimson Tide')

Particle physicists hunting for maddeningly elusive particles sometimes must feel like Mr. Hunter in the movie "Crimson Tide". The quarries which they are trying to mine seem so ephemeral, making their presence known in events with such slim probability margins, victims of nature's capricious dance of energy and matter, that intuition must sometimes seem as important as data. The hunt for such particles signifies some of the most intense efforts in extruding reality from nature's womb that human beings have ever put in.

No other particle exemplifies this uniquely human of all endeavors than the so-called Higgs boson. The man who bears the burden of imparting it its name is now a household name himself. Yet as the history of science often demonstrates, the real story is both more interesting and more complicated. It involves intense competition involving billions of dollars and thousands of careers of a kind rarely seen in science, and stories of glories and follies befitting the great tragedies. In his book "Massive", Ian Sample does a marvelous job of bringing this history to life.

Sample excels at three things. The first is the story of the two great laboratories that have mainly been involved in the race to the finish in discovering nature's building blocks- Fermilab and CERN. CERN was started in the 60s to give a boost to European physics after World War 2. Fermilab was lovingly built by the experimental physicist Robert Wilson, a former member of the Manhattan Project who was a first-rate amateur architect and saw accelerators as aesthetic things of beauty. Secondly, Sample does a nice job of explaining the reasons that led to the construction of these machines, the most complicated that mankind has ever constructed. Only human beings would put billions of dollars and immense manpower on the line purely for the purpose of satisfying man's curiosity of plumbing the depths of nature's deepest secrets. Sample also lays out the very human and social concerns that accompany such investigations. Lastly, Sample was lucky enough to get an extended interview with Peter Higgs, a shy man who very rarely does interviews. Higgs grew up in Scotland idolizing Paul Dirac and shared Dirac's view of a unifying beauty that would connect nature's disparate facts. In the late 1960s he wrote papers describing what is now called the Higgs boson. The papers were well-accepted in the US and Higgs's name soon began to be bandied about in seminars and meetings. As described below however, Higgs was not the only one postulating the theory.

So what exactly is the Higgs boson? A complete understanding would naturally need a background in theoretical physics, but the best analogy for the layman was given by a British scientist. Imagine a room full of young women who are happily chatting. In walks a handsome young man. As long as he is not noticed he can move freely across the room, but as soon as the young women spot him they cluster around him, impeding his movement. It's as though the young man has become heavier and has acquired mass from the "field" of women surrounding him. The Higgs then is the particle that imparts specific masses to all the other myriad particles discovered so far including quarks and leptons through its own field. It should be evident why it's important. The Higgs would be the crowning achievement in the Standard Model of particle physics which encompasses all particles and forced known until now except gravity.

However, the history of the Higgs particle is complicated. Sample does a great job of explaining why the credit belongs to six different people who reached the same conclusion that Higgs did. It seems that Higgs was not the first to publish, but he was the first one to clearly state the existence of a new particle. However, the most comprehensive theory of the Higgs field and particle came out later. If Nobel Prizes are to be awarded, it's not at all clear what three people should be picked, although Higgs's name seems obvious. The sociology of scientific discovery is as important as the facts and again illustrates that science is a much more haphazard and random process than is believed.

The search for the Higgs gathered tremendous momentum in the 80s and 90s. It intensified after accelerator laboratories spectacularly discovered two particles named the W and Z bosons that are responsible for mediating the electromagnetic and weak interactions (the electroweak force). These particles were predicted by Steven Weinberg, Abdus Salam and Sheldon Glashow in the 60s, and their prediction surely ranks as one of the greatest theoretical successes in modern physics. Once the theory predicted the masses of these particles, they were up for grabs. No experimentalist worth his or her salt would fail to relish nailing a concrete theoretical prediction of fundamental importance through a decisive experiment. Sample captures the pulse-quickening inter-Atlantic races to find these particles especially between CERN and Fermilab. The importance of these particles was so obvious that Nobel Prizes came in quick succession both to the theorists and the experimentalists. However the existence of the Higgs is also essential for the successful formulation of the electroweak theory, and signatures of the Higgs are thought to be produced whenever W and Z bosons are created. It again becomes obvious why finding the Higgs is so important; its existence would validate all those successes and Nobel Prizes, whereas a failure to find it would entail a stunningly hard look at some of particle physics's most fundamental notions.

These days the Large Hadron Collider (LHC) is all over the news. Yet the most exciting part of Sample's book describes not the LHC but the Large Electron Positron collider (LEP) at CERN which was the largest particle accelerator in the world at the time. Unlike protons, electrons and positrons are fundamental particles and crashing them together produces 'cleaner' results. There were some fascinating events associated with the LEP. The behemoth's circumference was 27 kilometers and it crisscrossed the Swiss-French border, so authorities had to seek permission to build the accelerator underneath some homes. It seems that French law is special just like their cheese and language; apparently if you build a house in France, it means that you own the entire ground beneath the house, all the way to the center of the earth. Suffice it to say that some negotiation with the homeowners was necessary to secure permission for underground construction. At one point the intensity of the beams inside the mammoth machine started to wax and wane. After many days of brainstorming a scientist had a hunch; it turns out that the the gravity of the moon and the sun sets up tides inside the crust of the earth. These tides put the calibration of the machine off by a millimeter, too small to be noticed by human beings, but thunderingly large for electron beams. In another case, the daily departure of a train from a nearby station sent surges of electricity into the ground and affected the beams. It seems like when you are building an accelerator you have to guard against the workings of the entire solar system.

The story of particle physics is also fraught with tragedies. One of the biggest described in the book was the construction of the Superconducting Supercollider in Texas. The SSC was supposed to be the answer to CERN and got enthusiastic backing from Reagan and Bush Sr. Unfortunately the budget spiraled out of hand, the infighting intensified, congressmen remained unconvinced and the collider never got built in spite of spending billions and affecting thousands of careers of scientists who had relocated. The fiasco just proved that public support for even projects like the LHC is never a sure thing, and scientists don't always excel at public relations.

Then of course there are all the doomsday scenarios and concerns which were raised about the LHC, from the formation of black holes to the world ending in myriad other ways. As Sample describes, these concerns go back to an accelerator at Brookhaven National Laboratory which would impact large gold ions together at furious velocities. The would-be Nobel laureate Frank Wilczek raised the theoretical yet vanishingly small probability of forming 'strangelets', entities akin to the fictitious substance 'Ice-9' in Kurt Vonnegut's novel 'Cat's Cradle'. These strangelets would coalesce together matter around themselves and form a superstable form of dead matter that would rapidly engulf the entire planet. The concern about strangelets pales in comparison however to the possibility of 'vacuum decay', in which our universe is thought to be in a perfectly happy but metastable state like a vase on a table. All it takes is a little nudge or a massive kick from a high-energy particle collision in our case to dislodge the vase or universe from its metastable state into a stable state of minimum energy. Gratifyingly, not only would this state mean the end of life as we know it but it would also mean the impossibility of life ever arising. Yes, all these scenarios seem straight out of the drug-induced, overactive imagination of a demented mind, but at least some of them are within the realm of theoretical possibility. Unfortunately when the result is the destruction of the planet, the words "improbable" and "vanishingly small" will never do much to assuage the public's fears. It just indicates that physicists will always have to grapple with public relations issues vastly more complex than the LHC.

Finally, we get a fascinating overview of the kinds of things which scientists hope to see in the LHC. The problem is that the generation of particles like the Higgs is a very low-probability event and is usually only a side-product of some other primary event. The situation is made more complicated by the immense difficulty of observing such fleeting glimpses in a hideously complex background of noise generated by the creation of other particles. Scientists working on these projects have to keep their eyes and instruments peeled for the one in a trillion event that may bring them glory. Whenever an event is observed, the scientists have to calculate the realm of probability in which it belongs. Usually if the event is outside five standard deviations ('5 sigma') then it is extremely likely to be real and not have occurred by chance alone. Not surprisingly, the observation and communication of these events is a tortuous thing. Publicity has to be avoided before you confirm such fleeting bits of probability, but leaks inevitably offer. And the media has seldom shown any restraint in announcing such potentially momentous discoveries which would bring glory, prizes and money to their originators. Scientists working today also have to deal with the presence of blogs and other instant communication conduits. As Sample narrates, at least in one case a physicist at CERN posted preliminary LHC results on the blog Cosmic Variance, and all hell broke loose. Scientists have to tread carefully especially in this era of instant data dissemination.

All this makes the scientists engaged in such endeavors live on the edge, and to us they appear like the explorers who have their eyes peeled to the sky looking out for the stray signal that would announce the presence of extraterrestrials. The mathematics of the Higgs boson is of course much more sound than that of alien contact, but the scientists who are looking for it are hanging on to such flimsy wisps of probability and interpretation that they surely must be questioning their own sanity sometimes.

In the end, even physicists are all too human. As Capt. Ramsey says, our rules are not always subject to little devils and angels sitting on our shoulders. And yet it seems that scientists like the Higgs hunters sometimes would be tempted to trust the hairs on the back of their head, especially when those hairs stand up straight at the glimpse of a peak in the graph, that 5-sigma event which would change everything. Maybe, just maybe.

Life (and chemistry) is a box of models

One of the most important challenges in teaching students chemistry is in conveying the fact that chemistry is essentially a milieu of models. Too often students can misinterpret the conceptual devices taught to them as "real" entities. While models seem to perpetually and cruelly banish the concept of "reality" itself to fanciful speculation at best, the real beauty of chemistry is in how the simplest of models can explain a vast range of diverse chemical phenomena. Students' understanding can only be enriched by communicating to them the value of models as a window into our world. How can we achieve this?

We can start by emphasizing the very fact. Very few of my chemistry teachers even mentioned the word "model" in their discourse, let alone emphasized the preponderance of models used in chemistry. One can claim that all of chemistry is in fact a model. The reason for this is not hard to grasp: models come to our aid when the world gets too complex. The complex nature of chemical systems wherein one cannot describe them using first principles lends especially this 'central science' to modeling.

You can start with the simplest fact taught in freshman chemistry class- the structure of methane as it is drawn on paper. The methane molecule of course exists in real life, but that does not mean that you can actually see four bonds growing out tetrahedrally from a central carbon. Recent advancements in techniques like scanning tunneling microscopy have brought an astoundingly real feel to molecules, but what you see is still diffuse electron density and not actual bonds. The tetrahedral representation of methane that we draw on paper is very much a model.

Once students realize that even their simple representations of molecules are models, the road ahead becomes easier. Since we are talking about methane, we will inevitably talk about hybridization and describe how the carbon is sp3 hybridized. But of course hybridization is merely a mathematical and conceptual device- and a very powerful one at that- and this needs to become clear. Hybridization in methane leads to discussion about hybridization in other molecules. This is usually followed by one of the most conceptually simple and useful models in chemistry where you can make back-of-the-envelope calculations to get real and useful results- VSEPR. VSEPR is a great example of a simple model that works in a great number of cases; asking whether it is "real" is futile. Thus, one can drive home the importance of modeling even in the first few sessions of chemistry 101.

Once these facts become clear, the floodgates can open. Students can cease to think of the world as real and still be happy. Think the famous Van der Waals "12-6" curve is real? Think again. It does a marvelous job of representing in simple terms an incredibly complex and delicate tension between attraction and repulsion engendered by point charges, dipoles and higher order terms, and it's no more than that. But it works! It's a disarmingly simple model that's even incorporated in popular molecular modeling programs. How about crystal field theory? Another fantastic model that does a great job of explaining the properties of transition metal complexes without being real. Of course, let's not even get started on that ubiquitous act that initiates a newbie into the world of organic chemistry- arrow pushing. That's the very epitome of modeling for you. And after this onslaught, students should have little trouble understanding that those ephemeral, seductive twin forms of benzene that seem to interconvert into each other on paper are pure fiction.

Want a book that teaches chemistry through models? You are in luck. One of the best books that conveys the reality of chemistry as model building also turns out to be one of the most influential scientific books of the 20th century- Linus Pauling's "The Nature of the Chemical Bond". In this book Pauling introduces dozens of ideas like polarization, hybridization, ionic and covalent character of bonds, resonance and hydrogen bonding. All of these are enshrined in his Valence Bond Theory. And all are models. If conveying the importance of models to students gives us an opportunity to introduce them to this classic text, the effort would already have been worthwhile.

So would students turn fatalistic and despondent once they have been convinced that the world is not real but is a model? Not at all. The singular fact that snatches hope from the jaws of defeat is the very fact that we can in fact build such models and understand the world. Think about it; we build models that are almost laughingly simplistic representations of a hideously complex reality that's probably going to remain out of our reach forever. And yet these apparent embarrassments help us understand protein folding, design new drugs against cancer, build solar cells, bake a cake and capture the smell of a rose in a bottle.

What more could we want.

Why are secondary amines the most basic?

A commentator on In the Pipeline remarked that in a series of compounds he was looking at, adding a methyl to a primary amide to turn it into a secondary amide surprisingly and "counterintuitively" increased its aqueous solubility.

But is it really that surprising? The remark made me recall the counterintuitive-looking trends in the basicity of amines that we learn about from college chemistry textbooks. Rationalizing these trends by considering tradeoffs is exactly the kind of process chemists revel in. The question is, among primary, secondary and tertiary amines, which class is the most basic?

The aqueous solubility of amines is dominantly governed by their basicity. The basicity is in turn dictated by two important effects: inductive effects from alkyl substituents, and the ability of the protonated amines to get solvated by water.

If you consider the first factor then you would predict tertiary amines to be the most basic since they have the largest number of alkyl substituents. However, they would also be the least favorably solvated because of these bulky, lipophilic alkyl groups hanging off them. In fact the steric hindrance created by the alkyl groups affects the solvation so badly that tertiary amines are usually the least basic among the three classes. By this token you would expect primary amines to be the best solvated and most basic, but in this case the inductive effect is weak so the solvation does not result in salvation.

Not surprisingly, it's the middle ground that wins. Secondary amines are solvated well-enough to be soluble, while also being enough pumped up by inductive effects to be reasonably basic. I suspect a similar argument applies to secondary amides. There could of course be other complicating factors like polar vs apolar solvents, but that's the simplest argument.

Trends in the basicity of amines provide a classic example of why chemistry is so interesting; it's deciphering the delicate trade-offs between various general factors in specific cases that gives chemists a buzz. The miraculous starts looking obvious.

P.S. As an aside, I wonder if someone has recently done a high-level theoretical calculation to dissect and validate these factors.

A graceful collapse
Vijay Pande's group at Stanford has become well-known for using the collective force of millions of CPUs around the world for simulating protein folding in the project known as Folding@home. One of the enduring challenges in simulating folding has been to sample the long timescales that are common in real-life folding events, and recent breakthroughs have made accessing such time domains realistic. We should expect long protein folding simulations to be within the reach of many non-specialists in the next few years.

In the latest issue of JACS, Pande's group provides an example of such advances by simulating the folding of a 39 residue protein called NTL9. The actual folding time is 1.5 ms so this is a substantially long MD simulation. To achieve this, Pande's group uses Graphic Processor Units (GPUs) of the kind that are found in video game modules. Over the last few years these units have made interesting biological phenomena accessible to chemists. C & EN has a nice article on the increasing use of GPUs for biomolecular simulation.

Pande's group also uses a set of statistical tools called Markov State Models (MSMs) to identify metastable folding states and the transition trajectories between them. MSMs provide a nifty strategy to bridge the results from several short trajectories (rather than running one long one).

What is endearing about the simulation is that that the correct structure doesn't form until much later and then quickly falls in place, like a lost kid suddenly remembering his place in the marching band. As can be seen in the video below, the missing piece of the puzzle is a short C-terminal part of a beta-sheet which seems to linger as part of an alpha helix while the rest of the sheet structure forms. After comfortably waltzing around as a little helical piece for a long time, it seems to suddenly remember its correct identity and snaps and collapses into place as part of the beta sheet. Very nice!

Admittedly, a 39 residue protein is minuscule compared to most typical proteins. But the results provide a neat proof of concept. Importantly, they also show that current force fields with implicit solvent models can be accurate enough for this kind of simulation. Further validation will test these force fields more stringently.

Voelz VA, Bowman GR, Beauchamp K, & Pande VS (2010). Molecular simulation of ab initio protein folding for a millisecond folder NTL9(1-39). Journal of the American Chemical Society, 132 (5), 1526-8 PMID: 20070076