The protein folding funnel and its discontents

Speaking of protein folding, here's something interesting. One of the most enduring views of protein folding from the last decade is that of an "energy funnel". The funnel was invented by the UCSD chemist Peter Wolynes in the 90s (the original paper is highly readable) and essentially depicts a plot of the configurational enthalpy (or effective energy) of the protein on the Y axis vs the configurational entropy on the X axis. In real situations this plot is multidimensional.

The funnel suggests a way out of Levinthal's paradox which contrasts the fast folding times for virtually all proteins with the vast amount of conformational space to be searched. According to the funnel viewpoint, the energy of the protein on the Y axis decreases and becomes more favorable even as the entropy on the X axis decreases, leading to fewer conformations to be searched and allowing the protein to rapidly find the native structure. The funnel has become a mainstay of descriptions of protein folding and has made its way into textbooks.

The funnel view of protein folding had always puzzled me a little for the simple reason that we usually think of the enthalpy and entropy of the protein (and in fact of any chemical system) as opposing factors. Entropy would hinder the protein even as it formed more "native" contacts and led to a favorable enthalpy. Yet the funnel seems to suggest a synergy between these two factors. Many papers have said that the funnel "guides" the protein to its correct conformational state. In this week's Nature Chemical Biology, one of the founding fathers of the field, Martin Karplus, sheds some light on this confusion and informs us that the traditional view of the funnel is indeed a little misleading.

To support his argument, Karplus illustrates two examples of protein folding studies using two kinds of systems. One is a lattice model system in which the protein is approximated by beads on a lattice. Native contacts in the protein are indicated by adjacent beads on the lattice. The other folding simulation is a standard molecular dynamics simulation of an alpha helix. In both cases the proteins are small (about 30 residues) but their behavior at low and high temperatures is intriguing.

At low temperatures, the folding landscape is more "rugged" and folding is slower. This is a well-established concept and it simply means that there is less energy for the protein to explore all the available local minima. At high temperature the landscape is "smooth" and the protein has enough energy to explore many conformational states. What is striking is that while the effective energy (enthalpy) at high temperature decreases smoothly all the way to the native state, the free energy (which is what we should really be worrying about) has a significant barrier. Thus this barrier has to come from entropy. The crucial thing to note is that at high temperatures, the free energy is dominated by the increasing unfavorable entropy engendered by the greater number of conformations that the protein has to search.

Ultimately it's easy to forget that the protein folding "funnel" is only a theoretical construct, an intuitive model. Has anyone actually observed a funnel for a real protein? As the article notes, for now the answer is a decided "No". Unfortunately it may be impossible to ever do so since to construct a real funnel one would need knowledge of every single conformational state that a protein visits on its way to folding. In addition since folding is a statistical phenomenon, one would also need knowledge of every starting trajectory. Needless to say, for now this is at best a pipe dream. However the funnel remains a useful construct provided we remember the subtleties and caveats that Karplus has described. Ultimately it's a model, and like other models it need not be real, but it should at least be useful.

Karplus, M. (2011). Behind the folding funnel diagram Nature Chemical Biology, 7 (7), 401-404 DOI: 10.1038/nchembio.565

Lindau 2011: What do scientists do after winning the Nobel Prize?

Most of us know about the prize-winning work of this year's Lindau Nobel Laureates, but how many of us keep track of what they did after winning the coveted honor? Scientists' lives after the Nobel Prize change dramatically. As former Lindau attendee Richard Ernst put it, they are now expected to be oracles on everything from international politics to religion, even when their knowledge of most other things is as limited as that of other people. There is no common thread; after winning the Prize, scientists' lives become as varied as those of all of us and in some cases a little more interesting. Here's a short portrait of life after the Nobel Prize illustrated with a select few examples...

Read the rest of the post on the Lindau blogs site...

The fine-tuning problem in protein folding: Is there a protein multiverse?

One of the deepest questions physicists have struggled with in the last half-decade is the so-called "fine-tuning problem". The fine-tuning problem asks why the values of the fundamental constants (Planck's constant, the speed of light, the mass of the electron etc.) are what they are.

The reason why physicists are so worried about the values of these constants is because presumably if the values were even a little different from what they are, the universe and life as we know them would not exist. For instance, even a slight weakening of the strong nuclear force that holds nucleons together would prevent the formation of atoms and thus of all complex matter. Similarly, a slight change in the electromagnetic force would fundamentally alter the interactions between atoms crucial for the formation of chemical bonds between the molecules of life.

There thus seems to be some factor during the evolution of the universe responsible for fine-tuning the values of the constants to their present values within an incredible window of accuracy. The fine-tuning problem is a real problem not least because some religious believers point to the unchangeable and precise values of the constants to be the work of some kind of intelligent designer.

In the last few decades there have been a few attempts to resolve the fine-tuning problem. Probably the most exotic and yet in some ways the most reasonable solution has been to assume the existence of multiple parallel universes. Multiple universes (or multiverses) were first proposed by Hugh Everett, a brilliant and troubled physicist who worked on nuclear weapons targeting, as a way around the so-called "measurement problem" in quantum mechanics. The measurement problem is fundamentally embedded in the quantum description of our world. The unsettling thing (and one that troubled Einstein) about quantum mechanics is that it assigns probabilities to certain events, but provides no answer as to why only one of those events materializes when we make a measurement. Everett worked around this conundrum by assuming that in fact all possible events actually do take place, but only one of them is part of our universe; the rest of the events also occur, but in parallel universes. Everett's interpretation which was regarded to be a fringe explanation for years (thus making it successfully into science fiction books) is now taken seriously by many physicists.

Being a problem associated with the most fundamental constants of nature, the fine-tuning problem makes its way into all "higher-level" sciences including chemistry and biology. In chemistry the fine-tuning problem takes on a fascinating form and entails asking why certain molecules have become fundamental to living systems while other more or less equivalent alternatives have been discarded during evolution. For instance, why alpha amino acids (and why not beta or gamma amino acids)? Why left-handed amino acids and right handed-sugars? Why phosphates and not sulfates or silicates? In retrospect one can think of answers to these questions based on factors like stability, versatility and ease of synthesis, but ultimately we may never know. However, the fine-tuning problem also manifests itself in one of the most fundamental processes in the workings of life; protein folding.

The protein folding problem is well-known; given an amino acid sequence, how can a protein fold into a single three-dimensional structure and reject the countless number of other possible structures it can fold into? What is even more remarkable about this problem is that several thousand of those other structures are almost equienergetic with the preferred folded structure and yet they do not form. In fact it is this energetic equivalency between several structures that plagues all modern computational protein folding algorithms; the problem is not so much to generate the one correct structure as it is to distinguish it from other structures that are very close to it in energy. The fundamental assumption in all these algorithms is that the correctly folded structure is the lowest-energy structure. But that does not mean it differs in energy from the other solutions disproportionately. Therein lies the rub.

Ever since I heard about the protein folding problem this issue has bothered me as I am sure it has others. Consider that the free energy difference between two different protein structures may be only 5 kcal/mol or so, about the energy of a single hydrogen bond. Yet a protein when it folds unerringly picks only one among the two structures. How can nature manage to pick the right solution every one of millions of times when it folds proteins inside our body each second? To put it another way, here's the "fine-tuning problem" in protein folding: why does a protein always adopt one and only one correct structure even when many other structures, very similar in energy and presumably in function, are available to it?

From a retrospective evolutionary standpoint the answer to this conundrum is perhaps not too surprising. Imagine what would happen if every time a newly synthesized copy of a given protein folded, it formed a slightly different structure. This heterogeneity and lack of quality control would play havoc with the intricate signaling networks in our body. Evolution simply cannot afford to have different three-dimensional structures for the same protein, no matter how slightly different they are. No wonder that quality control in protein folding is extreme. Of course nature does make occasional mistakes, but wrongly folded proteins are quickly degraded and destroyed.

Nonetheless, the original dilemma persists and metamorphoses into a further interesting question: isn't it possible for a protein structure that is slightly different from the one true structure to be functional? There are two possible answers here. Perhaps the alternative structure was functional during evolution at one point, but competition from the slightly better structure weeded out the former from the gene pool. If this is the case, could there be a chance that there is some unknown form of life in which this other slightly different yet perfectly reasonable structure still exists, happily doing its job with no evolutionary pressure around to discard it? The best way to answer this question is to compare proteins from different species, something that has been extensively done for years. But such a comparison usually reveals protein homology, in which the sequences themselves are slightly different and yet perform similar functions.

That's not what we are looking for. What we are looking for is "two" proteins with absolutely identical amino acid sequences which in two different creatures adopt slightly different three-dimensional structures and perform similar functions. Or they could even perform different functions, thus validating evolution as a force that puts slight differences to optimal use. Let us call these proteins with identical sequences but different functional folds "fold mutants". To my knowledge such fold mutants have not yet been found.

A second albeit more exotic solution to the fine-tuning problem appeals to a possible "protein multiverse". The argument here is that the kind of protein structures which we observe are indeed not the only feasible or functional ones. There are in fact other structures which are not only well-folded but also functional. For some reason, evolution, during its intricate dance of maintaining order, structure and function, chose to discard these structures in favor of ones that were more functionally relevant in this universe. However there is no reason why they could not have been picked in a different universe, where the laws were slightly different. There is another way to think of a protein multiverse; as a set of valleys and peaks where the valleys correspond to different folded structures. Such a metaphor has also been used by physicists to argue that our universe with its own set of fundamental constants corresponds to one local minimum in this "multiverse landscape", with other universes populating the other dips. Similarly we could imagine a protein multiverse landscape in which different protein folds occupy different valleys; we favor a particular fold only because it inhabits our own valley, but that does not stop other folds from corresponding to the others.

In a different universe, hemoglobin could have folded into a marginally different structure in which it bound not oxygen but some other small ligand like ammonia more efficiently. Such a fold mutant of hemoglobin would be useful to creatures which survive in an ammonia-rich environment (ammonia in fact has a greater temperature range as a liquid compared to water). Or one could imagine a fold mutant of carbonic anhydrase, which catalyzes the conversion of carbon dioxide to bicarbonate at a different pH or a different temperature. Fold mutants of known proteins could have every conceivable property different from their original "correctly" folded counterparts, including shape, size, polarizability and stability. The fold mutants could be exquisitely adopted to living conditions in their parents universe. Their special folds could be stabilized by environments differing from those found on earth in ionic strengths, hydrogen bonding capabilities and hydrophobicities. For a given protein, this alternative fold could in fact be the lowest in energy and its companion fold found in our universe could be slightly higher in energy.

This kind of speculation immediately suggests two explorations. One is to look for fold mutants in other parts of the universe. This search would be part of the search for extraterrestrial life that has been going on for years. But the point is that if we happen to find fold mutants of existing proteins on other planets or in other inhospitable environments, these mutants would provide powerful support for the solution of the fine-tuning problem. They would tell us that the fine-tuning problem exists only in our narrow-minded anthropocentric imagination, that there could indeed be many folds of the same protein that are robust and functional and that we just happen to inhabit a part of the universe that stabilizes our favorite fold.

The other more readily testable experiment asks if we can produce different functional folds from the same amino acid sequence by varying the experimental conditions. It's of course well-known to crystallographers and protein chemists that slight changes in physicochemical conditions can play havoc with the structure and function of their proteins. But most of the times these slight changes in conditions produce misfolded protein junk. Is there an example of someone slightly (or even radically) varying conditions in a test-tube and producing two different folds of the same protein that are both stable and functional? If there is one I would be very eager to know about it.

On the other hand, if it turns out that it's impossible to find two different functional folds for a single protein, such an observation might well lend credence to the physicists' multiverse with differing fundamental constants. It might well be that under the present values of fundamental constants, it is impossible to stabilize a slightly different protein fold and make it functional. Perhaps only a slight albeit conceptually radical restructuring of the fundamental constants could result in a universe that is friendly to fold mutants. Such a universe would still enable the creation of complex matter through the appropriate combination of the constants, but it would indeed result in life very different from what we know.

The protein multiverse could thus help resolve the fine-tuning problem in protein folding and make biochemists and physicists part of the same multiverse fraternity. More importantly, it could once again reinforce the diversity of creation. One could have different universes with the same fundamental constants but different protein folds or different universe with entirely different combinations of the constants themselves. Take your pick.

If uncovered, such diversity would only echo J B S Haldane's quote that the "universe is not only queerer than we suppose, but it is queerer than we can suppose".

Image source

Lindau 2011: From designing airplanes to designing proteins

An inspiration from the birth of aviation

A few weeks ago I visited the small coastal town of Kitty Hawk in North Carolina. Kitty Hawk is where the Wright brothers made their epoch-making first powered flight. Big stones mark the start and end points of the flight. There is a huge monument on top of a hill where they took off and then there are three stones at varying distances at ground level. The three stones indicate the distances covered on every flight; the brothers clearly got better at flying on every attempt.

The Wright brothers' story is inspiring not only because of the watershed in human history which they orchestrated but also because it shows the evolution of a technology at its best. The projects which the brothers undertook cost a few hundred dollars and should serve as a beacon of inspiration in this era of "big science" involving hundreds of millions of dollars. The brothers had a bicycle workshop in which they fashioned many of the components of their infant gliders. They drew inspiration from Otto Lillienthal who had been the first aviation pioneer to make successful glided flights; tragically, Lillienthal was killed on one of his flights, but not before saying "Kleine Opfer müssen gebracht werden!" ("Small sacrifices must be made!").

One of the most important lessons that the Wrights learnt from Lillienthal's adventures was the great value of building 'toy' models. Toy models start from the simplest possible systems which retain the essential features of a phenomenon and then work their way towards greater complexity. This philosophy has been used by many other pioneers of technology, including the scientists and engineers who made the moon landings possible...

Read the rest of the entry at the Lindau blogs website...

Putting the filosophy back into fysiks

How the Hippies Saved Physics: Science, Counterculture, and the Quantum Revival- David Kaiser

Does philosophy have a place in serious science? Many of the founders of modern physics certainly thought so. Einstein, Bohr, Heisenberg and Schrodinger were not just great scientists but they were equally enthusiastic and adept at pondering the philosophical implications of quantum theory. To some extent they were forced to confront such philosophical questions because the world that they were discovering was just so bizarre and otherworldly; particles could be waves and vice versa, cats (at least in principle) could be alive and dead, particles that were separated even by light years appeared to be able to communicate instantaneously with each other, and our knowledge of the subatomic world turned out to be fundamentally probabilistic.

However, as quantum theory matured into a powerful tool for calculation and concrete application, the new generation of physicists in general and American physicists in particular started worrying less about "what it means" and much more about "how to use it". American physicists had always been more pragmatic than their European counterparts and after World War 2, as the center of physics moved from Europe to the United States and as the Cold War necessitated a great application of science to defense, physicists turned completely from the philosophizing type to what was called the "shut up and calculate" kind; as long as quantum mechanics agrees spectacularly with experiment, why worry about what it means? Just learn how to use it. Yet this only swept epistemological questions under the rug.

Curiously, there emerged in the 1970s a quirky and small group of physicists in the Bay Area who tried to resurrect the age of philosopher-scientists. In "How the Hippies Saved Physics", David Kaiser wonderfully tells the very engaging story of this "Fundamental Fysiks" group and how it kept alive some of the deep philosophical questions that had haunted the founding fathers. The "Fysicists" came from a variety of backgrounds, but all of them had been dissatisfied; both by the dismal job market for physicists after the Cold War craze and more importantly by the purely practical approach toward physics which they learnt in graduate school. Interestingly they combined their deep questions about physics with the emerging hippie counterculture of the 60s and 70s and it's pretty clear from the book that they had great fun doing this; after all this was an age when non-conformity was encouraged. Discussions of physics concepts blended seamlessly with Eastern mysticism, forays into LSD-induced mind experiments, New Age workshops at the Esalen Institute in California and meanderings into telepathy, consciousness and parapsychology. Books like Fritjof Capra's "The Tao of Physics" which explored parallels between modern physics and Eastern religions only helped the movement. The small group of physicists was also fortunate to get funding from some unlikely sources, including self-help guru Werner Erhard and even the CIA who was interested in possible connections between ESP and physics. Not surprisingly, mainstream physicists often ignored and sometimes actively condemned such activities

However, as Kaiser describes in this fascinating volume, this ragtag group of countercultural philosopher-scientists achieved at least one crucial goal; they kept questions about the philosophical implications of quantum theory alive at a time when most physicists eschewed and disdained such questions. Gradually, they managed to get a handful of mainstream physicists interested in their philosophizing. Much of the connection of this philosophy to real physics centered about a remarkable result called Bell's theorem which essentially reinforced the spooky properties of quantum systems by showing that information in quantum systems can flow instantaneously between particles. Remarkably, this seemingly otherworldly idea of "quantum entanglement" (which gave some of the founding fathers heartburn) now lies at the foundation of some of the most cutting-edge areas of modern physics, including quantum computation and the new discipline of quantum information science. What was considered far-flung by mainstream physicists and kept alive by the Fundamental Fysiks group is now serious physics for many. In fact, at least a few physicists who put Bell's theorem to experimental test are regarded as candidates for a Nobel Prize (these especially include John Clauser, Alain Aspect and Anton Zeilinger who shared the prestigious Wolf Prize- often a forerunner to the Nobel Prize- in 2010).

In the end Kaiser wants to make the case that by keeping such once-disparaged philosophical concepts alive, the Fundamental Fysicists "saved physics". I am a little skeptical of this claim. They certainly managed to nurture and publicize the concepts, but it was the harnessing of these concepts by "real" physicists who were involved with the nuts and bolts of calculation and experiment that actually saved the concepts and kept them from turning into a purely philosophical mishmash. In addition, a lot of concepts that the New Age physicists bandied about belonged squarely in the realm of pseudoscience and the trend continues; people like Deepak Chopra commit gross violations of quantum mechanics on a daily basis. Unfortunately the line between science and non-science can be thin and one of the most intriguing discussions in Kaiser's book is this so-called "demarcation problem". How does one know if today's philosophy is tomorrow's cutting edge science or just noisy mumbo-jumbo? It's not always easy to say.

Nonetheless, I think Kaiser and the Fysicists make a really great general case for why philosophical questions in science have their own place and should not be rejected. For one thing, they are always fascinating in themselves and demonstrate the endless human quest for meaning and reality; as recent discussions indicate, the philosophical conundrums in physics have been far from answered and continue to be explored through even more bizarre ideas like parallel universes and multiple dimensions. And as this wonderful book shows, at least in some cases these discussions may lead to key advances by influencing mainstream physicists who validate them by subjecting them to the ultimate arbiter of truth in science- hard experiment.

Lindau 2011: The beginning

This year I am privileged to be invited again to write for and attend the 61st Meeting of Nobel Laureates in Lindau, Germany. This year's meeting is dedicated to Physiology or Medicine and the list of attendees provides a glimpse of the diversity and impact of biomedical research. These men and women have made enormous contributions to our understanding of biological systems, from elucidating structures and pathways to providing tools of inestimable value. My first post just went up and I will be linking to others as I write more. Here's the first one.

From messy to magical: Preparing for the future of medicine

In the early 1940s, as war raged over the continent, the British mathematician Freeman Dyson and the Indian physicist Harish Chandra were taking a walk in Cambridge. Harish Chandra was studying theoretical physics under the legendary Paul Dirac while Dyson was getting ready to spend a depressing time calculating bombing statistics at Bomber Command.

“I have decided to leave physics for mathematics”, quipped Harish Chandra. “I find physics messy, unrigorous, elusive”. “That’s interesting”, replied Dyson. “I am planning to leave mathematics for physics for exactly the same reason.” Leave their respective disciplines the two did, and both of them had highly distinguished careers in their new fields at the Institute for Advanced Study in Princeton.

I narrate this story because I can imagine almost exactly the same conversation taking place today between a biomedical researcher and any other kind of natural scientist. In fact it’s interesting to compare the status of medicine today with the status of physics when Dyson and Harish Chandra had their conversation. By 1940 physics had underwent a great revolution in the form of quantum mechanics and relativity. Yet there was much to be done and the “second revolution” was in the making. In retrospect it’s clear that very little was known about the strong and weak nuclear forces and nothing was known about the particle “zoo” that would be uncovered in the next few years. It took the efforts of many brilliant individuals to unify crucial concepts and make the whole structure look more consistent and complete.

Medicine in the year 2011 is like physics in the year 1940. Just like physics it has had a recent revolutionary past in the advent of molecular biology. Just like physics there is much of it that is “messy, unrigorous, elusive”. And it’s exactly these qualities that make it a field ripe for another revolution. The future beckons for medicine and biology today as it did for physics in 1940.

Read more at the Lindau blogs website...

God is not only unsubtle but she is malicious

This PNAS piece definitely takes the pick for the most suggestive abstract I have seen in recent history.

The picture above is of a butterfly pea flower. Look at it closely. Its scientific name is Clitoria ternatea. The paper talks about the biosynthesis of a protein isolated from the plant. One of its functions is to "speed up childbirth".

Things happen when nature's creations collide with human vocabulary. And no, there's wasn't an actual creator that engineered the relationship between the shape of the flower and the function of the protein. That's just us humans at our pattern-seeking best.