The future of science: Will models usurp theories?

This year's Nobel Prize for physics was awarded to Saul Perlmutter, Brian Schmidt and Adam Riess for their discovery of an accelerating universe, a finding leading to the startling postulate that 75% of our universe contains a hitherto unknown entity called dark energy. All three were considered favorite candidates for a long time so this is not surprising at all. The prize also underscores the continuing importance of cosmology since it had been awarded in 2o06 to George Smoot and John Mather, again for confirming the Big Bang and the universe's expansion.

This is an important discovery which stands on the shoulders of august minds and an exciting history. It continues a grand narrative that starts from Henrietta Swan Leavitt (who established a standard reference for calculating astronomical distances) through Albert Einstein (whose despised cosmological constant was resurrected by these findings) and Edwin Hubble, continuing through George Lemaitre and George Gamow (with their ideas about the Big Bang) and finally culminating in our current sophisticated understanding of the expanding universe. Anyone who wants to know more about the personalities and developments leading to today's event should read Richard Panek's excellent book "The 4 Percent Universe".

But what is equally interesting is the ignorance that the prizewinning discovery reveals. The prize was really awarded for the observation of an accelerating universe, not the explanation. Nobody really knows why the universe is accelerating. The current explanation for the acceleration consists of a set of different models, none of which has been definitively proven to explain the facts well enough. And this makes me wonder if such a proliferation of models without accompanying concrete theories is going to embody science in the future.

The twentieth century saw theoretical advances in physics that agreed with experiment to an astonishing degree of accuracy. The culmination of achievement in modern physics was surely quantum electrodynamics (QED) which is supposed to be the most accurate theory of physics we have. Since then we have had some successes in quantitatively correlating theory to experiment, most notably in the work on validating the Big Bang and the development of the standard model of particle physics. But dark energy- there's no theory for it that remotely approaches the rigor of QED when it comes to comparison with experiment.

Of course it's unfair to criticize dark energy since we are just getting started on tackling its mysteries. Maybe someday a comprehensive theory will be found, but given the complexity of what we are trying to achieve (essentially explain the nature of all the matter and energy in the universe) it seems likely that we may always be stuck with models, not actual theories. And this may be the case not just with cosmology but with other sciences. The fact is that the kinds of phenomena that science has been dealing with recently have been multifactorial, complex and emergent. The kind of mechanical, reductionist approaches that worked so well for atomic physics and molecular biology may turn out to be too impoverished for taking apart these phenomena. Take biology for instance. Do you think we could have a complete "theory" for the human brain that can quantitatively calculate all brain states leading to consciousness and our reaction to the external world? How about trying to build a "theory" for signal transduction that would allow us to not just predict but truly understand (in a holistic way) all the interactions with drugs and biomolecules that living organisms undergo? And then there's other complex phenomena like the economy, the weather and social networks. It seems wise to say that we don't anticipate real overarching theories for these phenomena anytime soon.

On the other hand, I think it's a sign of things to come that most of these fields are rife with explanatory models of varying accuracy and validity. Most importantly, modeling and simulation are starting to be considered as a respectable "third leg" of science, in addition to theory and experiment. One simple reason for this is the recognition that many of science's greatest current challenges may not be amenable to quantitative theorizing, and we may have to treat models of phenomena as independent, authoritative explanatory entities in their own right. We are already seeing this happen in chemistry, biology, climate science and social science, and I have been told that even cosmologists are now extensively relying on computational models of the universe. Admittedly these models are still far behind theory and experiment which have had head starts of about a thousand years. But there can be little doubt that such models can only become more accurate with increasing computational firepower. How accurate remains to be seen, but it's worth noting that there are already books that make a case for an independent, study-worthy philosophy of modeling and simulation. These books extol philosophers of science to treat models not just as convenient applications and representations of theories (which are then the only fundamental things worth studying) but as ultimate independent explanatory devices in themselves that deserve separate philosophical consideration.

Could this then be at least part of the future of science? A future where robust experimental observations are encompassed not by beautifully rigorous and complete theories like general relativity or QED but only by different models which are patched together through a combination of rigor, empirical data, fudge factors and plain old intuition? This would be a new kind of science, as useful in its applications as its old counterpart but rooting itself only in models and not in complete theories. Given the history of theoretical science, such a future may seem dark and depressing. That is because as the statistician George Box famously quipped, although some models are useful, all models are wrong. What Box meant was that models often feature unrealistic assumptions about all kinds of details that nonetheless allow us to reproduce the essential features of reality. Thus they can never provide the sure connection to "reality" that theories seem to. This is especially a problem when disparate models give the same answer to a question. In the absence of discriminating ideas, which model is then the "correct" one? The usual answer is "none of them", since they all do an equally good job of explaining the facts. But this view of science, where models that can be judged only on the basis of their utility are the ultimate arbiters of reality and where there is thus no sense of a unified theoretical framework, feels deeply unsettling. In this universe the "real" theory will always remain hidden behind a facade of models, much as reality is always hidden behind the event horizon of a black hole. Such a universe can hardly warm the cockles of the heart of those who are used to crafting grand narratives for life and the universe. However it may be the price we pay for more comprehensive understanding. In the future, Nobel Prizes may be frequently awarded for important observations for which there are no real theories, only models. The discovery of dark matter and energy and our current attempts to understand the brain and signal transduction could well be the harbingers of this new kind of science.

Should we worry about such a world rife with models and devoid of theories? Not necessarily. If there's one thing about science that we know, it's that it evolves. Grand explanatory theories have traditionally been supposed to be a key part- probably the key part- of the scientific enterprise. But this is mostly because of historical precedent as well a psychological urge for seeking elegance and unification. Such belief has been resoundingly validated in the past but it's utility may well have plateaued. I am not advocating some "end of science" scenario here - far from it - but as the recent history of string theory and theoretical physics in general demonstrates, even the most mathematically elegant and psychologically pleasing theories may have scant connection to reality. Because of the sheer scale and complexity of what we are trying to currently explain, we may have hit a roadblock in the application of the largely reductionist traditional scientific thinking which has served us so well for half a millennium

Ultimately what matters though is whether our constructs- theories, models, rules of thumb or heuristic pattern recognition- are up to the task of constructing consistent explanations of complex phenomena. The business of science is explanation, whether through unified narratives or piecemeal explanation is secondary. Although the former sounds more psychologically satisfying, science does not really care about stoking our egos. What is out there exists, and we do whatever's necessary and sufficient to unravel it.

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".

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