The Curious Wavefunction

The Curious Wavefunction

Musings on chemistry and the history and philosophy of science

Occam, me and a conformational medley


William of Occam, whose principle of parsimony has been used and misused (Image: WikiCommons)

The philosopher and writer Jim Holt who has written the sparkling new book “Why Does The World Exist?” recently wrote an op-ed column in the New York Times, gently reprimanding physicists to stop being ‘churlish’ and appreciate the centuries-old interplay between physics and philosophy. Holt’s point was that science and philosophy have always co-existed, even if their relationship has been more of an uneasy truce rather than an enthusiastic embrace. Some of the greatest physicists including Bohr and Einstein were also great philosophers.

Fortunately – or unfortunately – chemistry has had little to say about philosophy compared to physics. Chemistry is essentially an experimental science and for the longest time, theoretical chemistry had much less to contribute to chemistry than theoretical physics had to physics. This is now changing; people like Michael Weisberg, Eric Scerri and Roald Hoffmann proclaim themselves to to be bonafide philosophers of chemistry and bring valuable ideas to the discussion.

But the interplay between chemistry and philosophy is a topic for another post. In this post I want to explore one of the very few philosophical principles that chemists have embraced so wholeheartedly that they speak of it with the same familiar nonchalance with which they would toss around facts about acids and bases. This principle is Occam’s Razor, a sort of guiding vehicle that allows chemists to pick between competing explanations for a phenomenon or observation. Occam’s Razor owes its provenance to William of Occam, a 14th century Franciscan friar who dabbled in many branches of science and philosophy. Fully stated, the proposition tells us that “entities should not be multiplied unnecessarily” or that the fewer the assumptions and hypotheses underlying a particular analysis, the more preferred that analysis relative to those of equal explanatory power. More simply put, simple explanations are always better than complex explanations.

Sadly, the multiple derivate restatements of Occam’s Razor combined with our tendency to look for simple explanations can sometimes lead to erroneous results. Part of the blame lies not with Occam’s razor but with his interpreters; the main problem is that it’s not clear what “simple” and “complex” mean when applied to a natural law or phenomena. In addition, nature does not really care about what we perceive as simple or complex, and what may seem complex to us may appear perfectly simple to nature because it’s…real. This was driven home to me early on in my career.

Most of my research in graduate school was concerned with finding out the many conformations that complex organic molecules adopt in solution. Throw an organic molecule like ibuprofen in water and you don’t get a static picture of the molecule standing still; instead, there is free rotation about single bonds joining various atoms leading to multiple, rapidly interconverting shapes, or conformations, that are buffeted around by water like ships on the high seas. The exact percentage of each conformation in this dance is dictated by its energy; low-energy conformations are more prevalent than high-energy ones.

Different shapes of conformations of cyclohexane - a ring of six carbon atoms - ranked by energy (Image: Mcat review)

Since the existence of multiple conformations enabled by rotation around single bonds is a logical consequence of the basic principles of molecular structure, it would seem that this picture would be uncontroversial. Surprisingly though, it’s not always appreciated. The reason has to do with the fact that measurements of conformations by experimental techniques like nuclear magnetic resonance (NMR) spectroscopy always result in averages. This is because the time-scales for most of these techniques are longer than the time-scales needed for interconversion between conformations and therefore they cannot make out individual differences. The best analogy is that of a ceiling fan; when the fan is rotating fast, all we see is a contiguous disk because of the low time resolution of our eye. But we know that in reality, there are separate individual blades (see figure at end of post). NMR is like the eye that sees the disk and mistakes it for the fan.

Such is the problem with using experimental techniques to determine individual conformations of molecules. Their long time scales lead to average data to which a single, average structure is assigned. Clearly this is a flawed interpretation, but partly because of entrenched beliefs and partly because of lack of methods to tease apart individual conformations, scientists through the years have routinely published single structures as representing a more complex distribution of conformers. Such structures are sometimes called “virtual structures”, a moniker that reflects their illusory – essentially non-existent – nature. A lot of my work in graduate school was to use a method called NAMFIS (NMR Analysis of Molecular Flexibility In Solution) that combined average NMR data with theoretically calculated conformations to tease apart the data into individual conformations. Here's an article on NAMFIS that I wrote for college students.

When time came to give a talk on this research, a very distinguished scientist in the audience told me that he found it hard to digest this complicated picture of multiple conformations vying for a spot on the energy ladder. Wouldn’t the assumption of a single, clean, average structure be more pleasing? Wouldn’t Occam’s Razor favor this interpretation of the data? That was when I realized the limitations of Occam’s principle. The “complicated” picture of the multiple conformations was the real one in this case, and the simple picture of a single average conformation was unreal. In this case, it was the complicated and not the simple explanation that turned out to be the right one. This interpretation was validated when I also managed to find, among the panoply of conformations, one which bound to a crucial protein in the body and turned the molecule into a promising anticancer drug. The experience again drove home the point that nature doesn’t often care about what we scientists find simple or complex.

Recently Occam made another appearance, again in the context of molecular conformations. This time I was studying the diffusion of organic molecules through cell membranes, a process that’s of great significance in drug discovery since even your best test-tube drug is useless if it cannot get into a cell. A chemist from San Francisco has come up with a method to calculate different conformations of molecules. By looking at the lowest-energy conformation, he then predicts whether that conformation will be stable inside the lipid-rich cell membrane. Based on this he predicts whether the molecule will make it across. Now for me this posed a conundrum and I found myself in the shoes of my old inquisitor; we know that molecules have several conformations, so how can only the single, lowest-energy conformation matter in predicting membrane permeability?

I still don’t know the answer, but a couple of months ago another researcher did a more realistic calculation in which she did take all these other conformations into consideration. Her conclusion? More often than not the accuracy of the prediction becomes worse because by including more conformations, we are also including more noise. Someday perhaps we can take all those conformations into account without the accompanying noise. Would we then be both more predictive and more realistic? I don’t know.

These episodes from my own research underscores the rather complex and subtle nature of Occam’s Razor and its incarnation in scientific models. In the first case, the assumption of multiple conformations is both realistic and predictive. In the second, the assumption of multiple conformations is realistic but not predictive because the multiple-conformation model is not good enough for calculation. In the first case, a simple application of Occam’s razor is flawed while in the second, the flawed simple assumption actually leads to better predictions. Thus, sometimes simple assumptions can work not because the more complex ones are wrong, but because we simply lack the capacity to implement the more complex ones.

I am glad that my work with molecular conformations invariably led me to explore the quirky manifestations of Occam’s razor. And I am thankful to a well-known biochemist who put it best: “Nature doesn’t always shave with Occam’s Razor”. In science as in life, simple can be quite complicated, and complicated can turn out to be refreshingly simple.

A rotating ceiling fan - Occam's razor might lead us to think that the fan is a contiguous disk, but we know better.

The views expressed are those of the author and are not necessarily those of Scientific American.

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