Want to bind small molecules? Get a backbone

Here’s a paper from the Shoichet lab at UCSF that illustrates one of the major problems that drug designers encounter – predicting conformational changes (“entropy” to a physicist). What the study does is to plug a series of eight very simple congeneric ligands – benzene, methyl, ethyl and propyl benzene all the way to hexyl benzene - into a model protein cavity, in this case a lysozyme mutant, and observe the corresponding changes in protein conformation by solving the crystal structures. And the results aren’t exactly heartwarming for early phase drug discovery scientists.

Synthesizing congeneric series of ligands is a standard process in lead optimization and the elephant in the room which is often banished out of sight by drug designers is the possibility of large conformational changes in the protein caused by small changes in ligand structure (the other assumption is constancy in ligand binding orientation, and even that doesn’t always hold). The assumption is that any minor change in structure in the ligand would be accommodated by equivalent, small amino acid side chain movements in the protein.

This study shows that at best that assumption is a faith-based assumption which should always be considered provisional. What the authors observe is that instead of a smooth transition of amino acid side chain movements, you see a discrete and far more significant change in protein backbone movement, resulting in a subtle population of different states which bind the ligands. The difference in binding energy going from benzene to hexyl benzene is not too large – about 1.5 kcal/mol – but you are already seeing backbone movements. What is perhaps a bit more reassuring than this observation is that some of the discrete states are mirrored in lysozyme structures found in the PDB - but the authors looked at 121 structures to substantiate the result. Not the kind of numbers you would expect to find in the PDB for your typical novel drug discovery target.

The conclusions of the paper are a bit discomforting for at least two reasons. Firstly as mentioned above, drug designers often assume constancy or smooth and minor side chain changes in protein conformation when testing congeneric ligands in lead optimization. It’s quite clear that this is always a bit of a gamble: if something as simple as a change in molecular weight could lead to such divergent changes, what would small but important changes or reversals in polarity do? And then one also starts wondering how much weird or divergent SAR could potentially be explained by such unexpected backbone conformational changes.

Secondly, these kinds of changes pose a real problem for molecular modelers. As the paper says, you would need to go to pretty long MD (molecular dynamics) simulations or more radical protein modeling to look at backbone changes; even today, modeling backbone changes by either physics-based methods (like MD) or knowledge-based techniques (like Rosetta) is both less validated and more computationally expensive.

Lastly though, this study is another example of why drug discovery is hard even at a basic scientific level. Countless factors thwart the best intentions of drug designers at every stage, and uncertainty in predicting protein backbone conformational changes must rank pretty high on that list.

Occam, me and a conformational medley

Originally posted on the Scientific American Blog Network.

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 14^th 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. There are others. 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.

Conformations of the stevastelins: A reassessment

Shameless self-promotion: my paper on the conformational analysis of cyclic antiviral peptides called stevastelins is now online on the Biopolymers site. Here's a brief overview.

The stevastelins are cyclic peptides that show promising antiviral activity against the vaccinia viral VHR phosphatase. These peptides are phosphorylated in vivo before they can inhibit their target protein. A group in Germany previously did a meticulous analysis of four diastereometric analogs of these peptides which included their synthesis, biological characterization and conformational analysis. However, the conformational analysis was done using force field conformational searches from a single force field, constrained by variables from the NMR data (coupling constant derived dihedral angles and NOESY derived distances). Using such a protocol, the group concluded that each of the four diastereomers exists as a single conformational family in solution.

The problem with constrained conformational searches (or constrained molecular dynamics for that matter) is that they constitute a rather self-fulfilling exercise, with the assumption that there is in fact a single conformation of the molecule under question. However, as I have often discussed on this blog, any molecule with a couple of rotatable bonds is going to exist as multiple conformers in solution, so an assumption of a single conformation would be fuzzy unless supported by more data. NMR by itself is of scant value in determining these conformations for thermodynamic and kinetic reasons. Plus, analyzing conformations using a single force field can be fraught with ambiguity, since every force field comes with its own set of parameters and convergence criteria. Especially trusting energies from force fields can be dangerous. In this case, the stevastelin peptides have 9 rotatable bonds each, so I thought it worthwhile to apply our previously developed and applied NAMFIS (NMR Analysis of Molecular Flexibility In Solution) methodology combining NMR variables with structures from extensive conformational searches to the enumeration of the conformational behavior of these interesting molecules.

The paper essentially describes the conformational variability obtained for each of the diastereomers. Many of the conformations are very similar to the previously postulated families, but some are quite different. There are also some striking observations that are corroborated; for instance, the use of a d-serine truly seems to 'lock' the peptides in a single conformation. Such a lock could be effected to counter the entropic penalty that a multiconformational ensemble of molecules might have to pay. The instructive general observation is that subtle changes in sterechemistry at one or two chiral centers can dramatically affect conformational behavior, a fact that continues to surprise and confound medicinal chemists. I also note that if the NMR data for the phosphorylated peptides were available, an interesting comparison of the conformational pool for the phosphorylated and unphosphorylated counterparts could be attempted. This would shed light on whether phosphorylation leads to less conformational variability or simply increases the proportion of a chosen subset of conformations of the peptides.

Comments, criticism and general feelings of chagrin are welcomed.

Jogalekar, A. (2010). Conformations of stevastelin C3 analogs: Computational deconvolution of NMR data reveals conformational heterogeneity and novel motifs Biopolymers DOI: 10.1002/bip.21504

Constancy of the discodermolide hairpin motif

Our paper on the conformational analysis of discodermolide is now up on the ACS website. The following is a brief description of the work.

Discodermolide (DDM) is a well-known highly flexible polyketide that is the most potent microtubule polymerization agent known. In this capacity it functions very similar to taxol and the epothilones. However the binding mode of DDM will intimately depend on its conformations in solution.

To this end we have performed multiple force field conformational searches on DDM and the first surprising thing we noticed was that all four force fields located the same global minimum for the molecule in terms of geometry. This is surprising because, given the dissimilar parameterization criteria used in different force fields, minima obtained for flexible organic molecules are usually different for different force fields. Not only that, but all the minima closely superimposed on the x-ray structure of DDM which we call the "hairpin" motif. This is also surprising since the solid state structure of such a highly flexible molecule should not generally bear resemblance to a theoretically calculated global minimum.

Next, we used our NAMFIS methodology that combines parameters from conformational searches to coupling constants and interproton distances obtained from NMR data to determine DDM conformations in two solvents, water and DMSO. We were again surprised to see the x-ray/force field global minimum structure existing as a major component of the complex solution conformational ensemble. In many earlier studies, the x-ray structure has been located as a minor component so this too was unexpected.

However, this same structure has also been remarkably implicated as the bioactive conformation bound to tubulin by a series of elegant NMR experiments. To our knowledge, this is the first tubulin binder which has a single dominant preferred conformation in the solid-state, as a theoretical global minimum in multiple force field conformational searches, in solution as well as in the binding pocket of tubulin. In fact I personally don't know of any other molecule of this flexibility which exists as one dominant conformation in such extremely diverse environments; if this happened to every or even most molecules, drug discovery would suddenly become easier by an order of magnitude since all we would have to do to predict the binding mode of a drug would be to crystallize it or to look at its theoretical energy minima. To rationalize this very pronounced conformational preference of DDM, we analyze the energetics of three distributed synthons (methyl-hydroxy-methyl triads) in the molecule using molecular mechanics and quantum chemical methods; it seems that these three synthons modulate the conformational preferences of the molecule and essentially override other interactions with solvent, adjacent crystal entities, and amino acid elements in the protein.

Finally, we supplement this conformational analysis with a set of docking experiments which lead to a binding mode that is different from the earlier one postulated by NMR (as of now there is no x-ray structure of DDM bound to tubulin). We rationalize this binding mode in the light of SAR data for the molecule and describe why we prefer it to the previous one.

In summary then, DDM emerges as a unique molecule which seems to exist in one dominant conformation in highly dissimilar environments. The study also indicates the use of reinforcing synthons as modular elements to control conformation.

Jogalekar, A., Kriel, F., Shi, Q., Cornett, B., Cicero, D., & Snyder, J. (2009). The Discodermolide Hairpin Structure Flows from Conformationally Stable Modular Motifs Journal of Medicinal Chemistry DOI: 10.1021/jm9015284