The Curious Wavefunction

This is something I wanted to put out there. A colleague of mine reported a situation in which his flexible, complex organic molecule was becoming more soluble in water at low temperature and he was wondering why.

The most straightforward explanation that comes to my mind is this. When the molecule is flexible it naturally exists in several conformations in solution. The lipophilic conformations are going to be higher in energy since they are exposing non-polar groups to aqueous solvent. Conversely, the conformations that are nicely solvated and expose charged or polar groups to solvent are going to be low-energy.

At low temperatures, the higher-energy lipophilic conformations become inaccessible because of less energy in the system, leading to a preponderance of the low-energy polar conformations which are more soluble. Ergo the molecule becomes more soluble.

This can be studied by a couple of different ways, most notably by changing the solvent and altering the conformer population; previous studies have indicated that changes in solvent (say from polar to non-polar) only change populations, and not the conformations themselves.

Any other explanations?

Since we were on the subject of NMR and determining conformations, I think it would be pertinent to briefly discuss one of the more slippery basic concepts that I have seen a lot of chemistry students (naturally including myself) get plagued with; the difference between thermodynamics and kinetics. I find myself often besieged by a distinction between these two important ideas that encompass all of chemistry. Simply saying that thermodynamics is "where you go" and kinetics is "how you get there" is not enough of a light to always assuredly guide students through the sometimes dark corridors of structure and conformation.

Going beyond the fact that thermodynamics is defined by the equilibrium free energy difference (∆G) between reactants and products and that kinetics relates to the activation barrier (∆G^††) for getting from one to the other, I want to particularly discuss the importance of both these concepts for determining conformation by NMR spectroscopy.

There are two reasons why determining conformations in solution can become a particularly challenging endeavor. The first reason is thermodynamics. Again consider the all-important relation ∆G = -RTlnK which makes the equilibrium constant exquisitely sensitive to small changes in free energy (∆G). As mentioned before, an energy difference of only 1.8 kcal/mol between two conformations means that the more stable one exists to the extent of 96% while the minor one exists to the extent of only 4%. In practice such energy differences between conformers are seen all the time. A typical scenario for a flexible molecule in solution will posit a complex distribution of conformers being separated from each other by tiny energy differences ranging from say 0.5-3 kcal/mol. Again, the above exponential dependence of equilibrium constant K on ∆G means that the concentration of minor conformers which are higher in energy than the more stable ones by only 3 kcal/mol will be so tiny (~0.04%) as to be virtually non-existent. NMR typically cannot detect conformers which are less than 2-3% percent in solution (and it's too much to ask of NMR to do this), but such populations exist all the time.

Thus, thermodynamics is often the bane of NMR; in this case the technique is plagued by its low sensitivity

If thermodynamics is the bane, kinetics may be the nemesis. Rotational barriers between conformations (∆G^††) can be even tinier compared to thermal energy available to jostle molecules around at room temperature. For example, the classic rotational barrier for interconversion in ethane (whose origins are still debated by the way) is only 3 kcal/mol. Energy available at room temperature is about 20 kcal/mol which will make the ethane conformations interconvert like crazy. So even for energy barriers that are several kcal/mol, conformational interconversion is usually more than adequate to observe averaging of conformations and consequently all associated parameters- most importantly chemicals shifts and coupling constants- in NMR. The resolution time of NMR is on the order of tens of milliseconds, while conformational interconversion is on the order of tens of microseconds or less. Now in theory one can go to lower temperatures and 'freeze out' such motions. In many such experiments, line broadening at lower temperatures is observed, followed by separation of peaks at the relevant temperature. But consider that even for a barrier as high as 8-10 kcal/mol, NMR usually gives distinct, separate signals for the different conformers only at -100 degrees celsius. For barriers like those in ethane, the situation would be hopelessly challenging. As an aside, that means that sharp, well-defined resonances at room temperature do not indicate lack of conformational interconversion but can simply mean that conformational interconversion is fast compared to the NMR time scale.

Thus, kinetics is also often the bane of NMR; in this case the technique is plagued by low resolution time

Now there may be situations in which either thermodynamics or kinetics is favourable for carrying out an NMR conformational study. But for the typical flexible organic molecule, both these factors are usually pitted against the technique; rapid interconversion because of low rotational barriers, and low thermodynamic energy differences between conformers. Given this fact, it probably should not sound surprising to say that NMR is not that great a technique. However, as is well known to every chemist, its advantages far outweigh its drawbacks. Conformational studies comprise but one important aspect of countless NMR applications.

Nonetheless, when conformational studies are attempted, it should always be kept in mind that thermodynamics and kinetics have both conspired to make NMR an unattractive method for our purposes. Thermodynamics leads to low populations. Kinetics leads to averaging of populations. And yet the average information gained from NMR is invaluable and can shed light on individual solution conformations when combined with a deconvolution technique like NAMFIS or molecular dynamics. On the other hand, fitting the average data to a single conformation for a flexible molecule is inherently flawed and unrealistic. No one who has tried to take pictures of a horse race with a low-shutter speed camera should believe that NMR by itself is capable of teasing apart individual conformations in solution.

For determining conformations then, NMR alone does provide a wealth of data locked inside a safe. Peepholes in the door may illuminate some aspects of the system. But you need a key, best obtained from other sources, that will allow you to open the door and savor the treasures unearthed by NMR in their full glory.

I have been thinking a lot recently about studies in which people have determined the bound conformation of a ligand by transfer-NOESY experiments, essentially by transferring magnetization off another ligand to the protein and then back to the ligand of interest. With the known bound conformation of the first ligand, one can apparently locate the conformation of the second one. Many such unknown protein-bound conformations have been worked out. In my field of research, the ones which are relevant are of agents that bind to tubulin, especially discodermolide. In this case, the conformation of discodermolide was deduced via competition transfer-NOESY experiments with epothilone. These experiments are non-trivial to carry out and, as is the case for other biomolecular NMR studies, should be interpreted carefully. But in the end they look like nifty techniques that can shed light on unknown bioactive conformations, something that's very valuable for drug design.

Essentially it's again a problem of fitting the bound conformation NMR data to a single conformation. In solution we know for sure that this is a fallacious step. The (not so) obvious assumption in doing this for bound conformations is that there's got to be only one conformation in the active site too. But I have always wondered if a ligand in a protein active site could also have multiple conformations. MJ's comments on a past post and the discussion there makes me think that even in a protein active site, there could possibly be multiple conformations of a ligand, something that runs counter to what we conventionally think. How diverse those conformations might be is a different question; one would probably not expect large conformational changes. But even 'small' conformational changes could be significant enough to distinguish between different conformations in the active site. It's a problem worth thinking about.

A short holiday break and a rather protracted bout of the flu have kept me from blogging. So I will link to an article of mine that just got published in the magazine of the Chemical Society of the Indian Institute of Technology (IIT), Delhi. The article is written for the layman and talks about the importance of realizing that flexible molecules have multiple conformations in solution. Such conformations cannot be determined by NMR alone due to their rapid interconversion.

In the article, I describe NAMFIS (NMR Analysis of Molecular Flexibility In Solution), a joint computational-NMR approach which can derive a Boltzmann population for flexible molecules in solution. This information can be very useful for deducing, for example, the protein-bound conformation of a drug. But it can also be useful under other circumstances where determining conformation is important, such as for organic molecules assembling on a surface. Comments, criticism and questions are of course always welcome.

This paper explores the fallacy of determining conformational energies for polar organic molecules from molecular mechanics force fields. Using Taxol as a test case, it investigates how different force fields can produce downright contradictory results for energetic rankings of Taxol conformations.

The bottom line is simple; do NOT trust energies from force fields. Trust geometries. In case of energies force fields usually overemphasize electrostatic interactions because of lack of explicit solvent representation. Thus sometimes even geometries can be warped because of electrostatics overwhelming the optimization. The one thing force fields are good at calculating on the other hand is sterics.

Running a "complete" conformational search with multiple force fields will usually give you completely different geometries for the global minimum, or at least slightly different ones (depending on the molecule). Thus, trusting the global minimum conformation from any one force field is a big fallacy. Thinking that that global minimum will be the true global minimum in solution is nothing short of blasphemy. And for a bioactive molecule, thinking that the global minimum from a force field search will be the bioactive conformation is just...well, that just means you have been seduced by the dark side of the force field.

Lakdawala, A., Wang, M., Nevins, N., Liotta, D.C., Rusinska-Roszak, D., Lozynski, M., Snyder, J.P. (2001). . BMC Chemical Biology, 1(1), 2. DOI: 10.1186/1472-6769-1-2