Who's afraid of Big Bad Thermodynamics?

George Whitesides, in a trademark outfit.

In a talk at Northeastern University yesterday, George Whitesides asked the students in the audience if they had ever studied thermodynamics. Not a single hand went up.

Even accounting for the fact that some students might have been reluctant to flag themselves in a large audience, I find this staggering, especially if these students are planning to go into basic drug discovery research. But I can’t completely blame them. I happened to take one (mandatory) thermodynamics and one (non-mandatory) basic statistical mechanics class in college and was exposed to thermodynamics in graduate school through my work on conformational equilibria and NMR. But most of my fellow graduate students in organic and biochemistry had little inkling of thermodynamics; it certainly wasn't a part of their standard intellectual toolkit.

The problem’s made worse by misunderstandings about thermodynamics that seem to linger in students’ heads even later in their career. These misunderstandings stem from a larger rift between organic and physical chemistry; the latter is supposed to be highly mathematical and abstract and rather irrelevant to the former. This is in spite of the overwhelming importance of concepts from p-chem in classical physical organic chemistry. Sadly, classical physical organic chemistry itself is disappearing from the college and grad school curriculum, and an argument in favor of emphasizing thermodynamics is also a plug for not letting physical organic chemistry become a relic of the past. No other topic gives you as good a basic feel for structure, function and reactivity in organic chemistry.

But coming back to thermodynamics, this impression that many students have about thermodynamics being all about Maxwell relations and Carnot cycles and virial theorems is rather misleading. It’s not that these things are not important, it’s just that that’s not the kind of thermodynamics Whitesides was talking about when he was talking about drug discovery. Thermodynamics in drug discovery is often much less complicated than bonafide textbook thermodynamics. And it’s of foundational importance in the field since at its core, drug discovery is about understanding molecular recognition which is completely a thermodynamic phenomenon governed by free energy.

For a drug designer, the key thermodynamic circus to understand is the interplay between G, H, and S as manifested in the classic equation ∆G = ∆H – T∆S. It’s key to get a feel for how opposing values of H and S can lead to the same value of G, since this is at the heart of protein-drug recognition. It’s also important to know the different features of water, protein and solvent that contribute to changes in these parameters. Probably the most important thermodynamic effect that drug designers need to be aware of is the hydrophobic effect. They need to know that the hydrophobic effect is largely an entropic effect arising from the release of bound waters, although as Whitesides has himself demonstrated, reality can be more complicated. But the fact is that we simply cannot understand water without thermodynamics, and we cannot understand drug action without understanding water.

Also paramount is to understand the relationship between thermodynamics and kinetics, something that again benefits from studying reactions under thermodynamic and kinetic control and things like the Curtin-Hammet principle in classical physical organic chemistry. It’s crucial to know the difference between thermodynamic and kinetic stability, especially when one is dealing with small molecule and protein conformations. Finally, it’s enormously valuable to have a feel for a few key numbers, foremost among which may be the relationship between equilibrium constant and free energy; knowing this tells you for instance that it takes only a difference of 1.8 kcal/mol of free energy between two conformers to almost completely shift the conformational equilibrium on to the side of the more stable one. And when that difference is 3 kcal/mol, the higher-energy conformation is all gone, well beyond the detection limits of techniques like NMR. Speaking of which, a good understanding of thermodynamics also tells you why it’s incorrect to rely on average NMR data to tease apart the details of multiple conformations in solution.

All this knowledge about thermodynamics is ingrained more easily than complicated mathematical derivations of configuration integrals in free-energy perturbation theory. Students need to realize that the thermodynamics that they need to tackle drug discovery is a semi-quantitative blend of ideas relying much more on a rough feel for numbers and competing entropic and enthalpic effects. This kind of feel can lead to some very useful insights, for instance regarding relationships between G, H and S in the evolution of new drugs.

It’s time to incorporate this more general thermodynamics outlook in drug discovery classes and even in regular chemistry classes. It’s simple enough to be taught to undergraduates and bypasses the more sophisticated and intimidating ideas of statistical mechanics.

In yesterday’s conference, the chairman had the last laugh. Half-jokingly he emphasized that Northeastern’s chemistry course is ACS certified, which means that one semester of p-chem and thermodynamics are mandatory. Apparently Harvard’s is not. To which Whitesides replied that he can guarantee that you will find students at Harvard who are also not familiar with thermodynamics.

Whitesides's appeal to give pharmaceutical scientists-in-training a firm grounding in thermodynamics applies across the board. On top of Plato’s Academy there was rumored to be a sign which said “Let no one ignorant of geometry enter”. Perhaps one can make a similar case for thermodynamics in the pharmaceutical industry?

Note: 

I have often written about thermodynamics in drug design on my blog. A few potentially useful posts:

1. The strange case of enthalpy-entropy compensation.

2. The unbearable heat capacity of being.

3. A drug design class act.

4. Overturning hydrophobic assumptions.

5. ∆G, ∆G†† and All That: Implications for NMR.

Some useful references:

Ken Dill - Molecular Driving Forces

Jack Dunitz - Win some, lose some: Enthalpy-entropy compensation in weak intermolecular interactions (PDF).

Ken Dill - Dominant forces in protein folding.

George Whitesides - Designing ligands to bind tightly to proteins (book chapter PDF): Includes much of the material from Whitesides's talk.
Jonathan Chaires - Calorimetry and Thermodynamics in Drug Design.

Kinetics in drug discovery: The neglected child?

A couple of articles appearing in the last few months brought my attention to a topic that medicinal chemists don't always think about and need to pay more attention to; the important role of kinetics in drug discovery, especially in its early stages.

Anyone who is involved in drug discovery knows the importance of the dissociation constant that signifies the affinity of a therapeutic ligand for a protein. SAR around changing affinities (usually represented by Kd or IC50 values) drive lead design and optimization. But as some of the recent reviews note, the problem with this number is that it's a ratio of the on and off rates of binding of the ligand to the protein. A fast on rate and a fast off rate will give you the same number as a slow on and a slow off rate. But the two situations are not identical.

The most important point emphasized by these reviews is that slow off rates can sometimes lead to prolonged drug efficacy in ways that are not apparent from just the affinity. And this is quite logical if you consider that a slow off rate means that a ligand has a longer residence time in the protein's active site and is spending more time modulating its action. What this means in practice is that even compounds with relatively low affinities can have quite significant efficacies resulting from slow off rates.

So how do you modulate off rates? One good thing about off rates is that unlike on rates, they don't depend on concentration. The benefit of this is that you could have a compound which has a low concentration at the target site and is rapidly cleared away, but which nonetheless spends a lot of time in the protein and therefore provides good efficacy. The other good thing about off rates is that they are essentially dependent on the interactions between ligand and target. So you should in principle be able to improve them just by optimizing these interactions. Again, this won't result in better affinity if you are also slowing down on rates, but it might give you improved efficacy.

In part these studies remind us that we need to clearly distinguish between terms like affinity, IC50, efficacy and the other vocabulary of lingua pharmaceutica. But they also ask an important question; why aren't pharmaceutical scientists paying more attention to kinetic measurements in the early stages of drug discovery? That this is indeed the case became apparent when I looked at the website BindingDB which lists key biological, thermodynamic and kinetic parameters for ligands bound to popular targets. One prominent pharmaceutical target that I looked at had 277 different ligand structures bound to it along with many cases where affinities, IC50s and even free energies had been measured. But out of those 277 I could find only 5 cases (less than 2%) where on and off rates had been recorded. Clearly this is not a focus in preclinical drug discovery.

But as the recent article note, it should be. There are several cases of drugs - HIV protease inhibitors for instance - where differing efficacies for compounds with similar affinities essentially result from differing off rates and residence times. In fact as illustrated by the blood pressure lowering drug amlodipine, off rates can mean the difference between a best-in-class drug and the second-best contender; amlodipine is a better drug than others partly because of its longer residence time in the pocket of the calcium channel protein which it inhibits.

The neglect of kinetic rate measurements reminds me of an almost equal neglect of thermodynamic measurements by ITC. As described in other articles, careful measurement of enthalpy and entropy (and not just free energy) can be very useful in early stage drug discovery. This shouldn't be surprising at all; after all kinetics and thermodynamics are the twin pillars of protein-ligand binding, and you neglect them at your own peril.

∆G, ∆G†† and All That: Implications for NMR

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.