A Drug Design Class Act: ∆S or ∆H?

One of the most important relations in all of chemistry is the free energy relation ∆G = ∆H - T∆S. Tuning the potency of a ligand binding to a protein involves a fine balance between optimizing both entropy and enthalpy. In his review on the role of these two variables, Johns Hopkins's Ernesto Freire makes a very interesting observation; that for a given series of progressively improved set of drugs binding to a given protein, it's the enthalpy that becomes more and more favourable while the entropy pretty much starts out being favourable. Thus, it's enthalpy optimization that's the harder part in drug design.

Freire illustrates his observation by looking at two sets of famous drugs- HIV protease inhibitors and cholesterol-lowering statins. For example if we look at the progression of the protease inhibitors over time starting from about 1995 when we had good but not highly-potent drugs to about 2006 when we had greatly improved drugs, we essentially find the striking fact that while ∆S for drug binding was favourable to begin with in 1995, it's really a great improvement in ∆H that has made the drugs more potent through the years.

Thus Freire concludes that it's improving enthalpy of binding and not entropy that's the hard part in improving potency. The argument is fairly straightforward; favourable entropy depends on desolvation of the drug to get rid of water molecules, as well as displacement of water molecules from the active site by the drug. Both these events are more or less favourable for most drugs as most drugs are reasonably hydrophobic. Thus, high hydrophobicity can by itself confer favourable entropy. But tuning enthalpy is much harder for two reasons; first of all because as Freire notes, it is not possible yet to engineer hydrogen bonds to the tenths of angstroms needed for optimum energetic gain. Secondly, even a slight sub-optimal feature in hydrogen bonding can tip the scales because remember, the hydrogen bonds that the ligand forms with the protein are simply replacing strong hydrogen bonds that were previously formed with the surrounding water. Thus the new hydrogen bonds may not be as strong, and indeed may even be unfavourable with respect to the previous ones. From past discussions, recall that a mere 1.4 kcal/change in free energy from unfavourable hydrogen bonding can lead to a 10-fold loss in binding affinity ("Life is a 3 kcal/mol denizen"). Clearly one has to be careful while designing ligands to form hydrogen bonds. It's perhaps not surprising that hydrophobic effect-induced binding is the main stabilizing factor in both protein folding and ligand design; both man and nature apparently find it much easier to get binding affinity from hydrophobic interactions than polar ones.

These facts are borne out when we see the change in these two thermodynamic variables in the optimization of HIV protease inhibitors over time where, while ∆S is favourable to begin with, ∆H is actually positive and unfavourable at the beginning. Let's also not forget that potency is only the beginning for a ligand that needs to traverse many obstacles in order to be converted into a drug, including ADME-T optimization. Any one of these further modifications can modify the one or both of the thermodynamic variables and change the initially optimized potency.

However, since optimizing enthalpy is both more challenging and more important, Freire prescribes experimentally measuring the two variables as much as possible for every stage of the drug design process starting as early as possible. This can be best accomplished through Isothermal Titration Calorimetry (ITC) which can also shed light on enthalpy-entropy compensation, an important process in the binding of ligands.

Thermodynamic optimization is a tightrope walking act, a prelude to the ultimate juggling game that is drug design. Not only are you trying to balance several variables at once, but some of them are trying to actually pull you down. But simple strategies can quell at least some of these nefarious efforts and reward you with a fine ligand, if not drug.

Reference:
E Freire (2008). Do enthalpy and entropy distinguish first in class from best in class? Drug Discovery Today, 13 (19-20), 869-874 DOI: 10.1016/j.drudis.2008.07.005

Killing polyavians with a unistone: designing promiscuous drugs

Decapitate multiple avians by means of a single projectile (Kill many birds with a single stone)

There is an interesting review (doi:10.1016/j.sbi.2006.01.013) on the "rational" design of promiscuous ligands and drugs which target multiple receptors. The review tries to break with the current paradigm of drug discovery, that of highly selective and potent ligands targeting a single receptor. According to the authors, there is an addition to this paradigm of selective ligand design; instead, design promiscuous ligands that would modulate multiple targets and bring about the intended action. This may look like a somewhat suprising strategy, because we know that promiscuous ligands usually carry the risk of toxicity and off-target side effects. But the paradigm seems to be more subtle than that. Here are some points from the review that I found interesting:

1. Many drugs which were initially thought to be effective because of their selectivity are now recognised to be promiscuous, and perhaps effective because they are promiscuous. A most striking example is Gleevec. This way of thinking has also raised questions about kinase inhibitors in general; are they efficacious because of or inspite of their promiscuity?

2. In one study, it was found that the promiscuity of ligands inversely correlates with their molecular weight. This is not too surprising, considering that more complex ligands will have to fulfil multiple site interactions with the receptor, the probability of which will be lower than that for fewer points of interaction. To me, this also translates into the entropic difficulties of binding to receptors, with more complex ligands having to pay greater entropic penalties. Of course, 'more complex' in terms of higher molecular weight does not necessarily mean ligands with more rotatable bonds; it can just mean more flat rings. But the problem of multiple site interaction is still valid even for these. For nature, the best ligands would be those which have a highly favourable enthalpy of interaction with the receptor at a few well-defined points, without having to pay a high entropic cost. That is one of the reasons why so many of the potent molecules that nature has designed are small, planar, heterocyclic ligands. This concept also spills over into fields like kinase inhibitor design. For selective design, we usually try to strike some golden mean in terms of ligand complexity.

3. There are also promiscuous proteins, with the most well-known example being cytochrome P450. Tubulin is also a pretty promiscuous protein. Sadly, I don't think we really understand what features of a protein or ligand make it promiscuous. Hydrophobicity seems to be a common criterion, but the very word "common" indicates that it is spread across a wide range of protein and ligand classes. One interesting feature of another promiscuous protein, PXR, is that it seems to bind multiple configurations of the same ligand. I have always wanted to find an example of such a protein. Whether this is a strong criterion for promiscuity would be a very interesting proposition.

To me, it appears that promiscuity first of all is not as widely observed as we would think, especially in terms of ligand lipophilicity. Consider Taxol. To my knowledge, there is not a single protein other than Tubulin to which it binds so strongly, inspite of it being quite lipophilic. But clearly, lipophilicity itself cannot be a sufficient criterion for ligand promiscuity. Also, the high selectivity of taxol may be related to its relatively high molecular weight, with reference to the MW-promiscuity study. The point seems to be that although we know some examples of promiscuous proteins and promiscuous drugs, their general features seem not much different from other non-promiscuous molecules.

It seems then, that to have effective promiscuous drugs, what we need is not just rampant promiscuity but selective promiscuity (I know, sounds like an oxymoron). The way I think about it, it won't work if the drug is flagrantly promiscuous across diverse chemical classes. Simply throwing in a greasy compound into the cocktail of body chemistry may get you a wildly promiscuous inhibitor, but that would not be what you want for a drug.
Consider kinase inhibitors. We can almost take it for granted that an ideal, conpletely promiscuous kinase inhibitor that targets dozens of kinases across different classes cannot be made into a working drug. But one can think of a particular subset of kinases, intricately linked to each other through signal transduction pathways, very sensitive to modulation of each other and to modulation by small molecules, implicated in a disease such as cancer, and expressed in cancer cells constitutively. If, and this is a big if, one can design an inhibitor that will inhibit this unique chosen subset of kinases, then one could potentially have a very potent drug.

In light of the very selective and stringent promiscuity criteria above, I would think that if anything, it may be more difficult to design a truly potent and effective promiscuous inhibitor, compared to a highly selective inhibitor, except by serendepity. In the latter case, you have to selectively target one protein. In the former case, you may have to selectively target three of four proteins. That just sounds so difficult through rational drug design. Naturally, designing such inhibitors would entail an intimate understanding of signal transduction pathways.

How much water does it hold?

The last couple of days, in connection with the behaviour of water in protein active sites, I have been reading about water and the hydrophobic effect in general, and I found it fascinating how little we really know about both of these in general. For one thing, we still seem to have miles to go in understanding ice, bulk water, and the transition between the two. There was a debate between Richard Saykally of Cal Berkeley and Anders Nilsson of Stanford about the number of hydrogen bonds that a water molecule makes in bulk water. One would think that something as simple as this would have been unraveled by now. But nothing about water is simple. Nilsson published the pretty amazing contention that many water molecules in bulk liquid water at room temperature form only two hydrogen bonds. This would mean that those hydrogen bonds are unusually strong. This paper sparked heated debate, and Saykally was a vocal opponent, countering with his own experiments, and contending that it would be a walk across the street to Stockholm if Nilsson's viewpoint turned out to be true. I am no water expert, but the best value for the energy of an average hydrogen bond in bulk water that I have come across seems to be 1.5 kcal/mol (determined by Saykally), which can definitely be less than that in a protein active site. At least for now, this discussion of "average" hydrogen bonds generally sounds a little slippery to me.

I think that this whole issue of how much a hydrogen bond in bulk water is worth could affect how much gain in energy a water molecule displaced from a protein active site might gain. Friesner et al. in their recent publications indicate that water molecules which cannot form their full complement of hydrogen bonds in a protein active site because of confinement could get an enthalpic advantage if they are pushed out into solvent. I think there's much less ambiguity about the entropic advantage that such a water molecule could have. Then there's also Dunitz's whole argument about entropy-enthalpy compenstation (see previous post) which could factor in...I am still really groping about for coherence in this landscape.

As far as hydrophobic interactions are concerned, while the general idea that the hydrophobic effect is entropically driven seems correct, it also seems situation dependent, especially varying with the temperature. One of those basic important things to note is that the enthalpy of transfer for a nonpolar solute to water is close to zero, and can even be slightly favourable. But when two nonpolar surfaces in water aggregate, it's the entropy of disordering waters clustered around the solute that is very favourable. As usual, even these seemingly simple issues are draped in subtleties. Among others, Themis Lazaridis has explored this very interestingly in a review (2001), in which he cements the "classical" view of the hydrophobic effect. He also counters arguments about the similar energy of cavity creation in water compared to some other solvents by saying that while this may be true, the decomposition of factors contributing to the energy might be different for the two cases.

And finally, and I should have posted about this a long time back, Water In Biology, a great blog all about the molecular intricacies of water, from Philip Ball, staff writer for Nature and author of many excellent books, including H2O: A biography of water.

Water really seems like a testament to that quote by T.S. Eliot about coming back to the beginning again and again, and newly getting to know a place every time. There are just so many things about it we don't understand.

The strange case of entropy-enthalpy compensation

My original intention was to read about the role water molecules play in active sites, one thing led to another, and I ended up actually spending more time on the fascinating topic of entropy-enthalpy compensation. I drfited from water molecules to this topic primarily because of a 1995 paper by Jack Dunitz, in which he derives the conclusion that for a typical hydrogen bond, ~5 kcal/mol, there is entropy-enthalpy compensation, which means that that typical free energy of transfer of a hydrogen bond from bulk water to a protein active site can be close to zero. There were some assumptions in this paper, but the concept mostly seems to hold.

Entropy-enthalpy compensation (EEC) is actually a pretty logical concept. Let's say you are designing a ligand to bind a protein, and want to increase the binding affinity by adding hydrophobic groups on it. As you add these groups, the ligand will (usually) bind tighter because of increased vdW contacts as well as the hydrophobic effect, but the word "tighter" already indicates that it will do so with a loss in entropy. Thus, the gain in enthalpy of binding is offset by a loss in entropy. So even if you modify the ligand this, the resulting free energy of binding may be close to zero, or at least will stay constant because of these two opposing quantitites.

However, there are some pretty striking exceptions, and this came to light when I read a paper by George Whitesides in which his group was doing studies of ligand binding to carbonic anhydrase (CA). The authors observed that surprisingly, as they were adding more hydrophobic groups to some sulfonamide ligands by extending the side chain, they observed almost no change in the free energy of binding. In fact, they even observed this effect with different classes of side chains. Clearly, EEC was taking place. But remarkably, they observed that the effect was due to exactly the opposite of what usually happens; namely that the enthalpy was become more unfavourable and the entropy was becoming more favourable. Needless to say, this is not what one expects. The authors have proposed a nice model in which they believe there is some sort of negative cooperativity; as you add more atoms to the side chain, it somehow weakens the binding of the initial atoms that were previously binding better. This worsens the enthalpy of binding, and improves the entropy because the ligand becomes free to wiggle around more. Even though this model supports what is happening, the exact details of how it happens are not clear.

Clearly, EEC is an important concept in rational ligand and drug design. Formerly, it was thought to be a "phantom phenomenon", an artifact of experimental measurements and errors. But Whitesides contends that with the advent of Isothermal Titration Calorimetry (ITC), it has become known as a very real phenomenon. Practically, it means that small moelcules with relatively rigid structures could have the best potency and binding affinity, because we would then get a good and favourable increase in binding enthalpy, without having to pay the corresponding cost in entropy.

However, as I was reading this, I realised that while the chemist would aim to design such rigid high-binding ligands, nature already seems to have solved the EEC problem. Consider the various kinds of protein-protein interactions, where highly flexible loops are seen as recognition elements. Would a chemist ever design a loop for molecular reecognition? Yes and No. Yes, because designing such a loop would build in versatility and flexibility to explore conformational space. No because of the above-noted reasons, of attaining favourable entropy. So how does nature circumvent this problem? Clearly, there must be a way in which nature pays the cost of unfavourable entropy. A couple of ways come to mind:

1. Through the very existence of the protein! Consider how much penalty nature pays in synthesizing and compactly folding the protein in the first place. This entropy cost paves the way to a future, entropically less favourable situation.

2. Through 'steric confinment'. Loops are only a small part of a giant protein surface. The coming together of these surfaces is hydrophobically driven by the expulsion of water. Then it is relatively easy for loops to be recognised, as they are already close to the other surface. Again, the entropic cost has been paid by the rest of the protein surface.

3. Through optimizing the binding enthalpy so much, that unfavourable entropy is not so much of an issue. This is of course what chemists try to do all the time, but nature does it elegantly. Think of the umpteen number of cyclic peptides and macrocycles that nature uses for molecular recognition. Admittedly, one of the ways nature solves the EEC problem is by designing through evolution, ultra potent ligands, where a favourable ∆H compensates for an unfavourable ∆S

Once again, nature rules by striking the right balance through relentless optimization, and we have much to learn from it for tackling EEC

Culprit?

Mark Murcko who is the CTO of Vertex gave a nice keynote presentation on SBDD at the CHI conference. He was talking about our general ability to design drugs, when he said that a famous scientist he knew had told him once that we really know how to design ligands. This task by itself is quite challenging. Designing drugs, a much more difficult task, is firstly a multidisciplinary endeavor, while the former one is largely chemical in its broadest sense. Murcko said that the scientist was of the opinion that we really know only how to design ligands, and not really drugs in a rational way. By the way, Murcko did not entirely agree with him.

But Murcko thought it prudent to not name the scientist!

Yesterday, randomly flipping through a review by a well-known scientist, I came across this statement

"The ability to design drugs (so-called ‘ rational drug design ’) has been one of the long-term objectives of chemistry for 50 years. It is an exceptionally difficult problem, and many of its parts lie outside the expertise of chemistry. The much more limited problem – how to design tight-binding ligands (rational ligand design) – would seem to be one that chemistry could solve, but has also proved remarkably recalcitrant. The question is ‘Why is it so difficult ? ’ and the answer is ‘We still don’t entirely know’."

Needless to say, I get the very strong feeling that Murcko was talking about this particular scientist. I have to say that my own opinions swing toward those enumerated by the scientist. Care to guess who?? (One hint: conference and company location...)

Nature adores a vacuum?

Well, ok, nature does not actually adore a vacuum, but what are we then to make of Bruce Berne's newest PNAS piece, in which he talks about water molecules in protein active sites that are so horribly unhappy that they would almost let a vacuum take their place?

The article comes on the heels of Friesner et al.'s comprehensive JMC 06 Glide XP article, which was an impressively comprehensive instance of how computational chemists can take into consideration the detailed physical chemistry of protein-ligand/drug interactions. As usual, electrostatics, van der Waals interactions, and desolvation among other things are taken care of. As usual, it turns out that in most earlier studies, the 'other half'-water-had not been considered. No wonder attempts to explain diabolically strong interactions like that of streptavidin-biotin (the strongest protein-ligand interaction known) resulted in drastic underestimates of the binding energy. With their latest framework, Berne et al. seek to remedy this situation. They make a couple of elementary sounding but oft neglected and important points:

1. Water is not going to be happy in a place in a protein where it is surrounded by a hydrophobic enclosure.

2. It is not going to be happy if it cannot make its full complement of hydrogen bonds with the protein/with other water molecules.

3. Even if it can make such bonds, it is not going to be happy if there are only one or two configurations in which it can do so.

4. Clearly, such water molecules are going to be more than happy to be kicked out by ligand atoms which can form their full complement of h-bonds with protein residues. These bonds, if they form part of a ring or if they are in close vicinity, have been called correlated hydrogen bonds. As per the authors' interpretation, its is these correlated hydrogen bonds that give special binding stability to examples like the streptavidin-biotin complex.

Obviously, like all life forms, water aspires to that highest ideal- freedom.

In the PNAS article, Berne et al. examine three cases, including streptavidin and COX 2 binding, in which water seems to be simply aching to get of the protein cavity. In the case of streptavidin, five water molecules form a metastable ring as depicted above. They do manage to form bonds with each other and with protein residues, but they are hopelessly trapped on top and bottom by hydrophobic parts. In this case, as explained in the JMC piece, the atom-atom pairwise addition principle does not work for hydrophobic enclosures. Clearly, the sum of the parts is not equal to the whole here, and the effect of two hydrophobic atoms, one each on top and bottom, is different from the calculated pairwise sum of effects for two atoms .

The word "metastable" is the best word I can think of for describing this unhappy situation for water. Surreal, simmering, patient, but waiting to become free.

In the case of COX 2, I saw a few statements which neither me nor my advisor could make sense of at first. Aristotle notwithstanding, it seems that there are actually some solvation situations which are almost as bad as a vacuum. Or even worse? Consider what the authors have to say:

The Cox-2 active site was found to contain no persistent hydration sites and is in fact entirely devoid of solvent in 80% of the simulation, despite the cavity sterically accommodating approximately seven water molecules. The high excess chemical potential of the binding-cavity solvent is due to an inability of the water molecules to make hydrogen bonds with the surrounding hydrophobic protein residues and other water molecules...An extreme case of hydrophobic enclosure is observed in the Cox-2 binding cavity, where no energetically stable solvent configurations appear to exist; insertion of ligand hydrophobic groups into such a region of persistent vacuum will result in substantially larger free-energy liberation than would be expected if the binding cavity were treated as solvated.

Well...I second the study; water, that humble but amazingly complex liquid, has often been neglected and underestimated in studies of protein-drug-ligand interactions.

Almost concomitantly, Essex et al. have published a report in JACS, in which they examined the nature of water molecules in active sites. They find that most of the water molecules are displaceable. Not surprisingly, they conclude that the binding affinity of the ligand depends upon the nature and environment of the water molecules. It's a good statistical study.

A central point that is coming to light through such studies is that the absolute hydrophobicity/hydrophilicity of a ligand certainly does not constitute the whole story. This may well be kept in mind by medicinal chemists who aim at modulating these properties of drug-like molecules from SAR studies. Sometimes, a single well-positioned ligand atom which displaces one or two extremely metastable water molecules can lead to orders of magnitude of binding affinity, which cannot be predicted from absolute characteristics of the ligand.

As usual, quality, not quantity, matters.

Addendum:
Another nice 3 page review I found in the rarely read Chemical Biology and Drug Design again makes the case. The review explores the thermodynamic aspects of drug-protein binding, and says among other things:

As the major contributors to the binding enthalpy are polar groups, a common misconception is that enthalpically driven compounds must be highly polar and that consequently their bioavailability will be compromised. In fact, what is often observed experimentally is that compounds with the same number of polar groups have vastly different binding enthalpies...To generate a favorable binding enthalpy, it is not the number of polar groups that matters but the quality of their interactions with the target. It is better to have few groups that establish strong interactions than a large number of groups mostly paying the desolvation penalty.

Again, by a "few groups", all that is needed is two functional groups that can kick out a metastable water molecule, and your job might be done.