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