One of the most fun things about chemistry is that for every laundry list of examples, there is always a counterexample. The counterexample does not really violate any general principles, but it enriches our understanding of the principle by demonstrating its richness and complexity. And it keeps chemists busy.
One such key principle is the hydrophobic effect, an effect with an astounding range of applicability, from the origin of life to cake baking to drug design. Textbook definitions will tell you that the signature of the "classical" hydrophobic effect is a negative heat capacity change resulting from the union of two unfavorably solvated molecular entities. The nonpolar surface area of the solute is usually proportional to the change in heat capacity. The textbooks will also tell you that the hydrophobic effect is favorable principally because of entropy; the displacement of "unhappy" water molecules that are otherwise uncomfortably bound up in solvating a solute contributes to a net favorable change in free energy. Remember, free energy is composed of both enthalpy and entropy (∆G = ∆H - T∆S) and it's the latter term that's thought to lead to hydrophobic heaven.
But not always. Here's a nice example of a protein-ligand interaction where the improvements in free energy across a series of similar molecules comes not from entropy but from improved enthalpy with the entropy actually being unfavorable. A group from the University of Texas tested the binding of a series of tripeptides against the Grb2 protein SH2 domain. The exact details of the protein are not important; what's important is that the molecules only differed in the size of the cycloalkane ring in the central residue of the peptide- going from a cyclopropane to a cyclohexane. They found that the free energy of binding improves as you go from a 3-membered to a 5-membered ring but not for the reason you expect, namely a greater hydrophobic effect and entropic gain from the larger and more lipophilic rings.
Instead, when they experimentally break down the free energy into enthalpy and entropy using isothermal titration calorimetry (ITC), they find that all the gain in free energy is from enthalpy. They find that every extra methylene group contributes about 0.7 kcal/mol to the interaction. In fact the entropy becomes unfavorable, not favorable as you move up the series. There's another surprise waiting in the crystal structures of the complexes. There are a couple of ordered water molecules stuck in some of the complexes. Ordered water molecules are fixed in one place and are "unhappy", so you would expect these complexes to display unfavorable free energy. Again, you would be surprised. It's the ones without ordered water molecules that have worse free energy. The nail in the coffin of conventional hydrophobic thinking is driven by the observation that the free energy does not even correlate with decreased heat capacity, something that's supposed to be a hallmark of the "classical" hydrophobic effect.
Now it's probably not too surprising to find the enthalpy being favorable; after all as they note, you are making more Van der Waals contacts with the protein with larger rings and greater nonpolar surface area. But in most general cases this value is small, and the dominant contribution to the free energy is supposed to come from the "classical" hydrophobic effect with attendant displacement of waters. Not in this case where enthalpy dominates and entropy worsens. They don't really speculate much on why this may be happening. One factor that comes to my mind is the flexibility of the protein. The improved contacts between the larger rings and the protein may well be enforcing rigidity in the protein, leading to a sort of "ligand enthalpy - protein entropy" compensation. Unfortunately a comparison between bound and unbound protein is precluded by the fact that the free protein forms not a monomer but a domain-swapped dimer. In this case I think that molecular dynamics simulations might be able to shed some light on the flexibility of the free protein compared to the bound structures; it might especially be worthwhile to do this exercise in the absence of the apo structure
Nonetheless, this study provides a nice counterexample to the conventional thermodynamic signature of the hydrophobic effect. The textbooks probably don't need to be rewritten anytime soon, but chemists will continue to be frustrated, busy and amused as they keep trying to tame these unruly creatures, the annoying wrinkles in the data, into an organized whole.
Myslinski, J., DeLorbe, J., Clements, J., & Martin, S. (2011). Protein–Ligand Interactions: Thermodynamic Effects Associated with Increasing Nonpolar Surface Area Journal of the American Chemical Society DOI: 10.1021/ja2068752
How to calculate trigonometry functions
7 hours ago in Doc Madhattan