Gerhard Klebe's group at Marburg are studying inhibitors of thrombin in which they replace a cyclopentyl group by a cyclohexyl group. To their surprise they observe (DOI: 10.1002/anie.200701169) no change in binding affinity. Crystallography indicates no electron density for the part occupied by the cyclohexyl group but robust density for the cyclopentyl. The authors conclude that while the cyclohexyl binding is enthalpically unfavourable, entropically the six-membered ring can flip and twist and dance, which is favourable, and also does not provide much crystal density because of its flexibility. So unfavourable enthalpy is balanced by favourable entropy. MD simulations support this contention.
"What lesson can be learned from this example? Usually ligands are optimized in congeneric series. The addition of functional groups is expected to enhance binding; for example, the change from a five- to a six-membered ring should augment binding affinity by approximately 3–4 kJ/mol. However, even very similar ligands can exhibit very different binding properties that destroy a simple structure–activity relationship"Also, the gain in binding affinity from a methylene depends on the system. Model systems based on octanol-water partitioning offer a value of about 0.7 kcal/mol. But of course octanol unlike a protein does not have a problem reorienting itself around the substrate. Thus, the value can be less for a protein. On the other hand, in cases where an extra methylene or methyl just about fills the remaining space in a pocket and packs tightly can provide 5 times as much binding affinity. This is true for example in case of tRNA synthatases (I got this from Alan Fersht's excellent book) As usual, exceptions abound to the generalisations, and Klebe's study provides another interesting example.