The diagram below summarizes an interesting result recently reported by Hanson and co-workers (DOI: 10.1021/jo800706y. At ~neutral pH, compound 13 hydrolyses with a half life of 21 minutes, whereas 14 takes 840 minutes. Understanding this difference in reactivity may allow us to understand why some enzymes can catalyze the hydrolysis of peptides with an acceleration of up to twelve orders of magnitude.
The secret to understanding this behaviour lies in a technique known as conformational analysis, for which Derek Barton was awarded a Nobel prize. Indeed, the very molecules for which he first developed his technique were the decalins, of which molecule 13 is an example of a cis-decalin and 14 a trans-decalin. Barton’s insight was to recognize that both types of ring prefer to exist in chair conformations rather than the alternative boat shape.
The technique pioneered by Barton for estimating the energies of these various conformations is called Molecular Mechanics, and can be used to explain the difference in reactivity. Considering first molecule 13, one can calculate its molecular mechanics energy for two conformations, differing in whether the N-alkyl sidechain is equatorial (left) or axial (right).The equatorial form (green box) comes out about 5 kcal/mol lower in energy than the axial (red box). One can also calculate the energy of the product, which arises from the OH attacking the carbon of the amide (dashed lines), evicting ammonia, and forming a cyclic lactone. Here, the most stable product (by ~10 kcal/mol) is again that resulting from the green bond forming. From the simple relationship ΔG = -RT Ln K (where K describes the position of the equatorial/axial equilibrium), one can conclude that the ratio equatorial/axialis ~4000, i.e. the favoured reaction arises from the most abundant reactant. With the trans amide, the equatorial conformation (green box) is around 3 kcal/mol lower than the axial (red box), but now the most stable lactone product (by ~ 3 kcal/mol) arises (green bond) from the less stableaxial reactant. For reaction to occur, the equatorial reactant has to first isomerise to the axial, which imposes a ~3 kcal/mol penalty on the reaction. This is enough to slow the rate of the reaction significantly compared to the un-penalised cis-decalin reaction.