The consequences of translational and rotational entropy lost by small molecules on binding to proteins

When a small molecule binds to a protein, it loses a significant amount of rigid body translational and rotational entropy. Estimates of the associated energy barrier vary widely in the literature yet accurate estimates are important in the interpretation of results from fragment-based drug discovery techniques. This paper describes an analysis that allows the estimation of the rigid body entropy barrier from the increase in binding affinities that results when two fragments of known affinity and known binding mode are joined together. The paper reviews the relatively rare number of examples where good quality data is available. From the analysis of this data, we estimate that the barrier to binding, due to the loss of rigid-body entropy, is 15-20 kJ/mol, i.e. around 3 orders of magnitude in affinity at 298 K. This large barrier explains why it is comparatively rare to observe multiple fragments binding to non-overlapping adjacent sites in enzymes. The barrier is also consistent with medicinal chemistry experience where small changes in the critical binding regions of ligands are often poorly tolerated by enzymes.