Glucocorticoid receptor binding: A biphasic dependence on molecular size as revealed by the bilinear LinBiExp model

For corticosteroids, receptor-binding affinity (RBA) at the glucocorticoid receptor (GR) is a major determinant of therapeutic potential. Here, the results of a comprehensive quantitative analysis of relative RBA (rRBA) data obtained from more than a hundred active structures are reported. Because of a clear biphasic size-dependence, the recently introduced linearized biexponential (LinBiExp) model provided very good fit: for steroids that satisfy the main binding criteria at the GR, it accounts for close to 80% of the variability in the free energy of binding ΔG0 (or log rRBA) data by using only two descriptors: calculated molecular volume and an indicator variable for the presence of 6α/9α-halogen or cyclic 16,17-acetal moieties. Accordingly, binding is strongest for corticosteroids close to an ideal size that is large enough to provide as large nonspecific (van der Waals-type) interactions as possible, but is not too large to have difficulty fitting due to size-limitations at the binding site. Binding affinity is dramatically increased by 6α- or 9α-halogenation or introduction of a cyclic 16,17-acetal moiety (in average, about 7-fold), but there is no significant increase after the first substitution. Known highly active glucocorticoids, such as betamethasone 17-monopropionate, fluticasone propionate, or mometasone furoate, indeed satisfy both of these criteria. For small-enough structures, the obtained size-dependency (slope) of the free energy of binding suggest that, as long as only nonspecific interactions are involved, addition of a methylene-sized non-hydrogen atom to the ligand structure increases ΔG0 on average by about 1.5 kJ/mol, corresponding to an almost doubling of the binding affinity.