Entropy and Free Energy of a Mobile Loop Based on the Crystal Structures of the Free and Bound Proteins

A mobile loop changes its conformation from "open" (free enzyme) to "closed" upon ligand binding. The difference in the Helmholtz free energy, ΔF(loop) between these states sheds light on the mechanism of binding. With our "hypothetical scanning molecular dynamics" (HSMD-TI) method ΔF(loop) = F(free) - F(bound) where F(free) and F(bound) are calculated from two MD samples of the free and bound loop states; the contribution of water is obtained by a thermodynamic integration (TI) procedure. In previous work the free and bound loop structures were both attached to the same "template" which was "cut" from the crystal structure of the free protein. Our results for loop 287-290 of AcetylCholineEsterase agree with the experiment, ΔF(loop)~ -4 kcal/mol if the density of the TIP3P water molecules capping the loop is close to that of bulk water, i.e., N(water) = 140 - 180 waters in a sphere of a 18 Å radius. Here we calculate ΔF(loop) for the more realistic case, where two templates are "cut" from the crystal structures, 2dfp.pdb (bound) and 2ace.pdb (free), where N(water) = 40 - 160; this requires adding a computationally more demanding (second) TI procedure. While the results for N(water) ≤ 140 are computationally sound, ΔF(loop) is always positive (18 ± 2 kcal/mol for N(water) = 140). These (disagreeing) results are attributed to the large average B-factor, 41.6 of 2dfp (23.4 Å(2) for 2ace). While this conformational uncertainty is an inherent difficulty, the (unstable) results for N(water) = 160 suggest that it might be alleviated by applying different (initial) structural optimizations to each template.