Abstract
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.
Highlights
In recent years we have developed a new simulation method for calculating the absolute entropy, S and the absolute Helmholtz free energy, F called the hypothetical scanning Monte Carlo (HSMC), where molecular dynamics (MD) is used [1,2,3,4,5,6,7]
Later the implicit solvent was replaced by explicit solvent, i.e., the α-amylase loop was capped with 70 TIP3P [37] water molecules, which were moved in the MD
Starting from each optimized structure, an 1 ns MD trajectory was generated at 300 K, where the initial 0.5 ns part was used for equilibration and a sample of 1,000 structures was generated from the last part of the trajectory by retaining a structure to a sample every 0.5 ps
Summary
In recent years we have developed a new simulation method for calculating the absolute entropy, S and the absolute Helmholtz free energy, F called the hypothetical scanning Monte Carlo (HSMC) It would be more realistic to carry out the calculations with respect to two templates, which are cut separately from the free and bound x-ray structures This would require defining an additional TI procedure where the water-template interactions are gradually eliminated. The loop of AChE is treated here again, where the simulations are carried out with respect to two different templates which are cut from the free and bound crystal structures; this requires applying the (relatively) elaborate HSMD-TI procedure mentioned above. ΔFloop is calculated from relatively short trajectories (0.5 ns) where the loop remains in its original microstates (bound and free) In this context it should be pointed out that determining the exact limits of a microstate in conformational space is practically impossible and it is commonly defined by an MC or MD sample initiated from a microstate’s structure. That this is not an inherent limitation as in our present application of HSMD-TI to the avidin-biotin complex [54] part of the template is moved in the MD simulation since the size of the fluctuations remains under control
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