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Entropy 2010, 12(8), 1946-1974; doi:10.3390/e12081946

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

Department of Computational and Systems Biology, University of Pittsburgh School of Medicine, 3059 BST3, Pittsburgh, PA 15260, USA
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Received: 12 June 2010 / Revised: 2 August 2010 / Accepted: 17 August 2010 / Published: 25 August 2010
(This article belongs to the Special Issue Configurational Entropy)
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Abstract

A mobile loop changes its conformation from “open” (free enzyme) to “closed” upon ligand binding. The difference in the Helmholtz free energy, ΔFloop between these states sheds light on the mechanism of binding. With our “hypothetical scanning molecular dynamics” (HSMD-TI) method ΔFloop = FfreeFbound where Ffree and Fbound 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, ΔFloop~ −4 kcal/mol if the density of the TIP3P water molecules capping the loop is close to that of bulk water, i.e., Nwater = 140 − 180 waters in a sphere of a 18 Å radius. Here we calculate ΔFloop for the more realistic case, where two templates are “cut” from the crystal structures, 2dfp.pdb (bound) and 2ace.pdb (free), where Nwater = 40 − 160; this requires adding a computationally more demanding (second) TI procedure. While the results for Nwater ≤ 140 are computationally sound, ΔFloop is always positive (18 ± 2 kcal/mol for Nwater = 140). These (disagreeing) results are attributed to the large average B-factor, 41.6 of 2dfp (23.4 Å2 for 2ace). While this conformational uncertainty is an inherent difficulty, the (unstable) results for Nwater = 160 suggest that it might be alleviated by applying different (initial) structural optimizations to each template.
Keywords: absolute entropy; free energy; mobile loop; ligand binding absolute entropy; free energy; mobile loop; ligand binding
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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MDPI and ACS Style

Mihailescu, M.; Meirovitch, H. Entropy and Free Energy of a Mobile Loop Based on the Crystal Structures of the Free and Bound Proteins. Entropy 2010, 12, 1946-1974.

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