The configurational entropy of solute molecules is a crucially important quantity to study various biophysical processes. Consequently, it is necessary to establish an efficient quantitative computational method to calculate configurational entropy as accurately as possible. In the present paper, we investigate the quantitative performance of the quasi-harmonic and related computational methods, including widely used methods implemented in popular molecular dynamics (MD) software packages, compared with the Clausius method, which is capable of accurately computing the change of the configurational entropy upon temperature change. Notably, we focused on the choice of the coordinate systems (i.e., internal or Cartesian coordinates). The Boltzmann-quasi-harmonic (BQH) method using internal coordinates outperformed all the six methods examined here. The introduction of improper torsions in the BQH method improves its performance, and anharmonicity of proper torsions in proteins is identified to be the origin of the superior performance of the BQH method. In contrast, widely used methods implemented in MD packages show rather poor performance. In addition, the enhanced sampling of replica-exchange MD simulations was found to be efficient for the convergent behavior of entropy calculations. Also in folding/unfolding transitions of a small protein, Chignolin, the BQH method was reasonably accurate. However, the independent term without the correlation term in the BQH method was most accurate for the folding entropy among the methods considered in this study, because the QH approximation of the correlation term in the BQH method was no longer valid for the divergent unfolded structures.
A new method is developed for calculating hydration free energies (HFEs) of polyatomic solutes. The solute insertion is decomposed into the creation of a cavity in water matching the geometric characteristics of the solute at the atomic level (process 1) and the incorporation of solute-water van der Waals and electrostatic interactions (process 2). The angle-dependent integral equation theory combined with our morphometric approach and the three-dimensional interaction site model theory are applied to processes 1 and 2, respectively. Neither a stage of training nor parameterization is necessitated. For solutes with various sizes including proteins, the HFEs calculated by the new method are compared to those obtained using a molecular dynamics simulation based on solution theory in energy representation (the ER method developed by Matubayasi and co-workers), currently the most reliable tool. The agreement is very good especially for proteins. The new method is characterized by the following: The calculation can rapidly be finished; a solute possessing a significantly large total charge can be handled without difficulty; and since it yields not only the HFE but also its many physically insightful energetic and entropic components, it is best suited to the elucidation of mechanisms of diverse phenomena such as the receptor-ligand binding, different types of molecular recognition, and protein folding, denaturation, and association.
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