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WIREs Comput Mol Sci
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Direct methods for computing single‐molecule entropies from molecular simulations

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Assessing the actual role of entropic forces in controlling both the stability and activity of flexible molecules and macromolecules is a theoretical challenge that is gradually gaining more attention. The continuous improvements in computational algorithms and in hardware technologies are greatly expanding the sampling capability of molecular simulations, thereby making a direct positive impact on the feasibility and reliability of entropy predictions. However, more sophisticated theoretical approaches are also required in order to make substantial progress in the type and accuracy of entropy calculations. Focusing on the evaluation of the configurational entropy of single molecules, we highlight recent advances in different methodologies including Gaussian parametric approaches, nonparametric methods and normal mode calculations. For the nonparametric methodologies, we analyze more specifically the importance of correlation effects, the various formulations of the expansion approaches, the combination of nonparametric estimations of conformational entropy with normal mode calculations, the convenience of including bias corrections for mitigating the impact of insufficient sampling and, finally, their close relationship with the experimental measures of conformational motion. The overall consideration of these and other aspects shows that addition of the direct entropy methods to the standard palette of tools used in molecular modeling for data analysis and property estimation, will increase both the level of detail of the computer simulations and our understanding of molecular functions. WIREs Comput Mol Sci 2015, 5:1–26. doi: 10.1002/wcms.1195

Schematic representation of a potential energy surface as a set of disjoint harmonic wells associated with different conformers generated by molecular simulation methods. Each conformer is associated with the corresponding energy minimum and the nearby configurations located in the same basin.
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Comparison between the MLA and CC‐MLA conformational entropies for the 2.0 µs trajectory of the GPQEIAGQ peptide at different cutoff values. The minimum value of the CC‐MLA entropy (38.0 cal mol−1 K−1) is the best entropy estimation.
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Convergence plots of the conformational entropy of the GPQEIAGQ peptide (with 32 rotatable bonds) as obtained with the AMIE method at various orders with a 8.0 Å cutoff. The total Sconform represents a significant fraction (>10%) of the absolute entropy. Averaging the S(1) and S(2) values in the 1.0–2.0 µs interval gives 46.1 ± 0.1 and 38.7 ± 0.1 cal mol−1 K−1. Higher‐order approximations show worse convergence properties.
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GB‐based RRHO entropy calculated for 10,000 snapshots extracted at 200 ps intervals from the 2.0 µs MD simulation of the GPQEIAGQ peptide. The average values of the entropy components and their statistical uncertainties (standard error in parentheses and block‐average error in squared brackets) are also indicated. Note that Svib is clearly below the quasi‐harmonic/Schlitter Sconf estimations in Figure .
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Combining the RRHO and conformational entropy estimations.
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Convergence plots of the temperature‐weighted entropy for the GPQEIAGQ peptide as computed using ACCENT‐MM showing the first‐order and second‐order approximations. A total of 2 × 106 simulation frames were considered in the calculations. Note that the adoption of the BAT internal coordinates can result in negative values when computing the classical Sconf of single molecules.
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Convergence plots of the absolute Sconf entropy of a flexible peptide molecule (GPQEIAGQ) as computed with the Schlitter and quasi‐harmonic methods. Averaging the Sconf values in the 1.0–2.0 µs interval gives 818.1 ± 1.1 (Schlitter) and 788.9 ± 1.2 (QH) cal mol−1 K−1. The AMBER03 force field was used to represent the peptide atoms. The solute was immersed within an octahedral box of TIP3P waters and a 2.0 µs simulation was performed under NVT conditions (300 K). Further details of the simulation settings are identical to those described elsewhere (Ref ). The insets show the superposition of the most populated representative structures derived from clustering analyses in wireframe representation and the time evolution of the radius of gyration.
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Diagrammatic classification of the configurational entropy methods.
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Structure and Mechanism > Molecular Structures
Structure and Mechanism > Computational Biochemistry and Biophysics
Molecular and Statistical Mechanics > Molecular Dynamics and Monte-Carlo Methods

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