Carlsson Jens, Aqvist Johan
Department of Cell and Molecular Biology, Uppsala University, Biomedical Center, Box 596, Uppsala, Sweden.
Phys Chem Chem Phys. 2006 Dec 14;8(46):5385-95. doi: 10.1039/b608486a. Epub 2006 Sep 8.
The translational, rotational and conformational (vibrational) entropy contributions to ligand-receptor binding free energies are analyzed within the standard formulation of statistical thermodynamics. It is shown that the partitioning of the binding entropy into different components is to some extent arbitrary, but an appropriate method to calculate both translational and rotational entropy contributions to noncovalent association is by estimating the configurational volumes of the ligand in the bound and free states. Different approaches to calculating solute entropies using free energy perturbation calculations, configurational volumes based on root-mean-square fluctuations and covariance matrix based quasiharmonic analysis are illustrated for some simple molecular systems. Numerical examples for the different contributions demonstrate that theoretically derived results are well reproduced by the approximations. Calculation of solvent entropies, either using total potential energy averages or van't Hoff plots, are carried out for the case of ion solvation in water. Although convergence problems will persist for large and complex simulation systems, good agreement with experiment is obtained here for relative and absolute ion hydration entropies. We also outline how solvent and solute entropic contributions are taken into account in empirical binding free energy calculations using the linear interaction energy method. In particular it is shown that empirical scaling of the nonpolar intermolecular ligand interaction energy effectively takes into account size dependent contributions to the binding free energy.
在统计热力学的标准公式框架内，分析了配体 - 受体结合自由能的平动、转动和构象（振动）熵贡献。结果表明，将结合熵划分为不同组分在一定程度上是任意的，但计算非共价缔合的平动和转动熵贡献的一种合适方法是估计配体在结合态和游离态的构型体积。针对一些简单分子体系，阐述了使用自由能微扰计算、基于均方根涨落的构型体积以及基于协方差矩阵的准谐波分析来计算溶质熵的不同方法。不同贡献的数值示例表明，理论推导结果能被这些近似方法很好地重现。对于水中离子溶剂化的情况，采用总势能平均值或范特霍夫图来计算溶剂熵。尽管对于大型复杂模拟系统，收敛问题仍然存在，但在此处对于相对和绝对离子水合熵，与实验结果取得了良好的一致性。我们还概述了在使用线性相互作用能方法进行经验性结合自由能计算时，如何考虑溶剂和溶质的熵贡献。特别指出的是，非极性分子间配体相互作用能的经验标度有效地考虑了对结合自由能的尺寸依赖性贡献。
