Vorobjev Y N, Almagro J C, Hermans J
Department of Biochemistry and Biophysics, School of Medicine, University of North Carolina, Chapel Hill 27599-7260, USA.
Proteins. 1998 Sep 1;32(4):399-413.
A new method for calculating the total conformational free energy of proteins in water solvent is presented. The method consists of a relatively brief simulation by molecular dynamics with explicit solvent (ES) molecules to produce a set of microstates of the macroscopic conformation. Conformational energy and entropy are obtained from the simulation, the latter in the quasi-harmonic approximation by analysis of the covariance matrix. The implicit solvent (IS) dielectric continuum model is used to calculate the average solvation free energy as the sum of the free energies of creating the solute-size hydrophobic cavity, of the van der Waals solute-solvent interactions, and of the polarization of water solvent by the solute's charges. The reliability of the solvation free energy depends on a number of factors: the details of arrangement of the protein's charges, especially those near the surface; the definition of the molecular surface; and the method chosen for solving the Poisson equation. Molecular dynamics simulation in explicit solvent relaxes the protein's conformation and allows polar surface groups to assume conformations compatible with interaction with solvent, while averaging of internal energy and solvation free energy tend to enhance the precision. Two recently developed methods--SIMS, for calculation of a smooth invariant molecular surface, and FAMBE, for solution of the Poisson equation via a fast adaptive multigrid boundary element--have been employed. The SIMS and FAMBE programs scale linearly with the number of atoms. SIMS is superior to Connolly's MS (molecular surface) program: it is faster, more accurate, and more stable, and it smooths singularities of the molecular surface. Solvation free energies calculated with these two programs do not depend on molecular position or orientation and are stable along a molecular dynamics trajectory. We have applied this method to calculate the conformational free energy of native and intentionally misfolded globular conformations of proteins (the EMBL set of deliberately misfolded proteins) and have obtained good discrimination in favor of the native conformations in all instances.
本文提出了一种计算蛋白质在水溶剂中总构象自由能的新方法。该方法包括通过含显式溶剂（ES）分子的分子动力学进行相对简短的模拟，以生成宏观构象的一组微观状态。从模拟中获得构象能量和熵，后者通过协方差矩阵分析在准谐近似下得到。隐式溶剂（IS）介电连续介质模型用于计算平均溶剂化自由能，它是创建溶质尺寸疏水腔的自由能、范德华溶质 - 溶剂相互作用的自由能以及溶质电荷对水溶剂极化的自由能之和。溶剂化自由能的可靠性取决于许多因素：蛋白质电荷的排列细节，尤其是靠近表面的电荷；分子表面的定义；以及求解泊松方程所选择的方法。在显式溶剂中的分子动力学模拟使蛋白质构象松弛，并允许极性表面基团采取与溶剂相互作用相容的构象，而内能和溶剂化自由能的平均化倾向于提高精度。采用了两种最近开发的方法——用于计算平滑不变分子表面的SIMS和通过快速自适应多网格边界元求解泊松方程的FAMBE。SIMS和FAMBE程序与原子数呈线性比例关系。SIMS优于康诺利的MS（分子表面）程序：它更快、更准确、更稳定，并且能平滑分子表面的奇点。用这两个程序计算的溶剂化自由能不依赖于分子位置或取向，并且在分子动力学轨迹上是稳定的。我们已应用此方法计算蛋白质天然和故意错误折叠的球状构象（故意错误折叠蛋白质的EMBL数据集）的构象自由能，并在所有情况下都获得了有利于天然构象的良好区分。
