Richmond T J
J Mol Biol. 1984 Sep 5;178(1):63-89. doi: 10.1016/0022-2836(84)90231-6.
An analytical formula has been derived for the calculation of the solvent accessible surface area of a protein molecule or equivalently the surface area exterior to an arbitrary number of overlapping spheres. The directional derivative of this function with respect to atomic co-ordinates is provided to facilitate minimization procedures used with molecular docking algorithms and energy calculations. An analytical formula for the calculation of the volume enclosed within the accessible surface, the excluded volume, is also derived. Although the area function is not specific to the structures of proteins, the derivation was motivated by the need for a computationally feasible simulation of the hydrophobic effect in proteins. A computer program using the equations for area has been tested and has had limited application to the docking of protein alpha-helices. Possible relationships of the solvent excluded volume to hydrophobic interaction free energy and transfer free energy of solute molecules are derived from the statistical mechanics of solution.
已推导出一个解析公式，用于计算蛋白质分子的溶剂可及表面积，或者等效地计算任意数量重叠球体外部的表面积。提供了该函数相对于原子坐标的方向导数，以促进与分子对接算法和能量计算一起使用的最小化程序。还推导了一个用于计算可及表面内封闭体积（排除体积）的解析公式。尽管面积函数并非特定于蛋白质结构，但推导的动机是需要对蛋白质中的疏水效应进行计算上可行的模拟。一个使用面积方程的计算机程序已经经过测试，并在蛋白质α-螺旋对接方面有有限的应用。从溶液的统计力学中推导出溶剂排除体积与溶质分子的疏水相互作用自由能和转移自由能之间的可能关系。
