Department of Computer Science, Hunter College of the City University of New York, 695 Park Ave., New York, NY 10065, USA.
J Comput Chem. 2010 Dec;31(16):2889-99. doi: 10.1002/jcc.21584.
We present a general mathematical model that can be used to improve almost all fragment-based methods for ab initio calculation of total molecular energy. Fragment-based methods of computing total molecular energy mathematically decompose a molecule into smaller fragments, quantum-mechanically compute the energies of single and multiple fragments, and then combine the computed fragment energies in some particular way to compute the total molecular energy. Because the kernel energy method (KEM) is a fragment-based method that has been used with much success on many biological molecules, our model is presented in the context of the KEM in particular. In this generalized model, the total energy is not based on sums of all possible double-, triple-, and quadruple-kernel interactions, but on the interactions of precisely those combinations of kernels that are connected in the mathematical graph that represents the fragmented molecule. This makes it possible to estimate total molecular energy with high accuracy and no superfluous computation and greatly extends the utility of the KEM and other fragment-based methods. We demonstrate the practicality and effectiveness of our model by presenting how it has been used on the yeast initiator tRNA molecule, ytRN(i)(Met) (1YFG in the Protein Data Bank), with kernel computations using the Hartree-Fock equations with a limited basis of Gaussian STO-3G type.
我们提出了一个通用的数学模型，可用于改进几乎所有基于片段的从头计算总分子能量的方法。基于片段的计算总分子能量的方法从数学上把分子分解成较小的片段，量子力学地计算单个和多个片段的能量，然后以某种特定的方式组合计算得到的片段能量来计算总分子能量。由于核子能量法（KEM）是一种已经在许多生物分子上成功应用的基于片段的方法，因此我们的模型特别针对 KEM 进行了介绍。在这个广义模型中，总能量不是基于所有可能的双、三、四核子相互作用的总和，而是基于在表示碎片化分子的数学图中连接的核子的精确组合的相互作用。这使得以高精度和无多余计算来估计总分子能量成为可能，并极大地扩展了 KEM 和其他基于片段的方法的实用性。我们通过展示如何将其用于酵母起始 tRNA 分子 ytRN(i)(Met)（1YFG 在蛋白质数据库中）来证明我们模型的实用性和有效性，使用 Hartree-Fock 方程和有限的高斯 STO-3G 类型基进行核子计算。
