Yu Ning, Yennawar Hemant P, Merz Kenneth M
Department of Chemistry, The Pennsylvania State University, 104 Chemistry Research Building, University Park, Pennsylvania 16802, USA.
Acta Crystallogr D Biol Crystallogr. 2005 Mar;61(Pt 3):322-32. doi: 10.1107/S0907444904033669. Epub 2005 Feb 24.
A novel method is proposed in which combined restraints derived from linear-scaling semiempirical quantum-mechanical (QM) calculations and X-ray diffraction data are combined to refine crystal structures of proteins. Its performance has been tested on a small protein molecule, bovine pancreatic trypsin inhibitor (BPTI). The refinement involves minimization of the sum of a geometric energy function and an X-ray target function based on either the least-squares residual or the maximum-likelihood formalism. For comparison, similar refinement runs have also been performed using energy restraints derived from the force field available in the Crystallography & NMR System (CNS) program. The QM refinements were carried out with weights that were varied by several orders of magnitude and the optimal weights were identified by observing the trend in the final free R values, QM heats of formation and coordinate root-mean-square deviations (r.m.s.d.s) from the crystal structure. It is found that the QM weights are typically smaller but generally on the same scale as the molecular-mechanics (MM) weights for the respective X-ray target functions. The crystallographic R, free R, real-space R values and correlation coefficients based on the structures refined with the energy restraints derived from our QM calculations and Engh and Huber parameters are comparable, suggesting that the QM restraints are capable of maintaining reasonable stereochemistry to a similar degree as the force-field parameters. A detailed inspection of the structures refined with the QM and MM energy restraints reveals that one of the common differences between them and the crystal structure is that the strained bond angles in the crystal structure are corrected after energetically restrained refinements. Systematic differences in certain bond lengths between the QM-refined structures and the statistical averages of experimental structures have also been observed and discussed.
本文提出了一种新方法，即将线性标度半经验量子力学（QM）计算得出的组合约束与X射线衍射数据相结合，用于优化蛋白质的晶体结构。该方法已在一种小蛋白质分子——牛胰蛋白酶抑制剂（BPTI）上进行了测试。优化过程涉及基于最小二乘残差或最大似然形式，使几何能量函数和X射线目标函数之和最小化。为作比较，还使用了晶体学与核磁共振系统（CNS）程序中可用力场得出的能量约束进行了类似的优化运行。QM优化过程中权重变化了几个数量级，并通过观察最终自由R值、QM生成热以及与晶体结构的坐标均方根偏差（r.m.s.d.）趋势来确定最佳权重。结果发现，对于各自的X射线目标函数，QM权重通常较小，但与分子力学（MM）权重一般处于相同量级。基于用我们的QM计算得出的能量约束和Engh与Huber参数优化的结构所得到的晶体学R值、自由R值、实空间R值和相关系数具有可比性，这表明QM约束能够与力场参数一样在相似程度上维持合理的立体化学结构。对用QM和MM能量约束优化的结构进行详细检查发现，它们与晶体结构之间的一个常见差异是，在能量约束优化后，晶体结构中受应变的键角得到了校正。还观察并讨论了QM优化结构与实验结构统计平均值之间在某些键长上的系统差异。
