Department of Pharmacology, University of Texas Southwestern Medical Center at Dallas, Dallas, Texas 75390-9050, USA.
J Phys Chem B. 2011 Mar 31;115(12):3100-11. doi: 10.1021/jp1121382. Epub 2011 Mar 10.
In the companion paper, we presented a set of induced dipole interaction models using four types of screening functions, which include the Applequist (no screening), the Thole linear, the Thole exponential model, and the Thole Tinker-like (another form of exponential screening function) functions. In this work, we evaluate the performance of polarizability models using a large set of amino acid analog pairs in conformations that are frequently observed in protein structures as a benchmark. For each amino acid pair, we calculated quantum mechanical interaction energies at the MP2/aug-cc-pVTZ//MP2/6-311++G(d,p) level with the basis set superposition error (BSSE) correction and compared them with molecular mechanics results. Encouragingly, all polarizable models significantly outperform the additive F94 and F03 models (mimicking AMBER ff94/ff99 and ff03 force fields, respectively) in reproducing the BSSE-corrected quantum mechanical interaction energies. In particular, the root-mean-square errors (RMSEs) for three Thole models in Set A (where the 1-2 and 1-3 interactions are turned off and all 1-4 interactions are included) are 1.456, 1.417, and 1.406 kcal/mol for model AL (Thole Linear), model AE (Thole exponential), and model AT (Thole Tinker-like), respectively. In contrast, the RMSEs are 3.729 and 3.433 kcal/mol for F94 and F03 models, respectively. A similar trend was observed for the average unsigned errors (AUEs), which are 1.057, 1.025, 1.011, 2.219, and 2.070 kcal/mol for AL, AE, AT, F94/ff99, and F03, respectively. Analyses based on the trend line slopes indicate that the two fixed charge models substantially underestimate the relative strengths of noncharge-charge interactions by 24 (F03) and 35% (F94), respectively, whereas the four polarizable models overestimate the relative strengths by 5 (AT), 3 (AL, AE), and 13% (AA), respectively. Agreement was further improved by adjusting the van der Waals parameters. Judging from the notably improved accuracy in comparison with the fixed charge models, the polarizable models are expected to form the foundation for the development of high quality polarizable force fields for protein and nucleic acid simulations.
在配套论文中，我们提出了一组使用四种屏蔽函数的诱导偶极相互作用模型，包括 Applequist（无屏蔽）、Thole 线性、Thole 指数模型和 Thole Tinker-like（另一种指数屏蔽函数）函数。在这项工作中，我们使用一组在蛋白质结构中经常观察到的构象中的氨基酸类似物对作为基准，评估极化率模型的性能。对于每个氨基酸对，我们在 MP2/aug-cc-pVTZ//MP2/6-311++G(d,p)水平上使用基组叠加误差 (BSSE) 校正计算量子力学相互作用能，并将其与分子力学结果进行比较。令人鼓舞的是，所有极化率模型在重现 BSSE 校正的量子力学相互作用能方面都明显优于加性 F94 和 F03 模型（分别模拟 AMBER ff94/ff99 和 ff03 力场）。特别是，在 Set A 中，三个 Thole 模型的均方根误差 (RMSE) 对于关闭 1-2 和 1-3 相互作用且包含所有 1-4 相互作用的模型 AL（Thole Linear）、AE（Thole Exponential）和 AT（Thole Tinker-like）分别为 1.456、1.417 和 1.406 kcal/mol。相比之下，F94 和 F03 模型的 RMSE 分别为 3.729 和 3.433 kcal/mol。对于平均未加权误差 (AUE)，也观察到类似的趋势，分别为 AL、AE、AT、F94/ff99 和 F03 的 1.057、1.025、1.011、2.219 和 2.070 kcal/mol。基于趋势线斜率的分析表明，这两个固定电荷模型分别低估了非电荷-电荷相互作用的相对强度 24%（F03）和 35%（F94），而四个极化率模型则分别高估了相对强度 5%（AT）、3%（AL、AE）和 13%（AA）。通过调整范德华参数，进一步提高了一致性。与固定电荷模型相比，这些模型的准确性有了明显提高，预计将为蛋白质和核酸模拟开发高质量的极化力场奠定基础。
