Oberhofer Harald, Dellago Christoph
Department of Chemistry, University of Cambridge, Cambridge CB2 1EW, United Kingdom.
J Comput Chem. 2009 Aug;30(11):1726-36. doi: 10.1002/jcc.21290.
Hummer and Szabo recently presented a method based on the Jarzynski equality to calculate Helmholtz free energy profiles from nonequilibrium pathways obtained in simulations or experiments. In their approach, the free energy is reconstructed from weighted histograms. Here, we give a systematic derivation of the optimum weight, which--in principle--minimizes the statistical errors in the resulting free energy profiles. We then compare this optimum weight to Hummer and Szabo's original weight and several others by means of simulations of two one-dimensional models, for which the free energy profile is analytically known. In addition, we carry out simulations of a deca-alanine molecule pulled by a harmonic trap to assess the efficiency of the weights in a more realistic situation. In all cases, the weight of Hummer and Szabo performs very well leading to errors approximately equal to those obtained with a simplified version of the optimum weight. The performance of the optimum weight itself is unsatisfying due to statistical errors arising in the weight calculation.
赫默尔和萨博最近提出了一种基于雅津斯基等式的方法，用于从模拟或实验中获得的非平衡路径计算亥姆霍兹自由能分布。在他们的方法中，自由能是从加权直方图中重建的。在这里，我们给出了最优权重的系统推导，原则上，该权重能使所得自由能分布中的统计误差最小化。然后，我们通过对两个一维模型进行模拟，将这个最优权重与赫默尔和萨博的原始权重以及其他几个权重进行比较，这两个一维模型的自由能分布是可以通过解析得到的。此外，我们对由谐波阱拉动的十肽丙氨酸分子进行模拟，以评估这些权重在更实际情况下的效率。在所有情况下，赫默尔和萨博的权重表现非常好，导致的误差与使用简化版最优权重所获得的误差大致相等。由于权重计算中出现的统计误差，最优权重本身的性能并不令人满意。
