Shirts Michael R, Chodera John D
Department of Chemical Engineering, University of Virginia, Charlottesville, Virginia 22904, USA.
J Chem Phys. 2008 Sep 28;129(12):124105. doi: 10.1063/1.2978177.
We present a new estimator for computing free energy differences and thermodynamic expectations as well as their uncertainties from samples obtained from multiple equilibrium states via either simulation or experiment. The estimator, which we call the multistate Bennett acceptance ratio estimator (MBAR) because it reduces to the Bennett acceptance ratio estimator (BAR) when only two states are considered, has significant advantages over multiple histogram reweighting methods for combining data from multiple states. It does not require the sampled energy range to be discretized to produce histograms, eliminating bias due to energy binning and significantly reducing the time complexity of computing a solution to the estimating equations in many cases. Additionally, an estimate of the statistical uncertainty is provided for all estimated quantities. In the large sample limit, MBAR is unbiased and has the lowest variance of any known estimator for making use of equilibrium data collected from multiple states. We illustrate this method by producing a highly precise estimate of the potential of mean force for a DNA hairpin system, combining data from multiple optical tweezer measurements under constant force bias.
我们提出了一种新的估计器，用于从通过模拟或实验从多个平衡态获得的样本中计算自由能差、热力学期望值及其不确定性。我们将此估计器称为多态贝内特接受率估计器（MBAR），因为当仅考虑两个状态时，它简化为贝内特接受率估计器（BAR）。与用于组合多个状态数据的多重直方图重加权方法相比，MBAR具有显著优势。它不需要对采样的能量范围进行离散化以生成直方图，消除了由于能量分箱引起的偏差，并在许多情况下显著降低了计算估计方程解的时间复杂度。此外，还为所有估计量提供了统计不确定性的估计。在大样本极限下，MBAR是无偏的，并且在利用从多个状态收集的平衡数据的任何已知估计器中具有最低的方差。我们通过对DNA发夹系统的平均力势进行高精度估计来说明此方法，该估计结合了在恒定力偏置下的多个光镊测量数据。
