Optimal estimation of diffusion coefficients from single-particle trajectories
Optimal estimation of diffusion coefficients from single-particle trajectories
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DOI：
10.1103/physreve.89.022726
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发表时间：
2014-02-28
影响因子：
2.4
通讯作者：
Flyvbjerg, Henrik
中科院分区：
文献类型：
--
作者：
Vestergaard, Christian L.;Blainey, Paul C.;Flyvbjerg, Henrik
如何从单次延时记录的粒子轨迹中最佳地确定扩散粒子的扩散系数？我们用一个明确的、无偏的且实际上最优的基于协方差的估计器（CVE）来回答这个问题。该估计器是无回归的，并且远远优于基于测量的均方位移的常用方法。在实验相关的参数范围内，它也优于分析上难以处理且计算上要求更高的最大似然估计器（MLE）。对于柔性且波动的基材上的扩散情况，CVE 会因基材运动而产生偏差。然而，考虑到一些较长的时间序列和处于一定张力下的基底，扩展的 MLE 可以将基底上的粒子扩散与实验室框架中的基底运动分开。这提供了基准，可以消除 CVE 中底物波动引起的偏差。由此产生的无偏 CVE 对于波动基质上的短时间序列也是最佳的。我们将我们的估计器应用于在流动拉伸 DNA（一种波动底物）上扩散的人 8-氧代鸟嘌呤 DNA 甘醇酶蛋白，并发现如果不考虑底物波动，则扩散系数会被严重高估。
How does one optimally determine the diffusion coefficient of a diffusing particle from a single-time-lapse recorded trajectory of the particle? We answer this question with an explicit, unbiased, and practically optimal covariance-based estimator (CVE). This estimator is regression-free and is far superior to commonly used methods based on measured mean squared displacements. In experimentally relevant parameter ranges, it also outperforms the analytically intractable and computationally more demanding maximum likelihood estimator (MLE). For the case of diffusion on a flexible and fluctuating substrate, the CVE is biased by substrate motion. However, given some long time series and a substrate under some tension, an extended MLE can separate particle diffusion on the substrate from substrate motion in the laboratory frame. This provides benchmarks that allow removal of bias caused by substrate fluctuations in CVE. The resulting unbiased CVE is optimal also for short time series on a fluctuating substrate. We have applied our estimators to human 8-oxoguanine DNA glycolase proteins diffusing on flow-stretched DNA, a fluctuating substrate, and found that diffusion coefficients are severely overestimated if substrate fluctuations are not accounted for.