含测量噪声的单分子轨道中小时间序列样本引起的分子约束参数偏差的校正
Correcting for Bias of Molecular Confinement Parameters Induced by Small Time Series Sample Sizes in Single-Molecule Trajectories Containing Measurement Noise
摘要：
几个单分子研究的目的是可靠地提取参数表征分子限制或瞬态动力学捕获从实验观察。膜扩散研究中单粒子跟踪的开创性工作[Kusumi等人，生物物理学杂志，1993年]呼吁均方位移工具提取扩散率和其他参数量化程度的限制。最近，通过似然技术系统地处理多个噪声源（包括随机光子计数引起的噪声）的实际效用已在SPT界得到更广泛的实现。然而，有限的时间序列样本量引起的偏差并没有得到很大的关注。减轻有限采样引起的参数偏差对于任何旨在提高精度的科学努力都很重要，但偏差校正通常也是构建最佳参数估计值的重要步骤。在这篇文章中，演示了如何在基础数据显示布朗扩散并且观测值是用不可忽略的实验噪声测量的情况下（例如，由有限光子计数引起的噪声）。Tang和Chen [J. Econometrics，2009]的工作扩展到在存在测量噪声的情况下校正估计畜栏半径（SPT研究中通常用于量化限制的参数）的偏差。结果表明，所提出的方法是能够可靠地提取畜栏半径使用只有数百个离散采样的观察情况下，其他方法（包括MSD和贝叶斯技术）会遇到严重的困难。准确地统计表征瞬态限制的能力表明，在复杂的环境中量化限制和/或跳扩散的新技术。
英文摘要：
Several single-molecule studies aim to reliably extract parameters characterizing molecular confinement or transient kinetic trapping from experimental observations. Pioneering works from single particle tracking in membrane diffusion studies [Kusumi et al., Biophysical J., 1993] appealed to Mean Square Displacement tools for extracting diffusivity and other parameters quantifying the degree of confinement. More recently, the practical utility of systematically treating multiple noise sources (including noise induced by random photon counts) through likelihood techniques have been more broadly realized in the SPT community. However, bias induced by finite time series sample sizes has not received great attention. Mitigating parameter bias induced by finite sampling is important to any scientific endeavor aiming for high accuracy, but correcting for bias is also often an important step in the construction of optimal parameter estimates. In this article, it is demonstrated how a popular model of confinement can be corrected for finite sample bias in situations where the underlying data exhibits Brownian diffusion and observations are measured with non-negligible experimental noise (e.g., noise induced by finite photon counts). The work of Tang and Chen [J. Econometrics, 2009] is extended to correct for bias in the estimated corral radius (a parameter commonly used to quantify confinement in SPT studies) in the presence of measurement noise. It is shown that the approach presented is capable of reliably extracting the corral radius using only hundreds of discretely sampled observations in situations where other methods (including MSD and Bayesian techniques) would encounter serious difficulties. The ability to accurately statistically characterize transient confinement suggests new techniques for quantifying confined and/or hop diffusion in complex environments.
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