Calderon Christopher P
Numerica Corporation, 4850 Hahns Peak Drive, Loveland, Colorado 80538, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Jul;88(1):012707. doi: 10.1103/PhysRevE.88.012707. Epub 2013 Jul 9.
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 (SPT) in membrane diffusion studies [Kusumi et al., Biophys. J. 65, 2021 (1993)] appealed to mean square displacement (MSD) 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 has been more broadly realized in the SPT community. However, bias induced by finite-time-series sample sizes (unavoidable in practice) 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 exhibit 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 149, 65 (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 additional techniques for quantifying confined and/or hop diffusion in complex environments.
多项单分子研究旨在从实验观测中可靠地提取表征分子限制或瞬态动力学捕获的参数。膜扩散研究中单粒子追踪（SPT）的开创性工作[Kusumi等人，《生物物理杂志》65, 2021（1993）]诉诸均方位移（MSD）工具来提取扩散系数和其他量化限制程度的参数。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）的实际效用在SPT领域得到了更广泛的认识。然而，有限时间序列样本量引起的偏差（在实践中不可避免）尚未受到足够关注。减轻有限采样引起的参数偏差对于任何追求高精度的科学研究都很重要，而且校正偏差通常也是构建最优参数估计的重要一步。在本文中，展示了在基础数据呈现布朗扩散且观测值带有不可忽略的实验噪声（例如有限光子计数引起的噪声）的情况下，如何对一种流行的限制模型进行有限样本偏差校正。Tang和Chen的工作[《计量经济学杂志》149, 65（2009）]被扩展，以校正存在测量噪声时估计的“围栏半径”（SPT研究中常用于量化限制的一个参数）中的偏差。结果表明，所提出的方法能够在其他方法（包括MSD和贝叶斯技术）会遇到严重困难的情况下，仅使用数百个离散采样观测值就可靠地提取围栏半径。准确地从统计上表征瞬态限制的能力为量化复杂环境中的限制和/或跳跃扩散提出了额外的技术。
