Motion blur filtering: A statistical approach for extracting confinement forces and diffusivity from a single blurred trajectory
Motion blur filtering: A statistical approach for extracting confinement forces and diffusivity from a single blurred trajectory
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DOI：
10.1103/physreve.93.053303
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发表时间：
2016-05-12
影响因子：
2.4
通讯作者：
Calderon, Christopher P.
中科院分区：
文献类型：
--
作者：
Calderon, Christopher P.
单粒子追踪（SPT）可以帮助理解各种复杂的时空过程。然而，量化单个活细胞轨迹的扩散性和约束力由于轨迹间和轨迹内动力学异质性、热波动和细胞中经历的基础分子时间相关的约束动力学固有的（实验上可解析的）统计时间依赖性而变得复杂。定位不确定性和运动模糊等实验伪影使问题变得更加复杂。后者是由标记分子在单帧曝光时间内在不同空间位置发射光子引起的。上述实验伪影在测量的 SPT 时间序列中引入了虚假时间相关性，从而掩盖了感兴趣的信息（例如，限制力和扩散率）。我们开发了一种最大似然估计（MLE）技术，可以解耦上述噪声源，并通过时间序列方法系统地处理时间相关性。这最终允许使用可靠的算法来提取受限或非受限环境中的扩散率和有效力。我们说明了我们的方法如何避免均方位移或自相关技术固有的复杂性。我们的算法修改了已建立的卡尔曼滤波器（不处理运动模糊伪影）以提供基于可能性的时间序列估计过程。结果扩展了 A. J. Berglund 的运动模糊模型 [Phys. Rev. E 82, 011917 (2010)] 处理受限动力学。该方法还可以系统地利用图像分析提供的（可能与时间相关的）定位不确定性估计（如果可用）。该技术在时域 MLE 框架内明确处理限制和运动模糊，使用精确似然（时域方法有助于分析非平稳信号）。我们的估计器被证明在广泛的曝光时间（5 至 100 ms）、扩散系数（1 x 10(-3) 至 1 mu m(2)/s）和限制宽度（100 nm 至 2 mu m）范围内保持一致。我们证明，忽略运动模糊或限制可能会严重影响研究人员感兴趣的动力学参数的估计。该技术还允许人们在没有“基本事实”的情况下根据测量的个体轨迹检查统计模型假设。可靠且一致地提取表现出受限和/或非平稳动态的轨迹中的运动参数的能力，而不会影响估计的曝光时间伪影，预计将有助于直接比较从不同实验或成像模式获得的轨迹。提供了 Python 实现（开源代码将在 GitHub 上维护；另请参阅本文的补充材料）。
Single particle tracking (SPT) can aid in understanding a variety of complex spatiotemporal processes. However, quantifying diffusivity and confinement forces from individual live cell trajectories is complicated by inter- and intratrajectory kinetic heterogeneity, thermal fluctuations, and (experimentally resolvable) statistical temporal dependence inherent to the underlying molecule's time correlated confined dynamics experienced in the cell. The problem is further complicated by experimental artifacts such as localization uncertainty and motion blur. The latter is caused by the tagged molecule emitting photons at different spatial positions during the exposure time of a single frame. The aforementioned experimental artifacts induce spurious time correlations in measured SPT time series that obscure the information of interest (e.g., confinement forces and diffusivity). We develop a maximum likelihood estimation (MLE) technique that decouples the above noise sources and systematically treats temporal correlation via time series methods. This ultimately permits a reliable algorithm for extracting diffusivity and effective forces in confined or unconfined environments. We illustrate how our approach avoids complications inherent to mean square displacement or autocorrelation techniques. Our algorithm modifies the established Kalman filter (which does not handle motion blur artifacts) to provide a likelihood based time series estimation procedure. The result extends A. J. Berglund's motion blur model [Phys. Rev. E 82, 011917 (2010)] to handle confined dynamics. The approach can also systematically utilize (possibly time dependent) localization uncertainty estimates afforded by image analysis if available. This technique, which explicitly treats confinement and motion blur within a time domain MLE framework, uses an exact likelihood (time domain methods facilitate analyzing nonstationary signals). Our estimator is demonstrated to be consistent over a wide range of exposure times (5 to 100 ms), diffusion coefficients (1 x 10(-3) to 1 mu m(2)/s), and confinement widths (100 nm to 2 mu m). We demonstrate that neglecting motion blur or confinement can substantially bias estimation of kinetic parameters of interest to researchers. The technique also permits one to check statistical model assumptions against measured individual trajectories without "ground truth." The ability to reliably and consistently extract motion parameters in trajectories exhibiting confined and/or non-stationary dynamics, without exposure time artifacts corrupting estimates, is expected to aid in directly comparing trajectories obtained from different experiments or imaging modalities. A Python implementation is provided (open-source code will be maintained on GitHub; see also the Supplemental Material with this paper).