Department of Physics, Koç University, Istanbul, Turkey.
Microsc Microanal. 2012 Aug;18(4):781-92. doi: 10.1017/S1431927612000451.
Trajectories of individual molecules moving within complex environments such as cell cytoplasm and membranes or semiflexible polymer networks provide invaluable information on the organization and dynamics of these systems. However, when such trajectories are obtained from a sequence of microscopy images, they can be distorted due to the fact that the tracked molecule exhibits appreciable directed motion during the single-frame acquisition. We propose a new model of image formation for mobile molecules that takes the linear in-frame motion into account and develop an algorithm based on the maximum likelihood approach for retrieving the position and velocity of the molecules from single-frame data. The position and velocity information obtained from individual frames are further fed into a Kalman filter for interframe tracking of molecules that allows prediction of the trajectory of the molecule and further improves the precision of the position and velocity estimates. We evaluate the performance of our algorithm by calculations of the Cramer-Rao Lower Bound, simulations, and model experiments with a piezo-stage. We demonstrate tracking of molecules moving as fast as 7 pixels/frame (12.6 μm/s) within a mean error of 0.42 pixel (37.43 nm).
在细胞细胞质和膜或半刚性聚合物网络等复杂环境中，个体分子的轨迹提供了有关这些系统的组织和动力学的宝贵信息。然而，当从一系列显微镜图像中获得这些轨迹时，由于跟踪分子在单个帧采集期间表现出可观的定向运动，因此它们可能会失真。我们提出了一种新的用于移动分子的图像形成模型，该模型考虑了线性帧内运动，并基于最大似然方法开发了一种算法，用于从单帧数据中恢复分子的位置和速度。从单个帧获得的位置和速度信息进一步馈送到用于分子帧间跟踪的卡尔曼滤波器中，该滤波器允许预测分子的轨迹，并进一步提高位置和速度估计的精度。我们通过计算克拉美罗下限、模拟和带有压电台的模型实验来评估我们算法的性能。我们演示了对移动速度高达 7 像素/帧（12.6 μm/s）的分子的跟踪，平均误差为 0.42 像素（37.43nm）。
