Vahid Milad R, Hanzon Bernard, Ober Raimund J
Department of Biomedical EngineeringTexas A&M UniversityCollege StationTX77843USA.
Department of Biomedical Data ScienceStanford UniversityStanfordCA94305USA.
IEEE Trans Comput Imaging. 2020 Nov 23;7:98-113. doi: 10.1109/TCI.2020.3039951. eCollection 2021.
The advent of single molecule microscopy has revolutionized biological investigations by providing a powerful tool for the study of intercellular and intracellular trafficking processes of protein molecules which was not available before through conventional microscopy. In practice, pixelated detectors are used to acquire the images of fluorescently labeled objects moving in cellular environments. Then, the acquired fluorescence microscopy images contain the numbers of the photons detected in each pixel, during an exposure time interval. Moreover, instead of having the exact locations of detection of the photons, we only know the pixel areas in which the photons impact the detector. These challenges make the analysis of single molecule trajectories, from pixelated images, a complex problem. Here, we investigate the effect of pixelation on the parameter estimation of single molecule trajectories. In particular, we develop a stochastic framework to calculate the maximum likelihood estimates of the parameters of a stochastic differential equation that describes the motion of the molecule in living cells. We also calculate the Fisher information matrix for this parameter estimation problem. The analytical results are complicated through the fact that the observation process in a microscope prohibits the use of standard Kalman filter type approaches. The analytical framework presented here is illustrated with examples of low photon count scenarios for which we rely on Monte Carlo methods to compute the associated probability distributions.
单分子显微镜的出现为蛋白质分子的细胞间和细胞内运输过程研究提供了强大工具，彻底改变了生物学研究，而传统显微镜此前无法做到这一点。在实际操作中，像素化探测器用于获取在细胞环境中移动的荧光标记物体的图像。然后，所获取的荧光显微镜图像包含在曝光时间间隔内每个像素中检测到的光子数量。此外，我们并不知道光子的确切检测位置，只知道光子撞击探测器的像素区域。这些挑战使得从像素化图像分析单分子轨迹成为一个复杂问题。在此，我们研究像素化对单分子轨迹参数估计的影响。特别是，我们开发了一个随机框架来计算描述分子在活细胞中运动的随机微分方程参数的最大似然估计。我们还计算了此参数估计问题的费希尔信息矩阵。由于显微镜中的观测过程禁止使用标准卡尔曼滤波器类型的方法，分析结果变得复杂。这里给出的分析框架通过低光子计数场景的示例进行说明，对于这些示例，我们依靠蒙特卡罗方法来计算相关的概率分布。
