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 were 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. Therefore, the precise temporal information of detection of the photons is not available. 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 Cramer-Rao lower bound (CRLB), given by the inverse of the Fisher information matrix, on the variance of the parameter estimates. Even in cases that we have a small number of photons, the obtained results show that we are able to estimate the parameters of the molecule trajectory from simulated fluorescence microscopy images using our proposed method.

中文翻译：

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像素化对单分子轨迹参数估计的影响

单分子显微镜的出现彻底改变了生物学研究，为研究蛋白质分子的细胞间和细胞内运输过程提供了强大的工具，这是以前通过传统显微镜无法获得的。在实践中，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，获取的荧光显微镜图像包含每个像素中检测到的光子数量。因此，无法获得光子检测的精确时间信息。此外，我们只知道光子撞击探测器的像素区域，而不是光子检测的确切位置。这些挑战使得从像素化图像中分析单分子轨迹成为一个复杂的问题。在这里，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活细胞中分子运动的随机微分方程参数的最大似然估计。我们还根据参数估计的方差计算由 Fisher 信息矩阵的逆矩阵给出的 Cramer-Rao 下界 (CRLB)。即使在光子数量较少的情况下，获得的结果表明我们能够使用我们提出的方法从模拟荧光显微镜图像中估计分子轨迹的参数。