Wenchao Li, Shuo Li, Timothy C. Brown, Qiang Sun, Xuezhi Wang, Vladislav V. Yakovlev, Allison Kealy, Bill Moran, Andrew D. Greentree
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引用次数: 0
摘要
荧光显微镜对了解生物功能具有重要意义。然而,大多数荧光实验只是定性的,因为荧光粒子的绝对数量往往不能确定。此外,传统的测量荧光强度的方法不能区分两个或多个在同一光谱窗口中被激发和发射的荧光团,因为只能获得光谱窗口中的总强度。在这里,我们表明,通过使用光子数解析实验,我们能够确定许多不同物种的发射器数量及其发射概率,所有这些物种都具有相同的测量光谱特征。我们通过显示每个物种的发射器数量和从该物种收集光子的概率来说明我们的想法,对于一个,两个和三个其他无法分辨的荧光团。提出了一种卷积二项模型来表示多物种发射的光子计数。然后,利用期望最大化(EM)算法将测量到的光子数与期望卷积二项分布函数匹配。在应用EM算法时,为了解决陷入次优解的问题,引入矩量法对EM算法进行初始猜测。此外,还推导了相应的cram r - rao下界,并与仿真结果进行了比较。
Estimation of the number of single-photon emitters for multiple fluorophores with the same spectral signature
Fluorescence microscopy is of vital importance for understanding biological function. However, most fluorescence experiments are only qualitative inasmuch as the absolute number of fluorescent particles can often not be determined. Additionally, conventional approaches to measuring fluorescence intensity cannot distinguish between two or more fluorophores that are excited and emit in the same spectral window, as only the total intensity in a spectral window can be obtained. Here we show that, by using photon number resolving experiments, we are able to determine the number of emitters and their probability of emission for a number of different species, all with the same measured spectral signature. We illustrate our ideas by showing the determination of the number of emitters per species and the probability of photon collection from that species, for one, two and three otherwise unresolvable fluorophores. The convolution binomial model is presented to represent the counted photons emitted by multiple species. Then, the expectation-maximization (EM) algorithm is used to match the measured photon counts to the expected convolution binomial distribution function. In applying the EM algorithm, to leverage the problem of being trapped in a sub-optimal solution, the moment method is introduced to yield an initial guess for the EM algorithm. Additionally, the associated Cramér–Rao lower bound is derived and compared with the simulation results.