The photon counting histogram in fluorescence fluctuation spectroscopy
The photon counting histogram in fluorescence fluctuation spectroscopy
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DOI：
10.1016/s0006-3495(99)76912-2
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发表时间：
1999-07-01
影响因子：
3.4
通讯作者：
Gratton, E
中科院分区：
文献类型：
--
作者：
Chen, Y;Müller, JD;Gratton, E
荧光相关光谱（FCS）通常用于从荧光信号的自相关函数获得关于小体积中的荧光颗粒的数量和扩散系数的信息。在这里，我们证明了光子计数直方图（PCH）分析构成了一种新的工具，用于从荧光波动数据中提取数量，即，测量的每个分子的光子计数和观察体积内的平均分子数。荧光涨落实验的光子计数直方图，其中很少分子存在于激发体积中，表现出超泊松行为。与泊松分布相比，PCH的额外加宽是由于荧光强度波动。对于扩散粒子，这些强度波动是由不均匀的激发分布和在bar上的观察体积（N）中的粒子数量的波动引起的。通过Mandel公式给出了探测光子数与到达探测器的荧光强度之间的定量关系。基于该方程，考虑到双光子激发体积中的荧光强度分布，推导出了PCH随激发体积中分子数变化的理论表达式。对于单个分子种类，两个参数足以完全表征直方图，即观察体积内的分子的平均数量和每个采样时间内每个分子的检测到的光子计数。另一方面，多个分子种类的PCH是通过将每个种类的光子计数分布与其他种类的光子计数分布连续卷积而生成的。激发轮廓后的光子计数统计的两个相关的点扩散函数（PSF），三维高斯PSF常规采用共焦检测和高斯-洛伦兹PSF的平方双光子激发的影响，明确处理。用双光子激发源测得的光子计数分布与高斯-洛伦兹光束轮廓的平方计算的理论PCH在实验误差范围内一致。我们证明和讨论的平均粒子数的观察体积内的每分子每采样间隔后的光子计数分布的超泊松字符和检测到的光子计数的影响。
Fluorescence correlation spectroscopy (FCS) is generally used to obtain information about the number of fluorescent particles in a small volume and the diffusion coefficient from the autocorrelation function of the fluorescence signal. Here we demonstrate that photon counting histogram (PCH) analysis constitutes a novel tool for extracting quantities from fluorescence fluctuation data, i.e., the measured photon counts per molecule and the average number of molecules within the observation volume. The photon counting histogram of fluorescence fluctuation experiments, in which few molecules are present in the excitation volume, exhibits a super-Poissonian behavior. The additional broadening of the PCH compared to a Poisson distribution is due to fluorescence intensity fluctuations. For diffusing particles these intensity fluctuations are caused by an inhomogeneous excitation profile and the fluctuations in the number of particles in the observation volume (N) over bar. The quantitative relationship between the detected photon counts and the fluorescence intensity reaching the detector is given by Mandel's formula. Based on this equation and considering the fluorescence intensity distribution in the two-photon excitation volume, a theoretical expression for the PCH as a function of the number of molecules in the excitation volume is derived. For a single molecular species two parameters are sufficient to characterize the histogram completely, namely the average number of molecules within the observation volume and the detected photon counts per molecule per sampling time epsilon. The PCH for multiple molecular species, on the other hand, is generated by successively convoluting the photon counting distribution of each species with the others. The influence of the excitation profile upon the photon counting statistics for two relevant point spread functions (PSFs), the three-dimensional Gaussian PSF conventionally employed in confocal detection and the square of the Gaussian-Lorentzian PSF for two photon excitation, is explicitly treated. Measured photon counting distributions obtained with a two-photon excitation source agree, within experimental error with the theoretical PCHs calculated for the square of a Gaussian-Lorentzian beam profile. We demonstrate and discuss the influence of the average number of particles within the observation volume and the detected photon counts per molecule per sampling interval upon the super-Poissonian character of the photon counting distribution.