Analysis of fluctuations arising as fluorescent particles pass through a focused laser beam has enabled quantitative characterization of a broad range of molecular kinetic processes. Two key mathematical frameworks that have enabled these quantifications are fluorescence correlation spectroscopy (FCS) and photon counting histogram (PCH) analysis. Although these frameworks are effective and accurate when the focused laser beam is well approximated by an infinite Gaussian beam with a waist that is small compared to the size of the region over which the fluorescent particles can diffuse, they cannot be applied to situations in which this region is bounded at the nanoscale. We therefore derived general forms of the FCS and PCH frameworks for bounded systems. The finite-domain form of FCS differs from the classical form in its boundary and initial conditions and requires development of a new Fourier space solution for fitting data. Our finite-domain FCS predicts simulated data accurately and reduces to a previous model for the special case when the system is much larger than the Gaussian beam and can be considered to be infinite. We also derived the PCH form for the bounded systems. Our approach enables estimation of the concentration of diffusing fluorophores within a finite domain for the first time, to our knowledge. The method opens the possibility of quantification of kinetics in several systems for which this has never been possible.

中文翻译：

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有限、有界域中的荧光相关光谱和光子计数直方图

对荧光粒子通过聚焦激光束时出现的波动进行分析，可以对广泛的分子动力学过程进行定量表征。实现这些量化的两个关键数学框架是荧光相关光谱 (FCS) 和光子计数直方图 (PCH) 分析。尽管当聚焦激光束被无限高斯光束很好地近似时，这些框架是有效和准确的，该光束的腰围比荧光粒子可以扩散的区域的大小要小，但它们不能应用于以下情况：区域以纳米级为界。因此，我们推导出了有界系统的 FCS 和 PCH 框架的一般形式。FCS 的有限域形式在其边界和初始条件方面不同于经典形式，需要开发新的傅立叶空间解来拟合数据。我们的有限域 FCS 可以准确地预测模拟数据，并在系统远大于高斯光束并且可以被认为是无限大的特殊情况下简化为以前的模型。我们还推导出了有界系统的 PCH 形式。据我们所知，我们的方法首次能够估计有限域内扩散荧光团的浓度。该方法开启了在几个系统中对动力学进行量化的可能性，而这在以前是不可能的。我们的有限域 FCS 可以准确地预测模拟数据，并在系统远大于高斯光束并且可以被认为是无限大的特殊情况下简化为以前的模型。我们还推导出了有界系统的 PCH 形式。据我们所知，我们的方法首次能够估计有限域内扩散荧光团的浓度。该方法开启了在几个系统中对动力学进行量化的可能性，而这在以前是不可能的。我们的有限域 FCS 可以准确地预测模拟数据，并在系统远大于高斯光束并且可以被认为是无限大的特殊情况下简化为以前的模型。我们还推导出了有界系统的 PCH 形式。据我们所知，我们的方法首次能够估计有限域内扩散荧光团的浓度。该方法开启了在几个系统中对动力学进行量化的可能性，而这在以前是不可能的。