Fluorescence correlation spectroscopy (FCS) is commonly used to estimate diffusion and reaction rates. In FCS the fluorescence coming from a small volume is recorded and the autocorrelation function (ACF) of the fluorescence fluctuations is computed. Scaling out the fluctuations due to the emission process, this ACF can be related to the ACF of the fluctuations in the number of observed fluorescent molecules. In this paper the ACF of the molecule number fluctuations is studied theoretically, with no approximations, for a reaction-diffusion system in which the fluorescence changes with binding and unbinding. Theoretical ACFs are usually derived assuming that fluctuations in the number of molecules of one species are instantaneously uncorrelated to those of the others and obey Poisson statistics. Under these assumptions, the ACF derived in this paper is characterized only by the diffusive timescale of the fluorescent species and its total weight is the inverse of the mean number of observed fluorescent molecules. The theory is then scrutinized in view of previous experimental results which, for a similar system, gave a different total weight and correct estimates of other diffusive timescales. The total weight mismatch is corrected by assuming that the variance of the number of fluorescent molecules depends on the variance of the particle numbers of the other species, as in the variance decomposition formula. Including the finite acquisition time in its computation, it is shown that the ACF depends on various timescales of the system and that its total weight coincides with the one obtained with the variance decomposition formula. This calculation implies that diffusion coefficients of nonobservable species can be estimated with FCS experiments performed in reaction-diffusion systems. Ways to proceed in future experiments are also discussed.

中文翻译：

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反应扩散系统中荧光相关光谱实验中波动的量化

荧光相关光谱法（FCS）通常用于估计扩散和反应速率。在FCS中，记录了少量荧光，并计算了荧光波动的自相关函数（ACF）。消除由于发射过程引起的波动，该ACF可以与观察到的荧光分子数量波动的ACF有关。在本文中，对于荧光扩散随结合和解离而变化的反应扩散系统，没有近似地理论上研究了分子数目波动的ACF。理论上的ACF通常是假设一种物种的分子数量的瞬时波动与另一种分子的瞬时不相关并且服从泊松统计而得出的。在这些假设下，本文得出的ACF仅以荧光物质的扩散时间尺度为特征，其总重量是所观察到的荧光分子平均数的倒数。然后，根据先前的实验结果对这一理论进行审查，对于类似的系统，该实验结果给出了不同的总权重以及其他扩散时间尺度的正确估计。如方差分解公式中那样，通过假设荧光分子数目的方差取决于其他种类的粒子数的方差来校正总重量失配。在计算中包括有限采集时间，结果表明，ACF取决于系统的各种时标，并且其总权重与使用方差分解公式获得的权重一致。该计算暗示可以通过在反应扩散系统中进行的FCS实验来估计不可观察物种的扩散系数。还讨论了将来进行实验的方法。