Component Analysis of Photon Counting Histograms in Fluorescence Fluctuation Spectroscopy Experiments

An integrated approach based on the use of data mining methods is proposed in order to improve the efficiency of the analysis of photon counting histograms during study of the molecular composition of a substance by fluorescence fluctuation spectroscopy. The principal component method is used to test the hypothesis about cluster separability of the multidimensional experimental data. The reason for compression of the data cloud to characteristic nonlinearity, or so-called arcuate (arc-shaped) cloud, in the space of the first two principal components is investigated. Examples of simulated data sets of molecular systems with various brightness and concentration characteristics are considered. Interpretation and subsequent quantitative analysis of the data are complicated by nonlinear effects. It was established that the arcuate nature of the data cloud is a consequence of the presence of significant variation in one or more physical parameters and results and, in particular, from significant increase in the spread of the brightness or concentration parameters of the molecules. If only one type of molecule is being studied these parameters can provide additional indicators for assessing the quality of the experiments and can also be used for characterizing the system in the case of a mixture of various types of molecules. It was proposed to use normalization of local weighted smoothing of the scattering diagram to eliminate nonlinear effects in the space of the principal components.