How the Molecule Number Is Correctly Quantified in Two-Color Fluorescence Cross-Correlation Spectroscopy: Corrections for Cross-Talk and Quenching in Experiments

Fluorescence correlation spectroscopy (FCS) and two-color fluorescence cross-correlation spectroscopy (FCCS) are among the cutting-edge technologies for measuring molecule numbers at the single-molecule level in liquid phases. Yet, even after single molecule technologies caught up with theory, the techniques remained tools only for specialists able to navigate the formulas that give meaning to their observations. This original article aims at the derivations of relevant and useful quantification of molecule numbers for researchers with more diverse backgrounds who have begun probing questions previously unanswerable, except on the level of the molecule. The quantitation depends on the exact conditions of measurement. To some extent these are arbitrary, so that standard procedures are necessary in for valid comparisons of measurements among different data sets. To agree on and specify such procedures is one of the further aims here. No matter what fluorophores, which have, of course, to meet photophysical and photochemical requirements for FCS/FCCS, and optical setups/devices are used, the primary measurement signal arises from fluctuations of the mean molecule number in a confocal femtoliter or smaller probe region. Since FCS/FCCS relies on fluorescence emission measurements of rare events, one is looking for small signals on essentially zero background. Optical separation by FCCS setups is usually defined in terms of cross-talk and cross-excitation/cross-emission, respectively, which can be calculated and minimized by the experimenter from readily measurable quantities of the absorption/emission scenario for single labels and multiple labels n and m bound to or incorporated into the two-color molecules. Furthermore, this article derives relevant formulas for the quantification of molecule numbers under different experimental conditions with substantial quenching of the two-color molecules such as single labels and multiple labels n and m bound to or incorporated into the two-color molecules, high-density labeling of two-color molecules with multiple n green labels and one red label. Here, we summarize and extend the formulas to make them more generally applicable.