Correlation-matrix analysis of two-color coincidence events in single-molecule fluorescence experiments

We introduce a robust and relatively easy-to-use method to evaluate the quality of two-color (or more) fluorescence coincidence measurements based on close investigation of the coincidence correlation-matrix. This matrix contains temporal correlations between the number of detected bursts in individual channels and their coincidences. We show that the Euclidian norm of a vector Λ derived from elements of the correlation matrix takes a value between 0 and 2 depending on the relative coincidence frequency. We characterized the Λ-norm and its dependence on various experimental conditions by computer simulations and fluorescence microscopy experiments. Single-molecule experiments with two differently colored dye molecules diffusing freely in aqueous solution, a sample that generates purely random coincidence events, return a Λ-norm less than one, depending on the concentration of the fluorescent dyes. As perfect coincidence sample we monitored broad autofluorescence of 2.8 μm beads and determined the Λ-norm to be maximal and close to two. As in realistic diagnostic applications, we show that two-color coincidence detection of single-stranded DNA molecules, using differently labeled Molecular Beacons hybridizing to the same target, reveal a value between one and two representing a mixture of an optimal coincidence sample and a sample generating random coincidences. The Λ-norm introduced for data analysis provides a quantifiable measure for quickly judging the outcome of single-molecule coincidence experiments and estimating the quality of detected coincidences.