Parameter-free molecular counting from a single DNA-PAINT intensity trace

Localization microscopy techniques, like DNA-PAINT, enable one to localize single molecules with a precision far below the diffraction limit. When multiple molecules are close to each other, they result in a single cluster of localizations and they cannot be distinguished visually or counted. Here, we present a method to estimate the number of molecules and the blinking kinetics from a single raw intensity trace without any prior knowledge. The qPAINT method is commonly used to obtain quantitative information regarding the number of molecules in a cluster of DNA-PAINT binding events, but the counting relies on a priori knowledge about the hybridization kinetics of the complementary DNA strands, foremost the binding-rate k_on. Its value is either taken from literature or calibrations. Crucially, the binding rate depends strongly on temperature, buffer, and steric hindrance, which affects the estimate for the number of molecules. Recent qPAINT alternatives circumvent the k_on-dependence in molecular counting, but either requires a three-fold repetition of the experiment with different imager concentrations or is sensitive to signal processing. Here, we estimate the number of molecules and the binding constants k_on and k_off from a single raw intensity trace using cumulants. As all information is extracted from the time trace of the molecular cluster, our method does not require any calibration, prior knowledge, or signal processing. We apply the method to experimental data and demonstrate that we can accurately estimate the number of docking strands and binding kinetics for various number of docking strands and imager concentrations purely from a single trace. With this approach, we pave the way toward parameter-free absolute counting of individual assemblies, despite variations in unknown binding kinetics within the sample or between assemblies.