A theoretical high-density nanoscopy study leads to the design of UNLOC, an unsupervised algorithm

Among the superresolution microscopy techniques, the ones based on serially imaging sparse fluorescent particles enable the reconstruction of high-resolution images by localizing single molecules. Although challenging, single-molecule localization microscopy (SMLM) methods aim at listing the position of individual molecules leading a proper quantification of the stoichiometry and spatial organization of molecular actors. However, reaching the precision requested to localize accurately single molecules is mainly constrained by the signal-to-noise ratio (SNR) but also the density (Dframe), i.e., the number of fluorescent particles per μm2 per frame. Of central interest, we establish here a comprehensive theoretical study relying on both SNR and Dframe to delineate the achievable limits for accurate SMLM observations. We demonstrate that, for low-density hypothesis (i.e. one-Gaussian fitting hypothesis), any fluorescent particle biases the localization of a particle of interest when they are distant by less than ≈ 600 nm. Unexpectedly, we also report that even dim fluorescent particles should be taken into account to ascertain unbiased localization of any surrounding particles. Therefore, increased Dframe quickly deteriorates the localization precision, the image reconstruction and more generally the quantification accuracy. The first outcome is a standardized density-SNR space diagram to determine the achievable SMLM resolution expected with experimental data. Additionally, this study leads to the identification of the essential requirements for implementing UNLOC (UNsupervised particle LOCalization), an unsupervised and fast computing algorithm approaching the Cramér-Rao bound for particles at high-density per frame and without any prior on their intensity. UNLOC is available as an ImageJ plugin.