A Theoretical High-Density Nanoscopy Study Leads to the Design of UNLOC, a Parameter-free Algorithm

Abstract

Single-molecule localization microscopy (SMLM) enables the production of high-resolution images by imaging spatially isolated fluorescent particles. Although challenging, the result of SMLM analysis lists the position of individual molecules, leading to a valuable quantification of the stoichiometry and spatial organization of molecular actors. Both the signal/noise ratio and the density (D_frame), i.e., the number of fluorescent particles per μm² per frame, have previously been identified as determining factors for reaching a given SMLM precision. Establishing a comprehensive theoretical study relying on these two parameters is therefore of central interest to delineate the achievable limits for accurate SMLM observations. Our study reports that in absence of prior knowledge of the signal intensity α, the density effect on particle localization is more prominent than that anticipated from theoretical studies performed at known α. A first limit appears when, under a low-density hypothesis (i.e., one-Gaussian fitting hypothesis), any fluorescent particle distant by less than ∼600 nm from the particle of interest biases its localization. In fact, all particles should be accounted for, even those dimly fluorescent, to ascertain unbiased localization of any surrounding particles. Moreover, even under a high-density hypothesis (i.e., multi-Gaussian fitting hypothesis), a second limit arises because of the impossible distinction of particles located too closely. An increase in D_frame is thus likely to deteriorate the localization precision, the image reconstruction, and more generally the quantification accuracy. Our study firstly provides a density-signal/noise ratio space diagram for use as a guide in data recording toward reaching an achievable SMLM resolution. Additionally, it leads to the identification of the essential requirements for implementing UNLOC, a parameter-free and fast computing algorithm approaching the Cramér-Rao bound for particles at high-density per frame and without any prior knowledge of their intensity. UNLOC is available as an ImageJ plugin.