Nanoscale Pattern Extraction from Relative Positions of Sparse 3D Localizations

Abstract

Inferring the organization of fluorescently labeled nanosized structures from single molecule localization microscopy (SMLM) data, typically obscured by stochastic noise and background, remains challenging. To overcome this, we developed a method to extract high-resolution ordered features from SMLM data that requires only a low fraction of targets to be localized with high precision. First, experimentally measured localizations are analyzed to produce relative position distributions (RPDs). Next, model RPDs are constructed using hypotheses of how the molecule is organized. Finally, a statistical comparison is used to select the most likely model. This approach allows pattern recognition at sub-1% detection efficiencies for target molecules, in large and heterogeneous samples and in 2D and 3D data sets. As a proof-of-concept, we infer ultrastructure of Nup107 within the nuclear pore, DNA origami structures, and α-actinin-2 within the cardiomyocyte Z-disc and assess the quality of images of centrioles to improve the averaged single-particle reconstruction.

Assessment of 3D MINFLUX data for quantitative structural biology in cells

“…∆ xy distribution for the Nup96 localisations of Gwosch et al (2020) Fig. 1a (a), 3f (c) and 5c (e) and fits to them (b, d, f,) of nuclear porin models from 6-to 10-fold symmetry, including repeated single-molecule localisations ( σ xy ), intra- and inter-cluster distances within a NPC, and background≈inter-pore distances (Curd et al, 2020). Symmetry, nuclear pore diameter ( D ) and σ xy for the model selected by AICc (Curd et al, 2020) in each experiment (b, d, f).…”

“…1, we used the MATLAB function circlefit (https://uk.mathworks.com/matlabcentral/fileexchange/5557-circle-fit) to fit a circle to a set of ( x, y ) points, All the plots for Fig. 2 were generated using PERPL (https://bitbucket.org/apcurd/perpl-python3/) ((Curd et al, 2020)). The xy -model includes Gaussian clusters arranged symmetrically around a ring, repeated localizations of a single molecule (with s.d.…”

“…However, we recommend that experimentalists also perform initial testing of the resolution, detection efficiency and exploration of event filtering parameters on potential samples, to the extent this is possible, before choosing MINFLUX over other SMLM techniques. , intra-and inter-cluster distances within a NPC, and background≈inter-pore distances (Curd et al, 2020). Symmetry, nuclear pore diameter (D) and σxy for the model selected by AICc (Curd et al, 2020) in each experiment (b, d, f).…”

“…, intra-and inter-cluster distances within a NPC, and background≈inter-pore distances (Curd et al, 2020). Symmetry, nuclear pore diameter (D) and σxy for the model selected by AICc (Curd et al, 2020) in each experiment (b, d, f). Indications of resolved intra-cluster substructure in a (*).…”

Bayesian inference of multi-point macromolecular architecture mixtures at nanometre resolution

“…The over-estimation of pair-wise distances is well understood, with computational correction methods being available, [5], [6], [13]. In particular, in the case of isotropic Gaussian measurement errors the likelihood is analytically tractable in 1-3 dimensions, [5], [6], and has been used across a variety of applications, [20], [10]. In 3D, however, typically PSFs are anisotropic, with the resolution along the optical axis usually reduced relative to that in the focal plane.…”