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The resolution and accuracy of single-molecule localization microscopes (SMLMs) are routinely benchmarked using simulated data, calibration rulers, or comparisons to secondary imaging modalities. However, these methods cannot quantify the nanoscale accuracy of an arbitrary SMLM dataset. Here, we show that by computing localization stability under a well-chosen perturbation with accurate knowledge of the imaging system, we can robustly measure the confidence of individual localizations without ground-truth knowledge of the sample. We demonstrate that our method, termed Wasserstein-induced flux (WIF), measures the accuracy of various reconstruction algorithms directly on experimental 2D and 3D data of microtubules and amyloid fibrils. We further show that WIF confidences can be used to evaluate the mismatch between computational models and imaging data, enhance the accuracy and resolution of reconstructed structures, and discover hidden molecular heterogeneities. As a computational methodology, WIF is broadly applicable to any SMLM dataset, imaging system, and localization algorithm.

 

In soft matter, thermal energy causes molecules to continuously translate and rotate, even in crowded environments, thereby impacting the spatial organization and function of most molecular assemblies, such as lipid membranes. Directly measuring the orientation and spatial organization of large collections (>3000 molecules μm⁻²) of single molecules with nanoscale resolution remains elusive. In this paper, we utilize SMOLM, single‐molecule orientation localization microscopy, to directly measure the orientation spectra (3D orientation plus “wobble”) of lipophilic probes transiently bound to lipid membranes, revealing that Nile red's (NR) orientation spectra are extremely sensitive to membrane chemical composition. SMOLM images resolve nanodomains and enzyme‐induced compositional heterogeneity within membranes, where NR within liquid‐ordered vs. liquid‐disordered domains shows a ≈4° difference in polar angle and a ≈0.3π sr difference in wobble angle. As a new type of imaging spectroscopy, SMOLM exposes the organizational and functional dynamics of lipid‐lipid, lipid‐protein, and lipid‐dye interactions with single‐molecule, nanoscale resolution.

 

Imaging of both the positions and orientations of single fluorophores, termed single-molecule orientation-localization microscopy, is a powerful tool for the study of biochemical processes. However, the limited photon budget associated with single-molecule fluorescence makes high-dimensional imaging with isotropic, nanoscale spatial resolution a formidable challenge. Here we realize a radially and azimuthally polarized multi-view reflector (raMVR) microscope for the imaging of the three-dimensional (3D) positions and 3D orientations of single molecules, with precisions of 10.9 nm and 2.0° over a 1.5-μm depth range. The raMVR microscope achieves 6D super-resolution imaging of Nile red molecules transiently bound to lipid-coated spheres, accurately resolving their spherical morphology, despite refractive-index mismatch. By observing the rotational dynamics of Nile red, raMVR images also resolve the infiltration of lipid membranes by amyloid-beta oligomers without covalent labelling. Finally, we demonstrate 6D imaging of cell membranes, where the orientations of specific fluorophores reveal heterogeneity in membrane fluidity. With its nearly isotropic 3D spatial resolution and orientation measurement precision, we expect the raMVR microscope to enable 6D imaging of molecular dynamics within biological and chemical systems with exceptional detail. 

The past decade has brought many innovations in optical design for 3D super-resolution imaging of point-like emitters, but these methods often focus on single-emitter localization precision as a performance metric. Here, we propose a simple heuristic for designing a point spread function (PSF) that allows for precise measurement of the distance between two emitters. We discover that there are two types of PSFs that achieve high performance for resolving emitters in 3D, as quantified by the Cramér-Rao bounds for estimating the separation between two closely spaced emitters. One PSF is very similar to the existing Tetrapod PSFs; the other is a rotating single-spot PSF, which we call the crescent PSF. The latter exhibits excellent performance for localizing single emitters throughout a 1-µm focal volume (localization precisions of 7.3 nm inx, 7.7 nm iny, and 18.3 nm inzusing 1000 detected photons), and it distinguishes between one and two closely spaced emitters with superior accuracy (25-53% lower error rates than the best-performing Tetrapod PSF, averaged throughout a 1-µm focal volume). Our study provides additional insights into optimal strategies for encoding 3D spatial information into optical PSFs.

 

Dipole-spread function (DSF) engineering reshapes the images of a microscope to maximize the sensitivity of measuring the 3D orientations of dipole-like emitters. However, severe Poisson shot noise, overlapping images, and simultaneously fitting high-dimensional information–both orientation and position–greatly complicates image analysis in single-molecule orientation-localization microscopy (SMOLM). Here, we report a deep-learning based estimator, termed Deep-SMOLM, that achieves superior 3D orientation and 2D position measurement precision within 3% of the theoretical limit (3.8° orientation, 0.32 sr wobble angle, and 8.5 nm lateral position using 1000 detected photons). Deep-SMOLM also demonstrates state-of-art estimation performance on overlapping images of emitters, e.g., a 0.95 Jaccard index for emitters separated by 139 nm, corresponding to a 43% image overlap. Deep-SMOLM accurately and precisely reconstructs 5D information of both simulated biological fibers and experimental amyloid fibrils from images containing highly overlapped DSFs at a speed ~10 times faster than iterative estimators.

 

Interactions between biomolecules are characterized by where they occur and how they are organized, e.g., the alignment of lipid molecules to form a membrane. However, spatial and angular information are mixed within the image of a fluorescent molecule–the microscope’s dipole-spread function (DSF). We demonstrate the pixOL algorithm to simultaneously optimize all pixels within a phase mask to produce an engineered Green’s tensor–the dipole extension of point-spread function engineering. The pixOL DSF achieves optimal precision to simultaneously measure the 3D orientation and 3D location of a single molecule, i.e., 4.1° orientation, 0.44 sr wobble angle, 23.2 nm lateral localization, and 19.5 nm axial localization precisions in simulations over a 700 nm depth range using 2500 detected photons. The pixOL microscope accurately and precisely resolves the 3D positions and 3D orientations of Nile red within a spherical supported lipid bilayer, resolving both membrane defects and differences in cholesterol concentration in six dimensions.