Simultaneous orientation and 3D localization microscopy with a Vortex point spread function

Enhancing precision for simultaneous 3D localization and 3D orientation with structured illumination

Determining the three-dimensional (3D) position and orientation of molecules from limited fluorescence photons is challenging. Existing modulated illumination localization microscopy partially transfers the photon burden to excitation intensity gradients, advancing precision to the molecular scale. However, most simultaneous localization and orientation methods rely on polarization splitting in the detection path and are sensitive to the signal-to-background ratio. This sensitivity is further exacerbated by sequential structured illumination (SSI), potentially compromising robustness. Here, we introduce V-SIMFLUX, which integrates SSI and the Vortex PSF without polarization-splitting detection. Our theoretical analysis shows that V-SIMFLUX improves the precision of all estimated parameters, notably achieving a typical 2.9-fold improvement in lateral localization and a 1.7-fold enhancement in azimuthal orientation compared to conventional wide-field illumination.

Manipulation and analysis of large DNA molecules by controlling their dynamics using micro and nanogaps

Manipulation and analysis methods for large DNAs are critical for epidemiological, clinical, diagnostic, and fundamental research on bacteria, membrane vesicles, plants, yeast, and human cells. However, the physical properties of large DNAs often challenge their manipulation and analysis with high accuracy and speed using conventional methods such as gel electrophoresis and column-based methods. This review presents the approaches that leverage micrometer- and nanometer-sized gaps within microchannels to control the dynamics and conformations of large DNAs, thereby overcoming these challenges. By designing gap structures and migration conditions based on the relationship between gap parameters and the physical characteristics of large DNAs-such as diameter and persistence length-these methods enable swifter and more precise manipulation and analysis of large DNAs, including size separation, concentration, purification, and single-molecule analysis.

Resolving the Orientations of and Angular Separation Between a Pair of Dipole Emitters

We prove that it is impossible to distinguish two spatially coinciding fluorescent molecules from a single rotating molecule using polarization-sensitive imaging, even if one modulates the polarization of the illumination or the detection dipole-spread function (DSF). If the target is known to be a dipole pair, existing imaging methods perform poorly for measuring their angular separation. We propose simultaneously modulating the excitation polarization and DSF, which demonstrates robust discrimination between dipole pairs versus single molecules. Our method improves the precision of measuring centroid orientation by 50% and angular separation by two- to four-fold over existing techniques.

Spectrally Resolved Single-Molecule Orientation Imaging Reveals a Direct Correspondence between the Polarity and Microviscosity Experienced by Nile Red in Supported Lipid Bilayer Membranes

Molecular-level interactions among lipids, cholesterol, and water dictate the nanoscale membrane organization of lipid bilayers into liquid-ordered (Lo) and liquid-disordered (Ld) phases, characterized by different polarities and orders. Generally, solvatochromic dyes easily discriminate polarity difference between Lo and Ld phases, whereas molecular flippers and rotors show distinct photophysics depending on the membrane order. Despite progress in single-molecule spectral imaging and single-molecule orientation mapping, direct experimental proof linking polarity with microviscosity sensed by the same probe eludes us. Here, we demonstrate spectrally resolved single-molecule orientation localization microscopy to connect nanoscopic localization of a probe on a bilayer membrane with its emission spectra, three-dimensional dipole orientation, and rotational constraint offered by the local microenvironment and highlight the excellent correspondence between the polarity and order experienced by the same probe. This technique has the potential to address nanoscale heterogeneity and dynamics, especially in biology and material sciences.

Monitoring Dynamic Conformations of a Single Fluorescent Molecule Inside a Protein Cavity

Fluorescence nanoscopy and single-molecule methods are entering the realm of structural biology, breaking new ground for dynamic structural measurements at room temperature and liquid environments. Here, single-molecule localization microscopy, polarization-dependent single-molecule excitation, and protein engineering are combined to determine the orientation of a fluorophore forming hydrogen bonds inside a protein cavity. The observed conformations are in good agreement with molecular dynamics simulations, enabling a new, more realistic interplay between experiments and simulations to identify stable conformations and the key interactions involved. Furthermore, jumps between conformations can be monitored with a precision of 3° and a time resolution of a few seconds, confirming the potential of this methodology for retrieving dynamic structural information of nanoscopic biological systems under physiologically compatible conditions.

Single-molecule orientation-localization microscopy: Applications and approaches

Single-molecule orientation-localization microscopy (SMOLM) builds upon super-resolved localization microscopy by imaging orientations and rotational dynamics of individual molecules in addition to their positions. This added dimensionality provides unparalleled insights into nanoscale biophysical and biochemical processes, including the organization of actin networks, movement of molecular motors, conformations of DNA strands, growth and remodeling of amyloid aggregates, and composition changes within lipid membranes. In this review, we discuss recent innovations in SMOLM and cover three key aspects: (1) biophysical insights enabled by labeling strategies that endow fluorescent probes to bind to targets with orientation specificity; (2) advanced imaging techniques that leverage the physics of light-matter interactions and estimation theory to encode orientation information with high fidelity into microscope images; and (3) computational methods that ensure accurate and precise data analysis and interpretation, even in the presence of severe shot noise. Additionally, we compare labeling approaches, imaging hardware, and publicly available analysis software to aid the community in choosing the best SMOLM implementation for their specific biophysical application. Finally, we highlight future directions for SMOLM, such as the development of probes with improved photostability and specificity, the design of “smart” adaptive hardware, and the use of advanced computational approaches to handle large, complex datasets. This review underscores the significant current and potential impact of SMOLM in deepening our understanding of molecular dynamics, paving the way for future breakthroughs in the fields of biophysics, biochemistry, and materials science.

Calibration-free estimation of field dependent aberrations for single molecule localization microscopy across large fields of view

Image quality in single molecule localization microscopy (SMLM) depends largely on the accuracy and precision of the localizations. While under ideal imaging conditions the theoretically obtainable precision and accuracy are achieved, in practice this changes if (field dependent) aberrations are present. Currently there is no simple way to measure and incorporate these aberrations into the Point Spread Function (PSF) fitting, therefore the aberrations are often taken constant or neglected all together. Here we introduce a model-based approach to estimate the field-dependent aberration directly from single molecule data without a calibration step. This is made possible by using nodal aberration theory to incorporate the field-dependency of aberrations into our fully vectorial PSF model. This results in a limited set of aberration fit parameters that can be extracted from the raw frames without a bead calibration measurement, also in retrospect. The software implementation is computationally efficient, enabling fitting of a full 2D or 3D dataset within a few minutes. We demonstrate our method on 2D and 3D localization data of microtubuli and nuclear pore complexes over fields of view (FOV) of up to 180 μm and compare it with spline-based fitting and a deep learning based approach.

Single-Molecule Spectral Fluctuation Originates from the Variation in Dipole Orientation Connected to Accessible Vibrational Modes

Fluctuation in fluorescence emission of an immobilized single molecule is typically ascribed to the chromophore's intrinsic structural conformations and the influence of local environmental factors. Despite extensive research since its initial observation, a direct connection between these spectral fluctuations and the rearrangement of emission dipole orientations has remained elusive. Here, we elucidate this fundamental molecular behavior and its underlying mechanisms by employing unique single-molecule multidimensional tracking to simultaneously monitor both the emission spectrum and the three-dimensional dipole orientation of individual fluorophores. We present compelling evidence demonstrating a correlation between spectral fluctuations and dipolar rearrangements at room temperature. Our observations reveal that variations in the radiative relaxation probabilities among different vibronic emission bands, coupled with the interaction of associated vibrational modes, drive these spectral fluctuations. We identify significant out-of-plane dipole reorientations during pronounced spectral fluctuations, commonly known as spectral jumps, which primarily arise from transitions between dominant vibrational modes. Furthermore, we emphasize the potential for constructing vibrational spectra and optical nanoscopy with vibrational specificity, leveraging the vibronic emissions from single emitters.

POLCAM: instant molecular orientation microscopy for the life sciences

Current methods for single-molecule orientation localization microscopy (SMOLM) require optical setups and algorithms that can be prohibitively slow and complex, limiting widespread adoption for biological applications. We present POLCAM, a simplified SMOLM method based on polarized detection using a polarization camera, which can be easily implemented on any wide-field fluorescence microscope. To make polarization cameras compatible with single-molecule detection, we developed theory to minimize field-of-view errors, used simulations to optimize experimental design and developed a fast algorithm based on Stokes parameter estimation that can operate over 1,000-fold faster than the state of the art, enabling near-instant determination of molecular anisotropy. To aid in the adoption of POLCAM, we developed open-source image analysis software and a website detailing hardware installation and software use. To illustrate the potential of POLCAM in the life sciences, we applied our method to study α-synuclein fibrils, the actin cytoskeleton of mammalian cells, fibroblast-like cells and the plasma membrane of live human T cells.

Fundamental Limits in Measuring the Anisotropic Rotational Diffusion of Single Molecules

Many biophysical techniques, such as single-molecule fluorescence correlation spectroscopy, Förster resonance energy transfer, and fluorescence anisotropy, measure the translation and rotation of biomolecules to quantify molecular processes at the nanoscale. These methods often simplify data analysis by assuming isotropic rotational diffusion, e.g., that molecules wobble within a circular cone. This simplification ignores the anisotropy present in many biological contexts that may cause molecules to exhibit different degrees of diffusion in different directions. Here, we loosen this assumption and establish a theoretical framework for describing and measuring anisotropic rotational diffusion using fluorescence imaging. We show that anisotropic wobble is directly quantified by the eigenvalues of a 3-by-3 positive-semidefinite Hermitian matrix M consisting of the second-order moments of a molecule's transition dipole μ. This formalism enables us to model the influence of unavoidable shot noise using a Hermitian perturbation matrix E; the eigenvalues of E directly bound errors in measurements of wobble via Weyl's inequality. Quantifying various perturbations E reveals that anisotropic wobble measurements are generally more sensitive to errors compared to quantifying isotropic wobble. Moreover, severe shot noise can induce negative eigenvalues in estimates of M, thereby causing the anisotropic wobble measurement to fail. Our analysis, using Fisher information, shows that techniques with worse orientation measurement sensitivity experience stronger perturbations E and require larger signal to background ratios to measure anisotropic rotational diffusion accurately. Our work provides deep insights for improving the state of the art in imaging the orientations and anisotropic rotational diffusion of single molecules.

Scanning Electron Microscopy Imaging of Large DNA Molecules Using a Metal-Free Electro-Stain Composed of DNA-Binding Proteins and Synthetic Polymers

This paper presents the first scanning electron microscopy (SEM)-based DNA imaging in biological samples. This novel approach incorporates a metal-free electro-stain reagent, formulated by combining DNA-binding proteins and synthetic polymers to enhance the visibility of 2-nm-thick DNA under SEM. Notably, DNA molecules stain with proteins and polymers appear as dark lines under SEM. The resulting DNA images exhibit a thickness of 15.0±4.0 nm. As SEM is the primary platform, it integrates seamlessly with various chemically functionalized large surfaces with the aid of microfluidic devices. The approach allows high-resolution imaging of various DNA structures including linear, circular, single-stranded DNA and RNA, originating from nuclear and mitochondrial genomes. Furthermore, quantum dots are successfully visualized as bright labels that are sequence-specifically incorporated into DNA molecules, which highlights the potential for SEM-based optical DNA mapping. In conclusion, DNA imaging using SEM with the novel electro-stain offers electron microscopic resolution with the ease of optical microscopy.

Universal inverse modeling of point spread functions for SMLM localization and microscope characterization

The point spread function (PSF) of a microscope describes the image of a point emitter. Knowing the accurate PSF model is essential for various imaging tasks, including single-molecule localization, aberration correction and deconvolution. Here we present universal inverse modeling of point spread functions (uiPSF), a toolbox to infer accurate PSF models from microscopy data, using either image stacks of fluorescent beads or directly images of blinking fluorophores, the raw data in single-molecule localization microscopy (SMLM). Our modular framework is applicable to a variety of microscope modalities and the PSF model incorporates system- or sample-specific characteristics, for example, the bead size, field- and depth- dependent aberrations, and transformations among channels. We demonstrate its application in single or multiple channels or large field-of-view SMLM systems, 4Pi-SMLM, and lattice light-sheet microscopes using either bead data or single-molecule blinking data.

Large-FOV 3D localization microscopy by spatially variant point spread function generation

Accurate characterization of the microscopic point spread function (PSF) is crucial for achieving high-performance localization microscopy (LM). Traditionally, LM assumes a spatially invariant PSF to simplify the modeling of the imaging system. However, for large fields of view (FOV) imaging, it becomes important to account for the spatially variant nature of the PSF. Here, we propose an accurate and fast principal components analysis-based field-dependent 3D PSF generator (PPG3D) and localizer for LM. Through simulations and experimental three-dimensional (3D) single-molecule localization microscopy (SMLM), we demonstrate the effectiveness of PPG3D, enabling super-resolution imaging of mitochondria and microtubules with high fidelity over a large FOV. A comparison of PPG3D with a shift-variant PSF generator for 3D LM reveals a threefold improvement in accuracy. Moreover, PPG3D is approximately 100 times faster than existing PSF generators, when used in image plane-based interpolation mode. Given its user-friendliness, we believe that PPG3D holds great potential for widespread application in SMLM and other imaging modalities.

Universal inverse modelling of point spread functions for SMLM localization and microscope characterization

The point spread function (PSF) of a microscope describes the image of a point emitter. Knowing the accurate PSF model is essential for various imaging tasks, including single molecule localization, aberration correction and deconvolution. Here we present uiPSF (universal inverse modelling of Point Spread Functions), a toolbox to infer accurate PSF models from microscopy data, using either image stacks of fluorescent beads or directly images of blinking fluorophores, the raw data in single molecule localization microscopy (SMLM). The resulting PSF model enables accurate 3D super-resolution imaging using SMLM. Additionally, uiPSF can be used to characterize and optimize a microscope system by quantifying the aberrations, including field-dependent aberrations, and resolutions. Our modular framework is applicable to a variety of microscope modalities and the PSF model incorporates system or sample specific characteristics, e.g., the bead size, depth dependent aberrations and transformations among channels. We demonstrate its application in single or multiple channels or large field-of-view SMLM systems, 4Pi-SMLM, and lattice light-sheet microscopes using either bead data or single molecule blinking data.

Combining deep learning approaches and point spread function engineering for simultaneous 3D position and 3D orientation measurements of fluorescent single molecules

Point Spread Function (PSF) engineering is an effective method to increase the sensitivity of single-molecule fluorescence images to specific parameters. Classical phase mask optimization approaches have enabled the creation of new PSFs that can achieve, for example, localization precision of a few nanometers axially over a capture range of several microns with bright emitters. However, for complex high-dimensional optimization problems, classical approaches are difficult to implement and can be very time-consuming for computation. The advent of deep learning methods and their application to single-molecule imaging has provided a way to solve these problems. Here, we propose to combine PSF engineering and deep learning approaches to obtain both an optimized phase mask and a neural network structure to obtain the 3D position and 3D orientation of fixed fluorescent molecules. Our approach allows us to obtain an axial localization precision around 30 nanometers, as well as an orientation precision around 5 degrees for orientations and positions over a one micron depth range for a signal-to-noise ratio consistent with what is typical in single-molecule cellular imaging experiments.

Single-Molecule Orientation Imaging Reveals Two Distinct Binding Configurations on Amyloid Fibrils

Fluorescence readouts for an amyloid fibril sensor critically depend on its molecular interaction and local environment offered by the available structural motifs. Here we employ polarized points accumulation for imaging in nanoscale topography with intramolecular charge transfer probes transiently bound to amyloid fibrils to investigate the organization of fibril nanostructures and probe binding configurations. Besides the in-plane (θ ≈ 90°) mode for binding on the fibril surface parallel to the long fibril axis, we also observed a sizable population of over 60% out-of-plane (θ < 60°) dipoles for rotor probes experiencing a varying degree of orientational mobility. Highly confined dipoles exhibiting an out-of-plane configuration probably reflect tightly bound dipoles in the inner channel grooves, while the weakly bound ones on amyloid enjoy rotational flexibility. Our observation of an out-of-plane binding mode emphasizes the pivotal role played by the electron donor amino group toward fluorescence detection and hence the emergence of anchored probes alongside conventional groove binders.

Six-Dimensional Single-Molecule Imaging with Isotropic Resolution using a Multi-View Reflector Microscope

Imaging both the positions and orientations of single fluorophores, termed single-molecule orientation-localisation microscopy, is a powerful tool to study 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 realise a radially and azimuthally polarized multi-view reflector (raMVR) microscope for the imaging of the 3D positions and 3D orientations of single molecules, with precision 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 (NR) molecules transiently bound to lipid-coated spheres, accurately resolving their spherical morphology despite refractive-index mismatch. By observing the rotational dynamics of NR, 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.

Using fluorescent beads to emulate single fluorophores

We study the conditions under which fluorescent beads can be used to emulate single fluorescent molecules in the calibration of optical microscopes. Although beads are widely used due to their brightness and easy manipulation, there can be notable differences between the point spread functions (PSFs) they produce and those for single-molecule fluorophores, caused by their different emission patterns and sizes. We study theoretically these differences for various scenarios, e.g., with or without polarization channel splitting, to determine the conditions under which the use of beads as a model for single molecules is valid. We also propose methods to model the blurring due to the size difference and compensate for it to produce PSFs that are more similar to those for single molecules.

Fluorescence polarization modulation super-resolution imaging provides refined dynamics orientation processes in biological samples

Combining polarization modulation Fourier analysis and spatial information in a joint reconstruction algorithm for polarization-resolved fluorescence imaging provides not only a gain in spatial resolution but also a sensitive readout of anisotropy in cell samples.

Deep-SMOLM: deep learning resolves the 3D orientations and 2D positions of overlapping single molecules with optimal nanoscale resolution

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.

Axial accuracy in localization microscopy with 3D point spread function engineering

Single-molecule localization microscopy has developed into a widely used technique to overcome the diffraction limit and enables 3D localization of single-emitters with nanometer precision. A widely used method to enable 3D encoding is to use a cylindrical lens or a phase mask to engineer the point spread function (PSF). The performance of these PSFs is often assessed by comparing the precision they achieve, ignoring accuracy. Nonetheless, accurate localization is required in many applications, such as multi-plane imaging, measuring and modelling of physical processes based on volumetric data, and 3D particle averaging. However, there are PSF model mismatches in the localization schemes due to how reference PSFs are obtained, look-up-tables are created, or spots are fitted. Currently there is little insight in how these model mismatches give rise to systematic axial localization errors, how large these errors are, and how to mitigate them. In this theoretical and simulation work we use a vector PSF model, which incorporates super-critical angle fluorescence (SAF) and the appropriate aplanatic correction factor, to analyze the errors in z-localization. We introduce theory for defining the focal plane in SAF conditions and analyze the predicted axial errors for an astigmatic PSF, double-helix PSF, and saddle-point PSF. These simulations indicate that the absolute axial biases can be as large as 140 nm, 250 nm, and 120 nm for the astigmatic, saddle-point, and double-helix PSF respectively, with relative errors of more than 50%. Finally, we discuss potential experimental methods to verify these findings and propose a workflow to mitigate these effects.

Nanoscale organization of the pre-synapse: Tracking the neurotransmitter release machinery

Chemical communication is underpinned by the fusion of neurotransmitter-containing synaptic vesicles with the plasma membrane at active zones. With the advent of super-resolution microscopy, the door is now opened to unravel the dynamic remodeling of synapses underpinning learning and memory. Imaging proteins with conventional light microscopy cannot provide submicron information vital to determining the nanoscale organization of the synapse. We will first review the current super-resolution microscopy techniques available to investigate the localization and movement of synaptic proteins and how they have been applied to visualize the synapse. We discuss the new techniques and analytical approaches have provided comprehensive insights into synaptic organization in various model systems. Finally, this review provides a brief update on how these super-resolution techniques and analyses have opened the way to a much greater understanding of the synapse, the fusion and compensatory endocytosis machinery.

Simultaneous super-resolution estimation of single-molecule position and orientation with minimal photon fluxes

The orientation of a single molecule provides valuable information on fundamental biological processes. We report a technique for the simultaneous estimation of single-molecule 2D position and 2D orientation with ultra-high localization precision (∼2-nm precision with ∼500 photons under a typical 100-nm diameter of excitation beam pattern), which is also compatible with tracking in living cells. In the proposed method, the theoretical precision limits are calculated, and the localization and orientation performance along with potential applications are explored using numerical simulations. Compared to other camera-based orientation measurement methods, it is confirmed that the proposed method can obtain reasonable estimates even under very weak signals (∼15 photons). Moreover, the maximum likelihood estimator (MLE) is found to converge to the theoretical limit when the total number of photons is less than 100.

Deciphering a hexameric protein complex with Angstrom optical resolution

Cryogenic optical localization in three dimensions (COLD) was recently shown to resolve up to four binding sites on a single protein. However, because COLD relies on intensity fluctuations that result from the blinking behavior of fluorophores, it is limited to cases where individual emitters show different brightness. This significantly lowers the measurement yield. To extend the number of resolved sites as well as the measurement yield, we employ partial labeling and combine it with polarization encoding in order to identify single fluorophores during their stochastic blinking. We then use a particle classification scheme to identify and resolve heterogenous subsets and combine them to reconstruct the three-dimensional arrangement of large molecular complexes. We showcase this method (polarCOLD) by resolving the trimer arrangement of proliferating cell nuclear antigen (PCNA) and six different sites of the hexamer protein Caseinolytic Peptidase B (ClpB) of Thermus thermophilus in its quaternary structure, both with Angstrom resolution. The combination of polarCOLD and single-particle cryogenic electron microscopy (cryoEM) promises to provide crucial insight into intrinsic heterogeneities of biomolecular structures. Furthermore, our approach is fully compatible with fluorescent protein labeling and can, thus, be used in a wide range of studies in cell and membrane biology.

Dipole-spread-function engineering for simultaneously measuring the 3D orientations and 3D positions of fluorescent molecules

Interactions between biomolecules are characterized by both 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 for simultaneously optimizing 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 for measuring simultaneously 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 6 dimensions.

Photon efficient orientation estimation using polarization modulation in single-molecule localization microscopy

Combining orientation estimation with localization microscopy opens up the possibility to analyze the underlying orientation of biomolecules on the nanometer scale. Inspired by the recent improvement of the localization precision by shifting excitation patterns (MINFLUX, SIMFLUX), we have adapted the idea towards the modulation of excitation polarization to enhance the orientation precision. For this modality two modes are analyzed: i) normally incident excitation with three polarization steps to retrieve the in-plane angle of emitters and ii) obliquely incident excitation with p-polarization with five different azimuthal angles of incidence to retrieve the full orientation. Firstly, we present a theoretical study of the lower precision limit with a Cramér-Rao bound for these modes. For the oblique incidence mode we find a favorable isotropic orientation precision for all molecular orientations if the polar angle of incidence is equal to arccos ⁡ 2 / 3 ≈ 35 degrees. Secondly, a simulation study is performed to assess the performance for low signal-to-background ratios and how inaccurate illumination polarization angles affect the outcome. We show that a precision, at the Cramér-Rao bound (CRB) limit, of just 2.4 and 1.6 degrees in the azimuthal and polar angles can be achieved with only 1000 detected signal photons and 10 background photons per pixel (about twice better than reported earlier). Lastly, the alignment and calibration of an optical microscope with polarization control is described in detail. With this microscope a proof-of-principle experiment is carried out, demonstrating an experimental in-plane precision close to the CRB limit for signal photon counts ranging from 400 to 10,000.

Resolving the Three-Dimensional Rotational and Translational Dynamics of Single Molecules Using Radially and Azimuthally Polarized Fluorescence

We report a radially and azimuthally polarized (raPol) microscope for high detection and estimation performance in single-molecule orientation-localization microscopy (SMOLM). With 5000 photons detected from Nile red (NR) transiently bound within supported lipid bilayers (SLBs), raPol SMOLM achieves 2.9 nm localization precision, 1.5° orientation precision, and 0.17 sr precision in estimating rotational wobble. Within DPPC SLBs, SMOLM imaging reveals the existence of randomly oriented binding pockets that prevent NR from freely exploring all orientations. Treating the SLBs with cholesterol-loaded methyl-β-cyclodextrin (MβCD-chol) causes NR's orientational diffusion to be dramatically reduced, but curiously NR's median lateral displacements drastically increase from 20.8 to 75.5 nm (200 ms time lag). These jump diffusion events overwhelmingly originate from cholesterol-rich nanodomains within the SLB. These detailed measurements of single-molecule rotational and translational dynamics are made possible by raPol's high measurement precision and are not detectable in standard SMLM.

Robust and bias-free localization of individual fixed dipole emitters achieving the Cramér Rao bound for applications in cryo-single molecule localization microscopy

Single molecule localization microscopy (SMLM) has the potential to resolve structural details of biological samples at the nanometer length scale. Compared to room temperature experiments, SMLM performed under cryogenic temperature achieves higher photon yields and, hence, higher localization precision. However, to fully exploit the resolution it is crucial to account for the anisotropic emission characteristics of fluorescence dipole emitters with fixed orientation. In case of slight residual defocus, localization estimates may well be biased by tens of nanometers. We show here that astigmatic imaging in combination with information about the dipole orientation allows to extract the position of the dipole emitters without localization bias and down to a precision of 1 nm, thereby reaching the corresponding Cramér Rao bound. The approach is showcased with simulated data for various dipole orientations, and parameter settings realistic for real life experiments.

4polar-STORM polarized super-resolution imaging of actin filament organization in cells

Single-molecule localization microscopy provides insights into the nanometer-scale spatial organization of proteins in cells, however it does not provide information on their conformation and orientation, which are key functional signatures. Detecting single molecules' orientation in addition to their localization in cells is still a challenging task, in particular in dense cell samples. Here, we present a polarization-splitting scheme which combines Stochastic Optical Reconstruction Microscopy (STORM) with single molecule 2D orientation and wobbling measurements, without requiring a strong deformation of the imaged point spread function. This method called 4polar-STORM allows, thanks to a control of its detection numerical aperture, to determine both single molecules' localization and orientation in 2D and to infer their 3D orientation. 4polar-STORM is compatible with relatively high densities of diffraction-limited spots in an image, and is thus ideally placed for the investigation of dense protein assemblies in cells. We demonstrate the potential of this method in dense actin filament organizations driving cell adhesion and motility.

Single-Molecule Localization Microscopy of 3D Orientation and Anisotropic Wobble Using a Polarized Vortex Point Spread Function

Within condensed matter, single fluorophores are sensitive probes of their chemical environments, but it is difficult to use their limited photon budget to image precisely their positions, 3D orientations, and rotational diffusion simultaneously. We demonstrate the polarized vortex point spread function (PSF) for measuring these parameters, including characterizing the anisotropy of a molecule's wobble, simultaneously from a single image. Even when imaging dim emitters (∼500 photons detected), the polarized vortex PSF can obtain 12 nm localization precision, 4°-8° orientation precision, and 26° wobble precision. We use the vortex PSF to measure the emission anisotropy of fluorescent beads, the wobble dynamics of Nile red (NR) within supported lipid bilayers, and the distinct orientation signatures of NR in contact with amyloid-beta fibrils, oligomers, and tangles. The unparalleled sensitivity of the vortex PSF transforms single-molecule microscopes into nanoscale orientation imaging spectrometers, where the orientations and wobbles of individual probes reveal structures and organization of soft matter that are nearly impossible to perceive by using molecular positions alone.