Rotational mobility of single molecules affects localization accuracy in super-resolution fluorescence microscopy

Direct optical measurement of intramolecular distances with angstrom precision

Optical investigations of nanometer distances between proteins, their subunits, or other biomolecules have been the exclusive prerogative of Förster resonance energy transfer (FRET) microscopy for decades. In this work, we show that MINFLUX fluorescence nanoscopy measures intramolecular distances down to 1 nanometer-and in planar projections down to 1 angstrom-directly, linearly, and with angstrom precision. Our method was validated by quantifying well-characterized 1- to 10-nanometer distances in polypeptides and proteins. Moreover, we visualized the orientations of immunoglobulin subunits, applied the method in human cells, and revealed specific configurations of a histidine kinase PAS domain dimer. Our results open the door for examining proximities and interactions by direct position measurements at the intramacromolecular scale.

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.

Measurement of Molecular Height Using Cell Surface Optical Profilometry (CSOP)

The plasma membrane of cells is covered by proteins, glycoproteins, and glycolipids with molecular heights ranging from just a few nanometers to hundreds of nanometers. Formation of cell-cell contacts and signal transduction by individual receptors can be dependent on both the average height of a cell's glycocalyx and the specific height of individual receptors, sometimes with nanometer-scale sensitivity. While super-resolution imaging techniques allow molecular distances to be measured with the sub-diffraction limited resolution, typically 10 nm in the lateral direction and 100 nm in the axial direction, measurements of molecular heights at the single nanometer scale on native cell membranes have been difficult to obtain. Cell surface optical profilometry (CSOP) is a simple and rapid method that achieves nanometer height resolution by localizing fluorophores at the tip and base of cell surface molecules and determining their separation with high precision by radially averaging across many molecules. Here we describe how to make CSOP measurements of multi-domain proteins on model membrane surfaces as well as native cell surfaces.

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.

Time-modulated excitation for enhanced single-molecule localization microscopy

Structured illumination in single-molecule localization microscopy provides new information on the position of molecules and thus improves the localization precision compared to standard localization methods. Here, we used a time-shifted sinusoidal excitation pattern to modulate the fluorescence signal of the molecules whose position information is carried by the phase and recovered by synchronous demodulation. We designed two flexible fast demodulation systems located upstream of the camera, allowing us to overcome the limiting camera acquisition frequency and thus to maximize the collection of photons in the demodulation process. The temporally modulated fluorescence signal was then sampled synchronously on the same image, repeatedly during acquisition. This microscopy, called ModLoc, allows us to experimentally improve the localization precision by a factor of 2.4 in one direction, compared to classical Gaussian fitting methods. A temporal study and an experimental demonstration both show that the short lifetimes of the molecules in blinking regimes impose a modulation frequency in the kilohertz range, which is beyond the reach of current cameras. A demodulation system operating at these frequencies would thus be necessary to take full advantage of this new localization approach.

This article is part of the Theo Murphy meeting issue 'Super-resolution structured illumination microscopy (part 2)'.

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.

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.

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

Estimating the orientation and 3D position of rotationally constrained emitters with localization microscopy typically requires polarization splitting or a large engineered Point Spread Function (PSF). Here we utilize a compact modified PSF for single molecule emitter imaging to estimate simultaneously the 3D position, dipole orientation, and degree of rotational constraint from a single 2D image. We use an affordable and commonly available phase plate, normally used for STED microscopy in the excitation light path, to alter the PSF in the emission light path. This resulting Vortex PSF does not require polarization splitting and has a compact PSF size, making it easy to implement and combine with localization microscopy techniques. In addition to a vectorial PSF fitting routine we calibrate for field-dependent aberrations which enables orientation and position estimation within 30% of the Cramér-Rao bound limit over a 66 μm field of view. We demonstrate this technique on reorienting single molecules adhered to the cover slip, λ-DNA with DNA intercalators using binding-activated localization microscopy, and we reveal periodicity on intertwined structures on supercoiled DNA.

Polarization-resolved single-molecule tracking reveals strange dynamics of fluorescent tracers through a deep rubbery polymer network

Tracking the movement of fluorescent single-molecule (SM) tracers has provided several new insights into the local structure and dynamics in complex environments such as soft materials and biological systems. However, SM tracking (SMT) remains unreliable at molecular length scales, as the localization error (LE) of SM trajectories (∼30-50 nm) is considerably larger than the size of molecular tracers (∼1-2 nm). Thus, instances of tracer (im)mobility in heterogeneous media, which provide indicators for underlying anomalous-transport mechanisms, remain obscured within the realms of SMT. Since the translation of passive tracers in an isotropic media is associated with fast dipolar rotation, we propose that authentic pauses within the LE can be revealed by probing the hindrance of SM reorientational dynamics. Here, we demonstrate how polarization-resolved SMT (PR-SMT) can provide emission anisotropy at each super-localized position, thereby revealing the tumbling propensity of SMs during random walks. For rhodamine 6G tracers undergoing heterogeneous transport in a hydrated polyvinylpyrrolidone (PVP) network, analysis of PR-SMT trajectories enabled us to discern instances of genuine immobility and localized motion within the LE. Our investigations on 100 SMs in (plasticized) PVP films reveal a wide distribution of dwell times and pause frequencies, demonstrating that most probes intermittently experience complete translational and rotational immobilization. This indicates that tracers serendipitously encounter compact, rigid polymer cavities during transport, implying the existence of nanoscale glass-like domains sparsely distributed in a predominantly deep-rubbery polymer network far above the glass transition.

Cryogenic Super-Resolution Fluorescence and Electron Microscopy Correlated at the Nanoscale

We review the emerging method of super-resolved cryogenic correlative light and electron microscopy (srCryoCLEM). Super-resolution (SR) fluorescence microscopy and cryogenic electron tomography (CET) are both powerful techniques for observing subcellular organization, but each approach has unique limitations. The combination of the two brings the single-molecule sensitivity and specificity of SR to the detailed cellular context and molecular scale resolution of CET. The resulting correlative data is more informative than the sum of its parts. The correlative images can be used to pinpoint the positions of fluorescently labeled proteins in the high-resolution context of CET with nanometer-scale precision and/or to identify proteins in electron-dense structures. The execution of srCryoCLEM is challenging and the approach is best described as a method that is still in its infancy with numerous technical challenges. In this review, we describe state-of-the-art srCryoCLEM experiments, discuss the most pressing challenges, and give a brief outlook on future applications.

Three-dimensional single molecule localization close to the coverslip: a comparison of methods exploiting supercritical angle fluorescence

The precise spatial localization of single molecules in three dimensions is an important basis for single molecule localization microscopy (SMLM) and tracking. At distances up to a few hundred nanometers from the coverslip, evanescent wave coupling into the glass, also known as supercritical angle fluorescence (SAF), can strongly improve the axial precision, thus facilitating almost isotropic localization performance. Specific detection systems, introduced as Supercritical angle localization microscopy (SALM) or Direct optical nanoscopy with axially localized detection (DONALD), have been developed to exploit SAF in modified two-channel imaging schemes. Recently, our group has shown that off-focus microscopy, i.e., imaging at an intentional slight defocus, can perform equally well, but uses only a single detection arm. Here we compare SALM, off-focus imaging and the most commonly used 3D SMLM techniques, namely cylindrical lens and biplane imaging, regarding 3D localization in close proximity to the coverslip. We show that all methods gain from SAF, which leaves a high detection NA as the only major key requirement to unlock the SAF benefit. We find parameter settings for cylindrical lens and biplane imaging for highest z-precision. Further, we compare the methods in view of robustness to aberrations, fixed dipole emission and double-emitter events. We show that biplane imaging provides the best overall performance and support our findings by DNA-PAINT experiments on DNA-nanoruler samples. Our study sheds light on the effects of SAF for SMLM and is helpful for researchers who plan to employ localization-based 3D nanoscopy close to the coverslip.

Single-Molecule 3D Orientation Imaging Reveals Nanoscale Compositional Heterogeneity in Lipid Membranes

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.

Spatio-angular fluorescence microscopy III. Constrained angular diffusion, polarized excitation, and high-NA imaging

We investigate rotational diffusion of fluorescent molecules in angular potential wells, the excitation and subsequent emissions from these diffusing molecules, and the imaging of these emissions with high-NA aplanatic optical microscopes. Although dipole emissions only transmit six low-frequency angular components, we show that angular structured illumination can alias higher-frequency angular components into the passband of the imaging system. We show that the number of measurable angular components is limited by the relationships between three time scales: the rotational diffusion time, the fluorescence decay time, and the acquisition time. We demonstrate our model by simulating a numerical phantom in the limits of fast angular diffusion, slow angular diffusion, and weak potentials.

Molecular height measurement by cell surface optical profilometry (CSOP)

The physical dimensions of proteins and glycans on cell surfaces can critically affect cell function, for example, by preventing close contact between cells and limiting receptor accessibility. However, high-resolution measurements of molecular heights on native cell membranes have been difficult to obtain. Here we present a simple and rapid method that achieves nanometer height resolution by localizing fluorophores at the tip and base of cell surface molecules and determining their separation by radially averaging across many molecules. We use this method, which we call cell surface optical profilometry (CSOP), to quantify the height of key multidomain proteins on a model cell, as well as to capture average protein and glycan heights on native cell membranes. We show that average height of a protein is significantly smaller than its contour length, due to thermally driven bending and rotation on the membrane, and that height strongly depends on local surface and solution conditions. We find that average height increases with cell surface molecular crowding but decreases with solution crowding by solutes, both of which we confirm with molecular dynamics simulations. We also use experiments and simulations to determine the height of an epitope, based on the location of an antibody, which allows CSOP to profile various proteins and glycans on a native cell surface using antibodies and lectins. This versatile method for profiling cell surfaces has the potential to advance understanding of the molecular landscape of cells and the role of the molecular landscape in cell function.

Variable incidence angle linear dichroism (VALiD): a technique for unique 3D orientation measurement of fluorescent ensembles

A fundamental challenge with fluorophore orientation measurement is degeneracy, which is the inability to distinguish between multiple unique fluorophore orientations. Techniques exist for the non-degenerate measurement of the orientations of single, static fluorophores. However, such techniques are unsuitable for densely labeled and/or dynamic samples common to biological research. Accordingly, a rapid, widefield microscopy technique that can measure orientation parameters for ensembles of fluorophores in a non-degenerate manner is desirable. We propose that exciting samples with polarized light and multiple incidence angles could enable such a technique. We use Monte Carlo simulations to validate this approach for specific axially symmetric ensembles of fluorophores and obtain optimal experimental parameters for its future implementation.

VIPR: vectorial implementation of phase retrieval for fast and accurate microscopic pixel-wise pupil estimation

In microscopy, proper modeling of the image formation has a substantial effect on the precision and accuracy in localization experiments and facilitates the correction of aberrations in adaptive optics experiments. The observed images are subject to polarization effects, refractive index variations, and system specific constraints. Previously reported techniques have addressed these challenges by using complicated calibration samples, computationally heavy numerical algorithms, and various mathematical simplifications. In this work, we present a phase retrieval approach based on an analytical derivation of the vectorial diffraction model. Our method produces an accurate estimate of the system's phase information, without any prior knowledge about the aberrations, in under a minute.

Selective sequestration of signalling proteins in a membraneless organelle reinforces the spatial regulation of asymmetry in Caulobacter crescentus

Selective recruitment and concentration of signalling proteins within membraneless compartments is a ubiquitous mechanism for subcellular organization1-3. The dynamic flow of molecules into and out of these compartments occurs on faster timescales than for membrane-enclosed organelles, presenting a possible mechanism to control spatial patterning within cells. Here, we combine single-molecule tracking and super-resolution microscopy, light-induced subcellular localization, reaction-diffusion modelling and a spatially resolved promoter activation assay to study signal exchange in and out of the 200 nm cytoplasmic pole-organizing protein popZ (PopZ) microdomain at the cell pole of the asymmetrically dividing bacterium Caulobacter crescentus4-8. Two phospho-signalling proteins, the transmembrane histidine kinase CckA and the cytoplasmic phosphotransferase ChpT, provide the only phosphate source for the cell fate-determining transcription factor CtrA9-18. We find that all three proteins exhibit restricted rates of entry into and escape from the microdomain as well as enhanced phospho-signalling within, leading to a submicron gradient of activated CtrA-P19 that is stable and sublinear. Entry into the microdomain is selective for cytosolic proteins and requires a binding pathway to PopZ. Our work demonstrates how nanoscale protein assemblies can modulate signal propagation with fine spatial resolution, and that in Caulobacter, this modulation serves to reinforce asymmetry and differential cell fate of the two daughter cells.

Spatio-angular fluorescence microscopy I. Basic theory

We introduce the basic elements of a spatio-angular theory of fluorescence microscopy, providing a unified framework for analyzing systems that image single fluorescent dipoles and ensembles of overlapping dipoles that label biological molecules. We model an aplanatic microscope imaging an ensemble of fluorescent dipoles as a linear Hilbert-space operator, and we show that the operator takes a particularly convenient form when expressed in a basis of complex exponentials and spherical harmonics-a form we call the dipole spatio-angular transfer function. We discuss the implications of our analysis for all quantitative fluorescence microscopy studies and lay out a path toward a complete theory.

Spatio-angular fluorescence microscopy II. Paraxial 4f imaging

We investigate the properties of a single-view fluorescence microscope in a 4f geometry when imaging fluorescent dipoles without using the monopole or scalar approximations. We show that this imaging system has a spatio-angular band limit, and we exploit the band limit to perform efficient simulations. Notably, we show that information about the out-of-plane orientation of ensembles of in-focus fluorophores is recorded by paraxial fluorescence microscopes. Additionally, we show that the monopole approximation may cause biased estimates of fluorophore concentrations, but these biases are small when the sample contains either many randomly oriented fluorophores in each resolvable volume or unconstrained rotating fluorophores.

Fundamental Limits on Measuring the Rotational Constraint of Single Molecules Using Fluorescence Microscopy

Optical fluorescence imaging is capable of measuring both the translational and rotational dynamics of single molecules. However, unavoidable measurement noise will result in inaccurate estimates of rotational dynamics, causing a molecule to appear to be more rotationally constrained than it actually is. We report a mathematical framework to compute the fundamental limit of accuracy in measuring the rotational mobility of dipolelike emitters. By applying our framework to both in-plane and three-dimensional methods, we provide a means to choose the optimal orientation-measurement technique based on experimental conditions.

Single-molecule polarization microscopy of DNA intercalators sheds light on the structure of S-DNA

DNA structural transitions facilitate genomic processes, mediate drug-DNA interactions, and inform the development of emerging DNA-based biotechnology such as programmable materials and DNA origami. While some features of DNA conformational changes are well characterized, fundamental information such as the orientations of the DNA base pairs is unknown. Here, we use concurrent fluorescence polarization imaging and DNA manipulation experiments to probe the structure of S-DNA, an elusive, elongated conformation that can be accessed by mechanical overstretching. To this end, we directly quantify the orientations and rotational dynamics of fluorescent DNA-intercalated dyes. At extensions beyond the DNA overstretching transition, intercalators adopt a tilted (θ ~ 54°) orientation relative to the DNA axis, distinct from the nearly perpendicular orientation (θ ~ 90°) normally assumed at lower extensions. These results provide the first experimental evidence that S-DNA has substantially inclined base pairs relative to those of the standard (Watson-Crick) B-DNA conformation.

Nanometer-accuracy distance measurements between fluorophores at the single-molecule level

Measurements of macromolecular shapes provide insight into the mechanism of molecular machines. Distance measurements at the scale of biological macromolecules are often pursued by single-molecule fluorescence techniques. However, while single-molecule Förster resonance energy transfer can estimate distances of less than 8 nm, distances on the scale of 8 to 25 nm are difficult to determine. Here, we report two-color fluorescent distance measurement techniques capable of determining distances with ∼1-nm accuracy over a wide range of length scales. These methods can be implemented in high throughput on commonly available microscopes. As an example of their utility, we used our methods to uncover an unexpected conformational change in the antiparallel coiled-coil stalk of the dynein motor domain in different nucleotide states.

Light microscopy is a powerful tool for probing the conformations of molecular machines at the single-molecule level. Single-molecule Förster resonance energy transfer can measure intramolecular distance changes of single molecules in the range of 2 to 8 nm. However, current superresolution measurements become error-prone below 25 nm. Thus, new single-molecule methods are needed for measuring distances in the 8- to 25-nm range. Here, we describe methods that utilize information about localization and imaging errors to measure distances between two different color fluorophores with ∼1-nm accuracy at distances >2 nm. These techniques can be implemented in high throughput using a standard total internal reflection fluorescence microscope and open-source software. We applied our two-color localization method to uncover an unexpected ∼4-nm nucleotide-dependent conformational change in the coiled-coil “stalk” of the motor protein dynein. We anticipate that these methods will be useful for high-accuracy distance measurements of single molecules over a wide range of length scales.

mmSTORM: Multimodal localization based super-resolution microscopy

Super-resolution localization microscopy provides a powerful tool to study biochemical mechanisms at single molecule level. Although the lateral position of the fluorescent dye molecules can be determined routinely with high precision, measurement of other modalities such as 3D and multicolor without the degradation of the original super-resolved image is still in the focus. In this paper a dual-objective multimodal single molecule localization microscopy (SMLM) technique has been developed, optimized and tested. The proposed optical arrangement can be implemented onto a conventional inverted microscope without serious system modification. The performance of the method was tested using fluorescence beads, F-actin filaments and sarcomere structures. It was shown that the proposed imaging method does not degrade the image quality of the original SMLM 2D image but could provide information on the axial position or emission spectra of the dye molecules.

What we talk about when we talk about nanoclusters

Superresolution microscopy results have sparked the idea that many membrane proteins are not randomly distributed across the plasma membrane but are instead arranged in nanoclusters. Frequently, these new results seemed to confirm older data based on biochemical and electron microscopy experiments. Recently, however, it was recognized that multiple countings of the very same fluorescently labeled protein molecule can be easily confused with true protein clusters. Various strategies have been developed, which are intended to solve the problem of discriminating true protein clusters from imaging artifacts. We believe that there is currently no perfect algorithm for this problem; instead, different approaches have different strengths and weaknesses. In this review, we discuss single molecule localization microscopy in view of its ability to detect nanoclusters of membrane proteins. To capture the different views on nanoclustering, we chose an unconventional style for this article: we placed its scientific content in the setting of a fictive conference, where five researchers from different fields discuss the problem of detecting and quantifying nanoclusters. Using this style, we feel that the different approaches common for different research areas can be well illustrated. Similarities to a short story by Raymond Carver are not unintentional.

Switchable Fluorophores for Single-Molecule Localization Microscopy

The past decade has witnessed an explosion in the use of super-resolution fluorescence microscopy methods in biology and other fields. Single-molecule localization microscopy (SMLM) is one of the most widespread of these methods and owes its success in large part to the ability to control the on-off state of fluorophores through various chemical, photochemical, or binding-unbinding mechanisms. We provide here a comprehensive overview of switchable fluorophores in SMLM including a detailed review of all major classes of SMLM fluorophores, and we also address strategies for labeling specimens, considerations for multichannel and live-cell imaging, potential pitfalls, and areas for future development.

Imaging the three-dimensional orientation and rotational mobility of fluorescent emitters using the Tri-spot point spread function

Fluorescence photons emitted by single molecules contain rich information regarding their rotational motions, but adapting single-molecule localization microscopy (SMLM) to measure their orientations and rotational mobilities with high precision remains a challenge. Inspired by dipole radiation patterns, we design and implement a Tri-spot point spread function (PSF) that simultaneously measures the three-dimensional orientation and the rotational mobility of dipole-like emitters across a large field of view. We show that the orientation measurements done using the Tri-spot PSF are sufficiently accurate to correct the anisotropy-based localization bias, from 30 nm to 7 nm, in SMLM. We further characterize the emission anisotropy of fluorescent beads, revealing that both 20-nm and 100-nm diameter beads emit light significantly differently from isotropic point sources. Exciting 100-nm beads with linearly polarized light, we observe significant depolarization of the emitted fluorescence using the Tri-spot PSF that is difficult to detect using other methods. Finally, we demonstrate that the Tri-spot PSF detects rotational dynamics of single molecules within a polymer thin film that are not observable by conventional SMLM.

Fast photorefractive response in polymeric composites enabled by the control of chromophore free volume

The molecular orientation of a chromophore importantly affects the electro-optic characteristics of polymeric photorefractive composites. We designed methyl, ethyl, and isopropyl derivatives of 4-piperidinobenzylidene-malononitrile (PDCST) with the aim of enhancing molecular orientation properties, and investigated the effects of alkyl substitution on the electro-optic properties and response times of polymeric photorefractive composites. The three alkyl-substituted PDCSTs showed enhanced electro-optic responses and photorefractive grating buildup rates.

Fundamental Precision Bounds for Three-Dimensional Optical Localization Microscopy with Poisson Statistics

Point source localization is a problem of persistent interest in optical imaging. In particular, a number of widely used biological microscopy techniques rely on precise three-dimensional localization of single fluorophores. As emitter depth localization is more challenging than lateral localization, considerable effort has been spent on engineering the response of the microscope in a way that reveals increased depth information. Here, we prove the (sub)optimality of these approaches by deriving and comparing to the measurement-independent quantum Cramér-Rao bound (QCRB). We show that existing methods for depth localization with single-objective collection exceed the QCRB, and we gain insight into the bound by proposing an interferometer arrangement that approaches it. We also show that for light collection with two opposed objectives, an established interferometric technique globally reaches the QCRB in all three dimensions simultaneously, and so this represents an interesting case study from the point of view of quantum multiparameter estimation.

Nanoscale Membrane Budding Induced by CTxB and Detected via Polarized Localization Microscopy

For endocytosis and exocytosis, membranes transition among planar, budding, and vesicular topographies through nanoscale reorganization of lipids, proteins, and carbohydrates. However, prior attempts to understand the initial stages of nanoscale bending have been limited by experimental resolution. Through the implementation of polarized localization microscopy, this article reports the inherent membrane bending capability of cholera toxin subunit B (CTxB) in quasi-one-component-supported lipid bilayers. Membrane buds were first detected with <50 nm radius, grew to >200 nm radius, and extended into longer tubules with dependence on the membrane tension and CTxB concentration. Compared to the concentration of the planar-supported lipid bilayers, CTxB was (12 ± 4)× more concentrated on the positive curvature top and (26 ± 11)× more concentrated on the negative Gaussian curvature neck of the nanoscale membrane buds. CTxB is frequently used as a marker for liquid-ordered lipid phases; however, the coupling between CTxB and membrane bending provides an alternate understanding of CTxB-induced membrane reorganization. These findings allow for the reinterpretation of prior observations by correlating CTxB clustering and diffusion to CTxB-induced membrane bending. Single-particle tracking was performed on single lipids and CTxB to reveal the correlations among single-molecule diffusion, CTxB accumulation, and membrane topography. Slowed lipid and CTxB diffusion was observed at the nanoscale bud locations, suggesting a local increase in the effective membrane viscosity or molecular crowding upon membrane bending. These results suggest inherent CTxB-induced membrane bending as a mechanism for initiating CTxB internalization in cells that could be independent of clathrin, caveolin, actin, and lipid phase separation.

Three-Dimensional Localization of Single Molecules for Super-Resolution Imaging and Single-Particle Tracking

Single-molecule super-resolution fluorescence microscopy and single-particle tracking are two imaging modalities that illuminate the properties of cells and materials on spatial scales down to tens of nanometers or with dynamical information about nanoscale particle motion in the millisecond range, respectively. These methods generally use wide-field microscopes and two-dimensional camera detectors to localize molecules to much higher precision than the diffraction limit. Given the limited total photons available from each single-molecule label, both modalities require careful mathematical analysis and image processing. Much more information can be obtained about the system under study by extending to three-dimensional (3D) single-molecule localization: without this capability, visualization of structures or motions extending in the axial direction can easily be missed or confused, compromising scientific understanding. A variety of methods for obtaining both 3D super-resolution images and 3D tracking information have been devised, each with their own strengths and weaknesses. These include imaging of multiple focal planes, point-spread-function engineering, and interferometric detection. These methods may be compared based on their ability to provide accurate and precise position information on single-molecule emitters with limited photons. To successfully apply and further develop these methods, it is essential to consider many practical concerns, including the effects of optical aberrations, field dependence in the imaging system, fluorophore labeling density, and registration between different color channels. Selected examples of 3D super-resolution imaging and tracking are described for illustration from a variety of biological contexts and with a variety of methods, demonstrating the power of 3D localization for understanding complex systems.

Pointwise error estimates in localization microscopy

Pointwise localization of individual fluorophores is a critical step in super-resolution localization microscopy and single particle tracking. Although the methods are limited by the localization errors of individual fluorophores, the pointwise localization precision has so far been estimated using theoretical best case approximations that disregard, for example, motion blur, defocus effects and variations in fluorescence intensity. Here, we show that pointwise localization precision can be accurately estimated directly from imaging data using the Bayesian posterior density constrained by simple microscope properties. We further demonstrate that the estimated localization precision can be used to improve downstream quantitative analysis, such as estimation of diffusion constants and detection of changes in molecular motion patterns. Finally, the quality of actual point localizations in live cell super-resolution microscopy can be improved beyond the information theoretic lower bound for localization errors in individual images, by modelling the movement of fluorophores and accounting for their pointwise localization uncertainty.

Localization accuracy of gold nanoparticles in single particle orientation and rotational tracking

The Single Particle Orientation and Rotational Tracking (SPORT) technique, which utilizes anisotropic plasmonic gold nanorods and differential interference contrast (DIC) microscopy, has shown potential as an effective alternative to fluorescence-based techniques to decipher rotational motions on the cellular and molecular levels. However, localizing gold nanorods from their DIC images with high accuracy and precision is more challenging than the procedures applied in fluorescence or scattering microscopy techniques due to the asymmetric DIC point spread function with bright and dark parts superimposed over a grey background. In this paper, localization accuracy and inherited uncertainties from unique DIC image patterns are elucidated with the assistance of computer simulation. These discussions provide guidance for researchers to properly evaluate their data and avoid making claims beyond the technical limits. The understanding of the intrinsic localization errors and the principle of DIC microscopy leads us to propose a new localization strategy that utilizes the experimentally-measured shear distance of the DIC microscope to improve the localization accuracy.

TestSTORM: Versatile simulator software for multimodal super-resolution localization fluorescence microscopy

Optimization of sample, imaging and data processing parameters is an essential task in localization based super-resolution microscopy, where the final image quality strongly depends on the imaging of single isolated fluorescent molecules. A computational solution that uses a simulator software for the generation of test data stacks was proposed, developed and tested. The implemented advanced physical models such as scalar and vector based point spread functions, polarization sensitive detection, drift, spectral crosstalk, structured background etc., made the simulation results more realistic and helped us interpret the final super-resolved images and distinguish between real structures and imaging artefacts.

Polarization sensitive localization based super-resolution microscopy with a birefringent wedge

A practical method has been presented for polarization sensitive localization based super-resolution microscopy using a birefringent dual wedge. The measurement of the polarization degree at the single molecule level can reveal the chemical and physical properties of the local environment of the fluorescent dye molecule and can hence provide information about the sub-diffraction sized structure of biological samples. Polarization sensitive STORM imaging of the F-Actins proved correlation between the orientation of fluorescent dipoles and the axis of the fibril.

Single molecule optical measurements of orientation and rotations of biological macromolecules

Subdomains of macromolecules often undergo large orientation changes during their catalytic cycles that are essential for their activity. Tracking these rearrangements in real time opens a powerful window into the link between protein structure and functional output. Site-specific labeling of individual molecules with polarized optical probes and measurement of their spatial orientation can give insight into the crucial conformational changes, dynamics, and fluctuations of macromolecules. Here we describe the range of single molecule optical technologies that can extract orientation information from these probes, review the relevant types of probes and labeling techniques, and highlight the advantages and disadvantages of these technologies for addressing specific inquiries.

Molecular Water Lilies: Orienting Single Molecules in a Polymer Film by Solvent Vapor Annealing

The microscopic orientation and position of photoactive molecules is crucial to the operation of optoelectronic devices such as OLEDs and solar cells. Here, we introduce a shape-persistent macrocyclic molecule as an excellent fluorescent probe to simply measure (i) its orientation by rotating the excitation polarization and recording the strength of modulation in photoluminescence (PL) and (ii) its position in a film by analyzing the overall PL brightness at the molecular level. The unique shape, the absorption and the fluorescence properties of this probe yield information on molecular orientation and position. We control orientation and positioning of the probe in a polymer film by solvent vapor annealing (SVA). During the SVA process the molecules accumulate at the polymer/air interface, where they adopt a flat orientation, much like water lilies on the surface of a pond. The results are potentially significant for OLED fabrication and single-molecule spectroscopy (SMS) in general.

Surface Chemistry of Gold Nanorods

Gold nanorods have garnered a great deal of scientific interest because of their unique optical properties, and they have the potential to greatly impact many areas of science and technology. Understanding the structure and chemical makeup of their surfaces as well as how to tailor them is of paramount importance in the development of their successful applications. This Feature Article reviews the current understanding of the surface chemistry of as-synthesized gold nanorods, methods of tailoring the surface chemistry of gold nanorods with various inorganic and organic coatings/ligands, and the techniques employed to characterize ligands on the surface of gold nanorods as well as the associated measurement challenges. Specifically, we address the challenges of determining how thick the ligand shell is, how many ligands per nanorod are present on the surface, and where the ligands are located in regiospecific and mixed-ligand systems. We conclude with an outlook on the development of the surface chemistry of gold nanorods leading to the development of a synthetic nanoparticle surface chemistry toolbox analogous to that of synthetic organic chemistry and natural product synthesis.

Enhanced DNA imaging using super-resolution microscopy and simultaneous single-molecule orientation measurements

Single-molecule orientation measurements provide unparalleled insight into a multitude of biological and polymeric systems. We report a simple, high-throughput technique for measuring the azimuthal orientation and rotational dynamics of single fluorescent molecules, which is compatible with localization microscopy. Our method involves modulating the polarization of an excitation laser, and analyzing the corresponding intensities emitted by single dye molecules and their modulation amplitudes. To demonstrate our approach, we use intercalating and groove-binding dyes to obtain super-resolved images of stretched DNA strands through binding-induced turn-on of fluorescence. By combining our image data with thousands of dye molecule orientation measurements, we develop a means of probing the structure of individual DNA strands, while also characterizing dye-DNA interactions. This approach may hold promise as a method for monitoring DNA conformation changes resulting from DNA-binding proteins.

Deciphering the Structure and Function of Nuclear Pores Using Single-Molecule Fluorescence Approaches

Due to its central role in macromolecular trafficking and nucleocytoplasmic information transfer, the nuclear pore complex (NPC) has been studied in great detail using a wide spectrum of methods. Consequently, many aspects of its architecture, general function, and role in the life cycle of a cell are well understood. Over the last decade, fluorescence microscopy methods have enabled the real-time visualization of single molecules interacting with and transiting through the NPC, allowing novel questions to be examined with nanometer precision. While initial single-molecule studies focused primarily on import pathways using permeabilized cells, it has recently proven feasible to investigate the export of mRNAs in living cells. Single-molecule assays can address questions that are difficult or impossible to answer by other means, yet the complexity of nucleocytoplasmic transport requires that interpretation be based on a firm genetic, biochemical, and structural foundation. Moreover, conceptually simple single-molecule experiments remain technically challenging, particularly with regard to signal intensity, signal-to-noise ratio, and the analysis of noise, stochasticity, and precision. We discuss nuclear transport issues recently addressed by single-molecule microscopy, evaluate the limits of existing assays and data, and identify open questions for future studies. We expect that single-molecule fluorescence approaches will continue to be applied to outstanding nucleocytoplasmic transport questions, and that the approaches developed for NPC studies are extendable to additional complex systems and pathways within cells.

Lens-based fluorescence nanoscopy

The majority of studies of the living cell rely on capturing images using fluorescence microscopy. Unfortunately, for centuries, diffraction of light was limiting the spatial resolution in the optical microscope: structural and molecular details much finer than about half the wavelength of visible light (~200 nm) could not be visualized, imposing significant limitations on this otherwise so promising method. The surpassing of this resolution limit in far-field microscopy is currently one of the most momentous developments for studying the living cell, as the move from microscopy to super-resolution microscopy or 'nanoscopy' offers opportunities to study problems in biophysical and biomedical research at a new level of detail. This review describes the principles and modalities of present fluorescence nanoscopes, as well as their potential for biophysical and cellular experiments. All the existing nanoscopy variants separate neighboring features by transiently preparing their fluorescent molecules in states of different emission characteristics in order to make the features discernible. Usually these are fluorescent 'on' and 'off' states causing the adjacent molecules to emit sequentially in time. Each of the variants can in principle reach molecular spatial resolution and has its own advantages and disadvantages. Some require specific transitions and states that can be found only in certain fluorophore subfamilies, such as photoswitchable fluorophores, while other variants can be realized with standard fluorescent labels. Similar to conventional far-field microscopy, nanoscopy can be utilized for dynamical, multi-color and three-dimensional imaging of fixed and live cells, tissues or organisms. Lens-based fluorescence nanoscopy is poised for a high impact on future developments in the life sciences, with the potential to help solve long-standing quests in different areas of scientific research.

Quantitative nanoscale imaging of orientational order in biological filaments by polarized superresolution microscopy

Essential cellular functions as diverse as genome maintenance and tissue morphogenesis rely on the dynamic organization of filamentous assemblies. For example, the precise structural organization of DNA filaments has profound consequences on all DNA-mediated processes including gene expression, whereas control over the precise spatial arrangement of cytoskeletal protein filaments is key for mechanical force generation driving animal tissue morphogenesis. Polarized fluorescence is currently used to extract structural organization of fluorescently labeled biological filaments by determining the orientation of fluorescent labels, however with a strong drawback: polarized fluorescence imaging is indeed spatially limited by optical diffraction, and is thus unable to discriminate between the intrinsic orientational mobility of the fluorophore labels and the real structural disorder of the labeled biomolecules. Here, we demonstrate that quantitative single-molecule polarized detection in biological filament assemblies allows not only to correct for the rotational flexibility of the label but also to image orientational order of filaments at the nanoscale using superresolution capabilities. The method is based on polarized direct stochastic optical reconstruction microscopy, using dedicated optical scheme and image analysis to determine both molecular localization and orientation with high precision. We apply this method to double-stranded DNA in vitro and microtubules and actin stress fibers in whole cells.

Removing Orientation-Induced Localization Biases in Single-Molecule Microscopy Using a Broadband Metasurface Mask

Nanoscale localization of single molecules is a crucial function in several advanced microscopy techniques, including single-molecule tracking and wide-field super-resolution imaging ¹. To date, a central consideration of such techniques is how to optimize the precision of molecular localization. However, as these methods continue to push toward the nanometre size scale, an increasingly important concern is the localization accuracy. In particular, single fluorescent molecules emit with an anisotropic radiation pattern of an oscillating electric dipole, which can cause significant localization biases using common estimators ^2-5. Here we present the theory and experimental demonstration of a solution to this problem based on azimuthal filtering in the Fourier plane of the microscope. We do so using a high efficiency dielectric metasurface polarization/phase device composed of nanoposts with sub-wavelength spacing ⁶. The method is demonstrated both on fluorophores embedded in a polymer matrix, and in dL5 protein complexes that bind Malachite green ^{7, 8}.

Precise Three-Dimensional Scan-Free Multiple-Particle Tracking over Large Axial Ranges with Tetrapod Point Spread Functions

We employ a novel framework for information-optimal microscopy to design a family of point spread functions (PSFs), the Tetrapod PSFs, which enable high-precision localization of nanoscale emitters in three dimensions over customizable axial (z) ranges of up to 20 μm with a high numerical aperture objective lens. To illustrate, we perform flow profiling in a microfluidic channel and show scan-free tracking of single quantum-dot-labeled phospholipid molecules on the surface of living, thick mammalian cells.