Effect of aberration on height calibration in three-dimensional localization-based microscopy and particle tracking

Adaptive optics in super-resolution microscopy

Fluorescence microscopy has become a routine tool in biology for interrogating life activities with minimal perturbation. While the resolution of fluorescence microscopy is in theory governed only by the diffraction of light, the resolution obtainable in practice is also constrained by the presence of optical aberrations. The past two decades have witnessed the advent of super-resolution microscopy that overcomes the diffraction barrier, enabling numerous biological investigations at the nanoscale. Adaptive optics, a technique borrowed from astronomical imaging, has been applied to correct for optical aberrations in essentially every microscopy modality, especially in super-resolution microscopy in the last decade, to restore optimal image quality and resolution. In this review, we briefly introduce the fundamental concepts of adaptive optics and the operating principles of the major super-resolution imaging techniques. We highlight some recent implementations and advances in adaptive optics for active and dynamic aberration correction in super-resolution microscopy.

Addressing systematic errors in axial distance measurements in single-emitter localization microscopy

Nanoscale localization of point emitters is critical to several methods in optical fluorescence microscopy, including single-molecule super-resolution imaging and tracking. While the precision of the localization procedure has been the topic of extensive study, localization accuracy has been less emphasized, in part due to the challenge of producing an experimental sample containing unperturbed point emitters at known three-dimensional positions in a relevant geometry. We report a new experimental system which reproduces a widely-adopted geometry in high-numerical aperture localization microscopy, in which molecules are situated in an aqueous medium above a glass coverslip imaged with an oil-immersion objective. We demonstrate a calibration procedure that enables measurement of the depth-dependent point spread function (PSF) for open aperture imaging as well as imaging with engineered PSFs with index mismatch. We reveal the complicated, depth-varying behavior of the focal plane position in this system and discuss the axial localization biases incurred by common approximations of this behavior. We compare our results to theoretical calculations.

Depth-dependent PSF calibration and aberration correction for 3D single-molecule localization

Three-dimensional single molecule localization microscopy relies on the fitting of the individual molecules with a point spread function (PSF) model. The reconstructed images often show local squeezing or expansion in z. A common cause is depth-induced aberrations in conjunction with an imperfect PSF model calibrated from beads on a coverslip, resulting in a mismatch between measured PSF and real PSF. Here, we developed a strategy for accurate z-localization in which we use the imperfect PSF model for fitting, determine the fitting errors and correct for them in a post-processing step. We present an open-source software tool and a simple experimental calibration procedure that allow retrieving accurate z-positions in any PSF engineering approach or fitting modality, even at large imaging depths.

Direct characterization of the evanescent field in objective-type total internal reflection fluorescence microscopy

Total internal reflection fluorescence (TIRF) microscopy is a commonly used method for studying fluorescently labeled molecules in close proximity to a surface. Usually, the TIRF axial excitation profile is assumed to be single-exponential with a characteristic penetration depth, governed by the incident angle of the excitation laser beam towards the optical axis. However, in practice, the excitation profile does not only comprise the theoretically predicted single-exponential evanescent field, but also an additional non-evanescent contribution, supposedly caused by scattering within the optical path or optical aberrations. We developed a calibration slide to directly characterize the TIRF excitation field. Our slide features ten height steps ranging from 25 to 550 nanometers, fabricated from a polymer with a refractive index matching that of water. Fluorophores in aqueous solution above the polymer step layers sample the excitation profile at different heights. The obtained excitation profiles confirm the theoretically predicted exponential decay over increasing step heights as well as the presence of a non-evanescent contribution.

Real-time 3D single-molecule localization using experimental point spread functions

We present a real-time fitter for 3D single-molecule localization microscopy using experimental point spread functions (PSFs) that achieves minimal uncertainty in 3D on any microscope and is compatible with any PSF engineering approach. We used this method to image cellular structures and attained unprecedented image quality for astigmatic PSFs. The fitter compensates for most optical aberrations and makes accurate 3D super-resolution microscopy broadly accessible, even on standard microscopes without dedicated 3D optics.

Aberration-accounting calibration for 3D single-molecule localization microscopy

We propose a straightforward sample-based technique to calibrate the axial detection in 3D single-molecule localization microscopy. Using microspheres coated with fluorescent molecules, the calibration curves of point spread function-shaping or intensity-based measurements can be obtained over the imaging depth range. This experimental method takes into account the effect of the spherical aberration without requiring computational correction. We demonstrate its efficiency for astigmatic imaging in a 1.2 μm range above the coverslip.

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.

Recovering fluorophore concentration profiles from confocal images near lateral refractive index step changes

Optical aberrations due to refractive index mismatches occur in various types of microscopy due to refractive differences between the sample and the immersion fluid or within the sample. We study the effects of lateral refractive index differences by fluorescence confocal laser scanning microscopy due to glass or polydimethylsiloxane cuboids and glass cylinders immersed in aqueous fluorescent solution, thereby mimicking realistic imaging situations in the proximity of these materials. The reduction in fluorescence intensity near the embedded objects was found to depend on the geometry and the refractive index difference between the object and the surrounding solution. The observed fluorescence intensity gradients do not reflect the fluorophore concentration in the solution. It is suggested to apply a Gaussian fit or smoothing to the observed fluorescence intensity gradient and use this as a basis to recover the fluorophore concentration in the proximity of the refractive index step change. The method requires that the reference and sample objects have the same geometry and refractive index. The best results were obtained when the sample objects were also used for reference since small differences such as uneven surfaces will result in a different extent of aberration.

Fast Three-Dimensional Single-Particle Tracking in Natural Brain Tissue

Observation of molecular dynamics is often biased by the optical very heterogeneous environment of cells and complex tissue. Here, we have designed an algorithm that facilitates molecular dynamic analyses within brain slices. We adjust fast astigmatism-based three-dimensional single-particle tracking techniques to depth-dependent optical aberrations induced by the refractive index mismatch so that they are applicable to complex samples. In contrast to existing techniques, our online calibration method determines the aberration directly from the acquired two-dimensional image stream by exploiting the inherent particle movement and the redundancy introduced by the astigmatism. The method improves the positioning by reducing the systematic errors introduced by the aberrations, and allows correct derivation of the cellular morphology and molecular diffusion parameters in three dimensions independently of the imaging depth. No additional experimental effort for the user is required. Our method will be useful for many imaging configurations, which allow imaging in deep cellular structures.

Multifluorophore localization as a percolation problem: limits to density and precision

We show that the maximum desirable density of activated fluorophores in a superresolution experiment can be determined by treating the overlapping point spread functions as a problem in percolation theory. We derive a bound on the density of activated fluorophores, taking into account the desired localization accuracy and precision, as well as the number of photons emitted. Our bound on density is close to that reported in experimental work, suggesting that further increases in the density of imaged fluorophores will come at the expense of localization accuracy and precision.

Correcting field-dependent aberrations with nanoscale accuracy in three-dimensional single-molecule localization microscopy

The localization of single fluorescent molecules enables the imaging of molecular structure and dynamics with subdiffraction precision and can be extended to three dimensions using point spread function (PSF) engineering. However, the nanoscale accuracy of localization throughout a 3D single-molecule microscope's field of view has not yet been rigorously examined. By using regularly spaced subdiffraction apertures filled with fluorescent dyes, we reveal field-dependent aberrations as large as 50-100 nm and show that they can be corrected to less than 25 nm over an extended 3D focal volume. We demonstrate the applicability of this technique for two engineered PSFs, the double-helix PSF and the astigmatic PSF. We expect these results to be broadly applicable to 3D single-molecule tracking and superresolution methods demanding high accuracy.

Precisely and accurately localizing single emitters in fluorescence microscopy

Methods based on single-molecule localization and photophysics have brought nanoscale imaging with visible light into reach. This has enabled single-particle tracking applications for studying the dynamics of molecules and nanoparticles and contributed to the recent revolution in super-resolution localization microscopy techniques. Crucial to the optimization of such methods are the precision and accuracy with which single fluorophores and nanoparticles can be localized. We present a lucid synthesis of the developments on this localization precision and accuracy and their practical implications in order to guide the increasing number of researchers using single-particle tracking and super-resolution localization microscopy.

Eight years of single-molecule localization microscopy

Super-resolution imaging by single-molecule localization (localization microscopy) provides the ability to unravel the structural organization of cells and the composition of biomolecular assemblies at a spatial resolution that is well below the diffraction limit approaching virtually molecular resolution. Constant improvements in fluorescent probes, efficient and specific labeling techniques as well as refined data analysis and interpretation strategies further improved localization microscopy. Today, it allows us to interrogate how the distribution and stoichiometry of interacting proteins in subcellular compartments and molecular machines accomplishes complex interconnected cellular processes. Thus, it exhibits potential to address fundamental questions of cell and developmental biology. Here, we briefly introduce the history, basic principles, and different localization microscopy methods with special focus on direct stochastic optical reconstruction microscopy (dSTORM) and summarize key developments and examples of two- and three-dimensional localization microscopy of the last 8 years.

Correction of depth-dependent aberrations in 3D single-molecule localization and super-resolution microscopy

Single-molecule switching based super-resolution microscopy techniques have been extended into three dimensions through various 3D single-molecule localization methods. However, the localization accuracy in z can be severely degraded by the presence of aberrations, particularly the spherical aberration introduced by the refractive index mismatch when imaging into an aqueous sample with an oil immersion objective. This aberration confines the imaging depth in most experiments to regions close to the coverslip. Here we show a method to obtain accurate, depth-dependent z calibrations by measuring the point spread function (PSF) at the coverslip surface, calculating the microscope pupil function through phase retrieval, and then computing the depth-dependent PSF with the addition of spherical aberrations. We demonstrate experimentally that this method can maintain z localization accuracy over a large range of imaging depths. Our super-resolution images of a mammalian cell nucleus acquired between 0 and 2.5 μm past the coverslip show that this method produces accurate z localizations even in the deepest focal plane.

Extending microscopic resolution with single-molecule imaging and active control

Superresolution imaging of biological structures provides information beyond the optical diffraction limit. One class of superresolution techniques uses the power of single fluorescent molecules as nanoscale emitters of light combined with emission control, variously described by the acronyms PALM/FPALM/STORM and many others. Even though the acronyms differ and refer mainly to different active-control mechanisms, the underlying fundamental principles behind these "pointillist" superresolution imaging techniques are the same. Circumventing the diffraction limit requires two key steps. The first step (superlocalization) is the detection and localization of spatially separated single molecules. The second step actively controls the emitting molecules to ensure a very low concentration of single emitters such that they do not overlap in any one imaging frame. The final image is reconstructed from time-sequential imaging and superlocalization of the single emitting labels decorating the structure of interest. The statistical, imaging, and active-control strategies for achieving superresolution imaging with single molecules are reviewed.

Dynamic three-dimensional tracking of single fluorescent nanoparticles deep inside living tissue

Three-dimensional (3D) spatial information can be encoded in two-dimensional images of fluorescent nanoparticles by astigmatic imaging. We combined this method with light sheet microscopy for high contrast single particle imaging up to 200 µm deep within living tissue and real-time image analysis to determine 3D particle localizations with nanometer precision and millisecond temporal resolution. Axial information was instantly directed to the sample stage to keep a moving particle within the focal plane in an active feedback loop. We demonstrated 3D tracking of nanoparticles at an unprecedented depth throughout large cell nuclei over several thousand frames and a range of more than 10 µm in each spatial dimension, while simultaneously acquiring optically sectioned wide field images. We conclude that this 3D particle tracking technique employing light sheet microscopy presents a valuable extension to the nanoscopy toolbox.

Three-dimensional super-resolution imaging of the midplane protein FtsZ in live Caulobacter crescentus cells using astigmatism

Single-molecule super-resolution imaging provides a non-invasive method for nanometer-scale imaging and is ideally suited to investigations of quasi-static structures within live cells. Here, we extend the ability to image subcellular features within bacteria cells to three dimensions based on the introduction of a cylindrical lens in the imaging pathway. We investigate the midplane protein FtsZ in Caulobacter crescentus with super-resolution imaging based on fluorescent-protein photoswitching and the natural polymerization/depolymerization dynamics of FtsZ associated with the Z-ring. We quantify these dynamics and determine the FtsZ depolymerization time to be <100 ms. We image the Z-ring in live and fixed C. crescentus cells at different stages of the cell cycle and find that the FtsZ superstructure is dynamic with the cell cycle, forming an open shape during the stalked stage and a dense focus during the pre-divisional stage.

Single-image axial localization precision analysis for individual fluorophores

Bio-mechanism investigations demand single particle tracking with high spatial and temporal resolutions which require single fluorophore 3D localization measurements with matching precision and speed. Although the precision for lateral-localization measurements is well described by an analytical expression, for the axial direction, it is often obtained by repeating location measurements or by estimating a lower bound. Here, we report a precision expression for an axial-localization method that analyzes the standard deviations of single fluorophores' intensity profiles. Like the lateral-localization precision, this expression includes all relevant experimental effects measurable from a gaussian intensity profile of the fluorophore. This expression completes the precision analysis for single-image 3D localization of individual fluorophores and lifts the temporal resolution to the typical exposure timescales of milliseconds.

Three-dimensional superresolution colocalization of intracellular protein superstructures and the cell surface in live Caulobacter crescentus

Recently, single-molecule imaging and photocontrol have enabled superresolution optical microscopy of cellular structures beyond Abbe's diffraction limit, extending the frontier of noninvasive imaging of structures within living cells. However, live-cell superresolution imaging has been challenged by the need to image three-dimensional (3D) structures relative to their biological context, such as the cellular membrane. We have developed a technique, termed superresolution by power-dependent active intermittency and points accumulation for imaging in nanoscale topography (SPRAIPAINT) that combines imaging of intracellular enhanced YFP (eYFP) fusions (SPRAI) with stochastic localization of the cell surface (PAINT) to image two different fluorophores sequentially with only one laser. Simple light-induced blinking of eYFP and collisional flux onto the cell surface by Nile red are used to achieve single-molecule localizations, without any antibody labeling, cell membrane permeabilization, or thiol-oxygen scavenger systems required. Here we demonstrate live-cell 3D superresolution imaging of Crescentin-eYFP, a cytoskeletal fluorescent protein fusion, colocalized with the surface of the bacterium Caulobacter crescentus using a double-helix point spread function microscope. Three-dimensional colocalization of intracellular protein structures and the cell surface with superresolution optical microscopy opens the door for the analysis of protein interactions in living cells with excellent precision (20-40 nm in 3D) over a large field of view (12 12 μm).

Three-dimensional tracking of single mRNA particles in Saccharomyces cerevisiae using a double-helix point spread function

Optical imaging of single biomolecules and complexes in living cells provides a useful window into cellular processes. However, the three-dimensional dynamics of most important biomolecules in living cells remains essentially uncharacterized. The precise subcellular localization of mRNA-protein complexes plays a critical role in the spatial and temporal control of gene expression, and a full understanding of the control of gene expression requires precise characterization of mRNA transport dynamics beyond the optical diffraction limit. In this paper, we describe three-dimensional tracking of single mRNA particles with 25-nm precision in the x and y dimensions and 50-nm precision in the z dimension in live budding yeast cells using a microscope with a double-helix point spread function. Two statistical methods to detect intermittently confined and directed transport were used to quantify the three-dimensional trajectories of mRNA for the first time, using ARG3 mRNA as a model. Measurements and analysis show that the dynamics of ARG3 mRNA molecules are mostly diffusive, although periods of non-Brownian confinement and directed transport are observed. The quantitative methods detailed in this paper can be broadly applied to the study of mRNA localization and the dynamics of diverse other biomolecules in a wide variety of cell types.

Near-isotropic 3D optical nanoscopy with photon-limited chromophores

Imaging approaches based on single molecule localization break the diffraction barrier of conventional fluorescence microscopy, allowing for bioimaging with nanometer resolution. It remains a challenge, however, to precisely localize photon-limited single molecules in 3D. We have developed a new localization-based imaging technique achieving almost isotropic subdiffraction resolution in 3D. A tilted mirror is used to generate a side view in addition to the front view of activated single emitters, allowing their 3D localization to be precisely determined for superresolution imaging. Because both front and side views are in focus, this method is able to efficiently collect emitted photons. The technique is simple to implement on a commercial fluorescence microscope, and especially suitable for biological samples with photon-limited chromophores such as endogenously expressed photoactivatable fluorescent proteins. Moreover, this method is relatively resistant to optical aberration, as it requires only centroid determination for localization analysis. Here we demonstrate the application of this method to 3D imaging of bacterial protein distribution and neuron dendritic morphology with subdiffraction resolution.

Molecules and methods for super-resolution imaging

By looking at a fluorescently labeled structure one molecule at a time, it is possible to side-step the optical diffraction limit and obtain "super-resolution" images of small nanostructures. In the Moerner Lab, we seek to develop both molecules and methods to extend super-resolution fluorescence imaging. Methodologies and protocols for designing and characterizing fluorophores with switchable fluorescence required for super-resolution imaging are reported. These fluorophores include azido-DCDHF molecules, covalently linked Cy3-Cy5 dimers, and also the first example of a photoswitchable fluorescent protein, enhanced yellow fluorescent protein (EYFP). The imaging of protein superstructures in living Caulobacter crescentus bacteria is used as an example of the power of super-resolution imaging by single-molecule photoswitching to extract information beyond the diffraction limit. Finally, a new method is described for obtaining three-dimensional super-resolution information using a double-helix point-spread function.

Experimental characterization of 3D localization techniques for particle-tracking and super-resolution microscopy

Three-dimensional (3D) particle localization at the nanometer scale plays a central role in 3D particle tracking and 3D localization-based super-resolution microscopy. Here we introduce a localization algorithm that is independent of theoretical models and therefore generally applicable to a large number of experimental realizations. Applying this algorithm and a convertible experimental setup we compare the performance of the two major 3D techniques based on astigmatic distortions and on multiplane detection. In both methods we obtain experimental 3D localization accuracies in agreement with theoretical predictions and characterize the depth dependence of the localization accuracy in detail.