Superresolution localization methods

Tuning axial and lateral localization precision in 3D super-resolution microscopy with variable astigmatism

Astigmatism imaging is a three-dimensional (3D) single molecule fluorescence microscopy approach that yields super-resolved spatial information on a rapid time scale from a single image. It is ideally suited for resolving structures on a sub-micrometer scale and temporal behavior in the millisecond regime. While traditional astigmatism imaging utilizes a cylindrical lens, adaptive optics enables the astigmatism to be tuned for the experiment. We demonstrate here how the precisions in x, y, and z are inter-linked and vary with the astigmatism, z-position, and photon level. This experimentally driven and verified approach provides a guide for astigmatism selection in biological imaging strategies.

Locally adaptive thresholding centroid localization in confocal microscopy

We introduce an iteration-free approach, based on a centroid algorithm with a locally adaptive threshold, for nanometer-level peak position localization of the axial response signal in confocal microscopy. This approach has localization accuracies that are near theoretical limits, especially when there is a small number of sampling points within the discrete signal. The algorithm is also orders of magnitude faster compared to fitting schemes based on maximum likelihood estimation. Simulations and experiments demonstrate the localization performance of the approach.

SNR enhancement in brillouin microspectroscopy using spectrum reconstruction

Brillouin spectroscopy can suffer from low signal-to-noise ratios (SNRs). Such low SNRs can render common data analysis protocols unreliable, especially for SNRs below ∼10. In this work we exploit two denoising algorithms, namely maximum entropy reconstruction (MER) and wavelet analysis (WA), to improve the accuracy and precision in determination of Brillouin shifts and linewidth. Algorithm performance is quantified using Monte-Carlo simulations and benchmarked against the Cramér-Rao lower bound. Superior estimation results are demonstrated even at low SNRs (≥ 1). Denoising is furthermore applied to experimental Brillouin spectra of distilled water at room temperature, allowing the speed of sound in water to be extracted. Experimental and theoretical values were found to be consistent to within ±1% at unity SNR.

Single-molecule localization microscopy as nonlinear inverse problem

We present a statistical framework to model the spatial distribution of molecules based on a single-molecule localization microscopy (SMLM) dataset. The latter consists of a collection of spatial coordinates and their associated uncertainties. We describe iterative parameter-estimation algorithms based on this framework, as well as a sampling algorithm to numerically evaluate the complete posterior distribution. We demonstrate that the inverse computation can be viewed as a type of image restoration process similar to the classical image deconvolution methods, except that it is performed on SMLM images. We further discuss an application of our statistical framework in the task of particle fusion using SMLM data. We show that the fusion algorithm based on our model outperforms the current state-of-the-art in terms of both accuracy and computational cost.

Wavelength-scale errors in optical localization due to spin-orbit coupling of light

Far-field optical imaging techniques allow the determination of the position of point-like emitters and scatterers [1-3]. Although the optical wavelength sets a fundamental limit to the image resolution of unknown objects, the position of an individual emitter can in principle be estimated from the image with arbitrary precision. This is used for example in the determination of stars position [4] or in optical super-resolution microscopy [5]. Furthermore, precise position determination is an experimental prerequisite for the manipulation and measurement of individual quantum systems, such as atoms, ions, and solid-state-based quantum emitters [6-8]. Here we demonstrate that spin-orbit coupling of light in the emission of elliptically polarized emitters can lead to systematic, wavelength-scale errors in the estimation of the emitters position. Imaging a single trapped atom as well as a single sub-wavelength-diameter gold nanoparticle, we demonstrate a shift between the emitters measured and actual positions which is comparable to the optical wavelength. For certain settings, the expected shift can become arbitrarily large. Beyond optical imaging techniques, our findings could be relevant for the localization of objects using any type of wave that carries orbital angular momentum relative to the emitters position with a component orthogonal to the direction of observation.

Design, characterization and in vivo functioning of a light-dependent histidine protein kinase in the yeast Saccharomyces cerevisiae

Helical alignment of the α-helical linker of the LOV (light-oxygen-voltage) domain of YtvA from Bacillus subtilis with the α-helical linker of the histidine-protein kinase domain of the Sln1 kinase of the phospho-relay system for osmoregulation of Saccharomyces cerevisiae has been used to construct a light-modulatable histidine protein kinase. In vitro, illumination with blue light inhibits both the ATP-dependent phosphorylation of this hybrid kinase, as well as the phosphoryl transfer to Ypd1, the phosphoryl transfer domain of the Sln1 system. The helical alignment was carried out with conservation of the complete Jα helix of YtvA, as well as of the phosphorylatable histidine residue of the Sln1 kinase, with conservation of the hepta-helical motive of coiled-coil structures, recognizable in the helices of the two separate, constituent, proteins. Introduction of the gene encoding this hybrid histidine protein kinase into cells of S. cerevisiae in which the endogenous Sln1 kinase had been deleted, allowed us to modulate gene expression in the yeast cells with (blue) light. This was first demonstrated via the light-induced alteration of the expression level of the mannosyl-transferase OCH1, via a translational-fusion approach. As expected, illumination decreased the expression level of OCH1; the steady state decrease in saturating levels of blue light was about 40%. To visualize the in vivo functionality of this light-dependent regulation system, we fused the green fluorescent protein (GFP) to another regulatory protein, HOG1, which is also responsive to the Sln1 kinase. HOG1 is phosphorylated by the MAP-kinase-kinase Pbs2, which in turn is under control of the Sln1 kinase, via the phosphoryl transfer domain Ypd1. Fluorescence microscopy was used to show that illumination of cells that contained the combination of the hybrid kinase and the HOG1::GFP fusion protein, led to a persistent increase in the level of nuclear accumulation of HOG1, in contrast to salt stress, which-as expected-showed the well-characterized transient response. The system described in this study will be valuable in future studies on the role of cytoplasmic diffusion in signal transduction in eukaryotic cells.

Time-resolved molecule counting by photon statistics across the visible spectrum

In the past few years quantification of fluorescently labeled (bio-) molecules has become of increasing importance and several approaches have been developed to address this task. Counting by photon statistics measures the distribution of multiple photon detection events that carry information about the number and brightness of independently emitting fluorophores. The method enables absolute and non-destructive quantification, with the quality of estimates critically depending on the ability to accurately measure said photon statistics. Here, we present a combination of simulations and experiments that relate fundamental properties of fluorophores, i.e. their molecular brightness and photostability, to important experimental conditions, i.e. excitation power and acquisition time. Thereby, experimental settings and analysis parameters can be quantitatively evaluated, making counting by photon statistics a robust method for absolute counting of the number of emitters in a diffraction limited observation volume. We show that the time-resolution of counting varies with the fluorophore brightness and can be as fast as 10-100 ms. At the same time, the range of suitable fluorophores can be easily assessed. We evaluated the brightness and photostability of 16 organic dyes across the visible spectrum, providing information crucial for a range of single-molecule spectroscopy applications. This opens up exciting possibilities to analyze absolute stoichiometries in dynamic multi-component complexes.

Analysis and correction of errors in nanoscale particle tracking using the Single-pixel interior filling function (SPIFF) algorithm

Particle tracking, which is an essential tool in many fields of scientific research, uses algorithms that retrieve the centroid of tracked particles with sub-pixel accuracy. However, images in which the particles occupy a small number of pixels on the detector, are in close proximity to other particles or suffer from background noise, show a systematic error in which the particle sub-pixel positions are biased towards the center of the pixel. This "pixel locking" effect greatly reduces particle tracking accuracy. In this report, we demonstrate the severity of these errors by tracking experimental (and simulated) imaging data of optically trapped silver nanoparticles and single fluorescent proteins. We show that errors in interparticle separation, angle and mean square displacement are significantly reduced by applying the corrective Single-Pixel Interior Filling Function (SPIFF) algorithm. Our work demonstrates the potential ubiquity of such errors and the general applicability of SPIFF correction to many experimental fields.

Single-pixel interior filling function approach for detecting and correcting errors in particle tracking

We present a general method for detecting and correcting biases in the outputs of particle-tracking experiments. Our approach is based on the histogram of estimated positions within pixels, which we term the single-pixel interior filling function (SPIFF). We use the deviation of the SPIFF from a uniform distribution to test the veracity of tracking analyses from different algorithms. Unbiased SPIFFs correspond to uniform pixel filling, whereas biased ones exhibit pixel locking, in which the estimated particle positions concentrate toward the centers of pixels. Although pixel locking is a well-known phenomenon, we go beyond existing methods to show how the SPIFF can be used to correct errors. The key is that the SPIFF aggregates statistical information from many single-particle images and localizations that are gathered over time or across an ensemble, and this information augments the single-particle data. We explicitly consider two cases that give rise to significant errors in estimated particle locations: undersampling the point spread function due to small emitter size and intensity overlap of proximal objects. In these situations, we show how errors in positions can be corrected essentially completely with little added computational cost. Additional situations and applications to experimental data are explored in SI Appendix In the presence of experimental-like shot noise, the precision of the SPIFF-based correction achieves (and can even exceed) the unbiased Cramér-Rao lower bound. We expect the SPIFF approach to be useful in a wide range of localization applications, including single-molecule imaging and particle tracking, in fields ranging from biology to materials science to astronomy.

Optical and force nanoscopy in microbiology

Microbial cells have developed sophisticated multicomponent structures and machineries to govern basic cellular processes, such as chromosome segregation, gene expression, cell division, mechanosensing, cell adhesion and biofilm formation. Because of the small cell sizes, subcellular structures have long been difficult to visualize using diffraction-limited light microscopy. During the last three decades, optical and force nanoscopy techniques have been developed to probe intracellular and extracellular structures with unprecedented resolutions, enabling researchers to study their organization, dynamics and interactions in individual cells, at the single-molecule level, from the inside out, and all the way up to cell-cell interactions in microbial communities. In this Review, we discuss the principles, advantages and limitations of the main optical and force nanoscopy techniques available in microbiology, and we highlight some outstanding questions that these new tools may help to answer.

Single dish gradient screening of small molecule localization

Understanding trafficking in cells and tissues is one of the most critical steps in exploring the mechanisms and modes of action (MOAs) of a small molecule. Typically, deciphering the role of concentration presents one of the most difficult challenges associated with this task. Herein, we present a practical solution to this problem by developing concentration gradients within single dishes of cells. We demonstrate the method by evaluating fluorescently-labelled probes developed from two classes of natural products that have been identified as potential anti-cancer leads by STORM super-resolution microscopy.

Augmented 3D super-resolution of fluorescence-free nanoparticles using enhanced dark-field illumination based on wavelength-modulation and a least-cubic algorithm

Augmented three-dimensional (3D) subdiffraction-limited resolution of fluorescence-free single-nanoparticles was achieved with wavelength-dependent enhanced dark-field (EDF) illumination and a least-cubic algorithm. Various plasmonic nanoparticles on a glass slide (i.e., gold nanoparticles, GNPs; silver nanoparticles, SNPs; and gold nanorods, GNRs) were imaged and sliced in the z-direction to a thickness of 10 nm. Single-particle images were then compared with simulation data. The 3D coordinates of individual GNP, SNP, and GNR nanoparticles (x, y, z) were resolved by fitting the data with 3D point spread functions using a least-cubic algorithm and collation. Final, 3D super-resolution microscopy (SRM) images were obtained by resolving 3D coordinates and their Cramér-Rao lower bound-based localization precisions in an image space (530 nm × 530 nm × 300 nm) with a specific voxel size (2.5 nm × 2.5 nm × 5 nm). Compared with the commonly used least-square method, the least-cubic method was more useful for finding the center in asymmetric cases (i.e., nanorods) with high precision and accuracy. This novel 3D fluorescence-free SRM technique was successfully applied to resolve the positions of various nanoparticles on glass and gold nanospots (in vitro) as well as in a living single cell (in vivo) with subdiffraction limited resolution in 3D.

Optimal Drift Correction for Superresolution Localization Microscopy with Bayesian Inference

Single-molecule-localization-based superresolution microscopy requires accurate sample drift correction to achieve good results. Common approaches for drift compensation include using fiducial markers and direct drift estimation by image correlation. The former increases the experimental complexity and the latter estimates drift at a reduced temporal resolution. Here, we present, to our knowledge, a new approach for drift correction based on the Bayesian statistical framework. The technique has the advantage of being able to calculate the drifts for every image frame of the data set directly from the single-molecule coordinates. We present the theoretical foundation of the algorithm and an implementation that achieves significantly higher accuracy than image-correlation-based estimations.

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.

Localizing Proteins in Fixed Giardia lamblia and Live Cultured Mammalian Cells by Confocal Fluorescence Microscopy

Confocal fluorescence microscopy and electron microscopy (EM) are complementary methods for studying the intracellular localization of proteins. Confocal fluorescence microscopy provides a rapid and technically simple method to identify the organelle in which a protein localizes but only EM can identify the suborganellular compartment in which that protein is present. Confocal fluorescence microscopy, however, can provide information not obtainable by EM but required to understand the dynamics and interactions of specific proteins. In addition, confocal fluorescence microscopy of cells transfected with a construct encoding a protein of interest fused to a fluorescent protein tag allows live cell studies of the subcellular localization of that protein and the monitoring in real time of its trafficking. Immunostaining methods for confocal fluorescence microscopy are also faster and less involved than those for EM allowing rapid optimization of the antibody dilution needed and a determination of whether protein antigenicity is maintained under fixation conditions used for EM immunogold labeling. This chapter details a method to determine by confocal fluorescence microscopy the intracellular localization of a protein by transfecting the organism of interest, in this case Giardia lamblia, with the cDNA encoding the protein of interest and then processing these organisms for double label immunofluorescence staining after chemical fixation. Also presented is a method to identify the organelle targeting information in the presequence of a precursor protein, in this case the presequence of the precursor to the Euglena light harvesting chlorophyll a/b binding protein of photosystem II precursor (pLHCPII), using live cell imaging of mammalian COS7 cells transiently transfected with a plasmid encoding a pLHCPII presequence fluorescent protein fusion and stained with organelle-specific fluorescent dyes.

Super-resolution of fluorescence-free plasmonic nanoparticles using enhanced dark-field illumination based on wavelength-modulation

Super-resolution imaging of fluorescence-free plasmonic nanoparticles (NPs) was achieved using enhanced dark-field (EDF) illumination based on wavelength-modulation. Indistinguishable adjacent EDF images of 103-nm gold nanoparticles (GNPs), 40-nm gold nanorods (GNRs), and 80-nm silver nanoparticles (SNPs) were modulated at their wavelengths of specific localized surface plasmon scattering. The coordinates (x, y) of each NP were resolved by fitting their point spread functions with a two-dimensional Gaussian. The measured localization precisions of GNPs, GNRs, and SNPs were 2.5 nm, 5.0 nm, and 2.9 nm, respectively. From the resolved coordinates of NPs and the corresponding localization precisions, super-resolution images were reconstructed. Depending on the spontaneous polarization of GNR scattering, the orientation angle of GNRs in two-dimensions was resolved and provided more elaborate localization information. This novel fluorescence-free super-resolution method was applied to live HeLa cells to resolve NPs and provided remarkable sub-diffraction limit images.

Quantitative analysis of single-molecule superresolution images

This review highlights the quantitative capabilities of single-molecule localization-based superresolution imaging methods. In addition to revealing fine structural details, the molecule coordinate lists generated by these methods provide the critical ability to quantify the number, clustering, and colocalization of molecules with 10-50 nm resolution. Here we describe typical workflows and precautions for quantitative analysis of single-molecule superresolution images. These guidelines include potential pitfalls and essential control experiments, allowing critical assessment and interpretation of superresolution images.

Dynamics and organization of cortical microtubules as revealed by superresolution structured illumination microscopy

Plants employ acentrosomal mechanisms to organize cortical microtubule arrays essential for cell growth and differentiation. Using structured illumination microscopy (SIM) adopted for the optimal documentation of Arabidopsis (Arabidopsis thaliana) hypocotyl epidermal cells, dynamic cortical microtubules labeled with green fluorescent protein fused to the microtubule-binding domain of the mammalian microtubule-associated protein MAP4 and with green fluorescent protein-fused to the alpha tubulin6 were comparatively recorded in wild-type Arabidopsis plants and in the mitogen-activated protein kinase mutant mpk4 possessing the former microtubule marker. The mpk4 mutant exhibits extensive microtubule bundling, due to increased abundance and reduced phosphorylation of the microtubule-associated protein MAP65-1, thus providing a very useful genetic tool to record intrabundle microtubule dynamics at the subdiffraction level. SIM imaging revealed nano-sized defects in microtubule bundling, spatially resolved microtubule branching and release, and finally allowed the quantification of individual microtubules within cortical bundles. Time-lapse SIM imaging allowed the visualization of subdiffraction, short-lived excursions of the microtubule plus end, and dynamic instability behavior of both ends during free, intrabundle, or microtubule-templated microtubule growth and shrinkage. Finally, short, rigid, and nondynamic microtubule bundles in the mpk4 mutant were observed to glide along the parent microtubule in a tip-wise manner. In conclusion, this study demonstrates the potential of SIM for superresolution time-lapse imaging of plant cells, showing unprecedented details accompanying microtubule dynamic organization.