Fast maximum likelihood algorithm for localization of fluorescent molecules

Nanoscale imaging of quantum dot dimers using time-resolved super-resolution microscopy combined with scanning electron microscopy

Time-resolved super-resolution microscopy was used in conjunction with scanning electron microscopy to image individual colloidal CdSe/CdS semiconductor quantum dots (QD) and QD dimers. The photoluminescence (PL) lifetimes, intensities, and structural parameters were acquired with nanometer scale spatial resolution and sub-nanosecond time resolution. The combination of these two techniques was more powerful than either alone, enabling us to resolve the PL properties of individual QDs within QD dimers as they blinked on and off, measure interparticle distances, and identify QDs that may be participating in energy transfer. The localization precision of our optical imaging technique was ∼3 nm, low enough that the emission from individual QDs within the dimers could be spatially resolved. While the majority of QDs within dimers acted as independent emitters, at least one pair of QDs in our study exhibited lifetime and intensity behaviors consistent with resonance energy transfer from a shorter lifetime and lower intensity donor QD to a longer lifetime and higher intensity acceptor QD. For this case, we demonstrate how the combined super-resolution optical imaging and scanning electron microscopy data can be used to characterize the energy transfer rate.

Robust emitter localization with enhanced harmonic analysis

We present a non-iterative and model-free algorithm for three-dimensional (3D) single emitter localization. Our algorithm decodes the axial position and the emitter width via the ratio of the first and second Fourier harmonic. The retrieved width information is further used for dynamic extraction of the proper region of interest to robustly eliminate the outer noisy background, thus improving the localization precision over existing non-iterative algorithms. Using simulated and experimental datasets, we demonstrate that our algorithm achieves localization precision approaching the state-of-the-art iterative fitting-based methods in all three dimensions at two orders of magnitude faster speed, applicable in various 3D single-molecule localization techniques.

Potential quality improvement of stochastic optical localization nanoscopy images obtained by frame by frame localization algorithms

A data movie of stochastic optical localization nanoscopy contains spatial and temporal correlations, both providing information of emitter locations. The majority of localization algorithms in the literature estimate emitter locations by frame-by-frame localization (FFL), which exploit only the spatial correlation and leave the temporal correlation into the FFL nanoscopy images. The temporal correlation contained in the FFL images, if exploited, can improve the localization accuracy and the image quality. In this paper, we analyze the properties of the FFL images in terms of root mean square minimum distance (RMSMD) and root mean square error (RMSE). It is shown that RMSMD and RMSE can be potentially reduced by a maximum fold equal to the square root of the average number of activations per emitter. Analyzed and revealed are also several statistical properties of RMSMD and RMSE and their relationship with respect to a large number of data frames, bias and variance of localization errors, small localization errors, sample drift, and the worst FFL image. Numerical examples are taken and the results confirm the prediction of analysis. The ideas about how to develop an algorithm to exploit the temporal correlation of FFL images are also briefly discussed. The results suggest development of two kinds of localization algorithms: the algorithms that can exploit the temporal correlation of FFL images and the unbiased localization algorithms.

A multi-emitter fitting algorithm for potential live cell super-resolution imaging over a wide range of molecular densities

Multi-emitter fitting algorithms have been developed to improve the temporal resolution of single-molecule switching nanoscopy, but the molecular density range they can analyse is narrow and the computation required is intensive, significantly limiting their practical application. Here, we propose a computationally fast method, wedged template matching (WTM), an algorithm that uses a template matching technique to localise molecules at any overlapping molecular density from sparse to ultrahigh density with subdiffraction resolution. WTM achieves the localization of overlapping molecules at densities up to 600 molecules μm^-2 with a high detection sensitivity and fast computational speed. WTM also shows localization precision comparable with that of DAOSTORM (an algorithm for high-density super-resolution microscopy), at densities up to 20 molecules μm^-2 , and better than DAOSTORM at higher molecular densities. The application of WTM to a high-density biological sample image demonstrated that it resolved protein dynamics from live cell images with subdiffraction resolution and a temporal resolution of several hundred milliseconds or less through a significant reduction in the number of camera images required for a high-density reconstruction. WTM algorithm is a computationally fast, multi-emitter fitting algorithm that can analyse over a wide range of molecular densities. The algorithm is available through the website. https://doi.org/10.17632/bf3z6xpn5j.1.

Unraveling the Thousand Word Picture: An Introduction to Super-Resolution Data Analysis

Super-resolution microscopy provides direct insight into fundamental biological processes occurring at length scales smaller than light's diffraction limit. The analysis of data at such scales has brought statistical and machine learning methods into the mainstream. Here we provide a survey of data analysis methods starting from an overview of basic statistical techniques underlying the analysis of super-resolution and, more broadly, imaging data. We subsequently break down the analysis of super-resolution data into four problems: the localization problem, the counting problem, the linking problem, and what we've termed the interpretation problem.

Single-Molecule Imaging to Characterize the Transport Mechanism of the Nuclear Pore Complex

In the eukaryotic cell, a large macromolecular channel, known as the Nuclear Pore Complex (NPC), mediates all molecular transport between the nucleus and cytoplasm. In recent years, single-molecule fluorescence (SMF) imaging has emerged as a powerful tool to study the molecular mechanism of transport through the NPC. More recently, techniques such as single-molecule localization microscopy (SMLM) have enabled the spatial and temporal distribution of cargos, transport receptors and even structural components of the NPC to be determined with nanometre accuracy. In this protocol, we describe a method to study the position and/or motion of individual molecules transiting through the NPC with high spatial and temporal precision.

Quantitative evaluation of software packages for single-molecule localization microscopy

The quality of super-resolution images obtained by single-molecule localization microscopy (SMLM) depends largely on the software used to detect and accurately localize point sources. In this work, we focus on the computational aspects of super-resolution microscopy and present a comprehensive evaluation of localization software packages. Our philosophy is to evaluate each package as a whole, thus maintaining the integrity of the software. We prepared synthetic data that represent three-dimensional structures modeled after biological components, taking excitation parameters, noise sources, point-spread functions and pixelation into account. We then asked developers to run their software on our data; most responded favorably, allowing us to present a broad picture of the methods available. We evaluated their results using quantitative and user-interpretable criteria: detection rate, accuracy, quality of image reconstruction, resolution, software usability and computational resources. These metrics reflect the various tradeoffs of SMLM software packages and help users to choose the software that fits their needs.

Virtual-'light-sheet' single-molecule localisation microscopy enables quantitative optical sectioning for super-resolution imaging

Single-molecule super-resolution microscopy allows imaging of fluorescently-tagged proteins in live cells with a precision well below that of the diffraction limit. Here, we demonstrate 3D sectioning with single-molecule super-resolution microscopy by making use of the fitting information that is usually discarded to reject fluorophores that emit from above or below a virtual-'light-sheet', a thin volume centred on the focal plane of the microscope. We describe an easy-to-use routine (implemented as an open-source ImageJ plug-in) to quickly analyse a calibration sample to define and use such a virtual light-sheet. In addition, the plug-in is easily usable on almost any existing 2D super-resolution instrumentation. This optical sectioning of super-resolution images is achieved by applying well-characterised width and amplitude thresholds to diffraction-limited spots that can be used to tune the thickness of the virtual light-sheet. This allows qualitative and quantitative imaging improvements: by rejecting out-of-focus fluorophores, the super-resolution image gains contrast and local features may be revealed; by retaining only fluorophores close to the focal plane, virtual-'light-sheet' single-molecule localisation microscopy improves the probability that all emitting fluorophores will be detected, fitted and quantitatively evaluated.

A divide and conquer strategy for the maximum likelihood localization of low intensity objects

In cell biology and other fields the automatic accurate localization of sub-resolution objects in images is an important tool. The signal is often corrupted by multiple forms of noise, including excess noise resulting from the amplification by an electron multiplying charge-coupled device (EMCCD). Here we present our novel Nested Maximum Likelihood Algorithm (NMLA), which solves the problem of localizing multiple overlapping emitters in a setting affected by excess noise, by repeatedly solving the task of independent localization for single emitters in an excess noise-free system. NMLA dramatically improves scalability and robustness, when compared to a general purpose optimization technique. Our method was successfully applied for in vivo localization of fluorescent proteins.

Superresolution localization methods

Superresolution localization microscopy methods produce nanoscale images via a combination of intermittently active fluorescent probes and algorithms that can precisely determine the positions of these probes from single-molecule or few-molecule images. These algorithms vary widely in their underlying principles, complexity, and accuracy. In this review, we begin by surveying the principles of localization microscopy and describing the fundamental limits to localization precision. We then examine several different families of fluorophore localization algorithms, comparing their complexity, performance, and range of applicability (e.g., whether they require particular types of experimental information, are optimized for specific situations, or are more general). Whereas our focus is on the localization of single isotropic emitters in two dimensions, we also consider oriented dipoles, three-dimensional localization, and algorithms that can handle overlapping images of several nearby fluorophores. Throughout the review, we try to highlight practical advice for users of fluorophore localization algorithms, as well as open questions.

Light-sheet confined super-resolution using two-photon photoactivation

Light-sheet microscopy is a useful tool for performing biological investigations of thick samples and it has recently been demonstrated that it can also act as a suitable architecture for super-resolution imaging of thick biological samples by means of individual molecule localization. However, imaging in depth is still limited since it suffers from a reduction in image quality caused by scattering effects. This paper sets out to investigate the advantages of non-linear photoactivation implemented in a selective plane illumination configuration when imaging scattering samples. In particular, two-photon excitation is proven to improve imaging capabilities in terms of imaging depth and is expected to reduce light-sample interactions and sample photo-damage. Here, two-photon photoactivation is coupled to individual molecule localization methods based on light-sheet illumination (IML-SPIM), allowing super-resolution imaging of nuclear pH2AX in NB4 cells.

Fast and precise algorithm based on maximum radial symmetry for single molecule localization

We present an algorithm to estimate the location of single fluorescent molecule with both high speed and high precision. This algorithm is based on finding the subpixel position with maximum radial symmetry in a pixelated single molecule fluorescence image. Compared with conventional algorithms, this algorithm does not rely on point-spread-function or noise model. Through numerical simulation and experimental analysis, we found that this algorithm exhibits localization precision very close to the maximum likelihood estimator (MLE), while executes ∼1000 times faster than the MLE and ∼6 times faster than the fluoroBancroft algorithm.