Quantitative study of single molecule location estimation techniques

Cramér-Rao Lower Bound for Point Based Image Registration With Heteroscedastic Error Model for Application in Single Molecule Microscopy

The Cramér-Rao lower bound for the estimation of the affine transformation parameters in a multivariate heteroscedastic errors-in-variables model is derived. The model is suitable for feature-based image registration in which both sets of control points are localized with errors whose covariance matrices vary from point to point. With focus given to the registration of fluorescence microscopy images, the Cramér-Rao lower bound for the estimation of a feature's position (e.g., of a single molecule) in a registered image is also derived. In the particular case where all covariance matrices for the localization errors are scalar multiples of a common positive definite matrix (e.g., the identity matrix), as can be assumed in fluorescence microscopy, then simplified expressions for the Cramér-Rao lower bound are given. Under certain simplifying assumptions these expressions are shown to match asymptotic distributions for a previously presented set of estimators. Theoretical results are verified with simulations and experimental data.

Single-molecule spectroscopy and imaging over the decades

As of 2015, it has been 26 years since the first optical detection and spectroscopy of single molecules in condensed matter. This area of science has expanded far beyond the early low temperature studies in crystals to include single molecules in cells, polymers, and in solution. The early steps relied upon high-resolution spectroscopy of inhomogeneously broadened optical absorption profiles of molecular impurities in solids at low temperatures. Spectral fine structure arising directly from the position-dependent fluctuations of the number of molecules in resonance led to the attainment of the single-molecule limit in 1989 using frequency-modulation laser spectroscopy. In the early 1990s, a variety of fascinating physical effects were observed for individual molecules, including imaging of the light from single molecules as well as observations of spectral diffusion, optical switching and the ability to select different single molecules in the same focal volume simply by tuning the pumping laser frequency. In the room temperature regime, researchers showed that bursts of light from single molecules could be detected in solution, leading to imaging and microscopy by a variety of methods. Studies of single copies of the green fluorescent protein also uncovered surprises, especially the blinking and photoinduced recovery of emitters, which stimulated further development of photoswitchable fluorescent protein labels. All of these early steps provided important fundamentals underpinning the development of super-resolution microscopy based on single-molecule localization and active control of emitting concentration. Current thrust areas include extensions to three-dimensional imaging with high precision, orientational analysis of single molecules, and direct measurements of photodynamics and transport properties for single molecules trapped in solution by suppression of Brownian motion. Without question, a huge variety of studies of single molecules performed by many talented scientists all over the world have extended our knowledge of the nanoscale and many microscopic mechanisms previously hidden by ensemble averaging.

K-factor image deshadowing for three-dimensional fluorescence microscopy

The ability to track single fluorescent particles within a three dimensional (3D) cellular environment can provide valuable insights into cellular processes. In this paper, we present a modified nonlinear image decomposition technique called K-factor that reshapes the 3D point spread function (PSF) of an XYZ image stack into a narrow Gaussian profile. The method increases localization accuracy by ~60% with compare to regular Gaussian fitting, and improves minimal resolvable distance between overlapping PSFs by ~50%. The algorithm was tested both on simulated data and experimentally.

New results on the single molecule localization problem in two and three dimensions

Fluorescence microscopy is an optical microscopy technique which has been extensively used to study specifically- labeled subcellular objects, such as proteins, and their functions. The best possible accuracy with which an object of interest can be localized when imaged using a fluorescence microscope is typically calculated using the Cramer- Rao lower bound (CRLB). The calculation of the CRLB, however, so far relied on an analytical expression for the image of the object. This can pose challenges in practice since it is often difficult to find appropriate analytical models for the images of general objects. Even if an appropriate analytical model is available, the lack of knowledge about the precise values of imaging parameters might also impose difficulties in the calculation oxf the CRLB. To address these challenges, we have developed an approach that directly uses an experimentally collected image set to calculate the best possible localization accuracy for a general subcellular object in two and three dimensions. In this approach, we fit smoothly connected piecewise polynomials, known as splines, to the experimentally collected image set to provide a continuous model of the object. This continuous model can then be used for the calculation of the best possible localization accuracy.

Fluorescent Microspheres as Point Sources: A Localization Study

The localization of fluorescent microspheres is often employed for drift correction and image registration in single molecule microscopy, and is commonly carried out by fitting a point spread function to the image of the given microsphere. The mismatch between the point spread function and the image of the microsphere, however, calls into question the suitability of this localization approach. To investigate this issue, we subject both simulated and experimental microsphere image data to a maximum likelihood estimator that localizes a microsphere by fitting an Airy pattern to its image, and assess the suitability of the approach by evaluating the ability of the estimator to recover the true location of the microsphere with the best possible accuracy as determined based on the Cramér-Rao lower bound. Assessing against criteria based on the standard errors of the mean and the variance for an ideal estimator of the microsphere’s location, we find that microspheres up to 100 nm in diameter can in general be localized using a fixed width Airy pattern, and that microspheres as large as 1 μm in diameter can in general be localized using a floated width Airy pattern.

Fast weighted centroid algorithm for single particle localization near the information limit

A simple weighting scheme that enhances the localization precision of center of mass calculations for radially symmetric intensity distributions is presented. The algorithm effectively removes the biasing that is common in such center of mass calculations. Localization precision compares favorably with other localization algorithms used in super-resolution microscopy and particle tracking, while significantly reducing the processing time and memory usage. We expect that the algorithm presented will be of significant utility when fast computationally lightweight particle localization or tracking is desired.

Assessing resolution in super-resolution imaging

Resolution is a central concept in all imaging fields, and particularly in optical microscopy, but it can be easily misinterpreted. The mathematical definition of optical resolution was codified by Abbe, and practically defined by the Rayleigh Criterion in the late 19th century. The limit of conventional resolution was also achieved in this period, and it was thought that fundamental constraints of physics prevented further increases in resolution. With the recent development of a range of super-resolution techniques, it is necessary to revisit the concept of optical resolution. Fundamental differences in super-resolution modalities mean that resolution is not a directly transferrable metric between techniques. This article considers the issues in resolution raised by these new technologies, and presents approaches for comparing resolution between different super-resolution methods.

Investigation of the numerics of point spread function integration in single molecule localization

The computation of point spread functions, which are typically used to model the image profile of a single molecule, represents a central task in the analysis of single molecule microscopy data. To determine how the accuracy of the computation affects how well a single molecule can be localized, we investigate how the fineness with which the point spread function is integrated over an image pixel impacts the performance of the maximum likelihood location estimator. We consider both the Airy and the two-dimensional Gaussian point spread functions. Our results show that the point spread function needs to be adequately integrated over a pixel to ensure that the estimator closely recovers the true location of the single molecule with an accuracy that is comparable to the best possible accuracy as determined using the Fisher information formalism. Importantly, if integration with an insufficiently fine step size is carried out, the resulting estimates can be significantly different from the true location, particularly when the image data is acquired at relatively low magnifications. We also present a methodology for determining an adequate step size for integrating the point spread function.

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.

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.

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.

Measuring and overcoming limits of the Saffman-Delbrück model for soap film viscosities

We observe tracer particles diffusing in soap films to measure the two-dimensional (2D) viscous properties of the films. Saffman-Delbrück type models relate the single-particle diffusivity to parameters of the film (such as thickness h) for thin films, but the relation breaks down for thicker films. Notably, the diffusivity is faster than expected for thicker films, with the crossover at h/d = 5.2 ± 0.9 using the tracer particle diameter d. This indicates a crossover from purely 2D diffusion to diffusion that is more three-dimensional. We demonstrate that measuring the correlations of particle pairs as a function of their separation overcomes the limitations of the Saffman-Delbrück model and allows one to measure the viscosity of a soap film for any thickness.

Determination of localization accuracy based on experimentally acquired image sets: applications to single molecule microscopy

Fluorescence microscopy is a photon-limited imaging modality that allows the study of subcellular objects and processes with high specificity. The best possible accuracy (standard deviation) with which an object of interest can be localized when imaged using a fluorescence microscope is typically calculated using the Cramér-Rao lower bound, that is, the inverse of the Fisher information. However, the current approach for the calculation of the best possible localization accuracy relies on an analytical expression for the image of the object. This can pose practical challenges since it is often difficult to find appropriate analytical models for the images of general objects. In this study, we instead develop an approach that directly uses an experimentally collected image set to calculate the best possible localization accuracy for a general subcellular object. In this approach, we fit splines, i.e. smoothly connected piecewise polynomials, to the experimentally collected image set to provide a continuous model of the object, which can then be used for the calculation of the best possible localization accuracy. Due to its practical importance, we investigate in detail the application of the proposed approach in single molecule fluorescence microscopy. In this case, the object of interest is a point source and, therefore, the acquired image set pertains to an experimental point spread function.

An information-theoretic approach to designing the plane spacing for multifocal plane microscopy

Multifocal plane microscopy (MUM) is a 3D imaging modality which enables the localization and tracking of single molecules at high spatial and temporal resolution by simultaneously imaging distinct focal planes within the sample. MUM overcomes the depth discrimination problem of conventional microscopy and allows high accuracy localization of a single molecule in 3D along the z-axis. An important question in the design of MUM experiments concerns the appropriate number of focal planes and their spacings to achieve the best possible 3D localization accuracy along the z-axis. Ideally, it is desired to obtain a 3D localization accuracy that is uniform over a large depth and has small numerical values, which guarantee that the single molecule is continuously detectable. Here, we address this concern by developing a plane spacing design strategy based on the Fisher information. In particular, we analyze the Fisher information matrix for the 3D localization problem along the z-axis and propose spacing scenarios termed the strong coupling and the weak coupling spacings, which provide appropriate 3D localization accuracies. Using these spacing scenarios, we investigate the detectability of the single molecule along the z-axis and study the effect of changing the number of focal planes on the 3D localization accuracy. We further review a software module we recently introduced, the MUMDesignTool, that helps to design the plane spacings for a MUM setup.

Quantitative Aspects of Single Molecule Microscopy

Single molecule microscopy is a relatively new optical microscopy technique that allows the detection of individual molecules such as proteins in a cellular context. This technique has generated significant interest among biologists, biophysicists and biochemists, as it holds the promise to provide novel insights into subcellular processes and structures that otherwise cannot be gained through traditional experimental approaches. Single molecule experiments place stringent demands on experimental and algorithmic tools due to the low signal levels and the presence of significant extraneous noise sources. Consequently, this has necessitated the use of advanced statistical signal and image processing techniques for the design and analysis of single molecule experiments. In this tutorial paper, we provide an overview of single molecule microscopy from early works to current applications and challenges. Specific emphasis will be on the quantitative aspects of this imaging modality, in particular single molecule localization and resolvability, which will be discussed from an information theoretic perspective. We review the stochastic framework for image formation, different types of estimation techniques and expressions for the Fisher information matrix. We also discuss several open problems in the field that demand highly non-trivial signal processing algorithms.

Single molecule microscopy in 3D cell cultures and tissues

From the onset of the first microscopic visualization of single fluorescent molecules in living cells at the beginning of this century, to the present, almost routine application of single molecule microscopy, the method has well-proven its ability to contribute unmatched detailed insight into the heterogeneous and dynamic molecular world life is composed of. Except for investigations on bacteria and yeast, almost the entire story of success is based on studies on adherent mammalian 2D cell cultures. However, despite this continuous progress, the technique was not able to keep pace with the move of the cell biology community to adapt 3D cell culture models for basic research, regenerative medicine, or drug development and screening. In this review, we will summarize the progress, which only recently allowed for the application of single molecule microscopy to 3D cell systems and give an overview of the technical advances that led to it. While initially posing a challenge, we finally conclude that relevant 3D cell models will become an integral part of the on-going success of single molecule microscopy.

Optimal point spread function design for 3D imaging

To extract from an image of a single nanoscale object maximum physical information about its position, we propose and demonstrate a framework for pupil-plane modulation for 3D imaging applications requiring precise localization, including single-particle tracking and superresolution microscopy. The method is based on maximizing the information content of the system, by formulating and solving the appropriate optimization problem--finding the pupil-plane phase pattern that would yield a point spread function (PSF) with optimal Fisher information properties. We use our method to generate and experimentally demonstrate two example PSFs: one optimized for 3D localization precision over a 3  μm depth of field, and another with an unprecedented 5  μm depth of field, both designed to perform under physically common conditions of high background signals.

Effects of fixed pattern noise on single molecule localization microscopy

The newly developed scientific complementary metal oxide semiconductor (sCMOS) cameras are capable of realizing fast single molecule localization microscopy without sacrificing field-of-view, benefiting from their readout speed which is significantly higher than that of conventional charge-coupled device (CCD) cameras. However, the poor image uniformity (suffered from fixed pattern noise, FPN) is a major obstruction for widespread use of sCMOS cameras in single molecule localization microscopy. Here we present a quantitative investigation on the effects of FPN on single molecule localization microscopy via localization precision and localization bias. We found that FPN leads to almost no effect on localization precision, but introduces a certain amount of localization bias. However, for a commercial Hamamatsu Flash 4.0 sCMOS camera, such localization bias is usually <2 nm and thus can be neglected for most localization microscopy experiments. This study addresses the FPN concern which worries researchers, and thus will promote the application of sCMOS cameras in single molecule localization microscopy.

Designing the focal plane spacing for multifocal plane microscopy

Multifocal plane microscopy (MUM) has made it possible to study subcellular dynamics in 3D at high temporal and spatial resolution by simultaneously imaging distinct planes within the specimen. MUM allows high accuracy localization of a point source along the z-axis since it overcomes the depth discrimination problem of conventional single plane microscopy. An important question in MUM experiments is how the number of focal planes and their spacings should be chosen to achieve the best possible localization accuracy along the z-axis. Here, we propose approaches based on the Fisher information matrix and report spacing scenarios called strong coupling and weak coupling which yield an appropriate 3D localization accuracy. We examine the effect of numerical aperture, magnification, photon count, emission wavelength and extraneous noise on the spacing scenarios. In addition, we investigate the effect of changing the number of focal planes on the 3D localization accuracy. We also introduce a new software package that provides a user-friendly framework to find appropriate plane spacings for a MUM setup. These developments should assist in optimizing MUM experiments.

Single-molecule tracking in live cells reveals distinct target-search strategies of transcription factors in the nucleus

Gene regulation relies on transcription factors (TFs) exploring the nucleus searching their targets. So far, most studies have focused on how fast TFs diffuse, underestimating the role of nuclear architecture. We implemented a single-molecule tracking assay to determine TFs dynamics. We found that c-Myc is a global explorer of the nucleus. In contrast, the positive transcription elongation factor P-TEFb is a local explorer that oversamples its environment. Consequently, each c-Myc molecule is equally available for all nuclear sites while P-TEFb reaches its targets in a position-dependent manner. Our observations are consistent with a model in which the exploration geometry of TFs is restrained by their interactions with nuclear structures and not by exclusion. The geometry-controlled kinetics of TFs target-search illustrates the influence of nuclear architecture on gene regulation, and has strong implications on how proteins react in the nucleus and how their function can be regulated in space and time.

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.

SimpleSTORM: a fast, self-calibrating reconstruction algorithm for localization microscopy

Although there are many reconstruction algorithms for localization microscopy, their use is hampered by the difficulty to adjust a possibly large number of parameters correctly. We propose SimpleSTORM, an algorithm that determines appropriate parameter settings directly from the data in an initial self-calibration phase. The algorithm is based on a carefully designed yet simple model of the image acquisition process which allows us to standardize each image such that the background has zero mean and unit variance. This standardization makes it possible to detect spots by a true statistical test (instead of hand-tuned thresholds) and to de-noise the images with an efficient matched filter. By reducing the strength of the matched filter, SimpleSTORM also performs reasonably on data with high-spot density, trading off localization accuracy for improved detection performance. Extensive validation experiments on the ISBI Localization Challenge Dataset, as well as real image reconstructions, demonstrate the good performance of our algorithm.

High-density single-particle tracking: quantifying molecule organization and dynamics at the nanoscale

The organization and dynamics of proteins are fundamental parameters for cellular function. Their study, at the single-molecule level, provides precise information on molecular interactions. Over the last 30 years, the single-particle tracking imaging technique has proven its capability to efficiently quantify such parameters in many biological systems, with nanometric accuracy and millisecond temporal resolutions. Nevertheless, the low concentration of labeling required for single-molecule imaging usually prevents the extraction of large statistics. The advent of high-density single-molecule-based super-resolution techniques has revolutionized the field, allowing monitoring of thousands of biomolecules in the minute timescale and providing unprecedented insight into the molecular organization and dynamics of cellular compounds. In this issue, I will review the main principles of single-particle tracking, a highly interdisciplinary technique at the interface between microscopy, image analysis and labeling strategies. I will point out the advantages brought by high-density single-particle tracking which will be illustrated with a few recent biological results.

Single-molecule detection and tracking in plants

Combining optical properties with a limited choice of fluorophores turns single-molecule imaging in plants into a challenging task. This explains why the technique, despite its success in the field of animal cell biology, is far from being routinely applied in plant cell research. The same challenges, however, also apply to the application of single-molecule microscopy to any intact tissue or multicellular 3D cell culture. As recent and upcoming progress in fluorescence microscopy will permit single-molecule detection in the context of multicellular systems, plant tissue imaging will experience a huge benefit from this progress. In this review, we address every step of a single-molecule experiment, highlight the critical aspects of each and elaborate on optimizations and developments required for improvements. We relate each step to recent achievements, which have so far been conducted exclusively on the root epidermis of Arabidopsis thaliana seedlings with inclined illumination and show examples of single-molecule measurements using different cells or illumination schemes.

Fixed pattern noise in localization microscopy

Localization microscopy vastly improves the resolution achieved by fluorescence microscopy by fitting the positions of individual fluorophores. We examine the reconstructions produced by different fitting algorithms for instances of fixed pattern noise--systematic tendencies to alter estimated emitter positions according to their subpixel location in a way that does not reflect the ground truth structure. We show that while not readily visible at standard empirical signal strengths, fixed pattern noise can occur when performing sub-pixel fitting, and that its degree varies according to the algorithm used and the relative size of the pixels compared to the point spread function. For pixel sizes in the range 80-170 nm, this results in variations in accuracy of the order of 2-4 nm-comparatively small for many applications, but non-negligible in scenarios where very high accuracy is sought.

Troika of single particle tracking programing: SNR enhancement, particle identification, and mapping

Single particle tracking (SPT) techniques provide a microscopic approach to probe in vivo and in vitro structure and reactions. Automatic analysis of SPT data with high efficiency and accuracy spurs the development of SPT algorithms. In this perspective, we review a range of available techniques used in SPT analysis programs. In addition, we present an example SPT program step-by-step to provide a guide so that researchers can use, modify, and/or write a SPT program for their own purposes.

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.

Dynein motion switches from diffusive to directed upon cortical anchoring

Cytoplasmic dynein is a motor protein that exerts force on microtubules. To generate force for the movement of large organelles, dynein needs to be anchored, with the anchoring sites being typically located at the cell cortex. However, the mechanism by which dyneins target sites where they can generate large collective forces is unknown. Here, we directly observe single dyneins during meiotic nuclear oscillations in fission yeast and identify the steps of the dynein binding process: from the cytoplasm to the microtubule and from the microtubule to cortical anchors. We observed that dyneins on the microtubule move either in a diffusive or directed manner, with the switch from diffusion to directed movement occurring upon binding of dynein to cortical anchors. This dual behavior of dynein on the microtubule, together with the two steps of binding, enables dyneins to self-organize into a spatial pattern needed for them to generate large collective forces.

Real-time analysis and visualization for single-molecule based super-resolution microscopy

Accurate multidimensional localization of isolated fluorescent emitters is a time consuming process in single-molecule based super-resolution microscopy. We demonstrate a functional method for real-time reconstruction with automatic feedback control, without compromising the localization accuracy. Compatible with high frame rates of EM-CCD cameras, it relies on a wavelet segmentation algorithm, together with a mix of CPU/GPU implementation. A combination with Gaussian fitting allows direct access to 3D localization. Automatic feedback control ensures optimal molecule density throughout the acquisition process. With this method, we significantly improve the efficiency and feasibility of localization-based super-resolution microscopy.

A stochastic model for electron multiplication charge-coupled devices--from theory to practice

Electron multiplication charge-coupled devices (EMCCD) are widely used for photon counting experiments and measurements of low intensity light sources, and are extensively employed in biological fluorescence imaging applications. These devices have a complex statistical behaviour that is often not fully considered in the analysis of EMCCD data. Robust and optimal analysis of EMCCD images requires an understanding of their noise properties, in particular to exploit fully the advantages of Bayesian and maximum-likelihood analysis techniques, whose value is increasingly recognised in biological imaging for obtaining robust quantitative measurements from challenging data. To improve our own EMCCD analysis and as an effort to aid that of the wider bioimaging community, we present, explain and discuss a detailed physical model for EMCCD noise properties, giving a likelihood function for image counts in each pixel for a given incident intensity, and we explain how to measure the parameters for this model from various calibration images.

Single-molecule localization super-resolution microscopy: deeper and faster

For over a decade fluorescence microscopy has demonstrated the capacity to achieve single-molecule localization accuracies of a few nanometers, well below the ≈ 200 nm lateral and ≈ 500 nm axial resolution limit of conventional microscopy. Yet, only the recent development of new fluorescence labeling modalities, the increase in sensitivity of imaging hardware, and the creation of novel image analysis tools allow for the emergence of single-molecule-based super-resolution imaging techniques. Novel methods such as photoactivated localization microscopy and stochastic optical reconstruction microscopy can typically reach a tenfold increase in resolution compared to standard microscopy methods. Their implementation is relatively easy only requiring minimal changes to a conventional wide-field or total internal reflection fluorescence microscope. The recent translation of these two methods into commercial imaging systems has made them further accessible to researchers in biology. However, these methods are still evolving rapidly toward imaging live samples with high temporal resolution and depth. In this review, we recall the roots of single-molecule localization microscopy, summarize major recent developments, and offer perspective on potential applications.

Single-molecule super-resolution imaging in bacteria

Bacteria have evolved complex, multi-component cellular machineries to carry out fundamental cellular processes such as cell division/separation, locomotion, protein secretion, DNA transcription/replication, or conjugation/competence. Diffraction of light has so far restricted the use of conventional fluorescence microscopy to reveal the composition, internal architecture and dynamics of these important machineries. This review describes some of the more recent advances on single-molecule super-resolution microscopy methods applied to bacteria and highlights their application to chemotaxis, cell division, DNA segregation, and DNA transcription machineries. Finally, we discuss some of the lessons learned from this approach, and future perspectives.

Video-based tracking of single molecules exhibiting directed in-frame motion

Trajectories of individual molecules moving within complex environments such as cell cytoplasm and membranes or semiflexible polymer networks provide invaluable information on the organization and dynamics of these systems. However, when such trajectories are obtained from a sequence of microscopy images, they can be distorted due to the fact that the tracked molecule exhibits appreciable directed motion during the single-frame acquisition. We propose a new model of image formation for mobile molecules that takes the linear in-frame motion into account and develop an algorithm based on the maximum likelihood approach for retrieving the position and velocity of the molecules from single-frame data. The position and velocity information obtained from individual frames are further fed into a Kalman filter for interframe tracking of molecules that allows prediction of the trajectory of the molecule and further improves the precision of the position and velocity estimates. We evaluate the performance of our algorithm by calculations of the Cramer-Rao Lower Bound, simulations, and model experiments with a piezo-stage. We demonstrate tracking of molecules moving as fast as 7 pixels/frame (12.6 μm/s) within a mean error of 0.42 pixel (37.43 nm).

Maximum precision closed-form solution for localizing diffraction-limited spots in noisy images

Super-resolution techniques like PALM and STORM require accurate localization of single fluorophores detected using a CCD. Popular localization algorithms inefficiently assume each photon registered by a pixel can only come from an area in the specimen corresponding to that pixel (not from neighboring areas), before iteratively (slowly) fitting a Gaussian to pixel intensity; they fail with noisy images. We present an alternative; a probability distribution extending over many pixels is assigned to each photon, and independent distributions are joined to describe emitter location. We compare algorithms, and recommend which serves best under different conditions. At low signal-to-noise ratios, ours is 2-fold more precise than others, and 2 orders of magnitude faster; at high ratios, it closely approximates the maximum likelihood estimate.

Optical nanoscopy: from acquisition to analysis

Recent advances in far-field microscopy have demonstrated that fluorescence imaging is possible at resolutions well below the long-standing diffraction limit. By exploiting photophysical properties of fluorescent probe molecules, this new class of methods yields a resolving power that is fundamentally diffraction unlimited. Although these methods are becoming more widely used in biological imaging, they must be complemented by suitable data analysis approaches if their potential is to be fully realized. Here we review the basic principles of diffraction-unlimited microscopy and how these principles influence the selection of available algorithms for data analysis. Furthermore, we provide an overview of existing analysis strategies and discuss their application.

3D single molecule tracking and superresolution microscopy using multifocal plane microscopy

The study of cellular processes in three-dimensions is severely limited by the lack of imaging methodologies that allow for fast 3D tracking of cellular events and 3D superresolution imaging of sub-cellular structures. We have developed a 3D imaging modality, multifocal plane microscopy (MUM), that provides a powerful approach for 3D single molecule tracking and 3D superresolution microscopy. Here we review the technical challenges associated with 3D single molecule localization that is fundamental to both 3D tracking and 3D superresolution, and discuss how MUM overcomes these problems.

Fast maximum likelihood algorithm for localization of fluorescent molecules

A common task in microscopy is to fit an image of a fluorescent probe to a point spread function (PSF) in order to estimate the position of the probe. The PSF is often approximated as a Gaussian for mathematical simplicity. We show that the separable property of the Gaussian PSF enables a reduction of computational time from O(L2) to O(L), where L is the width (in pixels) of the image. When tested on realistic simulated data, our algorithm is able to localize the probes with precision close to the Cramér-Rao lower bound.

Wavelet analysis for single molecule localization microscopy

Localization of single molecules in microscopy images is a key step in quantitative single particle data analysis. Among them, single molecule based super-resolution optical microscopy techniques require high localization accuracy as well as computation of large data sets in the order of 10(5) single molecule detections to reconstruct a single image. We hereby present an algorithm based on image wavelet segmentation and single particle centroid determination, and compare its performance with the commonly used gaussian fitting of the point spread function. We performed realistic simulations at different signal-to-noise ratios and particle densities and show that the calculation time using the wavelet approach can be more than one order of magnitude faster than that of gaussian fitting without a significant degradation of the localization accuracy, from 1 nm to 4 nm in our range of study. We propose a simulation-based estimate of the resolution of an experimental single molecule acquisition.

Fast Fourier domain localization algorithm of a single molecule with nanometer precision

We present an algorithm to determine the location of a fluorescent molecule with nanometer-scale accuracy. A Fourier domain localization scheme based on zero-padded fast Fourier transform and phase gradient operators is used to obtain a powerful mathematical model for localizing the molecule without numerical fitting. Compared with conventional algorithms, our position estimator does not require prior background information or initial parameter estimation. Numerical simulations indicate that the proposed method exhibits high localization precision and small bias while executing almost as fast as the fluoroBancroft algorithm.

Fast, single-molecule localization that achieves theoretically minimum uncertainty

We describe an iterative algorithm that converges to the maximum likelihood estimate of the position and intensity of a single fluorophore. Our technique efficiently computes and achieves the Cramér-Rao lower bound, an essential tool for parameter estimation. An implementation of the algorithm on graphics processing unit hardware achieved more than 10(5) combined fits and Cramér-Rao lower bound calculations per second, enabling real-time data analysis for super-resolution imaging and other applications.

Optimized localization analysis for single-molecule tracking and super-resolution microscopy

We optimally localize isolated fluorescent beads and molecules imaged as diffraction-limited spots, determine the orientation of molecules, and present reliable formulae for the precisions of various localization methods. For beads, theory and experimental data both show that unweighted least-squares fitting of a Gaussian squanders one third of the available information, a popular formula for its precision exaggerates beyond Fisher's information limit, and weighted least-squares may do worse, while maximum likelihood fitting is practically optimal.