Fast, single-molecule localization that achieves theoretically minimum uncertainty

Optimal 3D single-molecule localization for superresolution microscopy with aberrations and engineered point spread functions

Photo-activation localization microscopy is a far-field superresolution imaging technique based on the localization of single molecules with subdiffraction limit precision. Known under acronyms such as PALM (photo-activated localization microscopy) or STORM (stochastic optical reconstruction microscopy), these techniques achieve superresolution by allowing only a sparse, random set of molecules to emit light at any given time and subsequently localizing each molecule with great precision. Recently, such techniques have been extended to three dimensions, opening up unprecedented possibilities to explore the structure and function of cells. Interestingly, proper engineering of the three-dimensional (3D) point spread function (PSF) through additional optics has been demonstrated to theoretically improve 3D position estimation and ultimately resolution. In this paper, an optimal 3D single-molecule localization estimator is presented in a general framework for noisy, aberrated and/or engineered PSF imaging. To find the position of each molecule, a phase-retrieval enabled maximum-likelihood estimator is implemented. This estimator is shown to be efficient, meaning it reaches the fundamental Cramer-Rao lower bound of x, y, and z localization precision. Experimental application of the phase-retrieval enabled maximum-likelihood estimator using a particular engineered PSF microscope demonstrates unmatched low-photon-count 3D wide-field single-molecule localization performance.

Super-resolution fluorescence imaging of chromosomal DNA

Super-resolution microscopy is a powerful tool for understanding cellular function. However one of the most important biomolecules - DNA - remains somewhat inaccessible because it cannot be effectively and appropriately labeled. Here, we demonstrate that robust and detailed super-resolution images of DNA can be produced by combining 5-ethynyl-2'-deoxyuridine (EdU) labeling using the 'click chemistry' approach and direct stochastic optical reconstruction microscopy (dSTORM). This method can resolve fine chromatin structure, and - when used in conjunction with pulse labeling - can reveal the paths taken by individual fibers through the nucleus. This technique should provide a useful tool for the study of nuclear structure and function.

Coordinate-based colocalization analysis of single-molecule localization microscopy data

Colocalization of differently labeled biomolecules is a valuable tool in fluorescence microscopy and can provide information on biomolecular interactions. With the advent of super-resolution microscopy, colocalization analysis is getting closer to molecular resolution, bridging the gap to other technologies such as fluorescence resonance energy transfer. Among these novel microscopic techniques, single-molecule localization-based super-resolution methods offer the advantage of providing single-molecule coordinates that, rather than intensity information, can be used for colocalization analysis. This requires adapting the existing mathematical algorithms for localization microscopy data. Here, we introduce an algorithm for coordinate-based colocalization analysis which is suited for single-molecule super-resolution data. In addition, we present an experimental configuration for simultaneous dual-color imaging together with a robust approach to correct for optical aberrations with an accuracy of a few nanometers. We demonstrate the potential of our approach for cellular structures and for two proteins binding actin filaments.

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.

Single-molecule-based super-resolution images in the presence of multiple fluorophores

Several super-resolution techniques exist, yet most require multiple lasers, use either large or weakly emitting fluorophores, or involve chemical manipulation. Here we show a simple technique that exceeds the standard diffraction limit by 5-15× on fixed samples, yet allows the user to localize individual fluorophores from among groups of crowded fluorophores. It relies only on bright, organic fluorophores and a sensitive camera, both of which are commercially available. Super-resolution is achieved by subtracting sequential images to find the fluorophores that photobleach (temporarily or permanently), photoactivate, or bind to the structure of interest in transitioning from one frame to the next. These fluorophores can then be localized via Gaussian fitting with selective frame averaging to achieve accuracies much better than the diffraction limit. The signal-to-noise ratio decreases with the square root of the number of nearby fluorophores, producing average single-molecule localization errors that are typically <30 nm. Surprisingly, one can often extract signal when there are approximately 20 fluorophores surrounding the fluorophore of interest. Examples shown include microtubules (in vitro and in fixed cells) and chromosomal DNA.

Model of bleaching and acquisition for superresolution microscopy controlled by a single wavelength

We consider acquisition schemes that maximize the fraction of images that contain only a single activated molecule (as opposed to multiple activated molecules) in superresolution localization microscopy of fluorescent probes. During a superresolution localization microscopy experiment, irreversible photobleaching destroys fluorescent molecules, limiting the ability to monitor the dynamics of long-lived processes. Here we consider experiments controlled by a single wavelength, so that the bleaching and activation rates are coupled variables. We use variational techniques and kinetic models to demonstrate that this coupling of bleaching and activation leads to very different optimal control schemes, depending on the detailed kinetics of fluorophore activation and bleaching. Likewise, we show that the robustness of the acquisition scheme is strongly dependent on the detailed kinetics of activation and bleaching.

ErbB1 dimerization is promoted by domain co-confinement and stabilized by ligand binding

The extent to which ligand occupancy and dimerization contribute to erbB1 signaling is controversial. To examine this, we utilized two-color Quantum Dot tracking for visualization of erbB1 homodimerization and quantification of the dimer off rate (k_off) on living cells. Kinetic parameters were extracted using a 3-state Hidden Markov Model to identify transition rates between free, co-confined, and dimerized states. We report that dimers composed of 2 ligand-bound receptors are long-lived and their k_off is independent of kinase activity. By comparison, unliganded dimers have >4-fold faster k_off. Transient co-confinement of receptors promotes repeated encounters and enhances dimer formation. Mobility decreases >6-fold when ligand-bound receptors dimerize. Blockade of erbB1 kinase activity or disruption of actin networks results in faster diffusion of receptor dimers. These results implicate both signal propagation and the cortical cytoskeleton in reduced mobility of signaling-competent erbB1 dimers.

High-density localization of active molecules using Structured Sparse Model and Bayesian Information Criterion

Localization-based super-resolution microscopy (or called localization microscopy) rely on repeated imaging and localization of active molecules, and the spatial resolution enhancement of localization microscopy is built upon the sacrifice of its temporal resolution. Developing algorithms for high-density localization of active molecules is a promising approach to increase the speed of localization microscopy. Here we present a new algorithm called SSM_BIC for such purpose. The SSM_BIC combines the advantages of the Structured Sparse Model (SSM) and the Bayesian Information Criterion (BIC). Through simulation and experimental studies, we evaluate systematically the performance between the SSM_BIC and the conventional Sparse algorithm in high-density localization of active molecules. We show that the SSM_BIC is superior in processing single molecule images with weak signal embedded in strong background.

Systems biology in immunology: a computational modeling perspective

Systems biology is an emerging discipline that combines high-content, multiplexed measurements with informatic and computational modeling methods to better understand biological function at various scales. Here we present a detailed review of the methods used to create computational models and to conduct simulations of immune function. We provide descriptions of the key data-gathering techniques employed to generate the quantitative and qualitative data required for such modeling and simulation and summarize the progress to date in applying these tools and techniques to questions of immunological interest, including infectious disease. We include comments on what insights modeling can provide that complement information obtained from the more familiar experimental discovery methods used by most investigators and the reasons why quantitative methods are needed to eventually produce a better understanding of immune system operation in health and disease.

Simultaneous multiple-emitter fitting for single molecule super-resolution imaging

Single molecule localization based super-resolution imaging techniques require repeated localization of many single emitters. We describe a method that uses the maximum likelihood estimator to localize multiple emitters simultaneously within a single, two-dimensional fitting sub-region, yielding an order of magnitude improvement in the tolerance of the analysis routine with regards to the single-frame active emitter density. Multiple-emitter fitting enables the overall performance of single-molecule super-resolution to be improved in one or more of several metrics that result in higher single-frame density of localized active emitters. For speed, the algorithm is implemented on Graphics Processing Unit (GPU) architecture, resulting in analysis times on the order of minutes. We show the performance of multiple emitter fitting as a function of the single-frame active emitter density. We describe the details of the algorithm that allow robust fitting, the details of the GPU implementation, and the other imaging processing steps required for the analysis of data sets.

Validating transcripts with probes and imaging technology

High-throughput gene expression screens provide a quantitative picture of the average expression signature of biological samples. However, the analysis of spatial gene expression patterns with single-cell resolution requires quantitative in situ measurement techniques. Here we describe recent technological advances in RNA fluorescence in situ hybridization (FISH) techniques that facilitate detection of individual fluorescently labeled mRNA molecules of practically any endogenous gene. These methods, which are based on advances in probe design, imaging technology and image processing, enable the absolute measurement of transcript abundance in individual cells with single-molecule resolution.

Confined activation and subdiffractive localization enables whole-cell PALM with genetically expressed probes

We demonstrate 3D superresolution microscopy in whole fixed cells using photoactivated localization microscopy (PALM). The use of the bright, genetically expressed fluorescent marker photoactivatable mCherry (PA-mCherry1) in combination with near diffraction-limited confinement of photoactivation using two-photon illumination and 3D localization methods allowed us to investigate a variety of cellular structures at <50 nm lateral and <100 nm axial resolution. Compared to existing methods, we substantially reduce excitation and bleaching of unlocalized markers, enabling 3D PALM imaging with high localization density in thick structures. Our 3D localization algorithms based on cross-correlation do not rely on idealized noise models or specific optical configurations, allowing flexible instrument design. Generation of appropriate fusion constructs and expression in Cos7 cells allowed us to image invaginations of the nuclear membrane, vimentin fibrils, the mitochondrial network, and the endoplasmic reticulum at depths greater than 8 μm.

PALM and STORM: unlocking live-cell super-resolution

Live-cell fluorescence light microscopy has emerged as an important tool in the study of cellular biology. The development of fluorescent markers in parallel with super-resolution imaging systems has pushed light microscopy into the realm of molecular visualization at the nanometer scale. Resolutions previously only attained with electron microscopes are now within the grasp of light microscopes. However, until recently, live-cell imaging approaches have eluded super-resolution microscopy, hampering it from reaching its full potential for revealing the dynamic interactions in biology occurring at the single molecule level. Here we examine recent advances in the super-resolution imaging of living cells by reviewing recent breakthroughs in single molecule localization microscopy methods such as PALM and STORM to achieve this important goal.

Single-molecule Photoswitching and Localization

Within only a few years super-resolution fluorescence imaging based on single-molecule localization and image reconstruction has attracted considerable interest because it offers a comparatively simple way to achieve a substantially improved optical resolution down to ∼20 nm in the image plane. Since super-resolution imaging methods such as photoactivated localization microscopy, fluorescence photoactivation localization microscopy, stochastic optical reconstruction microscopy, and direct stochastic optical reconstruction microscopy rely critically on exact fitting of the centre of mass and the shape of the point-spread-function of isolated emitters unaffected by neighbouring fluorophores, controlled photoswitching or photoactivation of fluorophores is the key parameter for resolution improvement. This review will explain the principles and requirements of single-molecule based localization microscopy, and compare different super-resolution imaging concepts and highlight their strengths and limitations with respect to applications in fixed and living cells with high spatio-temporal resolution.

Accuracy of the gaussian point spread function model in 2D localization microscopy

The gaussian function is simple and easy to implement as Point Spread Function (PSF) model for fitting the position of fluorescent emitters in localization microscopy. Despite its attractiveness the appropriateness of the gaussian is questionable as it is not based on the laws of optics. Here we study the effect of emission dipole orientation in conjunction with optical aberrations on the localization accuracy of position estimators based on a gaussian model PSF. Simulated image spots, calculated with all effects of high numerical aperture, interfaces between media, polarization, dipole orientation and aberrations taken into account, were fitted with a gaussian PSF based Maximum Likelihood Estimator. For freely rotating dipole emitters it is found that the gaussian works fine. The same, theoretically optimum, localization accuracy is found as if the true PSF were a gaussian, even for aberrations within the usual tolerance limit of high-end optical imaging systems such as microscopes (Marechal's diffraction limit). For emitters with a fixed dipole orientation this is not the case. Localization errors are found that reach up to 40 nm for typical system parameters and aberration levels at the diffraction limit. These are systematic errors that are independent of the total photon count in the image. The gaussian function is therefore inappropriate, and more sophisticated PSF models are a practical necessity.

Localization capability and limitation of electron-multiplying charge-coupled, scientific complementary metal-oxide semiconductor, and charge-coupled devices for superresolution imaging

Localization of a single fluorescent molecule is required in a number of superresolution imaging techniques for visualizing biological structures at cellular and subcellular levels. The localization capability and limitation of low-light detectors are critical for such a purpose. We present an updated evaluation on the performance of three typical low-light detectors, including a popular electron-multiplying CCD (EMCCD), a newly developed scientific CMOS (sCMOS), and a representative cooled CCD, for superresolution imaging. We find that under some experimental accessible conditions, the sCMOS camera shows a competitive and even better performance than the EMCCD camera, which has long been considered the detector of choice in the field of superresolution imaging.

Condensed mitotic chromosome structure at nanometer resolution using PALM and EGFP- histones

Photoactivated localization microscopy (PALM) and related fluorescent biological imaging methods are capable of providing very high spatial resolutions (up to 20 nm). Two major demands limit its widespread use on biological samples: requirements for photoactivatable/photoconvertible fluorescent molecules, which are sometimes difficult to incorporate, and high background signals from autofluorescence or fluorophores in adjacent focal planes in three-dimensional imaging which reduces PALM resolution significantly. We present here a high-resolution PALM method utilizing conventional EGFP as the photoconvertible fluorophore, improved algorithms to deal with high levels of biological background noise, and apply this to imaging higher order chromatin structure. We found that the emission wavelength of EGFP is efficiently converted from green to red when exposed to blue light in the presence of reduced riboflavin. The photon yield of red-converted EGFP using riboflavin is comparable to other bright photoconvertible fluorescent proteins that allow <20 nm resolution. We further found that image pre-processing using a combination of denoising and deconvolution of the raw PALM images substantially improved the spatial resolution of the reconstruction from noisy images. Performing PALM on Drosophila mitotic chromosomes labeled with H2AvD-EGFP, a histone H2A variant, revealed filamentous components of ∼70 nm. This is the first observation of fine chromatin filaments specific for one histone variant at a resolution approximating that of conventional electron microscope images (10-30 nm). As demonstrated by modeling and experiments on a challenging specimen, the techniques described here facilitate super-resolution fluorescent imaging with common biological samples.

Optical imaging of nanoscale cellular structures

Visualization of subcellular structures and their temporal evolution is of utmost importance to understand a vast range of biological processes. Optical microscopy is the method of choice for imaging live cells and tissues; it is minimally invasive, so processes can be observed over extended periods of time without generating artifacts due to intense light irradiation. The use of fluorescence microscopy is advantageous because biomolecules or supramolecular structures of interest can be labeled specifically with fluorophores, so the images reveal information on processes involving only the labeled molecules. The key restriction of optical microscopy is its moderate resolution, which is limited to about half the wavelength of light (∼200 nm) due to fundamental physical laws governing wave optics. Consequently, molecular processes taking place at spatial scales between 1 and 100 nm cannot be studied by regular optical microscopy. In recent years, however, a variety of super-resolution fluorescence microscopy techniques have been developed that circumvent the resolution limitation. Here, we present a brief overview of these techniques and their application to cellular biophysics.