Universal inverse modeling of point spread functions for SMLM localization and microscope characterization.

The point spread function (PSF) of a microscope describes the image of a point emitter. Knowing the accurate PSF model is essential for various imaging tasks, including single-molecule localization, aberration correction and deconvolution. Here we present universal inverse modeling of point spread functions (uiPSF), a toolbox to infer accurate PSF models from microscopy data, using either image stacks of fluorescent beads or directly images of blinking fluorophores, the raw data in single-molecule localization microscopy (SMLM). Our modular framework is applicable to a variety of microscope modalities and the PSF model incorporates system- or sample-specific characteristics, for example, the bead size, field- and depth- dependent aberrations, and transformations among channels. We demonstrate its application in single or multiple channels or large field-of-view SMLM systems, 4Pi-SMLM, and lattice light-sheet microscopes using either bead data or single-molecule blinking data.

DBlink: dynamic localization microscopy in super spatiotemporal resolution via deep learning.

Single-molecule localization microscopy (SMLM) has revolutionized biological imaging, improving the spatial resolution of traditional microscopes by an order of magnitude. However, SMLM techniques require long acquisition times, typically a few minutes, to yield a single super-resolved image, because they depend on accumulation of many localizations over thousands of recorded frames. Hence, the capability of SMLM to observe dynamics at high temporal resolution has always been limited. In this work, we present DBlink, a deep-learning-based method for super spatiotemporal resolution reconstruction from SMLM data. The input to DBlink is a recorded video of SMLM data and the output is a super spatiotemporal resolution video reconstruction. We use a convolutional neural network combined with a bidirectional long short-term memory network architecture, designed for capturing long-term dependencies between different input frames. We demonstrate DBlink performance on simulated filaments and mitochondria-like structures, on experimental SMLM data under controlled motion conditions and on live-cell dynamic SMLM. DBlink's spatiotemporal interpolation constitutes an important advance in super-resolution imaging of dynamic processes in live cells.

Design of optimal labeling patterns for optical genome mapping via information theory.

MOTIVATION: Optical genome mapping (OGM) is a technique that extracts partial genomic information from optically imaged and linearized DNA fragments containing fluorescently labeled short sequence patterns. This information can be used for various genomic analyses and applications, such as the detection of structural variations and copy-number variations, epigenomic profiling, and microbial species identification. Currently, the choice of labeled patterns is based on the available biochemical methods and is not necessarily optimized for the application. RESULTS: In this work, we develop a model of OGM based on information theory, which enables the design of optimal labeling patterns for specific applications and target organism genomes. We validated the model through experimental OGM on human DNA and simulations on bacterial DNA. Our model predicts up to 10-fold improved accuracy by optimal choice of labeling patterns, which may guide future development of OGM biochemical labeling methods and significantly improve its accuracy and yield for applications such as epigenomic profiling and cultivation-free pathogen identification in clinical samples. AVAILABILITY AND IMPLEMENTATION: https://github.com/yevgenin/PatternCode.

DeepOM: single-molecule optical genome mapping via deep learning.

MOTIVATION: Efficient tapping into genomic information from a single microscopic image of an intact DNA molecule is an outstanding challenge and its solution will open new frontiers in molecular diagnostics. Here, a new computational method for optical genome mapping utilizing deep learning is presented, termed DeepOM. Utilization of a convolutional neural network, trained on simulated images of labeled DNA molecules, improves the success rate in the alignment of DNA images to genomic references. RESULTS: The method is evaluated on acquired images of human DNA molecules stretched in nano-channels. The accuracy of the method is benchmarked against state-of-the-art commercial software Bionano Solve. The results show a significant advantage in alignment success rate for molecules shorter than 50 kb. DeepOM improves the yield, sensitivity, and throughput of optical genome mapping experiments in applications of human genomics and microbiology. AVAILABILITY AND IMPLEMENTATION: The source code for the presented method is publicly available at https://github.com/yevgenin/DeepOM.

Publisher Correction: DeepSTORM3D: dense 3D localization microscopy and PSF design by deep learning.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

DeepSTORM3D: dense 3D localization microscopy and PSF design by deep learning.

An outstanding challenge in single-molecule localization microscopy is the accurate and precise localization of individual point emitters in three dimensions in densely labeled samples. One established approach for three-dimensional single-molecule localization is point-spread-function (PSF) engineering, in which the PSF is engineered to vary distinctively with emitter depth using additional optical elements. However, images of dense emitters, which are desirable for improving temporal resolution, pose a challenge for algorithmic localization of engineered PSFs, due to lateral overlap of the emitter PSFs. Here we train a neural network to localize multiple emitters with densely overlapping Tetrapod PSFs over a large axial range. We then use the network to design the optimal PSF for the multi-emitter case. We demonstrate our approach experimentally with super-resolution reconstructions of mitochondria and volumetric imaging of fluorescently labeled telomeres in cells. Our approach, DeepSTORM3D, enables the study of biological processes in whole cells at timescales that are rarely explored in localization microscopy.

Diffractive optical system design by cascaded propagation.

Modern design of complex optical systems relies heavily on computational tools. These frequently use geometrical optics as well as Fourier optics. Fourier optics is typically used for designing thin diffractive elements, placed in the system's aperture, generating a shift-invariant Point Spread Function (PSF). A major bottleneck in applying Fourier Optics in many cases of interest, e.g. when dealing with multiple, or out-of-aperture elements, comes from numerical complexity. In this work, we propose and implement an efficient and differentiable propagation model based on the Collins integral, which enables the optimization of diffractive optical systems with unprecedented design freedom using backpropagation. We demonstrate the applicability of our method, numerically and experimentally, by engineering shift-variant PSFs via thin plate elements placed in arbitrary planes inside complex imaging systems, performing cascaded optimization of multiple planes, and designing optimal machine-vision systems by deep learning.

Monocular kilometer-scale passive ranging by point-spread function engineering.

Standard imaging systems are designed for 2D representation of objects, while information about the third dimension remains implicit, as imaging-based distance estimation is a difficult challenge. Existing long-range distance estimation technologies mostly rely on active emission of signal, which as a subsystem, constitutes a significant portion of the complexity, size and cost of the active-ranging apparatus. Despite the appeal of alleviating the requirement for signal-emission, passive distance estimation methods are essentially nonexistent for ranges greater than a few hundreds of meters. Here, we present monocular long-range, telescope-based passive ranging, realized by integration of point-spread-function engineering into a telescope, extending the scale of point-spread-function engineering-based ranging to distances where it has never been tested before. We provide experimental demonstrations of the optical system in a variety of challenging imaging scenarios, including adversarial weather conditions, dynamic targets and scenes of diversified textures, at distances extending beyond 1.7 km. We conclude with brief quantification of the effect of atmospheric turbulence on estimation precision, which becomes a significant error source in long-range optical imaging.

Multiplexed PSF Engineering for Three-Dimensional Multicolor Particle Tracking.

Three-dimensional spatiotemporal tracking of microscopic particles in multiple colors is a challenging optical imaging task. Existing approaches require a trade-off between photon efficiency, field of view, mechanical complexity, spectral specificity, and speed. Here, we introduce multiplexed point-spread-function engineering that achieves photon-efficient, 3D multicolor particle tracking over a large field of view. This is accomplished by first chromatically splitting the emission path of a microscope to different channels, engineering the point-spread function of each, and then recombining them onto the same region of the camera. We demonstrate our technique for simultaneously tracking five types of emitters in vitro as well as colocalization of DNA loci in live yeast cells.

Deep-ROCS: from speckle patterns to superior-resolved images by deep learning in rotating coherent scattering microscopy.

Rotating coherent scattering (ROCS) microscopy is a label-free imaging technique that overcomes the optical diffraction limit by adding up the scattered laser light from a sample obliquely illuminated from different angles. Although ROCS imaging achieves 150 nm spatial and 10 ms temporal resolution, simply summing different speckle patterns may cause loss of sample information. In this paper we present Deep-ROCS, a neural network-based technique that generates a superior-resolved image by efficient numerical combination of a set of differently illuminated images. We show that Deep-ROCS can reconstruct super-resolved images more accurately than conventional ROCS microscopy, retrieving high-frequency information from a small number (6) of speckle images. We demonstrate the performance of Deep-ROCS experimentally on 200 nm beads and by computer simulations, where we show its potential for even more complex structures such as a filament network.

VIPR: vectorial implementation of phase retrieval for fast and accurate microscopic pixel-wise pupil estimation.

In microscopy, proper modeling of the image formation has a substantial effect on the precision and accuracy in localization experiments and facilitates the correction of aberrations in adaptive optics experiments. The observed images are subject to polarization effects, refractive index variations, and system specific constraints. Previously reported techniques have addressed these challenges by using complicated calibration samples, computationally heavy numerical algorithms, and various mathematical simplifications. In this work, we present a phase retrieval approach based on an analytical derivation of the vectorial diffraction model. Our method produces an accurate estimate of the system's phase information, without any prior knowledge about the aberrations, in under a minute.

Single-Particle Diffusion Characterization by Deep Learning.

Diffusion plays a crucial role in many biological processes including signaling, cellular organization, transport mechanisms, and more. Direct observation of molecular movement by single-particle-tracking experiments has contributed to a growing body of evidence that many cellular systems do not exhibit classical Brownian motion but rather anomalous diffusion. Despite this evidence, characterization of the physical process underlying anomalous diffusion remains a challenging problem for several reasons. First, different physical processes can exist simultaneously in a system. Second, commonly used tools for distinguishing between these processes are based on asymptotic behavior, which is experimentally inaccessible in most cases. Finally, an accurate analysis of the diffusion model requires the calculation of many observables because different transport modes can result in the same diffusion power-law α, which is typically obtained from the mean-square displacements (MSDs). The outstanding challenge in the field is to develop a method to extract an accurate assessment of the diffusion process using many short trajectories with a simple scheme that is applicable at the nonexpert level. Here, we use deep learning to infer the underlying process resulting in anomalous diffusion. We implement a neural network to classify single-particle trajectories by diffusion type: Brownian motion, fractional Brownian motion and continuous time random walk. Further, we demonstrate the applicability of our network architecture for estimating the Hurst exponent for fractional Brownian motion and the diffusion coefficient for Brownian motion on both simulated and experimental data. These networks achieve greater accuracy than time-averaged MSD analysis on simulated trajectories while only requiring as few as 25 steps. When tested on experimental data, both net and ensemble MSD analysis converge to similar values; however, the net needs only half the number of trajectories required for ensemble MSD to achieve the same confidence interval. Finally, we extract diffusion parameters from multiple extremely short trajectories (10 steps) using our approach.

Multicolor localization microscopy and point-spread-function engineering by deep learning.

Deep learning has become an extremely effective tool for image classification and image restoration problems. Here, we apply deep learning to microscopy and demonstrate how neural networks can exploit the chromatic dependence of the point-spread function to classify the colors of single emitters imaged on a grayscale camera. While existing localization microscopy methods for spectral classification require additional optical elements in the emission path, e.g., spectral filters, prisms, or phase masks, our neural net correctly identifies static and mobile emitters with high efficiency using a standard, unmodified single-channel configuration. Furthermore, we show how deep learning can be used to design new phase-modulating elements that, when implemented into the imaging path, result in further improved color differentiation between species, including simultaneously differentiating four species in a single image.

Three-Dimensional Localization of Single Molecules for Super-Resolution Imaging and Single-Particle Tracking.

Single-molecule super-resolution fluorescence microscopy and single-particle tracking are two imaging modalities that illuminate the properties of cells and materials on spatial scales down to tens of nanometers or with dynamical information about nanoscale particle motion in the millisecond range, respectively. These methods generally use wide-field microscopes and two-dimensional camera detectors to localize molecules to much higher precision than the diffraction limit. Given the limited total photons available from each single-molecule label, both modalities require careful mathematical analysis and image processing. Much more information can be obtained about the system under study by extending to three-dimensional (3D) single-molecule localization: without this capability, visualization of structures or motions extending in the axial direction can easily be missed or confused, compromising scientific understanding. A variety of methods for obtaining both 3D super-resolution images and 3D tracking information have been devised, each with their own strengths and weaknesses. These include imaging of multiple focal planes, point-spread-function engineering, and interferometric detection. These methods may be compared based on their ability to provide accurate and precise position information on single-molecule emitters with limited photons. To successfully apply and further develop these methods, it is essential to consider many practical concerns, including the effects of optical aberrations, field dependence in the imaging system, fluorophore labeling density, and registration between different color channels. Selected examples of 3D super-resolution imaging and tracking are described for illustration from a variety of biological contexts and with a variety of methods, demonstrating the power of 3D localization for understanding complex systems.

Observing DNA in live cells.

The structural organization and dynamics of DNA are known to be of paramount importance in countless cellular processes, but capturing these events poses a unique challenge. Fluorescence microscopy is well suited for these live-cell investigations, but requires attaching fluorescent labels to the species under investigation. Over the past several decades, a suite of techniques have been developed for labeling and imaging DNA, each with various advantages and drawbacks. Here, we provide an overview of the labeling and imaging tools currently available for visualizing DNA in live cells, and discuss their suitability for various applications.

Fundamental Precision Bounds for Three-Dimensional Optical Localization Microscopy with Poisson Statistics.

Point source localization is a problem of persistent interest in optical imaging. In particular, a number of widely used biological microscopy techniques rely on precise three-dimensional localization of single fluorophores. As emitter depth localization is more challenging than lateral localization, considerable effort has been spent on engineering the response of the microscope in a way that reveals increased depth information. Here, we prove the (sub)optimality of these approaches by deriving and comparing to the measurement-independent quantum Cramér-Rao bound (QCRB). We show that existing methods for depth localization with single-objective collection exceed the QCRB, and we gain insight into the bound by proposing an interferometer arrangement that approaches it. We also show that for light collection with two opposed objectives, an established interferometric technique globally reaches the QCRB in all three dimensions simultaneously, and so this represents an interesting case study from the point of view of quantum multiparameter estimation.

Measurement-based estimation of global pupil functions in 3D localization microscopy.

We report the use of a phase retrieval procedure based on maximum likelihood estimation (MLE) to produce an improved, experimentally calibrated model of a point spread function (PSF) for use in three-dimensional (3D) localization microscopy experiments. The method estimates a global pupil phase function (which includes both the PSF and system aberrations) over the full axial range from a simple calibration scan. The pupil function is used to refine the PSF model and hence enable superior localizations from experimental data. To demonstrate the utility of the procedure, we apply it to experimental data acquired with a microscope employing a tetrapod PSF with a 6 µm axial range. The phase-retrieved model demonstrates significant improvements in both accuracy and precision of 3D localizations relative to the model based on scalar diffraction theory. The localization precision of the phase-retrieved model is shown to be near the limits imposed by estimation theory, and the reproducibility of the procedure is characterized and discussed. Code which performs the phase retrieval algorithm is provided.

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.

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.