Matthew D. Lew

Localizing and Tracking Single Nanoscale Emitters in Three Dimensions with High Spatiotemporal Resolution Using a Double-Helix Point Spread Function

Three-dimensional nanoscale localization and tracking of dim single emitters can be obtained with a widefield fluorescence microscope exhibiting a double-helix point spread function (DH-PSF). We describe in detail how the localization precision quantitatively depends upon the number of photons detected and the z position of the nanoscale emitter, thereby showing a approximately 10 nm localization capability along x, y, and z in the limit of weak emitters. Experimental measurements are compared to Fisher information calculations of the ultimate localization precision inherent in the DH-PSF. The DH-PSF, for the first time, is used to track single quantum dots in aqueous solution and a quantum dot-labeled structure inside a living cell in three dimensions.

Three-dimensional superresolution colocalization of intracellular protein superstructures and the cell surface in live Caulobacter crescentus

Recently, single-molecule imaging and photocontrol have enabled superresolution optical microscopy of cellular structures beyond Abbe’s diffraction limit, extending the frontier of noninvasive imaging of structures within living cells. However, live-cell superresolution imaging has been challenged by the need to image three-dimensional (3D) structures relative to their biological context, such as the cellular membrane. We have developed a technique, termed superresolution by power-dependent active intermittency and points accumulation for imaging in nanoscale topography (SPRAIPAINT) that combines imaging of intracellular enhanced YFP (eYFP) fusions (SPRAI) with stochastic localization of the cell surface (PAINT) to image two different fluorophores sequentially with only one laser. Simple light-induced blinking of eYFP and collisional flux onto the cell surface by Nile red are used to achieve single-molecule localizations, without any antibody labeling, cell membrane permeabilization, or thiol-oxygen scavenger systems required. Here we demonstrate live-cell 3D superresolution imaging of Crescentin-eYFP, a cytoskeletal fluorescent protein fusion, colocalized with the surface of the bacterium Caulobacter crescentus using a double-helix point spread function microscope. Three-dimensional colocalization of intracellular protein structures and the cell surface with superresolution optical microscopy opens the door for the analysis of protein interactions in living cells with excellent precision (20–40 nm in 3D) over a large field of view (12 × 12 μm).

Simultaneous, accurate measurement of the 3D position and orientation of single molecules

Recently, single molecule-based superresolution fluorescence microscopy has surpassed the diffraction limit to improve resolution to the order of 20 nm or better. These methods typically use image fitting that assumes an isotropic emission pattern from the single emitters as well as control of the emitter concentration. However, anisotropic single-molecule emission patterns arise from the transition dipole when it is rotationally immobile, depending highly on the molecule’s 3D orientation and z position. Failure to account for this fact can lead to significant lateral (x, y) mislocalizations (up to ∼50–200 nm). This systematic error can cause distortions in the reconstructed images, which can translate into degraded resolution. Using parameters uniquely inherent in the double-lobed nature of the Double-Helix Point Spread Function, we account for such mislocalizations and simultaneously measure 3D molecular orientation and 3D position. Mislocalizations during an axial scan of a single molecule manifest themselves as an apparent lateral shift in its position, which causes the standard deviation (SD) of its lateral position to appear larger than the SD expected from photon shot noise. By correcting each localization based on an estimated orientation, we are able to improve SDs in lateral localization from ∼2× worse than photon-limited precision (48 vs. 25 nm) to within 5 nm of photon-limited precision. Furthermore, by averaging many estimations of orientation over different depths, we are able to improve from a lateral SD of 116 (∼4× worse than the photon-limited precision; 28 nm) to 34 nm (within 6 nm of the photon limit).

Three-dimensional localization precision of the double-helix point spread function versus astigmatism and biplane.

Wide-field microscopy with a double-helix point spread function (DH-PSF) provides three-dimensional (3D) position information beyond the optical diffraction limit. We compare the theoretical localization precision for an unbiased estimator of the DH-PSF to that for 3D localization by astigmatic and biplane imaging using Fisher information analysis including pixelation and varying levels of background. The DH-PSF results in almost constant localization precision in all three dimensions for a 2 μm thick depth of field while astigmatism and biplane improve the axial localization precision over smaller axial ranges. For high signal-to-background ratio, the DH-PSF on average achieves better localization precision.

Corkscrew point spread function for far-field three-dimensional nanoscale localization of pointlike objects

We describe the corkscrew point spread function (PSF), which can localize objects in three dimensions throughout a 3.2 μm depth of field with nanometer precision. The corkscrew PSF rotates as a function of the axial (z) position of an emitter. Fisher information calculations show that the corkscrew PSF can achieve nanometer localization precision with limited numbers of photons. We demonstrate three-dimensional super-resolution microscopy with the corkscrew PSF by imaging beads on the surface of a triangular polydimethylsiloxane (PDMS) grating. With 99,000 photons detected, the corkscrew PSF achieves a localization precision of 2.7 nm in x, 2.1 nm in y, and 5.7 nm in z.

Rotational Mobility of Single Molecules Affects Localization Accuracy in Super-Resolution Fluorescence Microscopy

The asymmetric nature of single-molecule (SM) dipole emission patterns limits the accuracy of position determination in localization-based super-resolution fluorescence microscopy. The degree of mislocalization depends highly on the rotational mobility of SMs; only for SMs rotating within a cone half angle α > 60° can mislocalization errors be bounded to ≤10 nm. Simulations demonstrate how low or high rotational mobility can cause resolution degradation or distortion in super-resolution reconstructions.

The Role of Molecular Dipole Orientation in Single‐Molecule Fluorescence Microscopy and Implications for Super‐Resolution Imaging

Numerous methods for determining the orientation of single-molecule transition dipole moments from microscopic images of the molecular fluorescence have been developed in recent years. At the same time, techniques that rely on nanometer-level accuracy in the determination of molecular position, such as single-molecule super-resolution imaging, have proven immensely successful in their ability to access unprecedented levels of detail and resolution previously hidden by the optical diffraction limit. However, the level of accuracy in the determination of position is threatened by insufficient treatment of molecular orientation. Here we review a number of methods for measuring molecular orientation using fluorescence microscopy, focusing on approaches that are most compatible with position estimation and single-molecule super-resolution imaging. We highlight recent methods based on quadrated pupil imaging and on double-helix point spread function microscopy and apply them to the study of fluorophore mobility on immunolabeled microtubules.

Quantitative differential interference contrast microscopy based on structured-aperture interference

We report a quantitative differential interference contrast (DIC) microscope based on a structured-aperture (SA) wavefront sensor. Unlike a conventional DIC microscope, the SA-DIC microscope can separate the amplitude and the phase gradient information of the image wavefront, and form quantitative intensity and DIC images of the sample with good resolution; our prototype achieved resolution ~2 µm. Furthermore, due to the nonpolarization nature of the microscope, we were able to image birefringent samples without artifacts.

The double-helix microscope super-resolves extended biological structures by localizing single blinking molecules in three dimensions with nanoscale precision

The double-helix point spread function microscope encodes the axial (z) position information of single emitters in wide-field (x,y) images, thus enabling localization in three dimensions (3D) inside extended volumes. We experimentally determine the statistical localization precision σ of this approach using single emitters in a cell under typical background conditions, demonstrating σ < 20 nm laterally and <30 nm axially for N ≈ 1180 photons per localization. Combined with light-induced blinking of single-molecule labels, we present proof-of-concept imaging beyond the optical diffraction limit of microtubule network structures in fixed mammalian cells over a large axial range in three dimensions.

Correcting field-dependent aberrations with nanoscale accuracy in three-dimensional single-molecule localization microscopy

The localization of single fluorescent molecules enables the imaging of molecular structure and dynamics with subdiffraction precision and can be extended to three dimensions using point spread function (PSF) engineering. However, the nanoscale accuracy of localization throughout a 3D single-molecule microscopes field of view has not yet been rigorously examined. By using regularly spaced subdiffraction apertures filled with fluorescent dyes, we reveal field-dependent aberrations as large as 50-100 nm and show that they can be corrected to less than 25 nm over an extended 3D focal volume. We demonstrate the applicability of this technique for two engineered PSFs, the double-helix PSF and the astigmatic PSF. We expect these results to be broadly applicable to 3D single-molecule tracking and superresolution methods demanding high accuracy.