The double-helix point spread function enables precise and accurate measurement of 3D single-molecule localization and orientation

High-density volumetric super-resolution microscopy

Volumetric super-resolution microscopy typically encodes the 3D position of single-molecule fluorescence into a 2D image by changing the shape of the point spread function (PSF) as a function of depth. However, the resulting large and complex PSF spatial footprints reduce biological throughput and applicability by requiring lower labeling densities to avoid overlapping fluorescent signals. We quantitatively compare the density dependence of single-molecule light field microscopy (SMLFM) to other 3D PSFs (astigmatism, double helix and tetrapod) showing that SMLFM enables an order-of-magnitude speed improvement compared to the double helix PSF by resolving overlapping emitters through parallax. We demonstrate this optical robustness experimentally with high accuracy ( > 99.2 ± 0.1%, 0.1 locs μm-2) and sensitivity ( > 86.6 ± 0.9%, 0.1 locs μm-2) through whole-cell (scan-free) imaging and tracking of single membrane proteins in live primary B cells. We also exemplify high-density volumetric imaging (0.15 locs μm-2) in dense cytosolic tubulin datasets.

Quantifying nanoscopic alterations associated with mitochondrial dysfunction using three-dimensional single-molecule localization microscopy

Mitochondrial morphology provides unique insights into their integrity and function. Among fluorescence microscopy techniques, 3D super-resolution microscopy uniquely enables the analysis of mitochondrial morphological features individually. However, there is a lack of tools to extract morphological parameters from super-resolution images of mitochondria. We report a quantitative method to extract mitochondrial morphological metrics, including volume, aspect ratio, and local protein density, from 3D single-molecule localization microscopy images, with single-mitochondrion sensitivity. We validated our approach using simulated ground-truth SMLM images of mitochondria. We further tested our morphological analysis on mitochondria that have been altered functionally and morphologically in controlled manners. This work sets the stage to quantitatively analyze mitochondrial morphological alterations associated with disease progression on an individual basis.

Optimal sampling rate for 3D single molecule localization

Resolution of single molecule localization microscopy (SMLM) depends on the localization accuracy, which can be improved by utilizing engineered point spread functions (PSF) with delicate shapes. However, the intrinsic pixelation effect of the detector sensor will deteriorate PSFs under different sampling rates. The influence of the pixelation effect to the achieved 3D localization accuracy for different PSF shapes under different signal to background ratio (SBR) and pixel dependent readout noise has not been investigated in detail so far. In this work, we proposed a framework to characterize the 3D localization accuracy of pixelated PSF at different sampling rates. Four different PSFs (astigmatic PSF, double helix (DH) PSF, Tetrapod PSF and 4Pi PSF) were evaluated and the pixel size with optimal 3D localization performance were derived. This work provides a theoretical guide for the optimal design of sampling rate for 3D super resolution imaging.

MAxSIM: multi-angle-crossing structured illumination microscopy with height-controlled mirror for 3D topological mapping of live cells

Mapping 3D plasma membrane topology in live cells can bring unprecedented insights into cell biology. Widefield-based super-resolution methods such as 3D-structured illumination microscopy (3D-SIM) can achieve twice the axial ( ~ 300 nm) and lateral ( ~ 100 nm) resolution of widefield microscopy in real time in live cells. However, twice-resolution enhancement cannot sufficiently visualize nanoscale fine structures of the plasma membrane. Axial interferometry methods including fluorescence light interference contrast microscopy and its derivatives (e.g., scanning angle interference microscopy) can determine nanoscale axial locations of proteins on and near the plasma membrane. Thus, by combining super-resolution lateral imaging of 2D-SIM with axial interferometry, we developed multi-angle-crossing structured illumination microscopy (MAxSIM) to generate multiple incident angles by fast, optoelectronic creation of diffraction patterns. Axial localization accuracy can be enhanced by placing cells on a bottom glass substrate, locating a custom height-controlled mirror (HCM) at a fixed axial position above the glass substrate, and optimizing the height reconstruction algorithm for noisy experimental data. The HCM also enables imaging of both the apical and basal surfaces of a cell. MAxSIM with HCM offers high-fidelity nanoscale 3D topological mapping of cell plasma membranes with near-real-time ( ~ 0.5 Hz) imaging of live cells and 3D single-molecule tracking.

Polarization-sensitive direct laser patterning of azopolymer thin films with vortex beams

Laser patterning of thin films of materials is widely used for the fabrication of one-, two- and three-dimensional functional nanomaterials. Using structured laser beams with a complex structure of amplitude, phase, and polarization distributions allows one to significantly simplify and speed up the procedure of manufacturing nano- and microstructures with a complex shape, such as a spiral structure. Here, we demonstrate the use of vortex laser beams with a helical wavefront for the realization of spiral mass transfer in azopolymer films. The polarization sensitivity of this material allows us to demonstrate the formation of different three-dimensional structures in the case of linearly or circularly polarized vortex beams of different orders. The presented theoretical analysis shows that the profile of the fabricated structures is defined by the structure of the longitudinal component of the incident radiation, and thus can be easily controlled with the polarization state of the radiation without the need to change the amplitude-phase structure of the beam.

Axial accuracy in localization microscopy with 3D point spread function engineering

Single-molecule localization microscopy has developed into a widely used technique to overcome the diffraction limit and enables 3D localization of single-emitters with nanometer precision. A widely used method to enable 3D encoding is to use a cylindrical lens or a phase mask to engineer the point spread function (PSF). The performance of these PSFs is often assessed by comparing the precision they achieve, ignoring accuracy. Nonetheless, accurate localization is required in many applications, such as multi-plane imaging, measuring and modelling of physical processes based on volumetric data, and 3D particle averaging. However, there are PSF model mismatches in the localization schemes due to how reference PSFs are obtained, look-up-tables are created, or spots are fitted. Currently there is little insight in how these model mismatches give rise to systematic axial localization errors, how large these errors are, and how to mitigate them. In this theoretical and simulation work we use a vector PSF model, which incorporates super-critical angle fluorescence (SAF) and the appropriate aplanatic correction factor, to analyze the errors in z-localization. We introduce theory for defining the focal plane in SAF conditions and analyze the predicted axial errors for an astigmatic PSF, double-helix PSF, and saddle-point PSF. These simulations indicate that the absolute axial biases can be as large as 140 nm, 250 nm, and 120 nm for the astigmatic, saddle-point, and double-helix PSF respectively, with relative errors of more than 50%. Finally, we discuss potential experimental methods to verify these findings and propose a workflow to mitigate these effects.

Propagation-Invariant Off-Axis Elliptic Gaussian Beams with the Orbital Angular Momentum

We studied paraxial light beams, obtained by a continuous superposition of off-axis Gaussian beams with their phases chosen so that the whole superposition is invariant to free-space propagation, i.e., does not change its transverse intensity shape. Solving a system of five nonlinear equations for such superpositions, we obtained an analytical expression for a propagation-invariant off-axis elliptic Gaussian beam. For such an elliptic beam, an analytical expression was derived for the orbital angular momentum, which was shown to consist of two terms. The first one is intrinsic and describes the momentum with respect to the beam center and is shown to grow with the beam ellipticity. The second term depends parabolically on the distance between the beam center and the optical axis (similar to the Steiner theorem in mechanics). It is shown that the ellipse orientation in the transverse plane does not affect the normalized orbital angular momentum. Such elliptic beams can be used in wireless optical communications, since their superpositions do not interfere in space, if they do not interfere in the initial plane.

Single Particle Tracking: From Theory to Biophysical Applications

After three decades of developments, single particle tracking (SPT) has become a powerful tool to interrogate dynamics in a range of materials including live cells and novel catalytic supports because of its ability to reveal dynamics in the structure-function relationships underlying the heterogeneous nature of such systems. In this review, we summarize the algorithms behind, and practical applications of, SPT. We first cover the theoretical background including particle identification, localization, and trajectory reconstruction. General instrumentation and recent developments to achieve two- and three-dimensional subdiffraction localization and SPT are discussed. We then highlight some applications of SPT to study various biological and synthetic materials systems. Finally, we provide our perspective regarding several directions for future advancements in the theory and application of SPT.