Removing orientation-induced localization biases in single-molecule microscopy using a broadband metasurface mask, an experimental demonstration of azimuthal filtering
Nanoscale localization of single molecules is a crucial function in several advanced microscopy techniques, including single-molecule tracking and wide-field super-resolution imaging. Until now, a central consideration of such techniques is how to optimize the precision of molecular localization. However, as these methods continue to push towards the nanometre size scale, an increasingly important concern is the localization accuracy. In particular, single fluorescent molecules emit with an anisotropic radiation pattern of an oscillating electric dipole, which can cause significant localization biases using common estimators, especially with modest defocus. We have previously dealt with this problem using (a) polarized imaging with the DH-PSF (see Backlund et al. below), or (b) by noting that if the label is ona floppy tether, the error can be bounded (see Lew et al. below). Here we present the theory and experimental demonstration of an all-optical solution to this problem based on azimuthal filtering in the Fourier plane of the microscope (proposed by M.D. Lew and WEM, Opt. Lett. (2014), see below). To experimentally demonstrate azimuthal filtering, we use a high-efficiency dielectric metasurface polarization/phase device composed of dielectric nanoposts with subwavelength spacing. The removal of lateral position bias is demonstrated both on fluorophores embedded in a polymer matrix, and also for dL5 protein complexes that bind malachite green. The figure at left shows x-y localizations for two fluorophores of different orientation (red bar) moved in z for the standard PSF (upper) and for the Y-phi PSF (lower).
M. P. Backlund, A. Arbabi, P. N. Petrov, E. Arbabi, S. Saurabh, A. Faraon, and W. E. Moerner, "Removing orientation-induced localization biases in single-molecule microscopy using a broadband metasurface mask," Nat. Photonics 10, 459-462 (2016) (DOI: 10.1038/nphoton.2016.93, published online 16 May 2016). DOI [Slide]
Correcting field-dependent aberrations with nanoscale accuracy in three-dimensional single-molecule localization microscopy with a nanohole array
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 microscope's field of view has not 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 super-resolution methods demanding high accuracy.
Alex von Diezmann, Maurice Y. Lee, Matthew D. Lew, and W. E. Moerner, “Correcting field-dependent aberrations with nanoscale accuracy in three-dimensional single-molecule localization microscopy,” Optica 2, 985-993 (2015) (DOI: 10.1364/OPTICA.2.000985, published online November 19, 2015). DOI [Slide]
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 (3D) 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 to image flow profiles deep in the liquid. We also demonstrate scan-free tracking of single quantum-dot-labeled phospholipid molecules on the surface of living, thick mammalian cells. The tetrapod PSFs provide an important, non-rotating class of PSFs for flexible and deepimaging in three dimensions.
Yoav Shechtman, Lucien E. Weiss, Adam S. Backer, Steffen J. Sahl, and W. E. Moerner, “Precise Three-Dimensional Scan-Free Multiple-Particle Tracking over Large Axial Ranges with Tetrapod Point Spread Functions,” Nano Lett. 15, 4194-4199 (2015) (DOI: 10.1021/acs.nanolett.5b01396, published online May 5, 2015) DOI [Slide]
Azimuthal polarization filtering for accurate, precise, and robust single-molecule localization microscopy
Many single nanoemitters such as single molecules produce dipole radiation which leads to systematic position errors in both particle tracking and super-resolution microscopy. Via vectorial diffraction equations and simulations, we show that imaging only azimuthally polarized light in the microscope naturally avoids emission from the component of the transition dipole moment, resulting in negligible localization errors for all emitter orientations and degrees of objective lens misfocus. Furthermore, localization accuracy is maintained even in the presence of aberrations resulting from imaging in mismatched media.
Matthew D. Lew and W. E. Moerner, “Azimuthal polarization filtering for accurate, precise, and robust single-molecule localization microscopy,” Nano Letters 14, 6407-6413 (2014), (DOI:10.1021/nl502914k, published online October 1, 2014) DOI [Slide]
Optimal Point-Spread Function Design for 3D Imaging
Single emitter position determination from a single snapshot is an essential element of particle tracking and single-molecule active control microscopy (SMACM). The precision to which the 3D position of an emitter can be determined is a function of many parameters, such as emitter brightness, background fluorescence, and importantly – the shape of the PSF. 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. 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 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.
Yoav Shechtman, Steffen J. Sahl, Adam S. Backer, and W. E. Moerner, “Optimal Point Spread Function Design for 3D Imaging,” Phys. Rev. Lett. 113, 133902 (2014), published online September 26, 2014. DOI [Slide]
Quantifying Transient 3D Dynamical Phenomena of Single mRNA Particles in Live Yeast Cell Measurements
Single-particle tracking (SPT) has been extensively used to obtain information about diffusion and directed motion in a wide range of biological applications. Recently, new methods have appeared for obtaining precise (10s of nm) spatial information in three dimensions (3D) with high temporal resolution (measurements obtained every 4ms), which promise to more accurately sense the true dynamical behavior in the natural 3D cellular environment. Despite the quantitative 3D tracking information, the range of mathematical methods for extracting information about the underlying system has been limited mostly to mean-squared displacement analysis and other techniques not accounting for complex 3D kinetic interactions. There is a great need for new analysis tools aiming to more fully extract the biological information content from in vivo SPT measurements. High-resolution SPT experimental data has enormous potential to objectively scrutinize various proposed mechanistic schemes arising from theoretical biophysics and cell biology. At the same time, methods for rigorously checking the sta tistical consistency of both model assumptions and estimated parameters against observed experimental data (i.e. goodness-of-t tests) have not received great attention. We demonstrate methods enabling (1) estimation of the parameters of 3D stochastic differential equation (SDE) models of the underlying dynamics given only one trajectory; and (2) construction of hypothesis tests checking the consistency of the tted model with the observed trajectory so that extracted parameters are not over-interpreted (the tools are applicable to linear or nonlinear SDEs calibrated from non-stationary time series data). The approach is demonstrated on high-resolution 3D trajectories of single ARG3 mRNA particles in yeast cells in order to show the power of the methods in detecting signatures of transient directed transport. The methods presented are generally relevant to a wide variety of 2D and 3D SPT tracking pplications.
Christopher P. Calderon, Michael A. Thompson, Jason M. Casolari, Randy C. Paffenroth, and W. E. Moerner, “Quantifying Transient 3D Dynamical Phenomena of Single mRNA Particles in Live Yeast Cell Measurements,” Michael D. Fayer Festschrift, J. Phys. Chem. B 117, 15701-15713 (2013) published online September 9, 2013. DOI[Slide]
Single-molecule orientation measurements with a quadrated pupil
This paper presents a means of measuring the dipole orientation of a fluorescent, orientationally fixed single molecule (SM), which uses a specially designed phase mask, termed a “quadrated pupil,” conjugate to the back focal plane (BFP) of a conventional widefield microscope. The method leverages the spatial anisotropy of the far-field emission pattern of a dipole emitter, and makes this anisotropy amenable to quantitative analysis at the image plane. In comparison to older image-fitting techniques that infer orientation by matching simulations to defocused or excessively magnified images, the quadrated pupil approach is more robust to minor modeling discrepancies and optical aberrations. Precision on the order of 1-5 degrees is achieved in proof-of-concept experiments for both azimuthal (φ) and polar (θ) angles without defocusing. Since the phase mask is implemented on a liquid-crystal spatial light modulator (SLM) that may be deactivated without any mechanical perturbation of the sample or imaging system, the technique may be readily integrated into clear aperture imaging studies.
Adam S. Backer, Mikael P. Backlund, Matthew D. Lew, and W. E. Moerner, “Single-molecule orientation measurements with a quadrated pupil,” Optics Lett. 38, 1521-1523 (2013), published online March 15, 2013. DOI[Slide]
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. This effect depends upon axial position of the molecule with respect to the focal plane. More importantly, in actual experiments, the degree of mislocalization depends highly on the rotational mobility of the SM; 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 (orientational) mobility can cause resolution degradation or distortion in super-resolution reconstructions. The design of optimal fluorescent label attachments may be altered to affect the local orientational mobility of the fluorophore.
Matthew D. Lew*, Mikael P. Backlund*, and W. E. Moerner (*equal contributions), “Rotational Mobility of Single Molecules Affects Localization Accuracy in Super-Resolution Fluorescence Microscopy,” Nano Lett. 13, 3967- 3972 (2013), published online January 29, 2013. DOI[Slide]
Simultaneous, Accurate Subdiffraction Measurement of the 3D Position and Orientation of Single Molecules Enabled by the Double-Helix Point Spread Function Microscope
Recently, single-molecule-based super-resolution fluorescence microscopy has surpassed the diffraction limit to improve resolution to the order of 20 nm or better. These methods typically employ 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 three-dimensional (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 of its lateral position to appear larger than that expected from photon shot noise. By correcting each localization based on an estimated orientation, we are able to improve standard deviations in lateral localization from ~2x worse than photon-limited precision (48 nm 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 standard deviation of 116 nm (~4x worse than the photon-limited precision, 28 nm) to 34 nm (within 6 nm of the photon limit).
Mikael P. Backlund*, Matthew D. Lew*, Adam S. Backer, Steffen J. Sahl, Ginni Grover, Anurag Agrawal, Rafael Piestun, and W. E. Moerner (equal contributions), “Simultaneous, accurate measurement of the 3D position and orientation of single molecules,” Proc. Nat. Acad. Sci. (USA) 109, 19087-19092 (2012), published online 5 November 2012. DOI[Slide]
Three-Dimensional Super-Resolution Imaging of the Midplane Protein FtsZ in Live Caulobacter crescentus Cells Using Astigmatism
Single-molecule super-resolution imaging provides a non-invasive method for nanometer-scale imaging and is ideally suited to investigations of quasi-static structures within live cells. Here, we extend the ability to image subcellular features within bacteria cells to three dimensions based on the introduction of a cylindrical lens in the imaging pathway. We investigate the midplane protein FtsZ in Caulobacter crescentus with super-resolution imaging based on fluorescent-protein photoswitching and the natural polymerization/depolymerization dynamics of FtsZ associated with the Z-ring. We quantify these dynamics and determine the FtsZ depolymerization time to be < 100 ms. We image the Z-ring in live and fixed C. crescentus cells at different stages of the cell cycle and find that the FtsZ superstructure is dynamic with the cell cycle, forming an open shape during the stalked stage and a dense focus during the pre-divisional stage.
Julie Biteen, Erin D. Goley, Lucy Shapiro, and W. E. Moerner, “Three-Dimensional Super-Resolution Imaging of the Midplane Protein FtsZ in Live Caulobacter crescentus Cells Using Astigmatism, ChemPhysChem 13, 1007-1012 (2012), published online January 20, 2012. DOI [Slide]
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.
Hsiao-lu D. Lee*, Steffen J. Sahl*, Matthew D. Lew, and W. E. Moerner, “The double-helix microscope super-resolves extended biological structures by localizing single blinking molecules in three dimensions with nanoscale precision,” Appl. Phys. Lett. 100, 153701 (2012), published online 9 April 2012. DOI [Slide]
Three-dimensional super-resolution co-localization of intracellular protein superstructures and the cell surface in live Caulobacter crescentus
Recently, single-molecule imaging and photocontrol have enabled super-resolution optical microscopy of cellular structures beyond Abbe’s diffraction limit, opening a new frontier in noninvasive imaging of structures within living cells. However, live cell super-resolution imaging has been challenged by the need to image 3D structures relative to their biological context, such as the cellular membrane. We have developed a technique, termed Super-resolution by PoweR-dependent Active Intermittency and Points Accumulation for Imaging in Nanoscale Topography (SPRAIPAINT) that combines imaging of intracellular 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 super-resolution imaging of Crescentin-eYFP, a cytoskeletal fluorescent protein fusion, co-localized with the surface of the bacterium Caulobacter crescentus using a double helix point spread function microscope. Three-dimensional co-localization of intracellular protein structures and the cell surface with super-resolution optical microscopy opens the door for the analysis of protein interactions in living cells with excellent precision (20-30 nm in 3D) over a large field of view (12×12 μm).
Matthew D. Lew*, Steven F. Lee*, Jerod L. Ptacin, Marissa K. Lee, Robert J. Twieg, Lucy Shapiro, and W. E. Moerner, “Three-dimensional super-resolution co-localization of intracellular protein superstructures and the cell surface in live Caulobacter crescentus,” Proc. Nat. Acad. Sci. (USA) 108, E1102-E1110 (2011) and 108, 18577-18578 (2011), published online 26 October 2011. [Slide]
[Journal Link] [MOVIE 7.7MB .wmv-see SI Videos for more]
Corkscrew point spread function for far-field three-dimensional nanoscale localization of point-like objects
We have developed a new point spread function (PSF), termed the corkscrew PSF, which can localize objects in three dimensions throughout a 3.2 µm depth of field with nanometer precision using a wide-field imaging microscope. 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 fluorescent beads on the surface of a triangular 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. This new PSF should provide a useful complement to the DH-PSF for 3D imaging with wide-field microscopy.
Matthew D. Lew, Steven F. Lee, Majid Badieirostami, and W. E. Moerner, “Corkscrew point spread function for far-field three-dimensional nanoscale localization of point-like objects," Optics Letters 36, 202-204 (2011), published online December 14, 2010. [Slide]
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.
Majid Badieirostami, Matthew D. Lew, Michael A. Thompson,, and W. E. Moerner, “Three-Dimensional Localization Precision of the Double-Helix Point Spread Function versus Astigmatism and Biplane," Applied Physics Letters 97, 161103 (2010), published online October 18, 2010. [Journal Link]
Tracking mRNA in Live Yeast Cells Beyond the Diffraction Limit in 3D
Optical imaging of single biomolecules and complexes in living cells provides a useful window into cellular processes. However, the three-dimensional dynamics of most important biomolecules in living cells remains essentially uncharacterized. The precise subcellular localization of mRNA-protein complexes plays a critical role in the spatial and temporal control of gene expression, and a full understanding of the control of gene expression requires precise characterization of mRNA transport dynamics beyond the optical diffraction limit. In this paper, we describe three-dimensional tracking of single mRNA particles with 25 nm precision in the x and y dimensions and 50 nm precision in the z dimension in live budding yeast cells using a microscope with a double-helix point spread function. Two statistical methods to detect intermittently confined and directed transport were used to quantify the three-dimensional trajectories of mRNA for the first time, using ARG3 mRNA as a model. Measurements and analysis show that the dynamics of ARG3 mRNA molecules are mostly diffusive, although periods of non-Brownian confinement and directed transport are observed. The quantitative methods detailed in this paper can be broadly applied to the study of mRNA localization and the dynamics of diverse other biomolecules in a wide variety of cell types.
Michael A. Thompson, Jason Casolari, Majid Badieirostami, Patrick O. Brown, and W. E. Moerner, “Three-dimensional tracking of single mRNA particles in Saccharomyces cerevisiae using a double-helix point spread function," Proc. Nat. Acad. Sci. (USA) 107, 17864-17871 (2010), published online October 4, 2010. [Slide]
[Journal Link][Free access pdf]
Localizing and Tracking Single Nanoscale Emitters in Three Dimensions with High Spatiotemporal Resolution Using a Double-Helix Point Spread Function - Quantifying Localization Precision with Measurement and Fisher Information
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 ~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.
M. A. Thompson*, M. D. Lew*, M. Badieirostami, and W. E. Moerner, (*equal contributions), “Localizing
and Tracking Single Nanoscale Emitters in Three Dimensions with High Spatio-Temporal Resolution Using a
Double-Helix Point Spread Function,” Nano Letters 10, 211 (2010), published online December 15, 2009.
Journal Link] [Movie - see SM movies page]
In vivo Three-Dimensional Superresolution Fluorescence Tracking using a Double-Helix Point Spread Function
The point spread function (PSF) of a widefield fluorescence microscope is not suitable for three-dimensional super-resolution imaging. We characterize the localization precision of a unique method for 3D superresolution imaging featuring a double-helix point spread function (DH-PSF). The DH-PSF is designed to have two lobes that rotate about their midpoint in any transverse plane as a function of the axial position of the emitter. In effect, the PSF appears as a double helix in three dimensions. By comparing the Cramer-Rao bound of the DH-PSF with the standard PSF as a function of the axial position, we show that the DH-PSF has a higher and more uniform localization precision than the standard PSF throughout a 2 μm depth of field. Comparisons between the DH-PSF and other methods for 3D super-resolution are briefly discussed. We also illustrate the applicability of the DH-PSF for imaging weak emitters in biological systems by tracking the movement of quantum dots in glycerol and in live cells.
M. D. Lew, M. A. Thompson, M. Badieirostami, and W. E. Moerner, “In-vivo Three-Dimensional Superresolution Fluorescence Tracking using a Double-Helix Point Spread Function,” Proc. SPIE 7571, 75710Z-1-75710Z-13 (2010).[Journal Link]
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