Dipole-spread-function engineering for simultaneously measuring the 3D orientations and 3D positions of fluorescent molecules

Fundamental Limits in Measuring the Anisotropic Rotational Diffusion of Single Molecules

Many biophysical techniques, such as single-molecule fluorescence correlation spectroscopy, Förster resonance energy transfer, and fluorescence anisotropy, measure the translation and rotation of biomolecules to quantify molecular processes at the nanoscale. These methods often simplify data analysis by assuming isotropic rotational diffusion, e.g., that molecules wobble within a circular cone. This simplification ignores the anisotropy present in many biological contexts that may cause molecules to exhibit different degrees of diffusion in different directions. Here, we loosen this assumption and establish a theoretical framework for describing and measuring anisotropic rotational diffusion using fluorescence imaging. We show that anisotropic wobble is directly quantified by the eigenvalues of a 3-by-3 positive-semidefinite Hermitian matrix M consisting of the second-order moments of a molecule's transition dipole μ. This formalism enables us to model the influence of unavoidable shot noise using a Hermitian perturbation matrix E; the eigenvalues of E directly bound errors in measurements of wobble via Weyl's inequality. Quantifying various perturbations E reveals that anisotropic wobble measurements are generally more sensitive to errors compared to quantifying isotropic wobble. Moreover, severe shot noise can induce negative eigenvalues in estimates of M, thereby causing the anisotropic wobble measurement to fail. Our analysis, using Fisher information, shows that techniques with worse orientation measurement sensitivity experience stronger perturbations E and require larger signal to background ratios to measure anisotropic rotational diffusion accurately. Our work provides deep insights for improving the state of the art in imaging the orientations and anisotropic rotational diffusion of single molecules.

Membrane topography and the overestimation of protein clustering in single molecule localisation microscopy - identification and correction

According to single-molecule localisation microscopy almost all plasma membrane proteins are clustered. We demonstrate that clusters can arise from variations in membrane topography where the local density of a randomly distributed membrane molecule to a degree matches the variations in the local amount of membrane. Further, we demonstrate that this false clustering can be differentiated from genuine clustering by using a membrane marker to report on local variations in the amount of membrane. In dual colour live cell single molecule localisation microscopy using the membrane probe DiI alongside either the transferrin receptor or the GPI-anchored protein CD59, we found that pair correlation analysis reported both proteins and DiI as being clustered, as did its derivative pair correlation-photoactivation localisation microscopy and nearest neighbour analyses. After converting the localisations into images and using the DiI image to factor out topography variations, no CD59 clusters were visible, suggesting that the clustering reported by the other methods is an artefact. However, the TfR clusters persisted after topography variations were factored out. We demonstrate that membrane topography variations can make membrane molecules appear clustered and present a straightforward remedy suitable as the first step in the cluster analysis pipeline.

Resolving the Nanoscale Structure of β-Sheet Peptide Self-Assemblies Using Single-Molecule Orientation-Localization Microscopy

Synthetic peptides that self-assemble into cross-β fibrils are versatile building blocks for engineered biomaterials due to their modularity and biocompatibility, but their structural and morphological similarities to amyloid species have been a long-standing concern for their translation. Further, their polymorphs are difficult to characterize by using spectroscopic and imaging techniques that rely on ensemble averaging to achieve high resolution. Here, we utilize Nile red (NR), an amyloidophilic fluorogenic probe, and single-molecule orientation-localization microscopy (SMOLM) to characterize fibrils formed by the designed amphipathic enantiomers KFE8L and KFE8D and the pathological amyloid-beta peptide Aβ42. Importantly, NR SMOLM reveals the helical (bilayer) ribbon structure of both KFE8 and Aβ42 and quantifies the precise tilt of the fibrils' inner and outer backbones in relevant buffer conditions without the need for covalent labeling or sequence mutations. SMOLM also distinguishes polymorphic branched and curved morphologies of KFE8, whose backbones exhibit much more heterogeneity than those of typical straight fibrils. Thus, SMOLM is a powerful tool to interrogate the structural differences and polymorphism between engineered and pathological cross-β-rich fibrils.

Fluorescence Microscopy: a statistics-optics perspective

Fundamental properties of light unavoidably impose features on images collected using fluorescence microscopes. Modeling these features is ever more important in quantitatively interpreting microscopy images collected at scales on par or smaller than light's wavelength. Here we review the optics responsible for generating fluorescent images, fluorophore properties, microscopy modalities leveraging properties of both light and fluorophores, in addition to the necessarily probabilistic modeling tools imposed by the stochastic nature of light and measurement.

Resolving the nanoscale structure of β-sheet assemblies using single-molecule orientation-localization microscopy

Synthetic peptides that self-assemble into cross-β fibrils have remarkable utility as engineered biomaterials due to their modularity and biocompatibility, but their structural and morphological similarity to amyloid species has been a long-standing concern for their translation. Further, their polymorphs are difficult to characterize using spectroscopic and imaging techniques that rely on ensemble averaging to achieve high resolution. Here, we utilize single-molecule orientation-localization microscopy (SMOLM) to characterize fibrils formed by the designed amphipathic enantiomers, KFE8L and KFE8D, and the pathological amyloid-beta peptide Aβ42. SMOLM reveals that the orientations of Nile red, as it transiently binds to both KFE8 and Aβ42, are consistent with a helical (bilayer) ribbon structure and convey the precise tilt of the fibrils' inner and outer backbones. SMOLM also finds polymorphic branched and curved morphologies of KFE8 whose backbones exhibit much more heterogeneity than those of more typical straight fibrils. Thus, SMOLM is a powerful tool to interrogate the structural differences and polymorphism between engineered and pathological cross β-rich fibrils.

Combining deep learning approaches and point spread function engineering for simultaneous 3D position and 3D orientation measurements of fluorescent single molecules

Point Spread Function (PSF) engineering is an effective method to increase the sensitivity of single-molecule fluorescence images to specific parameters. Classical phase mask optimization approaches have enabled the creation of new PSFs that can achieve, for example, localization precision of a few nanometers axially over a capture range of several microns with bright emitters. However, for complex high-dimensional optimization problems, classical approaches are difficult to implement and can be very time-consuming for computation. The advent of deep learning methods and their application to single-molecule imaging has provided a way to solve these problems. Here, we propose to combine PSF engineering and deep learning approaches to obtain both an optimized phase mask and a neural network structure to obtain the 3D position and 3D orientation of fixed fluorescent molecules. Our approach allows us to obtain an axial localization precision around 30 nanometers, as well as an orientation precision around 5 degrees for orientations and positions over a one micron depth range for a signal-to-noise ratio consistent with what is typical in single-molecule cellular imaging experiments.

Six-Dimensional Single-Molecule Imaging with Isotropic Resolution using a Multi-View Reflector Microscope

Imaging both the positions and orientations of single fluorophores, termed single-molecule orientation-localisation microscopy, is a powerful tool to study biochemical processes. However, the limited photon budget associated with single-molecule fluorescence makes high-dimensional imaging with isotropic, nanoscale spatial resolution a formidable challenge. Here, we realise a radially and azimuthally polarized multi-view reflector (raMVR) microscope for the imaging of the 3D positions and 3D orientations of single molecules, with precision of 10.9 nm and 2.0° over a 1.5 μm depth range. The raMVR microscope achieves 6D super-resolution imaging of Nile red (NR) molecules transiently bound to lipid-coated spheres, accurately resolving their spherical morphology despite refractive-index mismatch. By observing the rotational dynamics of NR, raMVR images also resolve the infiltration of lipid membranes by amyloid-beta oligomers without covalent labelling. Finally, we demonstrate 6D imaging of cell membranes, where the orientations of specific fluorophores reveal heterogeneity in membrane fluidity. With its nearly isotropic 3D spatial resolution and orientation measurement precision, we expect the raMVR microscope to enable 6D imaging of molecular dynamics within biological and chemical systems with exceptional detail.

Using fluorescent beads to emulate single fluorophores

We study the conditions under which fluorescent beads can be used to emulate single fluorescent molecules in the calibration of optical microscopes. Although beads are widely used due to their brightness and easy manipulation, there can be notable differences between the point spread functions (PSFs) they produce and those for single-molecule fluorophores, caused by their different emission patterns and sizes. We study theoretically these differences for various scenarios, e.g., with or without polarization channel splitting, to determine the conditions under which the use of beads as a model for single molecules is valid. We also propose methods to model the blurring due to the size difference and compensate for it to produce PSFs that are more similar to those for single molecules.

Calcite-Assisted Localization and Kinetics (CLocK) Microscopy

Localization-based super-resolution imaging techniques have improved the spatial resolution of optical microscopy well below the diffraction limit, yet encoding additional information into super-resolved images, such as anisotropy and orientation, remains a challenge. Here we introduce calcite-assisted localization and kinetics (CLocK) microscopy, a multiparameter super-resolution imaging technique easily integrated into any existing optical microscope setup at low cost and with straightforward analysis. By placing a rotating calcite crystal in the infinity space of an optical microscope, CLocK microscopy provides immediate polarization and orientation information while maintaining the ability to localize an emitter/scatterer with <10 nm resolution. Further, kinetic information an order of magnitude shorter than the integration time of the camera is encoded in the unique point spread function of a CLocK image, allowing for new mechanistic insight into dynamic processes such as single-nanoparticle dissolution and single-molecule surface-enhanced Raman scattering.

Monitoring non-specific adsorption at solid-liquid interfaces by supercritical angle fluorescence microscopy

Supercritical angle fluorescence (SAF) microscopy is a novel imaging tool based on the use of distance-dependent fluorophore emission patterns to provide accurate locations of fluorophores relative to a surface. This technique has been extensively used to construct accurate cellular images and to detect surface phenomena in a static environment. However, the capability of SAF microscopy in monitoring dynamic surface phenomena and changes in millisecond intervals is underexplored in the literature. Here, we report on a hardware add-on for a conventional inverted microscope coupled with a post-processing Python module that extends the capability of SAF microscopy to monitor dynamic surface adsorption in sub-second intervals, thereby greatly expanding the potential of this tool to study surface interactions, such as surface fouling and competitive surface adhesion. The Python module enables researchers to automatically extract SAF profiles from each image. We first assessed the performance of the system by probing the specific binding of biotin-fluorescein conjugates to a neutravidin-coated cover glass in the presence of non-binding fluorescein. The SAF emission was observed to increase with the quantity of bound fluorophore on the cover glass. However, a high concentration of unbound fluorophore also contributed to overall SAF emission, leading to over-estimation in surface-bound fluorescence. To expand the applications of SAF in monitoring surface phenomena, we monitored the non-specific surface adsorption of BSA and non-ionic surfactants on a Teflon-AF surface. Solution mixtures of bovine serum albumin (BSA) and nine Pluronic/Tetronic surfactants were exposed to a Teflon-AF surface. No significant BSA adsorption was observed in all BSA-surfactant solution mixtures with negligible SAF intensity. Finally, we monitored the adsorption dynamics of BSA onto the Teflon-AF surface and observed rapid BSA adsorption on Teflon-AF surface within 10 s of addition. The adsorption rate constant (k_a) and half-life of BSA adsorption on Teflon-AF were determined to be 0.419 ± 0.004 s^-1 and 1.65 ± 0.016 s, respectively, using a pseudo-first-order adsorption equation.

Deep learning in single-molecule imaging and analysis: recent advances and prospects

Single-molecule microscopy is advantageous in characterizing heterogeneous dynamics at the molecular level. However, there are several challenges that currently hinder the wide application of single molecule imaging in bio-chemical studies, including how to perform single-molecule measurements efficiently with minimal run-to-run variations, how to analyze weak single-molecule signals efficiently and accurately without the influence of human bias, and how to extract complete information about dynamics of interest from single-molecule data. As a new class of computer algorithms that simulate the human brain to extract data features, deep learning networks excel in task parallelism and model generalization, and are well-suited for handling nonlinear functions and extracting weak features, which provide a promising approach for single-molecule experiment automation and data processing. In this perspective, we will highlight recent advances in the application of deep learning to single-molecule studies, discuss how deep learning has been used to address the challenges in the field as well as the pitfalls of existing applications, and outline the directions for future development.

Deep-SMOLM: deep learning resolves the 3D orientations and 2D positions of overlapping single molecules with optimal nanoscale resolution

Dipole-spread function (DSF) engineering reshapes the images of a microscope to maximize the sensitivity of measuring the 3D orientations of dipole-like emitters. However, severe Poisson shot noise, overlapping images, and simultaneously fitting high-dimensional information-both orientation and position-greatly complicates image analysis in single-molecule orientation-localization microscopy (SMOLM). Here, we report a deep-learning based estimator, termed Deep-SMOLM, that achieves superior 3D orientation and 2D position measurement precision within 3% of the theoretical limit (3.8° orientation, 0.32 sr wobble angle, and 8.5 nm lateral position using 1000 detected photons). Deep-SMOLM also demonstrates state-of-art estimation performance on overlapping images of emitters, e.g., a 0.95 Jaccard index for emitters separated by 139 nm, corresponding to a 43% image overlap. Deep-SMOLM accurately and precisely reconstructs 5D information of both simulated biological fibers and experimental amyloid fibrils from images containing highly overlapped DSFs at a speed ~10 times faster than iterative estimators.