Resolving the Three-Dimensional Rotational and Translational Dynamics of Single Molecules Using Radially and Azimuthally Polarized Fluorescence

Enhancing precision for simultaneous 3D localization and 3D orientation with structured illumination

Determining the three-dimensional (3D) position and orientation of molecules from limited fluorescence photons is challenging. Existing modulated illumination localization microscopy partially transfers the photon burden to excitation intensity gradients, advancing precision to the molecular scale. However, most simultaneous localization and orientation methods rely on polarization splitting in the detection path and are sensitive to the signal-to-background ratio. This sensitivity is further exacerbated by sequential structured illumination (SSI), potentially compromising robustness. Here, we introduce V-SIMFLUX, which integrates SSI and the Vortex PSF without polarization-splitting detection. Our theoretical analysis shows that V-SIMFLUX improves the precision of all estimated parameters, notably achieving a typical 2.9-fold improvement in lateral localization and a 1.7-fold enhancement in azimuthal orientation compared to conventional wide-field illumination.

Resolving the Orientations of and Angular Separation Between a Pair of Dipole Emitters

We prove that it is impossible to distinguish two spatially coinciding fluorescent molecules from a single rotating molecule using polarization-sensitive imaging, even if one modulates the polarization of the illumination or the detection dipole-spread function (DSF). If the target is known to be a dipole pair, existing imaging methods perform poorly for measuring their angular separation. We propose simultaneously modulating the excitation polarization and DSF, which demonstrates robust discrimination between dipole pairs versus single molecules. Our method improves the precision of measuring centroid orientation by 50% and angular separation by two- to four-fold over existing techniques.

Spectrally Resolved Single-Molecule Orientation Imaging Reveals a Direct Correspondence between the Polarity and Microviscosity Experienced by Nile Red in Supported Lipid Bilayer Membranes

Molecular-level interactions among lipids, cholesterol, and water dictate the nanoscale membrane organization of lipid bilayers into liquid-ordered (Lo) and liquid-disordered (Ld) phases, characterized by different polarities and orders. Generally, solvatochromic dyes easily discriminate polarity difference between Lo and Ld phases, whereas molecular flippers and rotors show distinct photophysics depending on the membrane order. Despite progress in single-molecule spectral imaging and single-molecule orientation mapping, direct experimental proof linking polarity with microviscosity sensed by the same probe eludes us. Here, we demonstrate spectrally resolved single-molecule orientation localization microscopy to connect nanoscopic localization of a probe on a bilayer membrane with its emission spectra, three-dimensional dipole orientation, and rotational constraint offered by the local microenvironment and highlight the excellent correspondence between the polarity and order experienced by the same probe. This technique has the potential to address nanoscale heterogeneity and dynamics, especially in biology and material sciences.

Single-molecule orientation-localization microscopy: Applications and approaches

Single-molecule orientation-localization microscopy (SMOLM) builds upon super-resolved localization microscopy by imaging orientations and rotational dynamics of individual molecules in addition to their positions. This added dimensionality provides unparalleled insights into nanoscale biophysical and biochemical processes, including the organization of actin networks, movement of molecular motors, conformations of DNA strands, growth and remodeling of amyloid aggregates, and composition changes within lipid membranes. In this review, we discuss recent innovations in SMOLM and cover three key aspects: (1) biophysical insights enabled by labeling strategies that endow fluorescent probes to bind to targets with orientation specificity; (2) advanced imaging techniques that leverage the physics of light-matter interactions and estimation theory to encode orientation information with high fidelity into microscope images; and (3) computational methods that ensure accurate and precise data analysis and interpretation, even in the presence of severe shot noise. Additionally, we compare labeling approaches, imaging hardware, and publicly available analysis software to aid the community in choosing the best SMOLM implementation for their specific biophysical application. Finally, we highlight future directions for SMOLM, such as the development of probes with improved photostability and specificity, the design of “smart” adaptive hardware, and the use of advanced computational approaches to handle large, complex datasets. This review underscores the significant current and potential impact of SMOLM in deepening our understanding of molecular dynamics, paving the way for future breakthroughs in the fields of biophysics, biochemistry, and materials science.

Single-Molecule Spectral Fluctuation Originates from the Variation in Dipole Orientation Connected to Accessible Vibrational Modes

Fluctuation in fluorescence emission of an immobilized single molecule is typically ascribed to the chromophore's intrinsic structural conformations and the influence of local environmental factors. Despite extensive research since its initial observation, a direct connection between these spectral fluctuations and the rearrangement of emission dipole orientations has remained elusive. Here, we elucidate this fundamental molecular behavior and its underlying mechanisms by employing unique single-molecule multidimensional tracking to simultaneously monitor both the emission spectrum and the three-dimensional dipole orientation of individual fluorophores. We present compelling evidence demonstrating a correlation between spectral fluctuations and dipolar rearrangements at room temperature. Our observations reveal that variations in the radiative relaxation probabilities among different vibronic emission bands, coupled with the interaction of associated vibrational modes, drive these spectral fluctuations. We identify significant out-of-plane dipole reorientations during pronounced spectral fluctuations, commonly known as spectral jumps, which primarily arise from transitions between dominant vibrational modes. Furthermore, we emphasize the potential for constructing vibrational spectra and optical nanoscopy with vibrational specificity, leveraging the vibronic emissions from single emitters.

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.

Optical characterization of a single molecule complete spatial orientation using intra-molecular triplet-triplet absorption

Progress in single molecule fluorescence experiments have enabled an in-depth characterization of fluorophores, ranging from their photophysical rates to the orientation of their emission dipole moments in three dimensions. However, one crucial spatial information remains elusive: the molecule orientation relative to its emission dipole moment. One can retrieve the latter only by the use of another non-colinear transition dipole moment. We experimentally demonstrate the optical retrieval of this information for single terrylene (Tr) molecules in a 30 nm thin para-terphenyl matrix. We show, through second-order correlation measurements at varying excitation power and polarization, that Tr molecules experience an optically induced deshelving of their triplet states, mediated by two orthogonal intra-molecular triplet-triplet absorption dipole moments. We take advantage of these two transition dipole moments to retrieve the full orientation of the Tr molecule, employing a 3-level scheme for the molecule photophysics and analytical calculations for the exciting electric field distribution. This modelling approach enables us to accurately describe both varying power and polarization measurements, giving access to the molecule's photophysical rates and to its complete orientation in three dimensions. This includes the orientation of the singlet emission dipole moment in the laboratory frame, and the orientation of the molecule plane with respect to the singlet emission dipole moment.

Single-Molecule Orientation Imaging Reveals the Nano-Architecture of Amyloid Fibrils Undergoing Growth and Decay

Amyloid-beta (Aβ42) aggregates are characteristic Alzheimer's disease signatures, but probing how their nanoscale architectures influence their growth and decay remains challenging using current technologies. Here, we apply time-lapse single-molecule orientation-localization microscopy (SMOLM) to measure the orientations and rotational "wobble" of Nile blue (NB) molecules transiently binding to Aβ42 fibrils. We correlate fibril architectures measured by SMOLM with their growth and decay over the course of 5 to 20 min visualized by single-molecule localization microscopy (SMLM). We discover that stable Aβ42 fibrils tend to be well-ordered and signified by well-aligned NB orientations and small wobble. SMOLM also shows that increasing order and disorder are signatures of growing and decaying fibrils, respectively. We also observe SMLM-invisible fibril remodeling, including steady growth and decay patterns that conserve β-sheet organization. SMOLM reveals that increased fibril architectural heterogeneity is correlated with dynamic remodeling and that large-scale fibril remodeling tends to originate from strongly heterogeneous local regions.

Mechanical stability of polarization signatures in biological tissue characterization

Mueller matrix imaging polarimetry (MMIP) is a promising technique for investigating structural abnormalities in pathological diagnosis. The characterization stability of polarization signatures, described by Mueller matrix parameters (MMPs), correlates with the mechanical state of the biological medium. In this study, we developed an MMIP system capable of applying quantitative forces to samples and measuring the resulting polarization signatures. Mechanical stretching experiments were conducted on a mimicking phantom and a tissue sample at different force scales. We analyzed the textural features and data distribution of MMP images and evaluated the force effect on the characterization of MMPs using the structural similarity index. The results demonstrate that changes in the mechanical microenvironment (CMM) can cause textural fluctuations in MMP images, interfering with the stability of polarization signatures. Specifically, parameters of anisotropic orientation, retardance, and optical rotation are the most sensitive to CMM, inducing a dramatic change in the overall image texture, while other parameters (e.g., polarization, diattenuation, and depolarization) exhibit locality in their response to CMM. For some MMPs, CMM can enhance regional textural contrasts. This study elucidates the mechanical stability of polarization signatures in biological tissue characterization and provides a valuable reference for further research toward minimizing CMM influence.

Single-Molecule Orientation Imaging Reveals the Nano-Architecture of Amyloid Fibrils Undergoing Growth and Decay

Amyloid-beta ( A β 42 ) aggregates are characteristic signatures of Alzheimer's disease, but probing how their nanoscale architectures influence their growth and decay remains challenging using current technologies. Here, we apply time-lapse single-molecule orientation-localization microscopy (SMOLM) to measure the orientations and rotational "wobble" of Nile blue (NB) molecules transiently binding to A β 42 fibrils. We quantify correlations between fibril architectures, measured by SMOLM, and their growth and decay visualized by single-molecule localization microscopy (SMLM). We discover that stable A β 42 fibrils tend to be well-ordered, signified by well-aligned NB orientations and small wobble. SMOLM also shows that increasing order and disorder are signatures of growing and decaying A β 42 fibrils, respectively. We also observe SMLM-invisible fibril remodeling, including steady growth and decay patterns that conserve β -sheet organization. SMOLM reveals that increased heterogeneity in fibril architectures is correlated with more dynamic remodeling and that large-scale fibril remodeling tends to originate from local regions that exhibit strong heterogeneity.

Getting the Most Out of Fluorogenic Probes: Challenges and Opportunities in Using Single-Molecule Fluorescence to Image Electro- and Photocatalysis

Single-molecule fluorescence microscopy enables the direct observation of individual reaction events at the surface of a catalyst. It has become a powerful tool to image in real time both intra- and interparticle heterogeneity among different nanoscale catalyst particles. Single-molecule fluorescence microscopy of heterogeneous catalysts relies on the detection of chemically activated fluorogenic probes that are converted from a nonfluorescent state into a highly fluorescent state through a reaction mediated at the catalyst surface. This review article describes challenges and opportunities in using such fluorogenic probes as proxies to develop structure-activity relationships in nanoscale electrocatalysts and photocatalysts. We compare single-molecule fluorescence microscopy to other microscopies for imaging catalysis in situ to highlight the distinct advantages and limitations of this technique. We describe correlative imaging between super-resolution activity maps obtained from multiple fluorogenic probes to understand the chemical origins behind spatial variations in activity that are frequently observed for nanoscale catalysts. Fluorogenic probes, originally developed for biological imaging, are introduced that can detect products such as carbon monoxide, nitrite, and ammonia, which are generated by electro- and photocatalysts for fuel production and environmental remediation. We conclude by describing how single-molecule imaging can provide mechanistic insights for a broader scope of catalytic systems, such as single-atom catalysts.

Single-Molecule Orientation Imaging Reveals Two Distinct Binding Configurations on Amyloid Fibrils

Fluorescence readouts for an amyloid fibril sensor critically depend on its molecular interaction and local environment offered by the available structural motifs. Here we employ polarized points accumulation for imaging in nanoscale topography with intramolecular charge transfer probes transiently bound to amyloid fibrils to investigate the organization of fibril nanostructures and probe binding configurations. Besides the in-plane (θ ≈ 90°) mode for binding on the fibril surface parallel to the long fibril axis, we also observed a sizable population of over 60% out-of-plane (θ < 60°) dipoles for rotor probes experiencing a varying degree of orientational mobility. Highly confined dipoles exhibiting an out-of-plane configuration probably reflect tightly bound dipoles in the inner channel grooves, while the weakly bound ones on amyloid enjoy rotational flexibility. Our observation of an out-of-plane binding mode emphasizes the pivotal role played by the electron donor amino group toward fluorescence detection and hence the emergence of anchored probes alongside conventional groove binders.

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.

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.

Simultaneous super-resolution estimation of single-molecule position and orientation with minimal photon fluxes

The orientation of a single molecule provides valuable information on fundamental biological processes. We report a technique for the simultaneous estimation of single-molecule 2D position and 2D orientation with ultra-high localization precision (∼2-nm precision with ∼500 photons under a typical 100-nm diameter of excitation beam pattern), which is also compatible with tracking in living cells. In the proposed method, the theoretical precision limits are calculated, and the localization and orientation performance along with potential applications are explored using numerical simulations. Compared to other camera-based orientation measurement methods, it is confirmed that the proposed method can obtain reasonable estimates even under very weak signals (∼15 photons). Moreover, the maximum likelihood estimator (MLE) is found to converge to the theoretical limit when the total number of photons is less than 100.

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

Interactions between biomolecules are characterized by both where they occur and how they are organized, e.g., the alignment of lipid molecules to form a membrane. However, spatial and angular information are mixed within the image of a fluorescent molecule-the microscope's dipole-spread function (DSF). We demonstrate the pixOL algorithm for simultaneously optimizing all pixels within a phase mask to produce an engineered Green's tensor-the dipole extension of point-spread function engineering. The pixOL DSF achieves optimal precision for measuring simultaneously the 3D orientation and 3D location of a single molecule, i.e., 4.1° orientation, 0.44 sr wobble angle, 23.2 nm lateral localization, and 19.5 nm axial localization precisions in simulations over a 700-nm depth range using 2500 detected photons. The pixOL microscope accurately and precisely resolves the 3D positions and 3D orientations of Nile red within a spherical supported lipid bilayer, resolving both membrane defects and differences in cholesterol concentration in 6 dimensions.

Photon efficient orientation estimation using polarization modulation in single-molecule localization microscopy

Combining orientation estimation with localization microscopy opens up the possibility to analyze the underlying orientation of biomolecules on the nanometer scale. Inspired by the recent improvement of the localization precision by shifting excitation patterns (MINFLUX, SIMFLUX), we have adapted the idea towards the modulation of excitation polarization to enhance the orientation precision. For this modality two modes are analyzed: i) normally incident excitation with three polarization steps to retrieve the in-plane angle of emitters and ii) obliquely incident excitation with p-polarization with five different azimuthal angles of incidence to retrieve the full orientation. Firstly, we present a theoretical study of the lower precision limit with a Cramér-Rao bound for these modes. For the oblique incidence mode we find a favorable isotropic orientation precision for all molecular orientations if the polar angle of incidence is equal to arccos ⁡ 2 / 3 ≈ 35 degrees. Secondly, a simulation study is performed to assess the performance for low signal-to-background ratios and how inaccurate illumination polarization angles affect the outcome. We show that a precision, at the Cramér-Rao bound (CRB) limit, of just 2.4 and 1.6 degrees in the azimuthal and polar angles can be achieved with only 1000 detected signal photons and 10 background photons per pixel (about twice better than reported earlier). Lastly, the alignment and calibration of an optical microscope with polarization control is described in detail. With this microscope a proof-of-principle experiment is carried out, demonstrating an experimental in-plane precision close to the CRB limit for signal photon counts ranging from 400 to 10,000.