Computational Modelling Enables Robust Multidimensional Nanoscopy

The following sections are included: Present State of Computational Modelling in Fluorescence Nanoscopy Recent Contributions to Computational Modelling in Fluorescence Nanoscopy Outlook on Computational Modelling in Fluorescence Nanoscopy Acknowledgments Reference

Quantum limits for precisely estimating the orientation and wobble of dipole emitters

Precisely measuring molecular orientation is key to understanding how molecules organize and interact in soft matter, but the maximum theoretical limit of measurement precision has yet to be quantified. We use quantum estimation theory and Fisher information (QFI) to derive a fundamental bound on the precision of estimating the orientations of rotationally fixed molecules. While direct imaging of the microscope pupil achieves the quantum bound, it is not compatible with widefield imaging, so we propose an interferometric imaging system that also achieves QFI-limited measurement precision. Extending our analysis to rotationally diffusing molecules, we derive conditions that enable a subset of second-order dipole orientation moments to be measured with quantum-limited precision. Interestingly, we find that no existing techniques can measure all second moments simultaneously with QFI-limited precision; there exists a fundamental trade-off between precisely measuring the mean orientation of a molecule versus its wobble. This theoretical analysis provides crucial insight for optimizing the design of orientation-sensitive imaging systems

Fundamental limits of measuring single-molecule rotational mobility

Various methods exist for measuring molecular orientation, thereby providing insight into biochemical activities at nanoscale. Since fluorescence intensity and not electric field is detected, these methods are limited to measuring even-order moments of molecular orientation. However, any measurement noise, for example photon shot noise, will result in nonzero measurements of any of these even-order moments, thereby causing rotationally-free molecules to appear to be partially constrained. Here, we build a model to quantify measurement errors in rotational mobility. Our theoretical framework enables scientists to choose the optimal single-molecule orientation measurement technique for any desired measurement accuracy and photon budget

A robust statistical estimation (RoSE) algorithm jointly recovers the 3D location and intensity of single molecules accurately and precisely

In single-molecule (SM) super-resolution microscopy, the complexity of a biological structure, high molecular density, and a low signal-to-background ratio (SBR) may lead to imaging artifacts without a robust localization algorithm. Moreover, engineered point spread functions (PSFs) for 3D imaging pose difficulties due to their intricate features. We develop a Robust Statistical Estimation algorithm, called RoSE, that enables joint estimation of the 3D location and photon counts of SMs accurately and precisely using various PSFs under conditions of high molecular density and low SBR

Long-term, super-resolution imaging of amyloid structures using transient amyloid binding microscopy

Amyloid fibrils and tangles are signatures of Alzheimer disease, but nanometer-sized aggregation intermediates are hypothesized to be the structures most toxic to neurons. The structures of these oligomers are too small to be resolved by conventional light microscopy. We have developed a simple and versatile method, called transient amyloid binding (TAB), to image amyloid structures with nanoscale resolution using amyloidophilic dyes, such as Thioflavin T, without the need for covalent labeling or immunostaining of the amyloid protein. Transient binding of ThT molecules to amyloid structures over time generates photon bursts that are used to localize single fluorophores with nanometer precision. Continuous replenishment of fluorophores from the surrounding solution minimizes photobleaching, allowing us to visualize a single amyloid structure for hours to days. We show that TAB microscopy can image both the oligomeric and fibrillar stages of amyloid-β aggregation. We also demonstrate that TAB microscopy can image the structural remodeling of amyloid fibrils by epi-gallocatechin gallate. Finally, we utilize TAB imaging to observe the non-linear growth of amyloid fibrils

Imaging the Three-Dimensional Orientation and Rotational Mobility of Fluorescent Emitters using the Tri-Spot Point Spread Function

Fluorescence photons emitted by single molecules contain rich information regarding their rotational motions, but adapting single-molecule localization microscopy (SMLM) to measure their orientations and rotational mobilities with high precision remains a challenge. Inspired by dipole radiation patterns, we design and implement a Tri-spot point spread function (PSF) that simultaneously measures the three-dimensional orientation and the rotational mobility of dipole-like emitters across a large field of view. We show that the orientation measurements done using the Tri-spot PSF are sufficiently accurate to correct the anisotropy-based localization bias, from 30 nm to 7 nm, in SMLM. We further characterize the emission anisotropy of fluorescent beads, revealing that both 20-nm and 100-nm diameter beads emit light significantly differently from isotropic point sources. Exciting 100-nm beads with linearly polarized light, we observe significant depolarization of the emitted fluorescence using the Tri-spot PSF that is difficult to detect using other methods. Finally, we demonstrate that the Tri-spot PSF detects rotational dynamics of single molecules within a polymer thin film that are not observable by conventional SMLM

Measuring localization confidence for quantifying accuracy and heterogeneity in single-molecule super-resolution microscopy

We present a computational method, termed Wasserstein-induced flux (WIF), to robustly quantify the accuracy of individual localizations within a single-molecule localization microscopy (SMLM) dataset without ground- truth knowledge of the sample. WIF relies on the observation that accurate localizations are stable with respect to an arbitrary computational perturbation. Inspired by optimal transport theory, we measure the stability of individual localizations and develop an efficient optimization algorithm to compute WIF. We demonstrate the advantage of WIF in accurately quantifying imaging artifacts in high-density reconstruction of a tubulin network. WIF represents an advance in quantifying systematic errors with unknown and complex distributions, which could improve a variety of downstream quantitative analyses that rely upon accurate and precise imaging. Furthermore, thanks to its formulation as layers of simple analytical operations, WIF can be used as a loss function for optimizing various computational imaging models and algorithms even without training data

Erratum: Imaging the three‐dimensional orientation and rotational mobility of fluorescent emitters using the Tri‐spot point spread function

In the original paper, a calibration error exists in the image-formation model used to analyze experimental images taken by our microscope, causing a bias in the orientation measurements in Figs. 2 and 3. The updated measurements are shown in Fig. E1. We have also updated the supplementary material for the original article to discuss the revised PSF model and estimation algorithms (supplementary material 2) and show the revised model and measurements (Figs. S1, S3, S7, S8, and S10–S13)