An official website of the United States government
Precisely measuring the three-dimensional position and orientation of individual fluorophores is challenging due to the substantial photon shot noise in single-molecule experiments. Facing this limited photon budget, numerous techniques have been developed to encode 2D and 3D position and 2D and 3D orientation information into fluorescence images. In this work, we adapt classical and quantum estimation theory and propose a mathematical framework to derive the best possible precision for measuring the position and orientation of dipole-like emitters for any fixed imaging system. We find that it is impossible to design an instrument that achieves the maximum sensitivity limit for measuring all possible rotational motions. Further, our vectorial dipole imaging model shows that the best quantum-limited localization precision is 4%–8% worse than that suggested by a scalar monopole model. Overall, we conclude that no single instrument can be optimized for maximum precision across all possible 2D and 3D localization and orientation measurement tasks.
more »
« less
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.
more »
« less
- Award ID(s):
- 1653777
- PAR ID:
- 10094973
- Date Published:
- Journal Name:
- Proc. SPIE 10884, Single Molecule Spectroscopy and Superresolution Imaging XII
- Page Range / eLocation ID:
- 1088412
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Simultaneous measurements of single-molecule positions and orientations provide critical insight into a variety of biological and chemical processes. Various engineered point spread functions (PSFs) have been introduced for measuring the orientation and rotational diffusion of dipole-like emitters, but the widely used Cramér-Rao bound (CRB) only evaluates performance for one specific orientation at a time. Here, we report a performance metric, termed variance upper bound (VUB), that yields a global maximum CRB for all possible molecular orientations, thereby enabling the measurement performance of any PSF to be computed efficiently ( faster than calculating average CRB). Our VUB reveals that the simple polarized standard PSF provides robust and precise orientation measurements if emitters are near a refractive index interface. Using this PSF, we measure the orientations and positions of Nile red (NR) molecules transiently bound to amyloid aggregates. Our super-resolved images reveal the main binding mode of NR on amyloid fiber surfaces, as well as structural heterogeneities along amyloid fibrillar networks, that cannot be resolved by single-molecule localization alone.more » « less
-
Abstract The nature of dark matter is unknown and calls for a systematical search. For axion dark matter, such a search relies on finding feeble random noise arising from the weak coupling between dark matter and microwave haloscopes. We model such process as a quantum channel and derive the fundamental precision limit of noise sensing. An entanglement-assisted strategy based on two-mode squeezed vacuum is thereby demonstrated optimal, while the optimality of a single-mode squeezed vacuum is found limited to the lossless case. We propose a “nulling” measurement (squeezing and photon counting) to achieve the optimal performances. In terms of the scan rate, even with 20-decibel of strength, single-mode squeezing still underperforms the vacuum limit which is achieved by photon counting on vacuum input; while the two-mode squeezed vacuum provides large and close-to-optimum advantage over the vacuum limit, thus more exotic quantum resources are no longer required. Our results highlight the necessity of entanglement assistance and microwave photon counting in dark matter search.more » « less
-
Abstract In soft matter, thermal energy causes molecules to continuously translate and rotate, even in crowded environments, thereby impacting the spatial organization and function of most molecular assemblies, such as lipid membranes. Directly measuring the orientation and spatial organization of large collections (>3000 molecules μm−2) of single molecules with nanoscale resolution remains elusive. In this paper, we utilize SMOLM, single‐molecule orientation localization microscopy, to directly measure the orientation spectra (3D orientation plus “wobble”) of lipophilic probes transiently bound to lipid membranes, revealing that Nile red's (NR) orientation spectra are extremely sensitive to membrane chemical composition. SMOLM images resolve nanodomains and enzyme‐induced compositional heterogeneity within membranes, where NR within liquid‐ordered vs. liquid‐disordered domains shows a ≈4° difference in polar angle and a ≈0.3π sr difference in wobble angle. As a new type of imaging spectroscopy, SMOLM exposes the organizational and functional dynamics of lipid‐lipid, lipid‐protein, and lipid‐dye interactions with single‐molecule, nanoscale resolution.more » « less
-
Abstract Fossil footprints (i.e., tracks) were believed to document arch anatomical evolution, although our recent work has shown that track arches record foot kinematics instead. Analyses of track arches can thereby inform the evolution of human locomotion, although quantifying this 3‐D aspect of track morphology is difficult. Here, we present a volumetric method for measuring the arches of 3‐D models of human tracks and feet, using both Autodesk Maya and Blender software. The method involves generation of a 3‐D object that represents the space beneath the longitudinal arch, and measurement of that arch object's geometry and spatial orientation. We provide relevant tools and guidance for users to apply this technique to their own data. We present three case studies to demonstrate potential applications. These include, (1) measuring the arches of static and dynamic human feet, (2) comparing the arches of human tracks with the arches of the feet that made them, and (3) direct comparisons of human track and foot arch morphology throughout simulated track formation. The volumetric measurement tool proved robust for measuring 3‐D models of human tracks and feet, in static and dynamic contexts. This tool enables researchers to quantitatively compare arches of fossil hominin tracks, in order to derive biomechanical interpretations from them, and/or offers a different approach for quantifying foot morphology in living humans.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1117/12.2506712
