Single-molecule orientation localization microscopy I: fundamental limits.

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.

[1]  J. Goodman.  Introduction to Fourier optics , 1969 .

[2]  J. Lippincott-Schwartz,et al.  Interferometric fluorescent super-resolution microscopy resolves 3D cellular ultrastructure , 2009, Proceedings of the National Academy of Sciences.

[3]  Adam S. Backer,et al.  Enhanced DNA imaging using super-resolution microscopy and simultaneous single-molecule orientation measurements , 2016, 2016 Conference on Lasers and Electro-Optics (CLEO).

[4]  Stefano Pirandola,et al.  Ultimate Precision Bound of Quantum and Subwavelength Imaging. , 2016, Physical review letters.

[5]  Nadine Gottschalk,et al.  Fundamentals Of Photonics , 2016 .

[6]  D. Axelrod.  Fluorescence excitation and imaging of single molecules near dielectric‐coated and bare surfaces: a theoretical study , 2012, Journal of microscopy.

[7]  Matthew D Lew,et al.  The role of molecular dipole orientation in single-molecule fluorescence microscopy and implications for super-resolution imaging. , 2014, Chemphyschem : a European journal of chemical physics and physical chemistry.

[8]  J. Lippincott-Schwartz,et al.  Imaging Intracellular Fluorescent Proteins at Nanometer Resolution , 2006, Science.

[9]  Lukas Novotny,et al.  Single-molecule orientations determined by direct emission pattern imaging , 2004 .

[10]  Matthew D. Lew,et al.  Single-molecule orientation localization microscopy II: a performance comparison. , 2020, Journal of the Optical Society of America. A, Optics, image science, and vision.

[11]  Daniel Choquet,et al.  New Concepts in Synaptic Biology Derived from Single-Molecule Imaging , 2008, Neuron.

[12]  Handler,et al.  Spatio-angular fluorescence microscopy II. Paraxial 4f imaging. , 2019, Journal of the Optical Society of America. A, Optics, image science, and vision.

[13]  P. L. La Riviere,et al.  Spatio-angular fluorescence microscopy III. Constrained angular diffusion, polarized excitation, and high-NA imaging. , 2020, Journal of the Optical Society of America. A, Optics, image science, and vision.

[14]  Michael D. Mason,et al.  Ultra-high resolution imaging by fluorescence photoactivation localization microscopy. , 2006, Biophysical journal.

[15]  Tianben Ding,et al.  Single-molecule orientation localization microscopy for resolving structural heterogeneities between amyloid fibrils , 2020, bioRxiv.

[16]  Mankei Tsang,et al.  Quantum limit to subdiffraction incoherent optical imaging , 2018, Physical Review A.

[17]  Z Hradil,et al.  Optimal measurements for resolution beyond the Rayleigh limit. , 2017, Optics letters.

[18]  Adam S. Backer,et al.  Extending Single-Molecule Microscopy Using Optical Fourier Processing , 2014, The journal of physical chemistry. B.

[19]  W. E. Moerner,et al.  Azimuthal Polarization Filtering for Accurate, Precise, and Robust Single-Molecule Localization Microscopy , 2014, Nano letters.

[20]  Jörg Enderlein,et al.  Orientation imaging of single molecules by wide-field epifluorescence microscopy , 2003 .

[21]  Single-molecule orientation localization microscopy for resolving structural heterogeneities between amyloid fibrils. , 2020, Optica.

[22]  M. L.,et al.  Variable incidence angle linear dichroism (VALiD): a technique for unique 3D orientation measurement of fluorescent ensembles , 2020 .

[23]  R. Hochstrasser,et al.  Wide-field subdiffraction imaging by accumulated binding of diffusing probes , 2006, Proceedings of the National Academy of Sciences.

[24]  S. Hell,et al.  Two-color nanoscopy of three-dimensional volumes by 4Pi detection of stochastically switched fluorophores , 2011, Nature Methods.

[25]  J. Ellenberg,et al.  MINFLUX nanoscopy delivers 3D multicolor nanometer resolution in cells , 2020, Nature Methods.

[26]  Jordan R. Myers,et al.  Ultra-High Resolution 3D Imaging of Whole Cells , 2016, Cell.

[27]  S. Stallinga.  Effect of rotational diffusion in an orientational potential well on the point spread function of electric dipole emitters. , 2015, Journal of the Optical Society of America. A, Optics, image science, and vision.

[28]  Matthew D. Lew,et al.  Fundamental Limits on Measuring the Rotational Constraint of Single Molecules Using Fluorescence Microscopy. , 2018, Physical review letters.

[29]  H. Flyvbjerg,et al.  Optimized localization-analysis for single-molecule tracking and super-resolution microscopy , 2010, Nature Methods.

[30]  Andrei Faraon,et al.  Removing Orientation-Induced Localization Biases in Single-Molecule Microscopy Using a Broadband Metasurface Mask , 2016, Nature Photonics.

[31]  Mankei Tsang,et al.  Quantum theory of superresolution for two incoherent optical point sources , 2015, 1511.00552.

[32]  Sudhakar Prasad,et al.  Quantum-limited superlocalization and superresolution of a source pair in three dimensions , 2018, Physical Review A.

[33]  W E Moerner,et al.  A bisected pupil for studying single-molecule orientational dynamics and its application to three-dimensional super-resolution microscopy. , 2014, Applied physics letters.

[34]  W E Moerner,et al.  Determining the rotational mobility of a single molecule from a single image: a numerical study. , 2015, Optics express.

[35]  Sjoerd Stallinga,et al.  Localization microscopy at doubled precision with patterned illumination , 2019, bioRxiv.

[36]  Yoav Shechtman,et al.  Fundamental Precision Bounds for Three-Dimensional Optical Localization Microscopy with Poisson Statistics. , 2018, Physical review letters.

[37]  J. Enderlein,et al.  Fluorescence polarization filtering for accurate single molecule localization , 2020 .

[38]  W. E. Moerner,et al.  Exploring bacterial cell biology with single-molecule tracking and super-resolution imaging , 2013, Nature Reviews Microbiology.

[39]  P. L. La Riviere,et al.  Spatio-angular fluorescence microscopy I. Basic theory. , 2018, Journal of The Optical Society of America A-optics Image Science and Vision.

[40]  T. Moon,et al.  Mathematical Methods and Algorithms for Signal Processing , 1999 .

[41]  Oumeng Zhang,et al.  Quantum limits for precisely estimating the orientation and wobble of dipole emitters , 2020, Physical review research.

[42]  Eric R. Prossnitz,et al.  Full characterization of GPCR monomer–dimer dynamic equilibrium by single molecule imaging , 2011, The Journal of cell biology.

[43]  J. Elf,et al.  Nanometer resolution imaging and tracking of fluorescent molecules with minimal photon fluxes , 2016, Science.

[44]  Ashis Sen Gupta,et al.  Tests for Standardized Generalized Variances of Multivariate Normal Populations of Possibly Different Dimensions. , 1981 .

[45]  Matthew D. Lew,et al.  Single-molecule 3D orientation imaging reveals nanoscale compositional heterogeneity in lipid membranes , 2020, bioRxiv.

[46]  Mankei Tsang,et al.  Quantum limit for two-dimensional resolution of two incoherent optical point sources , 2016, 2016 Conference on Lasers and Electro-Optics (CLEO).

[47]  T. Tachikawa,et al.  Evidence for crystal-face-dependent TiO2 photocatalysis from single-molecule imaging and kinetic analysis. , 2011, Journal of the American Chemical Society.

[48]  Michael J Rust,et al.  Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM) , 2006, Nature Methods.

[49]  Sophie Brasselet,et al.  Birefringent Fourier filtering for single molecule coordinate and height super-resolution imaging with dithering and orientation , 2019, Nature Communications.

[50]  Klaus Schulten,et al.  Angular measurements of the dynein ring reveal a stepping mechanism dependent on a flexible stalk , 2017, Proceedings of the National Academy of Sciences.

[51]  Mankei Tsang,et al.  Quantum limits to optical point-source localization , 2014, 1411.2954.