Fundamental limits in single-molecule orientation measurements

Directionality inherent in the polarization of light affords the means of performing robust dynamic orientational measurements of molecules and asymmetric scatterers. In this paper, the precision with which measurements of this kind can be made is quantified for a number of common polarization- based measurement architectures using a metric derived from Fisher information. Specifically, a fundamental limit of 0.5radian per detected photon (on average) is found, thus highlighting the importance of maximizing photon numbers by correct fluorophore selection. Informational dips, whereby measurement precision is degraded, are shown to arise in many realistic measurement scenarios, particularly for inference from null readings. The severity of these precision losses is therefore considered, and it is shown to decrease with increased system redundancy. Contamination of measured data from coherently and incoherently radiating extraneous sources, furthermore, causes a loss of precision. Analytic and numerical results are hence also presented in this vein.

[1]  Peter Török,et al.  A priori information and optimisation in polarimetry. , 2008, Optics express.

[2]  H. Cramér.  Mathematical methods of statistics , 1947 .

[3]  B. Hecht,et al.  Three-dimensional optical polarization tomography of single molecules , 2003 .

[4]  Jörg Enderlein,et al.  Image Analysis of Defocused Single-Molecule Images for Three-Dimensional Molecule Orientation Studies , 2004 .

[5]  M. Lohse,et al.  Rotational diffusion of the α(2a) adrenergic receptor revealed by FlAsH labeling in living cells. , 2011, Biophysical journal.

[6]  D. Chemla,et al.  Single Molecule Dynamics Studied by Polarization Modulation. , 1996, Physical review letters.

[7]  R. M. A. Azzam,et al.  Division-of-amplitude Photopolarimeter (DOAP) for the Simultaneous Measurement of All Four Stokes Parameters of Light , 1982 .

[8]  David J. Norris,et al.  SIMULTANEOUS IMAGING OF INDIVIDUAL MOLECULES ALIGNED BOTH PARALLEL AND PERPENDICULAR TO THE OPTIC AXIS , 1998 .

[9]  M. Irving,et al.  Model-independent analysis of the orientation of fluorescent probes with restricted mobility in muscle fibers. , 1999, Biophysical journal.

[10]  P. Török,et al.  Computational methods in vectorial imaging , 2011 .

[11]  C. R. Rao,et al.  Information and the Accuracy Attainable in the Estimation of Statistical Parameters , 1992 .

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

[13]  R. Fisher,et al.  On the Mathematical Foundations of Theoretical Statistics , 1922 .

[14]  Moungi G. Bawendi,et al.  Room temperature measurements of the 3D orientation of single CdSe quantum dots using polarization microscopy , 2003, Proceedings of the National Academy of Sciences of the United States of America.

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

[16]  Peter Török,et al.  Electromagnetic diffraction of light focused through a planar interface between materials of mismatched refractive indices: an integral representation , 1995 .

[17]  Michael Unser,et al.  Super-resolution orientation estimation and localization of fluorescent dipoles using 3-D steerable filters. , 2009, Optics express.

[18]  D. Axelrod,et al.  Total Internal Reflection Fluorescence Microscopy , 2016 .

[19]  J. Lakowicz.  Principles of fluorescence spectroscopy , 1983 .

[20]  H. V. Hulst.  Light Scattering by Small Particles , 1957 .

[21]  Kevin F. Lee,et al.  Direct measurement of the angular dependence of ionization for N2, O2, and CO2 in intense laser fields. , 2007, Physical review letters.

[22]  Tony Wilson,et al.  Theory for confocal and conventional microscopes imaging small dielectric scatterers , 1998 .

[23]  Tsu-Wei Nee,et al.  Scattering polarization by anisotropic biomolecules. , 2008, Journal of the Optical Society of America. A, Optics, image science, and vision.

[24]  E. Betzig,et al.  Live-cell photoactivated localization microscopy of nanoscale adhesion dynamics , 2008, Nature Methods.

[25]  Peter Török,et al.  Determination of the three-dimensional orientation of single molecules. , 2008, Optics letters.

[26]  Carl Paterson,et al.  Stokes polarimeter optimization in the presence of shot and Gaussian noise , 2009, Optics express.

[27]  S. Götzinger,et al.  A single-molecule optical transistor , 2009, Nature.

[28]  S. Ram,et al.  Localization accuracy in single-molecule microscopy. , 2004, Biophysical journal.

[29]  P. Török,et al.  Calculation of the image of an arbitrary vectorial electromagnetic field. , 2007, Optics express.

[30]  R. Azzam,et al.  Arrangement of four photodetectors for measuring the state of polarization of light. , 1985, Optics letters.

[31]  Novotny,et al.  Orientational imaging of single molecules by annular illumination , 2000, Physical review letters.

[32]  Matthew R. Foreman,et al.  Information and resolution in electromagnetic optical systems , 2010 .

[33]  B. Drévillon,et al.  Broadband Division-of-Amplitude Polarimeter Based on Uncoated Prisms. , 1998, Applied optics.

[34]  B. Frieden,et al.  Physics from Fisher Information: A Unification , 1998 .

[35]  N. Thompson,et al.  Total internal reflection fluorescence. , 1984, Annual review of biophysics and bioengineering.

[36]  R. Oldenbourg,et al.  New polarized light microscope with precision universal compensator , 1995, Journal of microscopy.

[37]  M. Dahan,et al.  Orientational imaging and tracking of single CdSe nanocrystals by defocused microscopy , 2005 .

[38]  Tony Wilson,et al.  Imaging properties of high aperture multiphoton fluorescence scanning optical microscopes , 1999 .

[39]  P. D. Higdon,et al.  On the general properties of polarised light conventional and confocal microscopes , 1998 .

[40]  S. Stallinga,et al.  Accuracy of the gaussian point spread function model in 2D localization microscopy. , 2010, Optics express.

[41]  Rafael Piestun,et al.  Polarization sensitive, three-dimensional, single-molecule imaging of cells with a double-helix system. , 2009, Optics express.

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

[43]  L. Mets,et al.  Nanometer-localized multiple single-molecule fluorescence microscopy. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[44]  M. Foreman.  Informational Limits in Optical Polarimetry and Vectorial Imaging , 2012 .

[45]  Peter R T Munro,et al.  Inversion of the Debye-Wolf diffraction integral using an eigenfunction representation of the electric fields in the focal region. , 2008, Optics express.

[46]  Andrew R. Harvey,et al.  Experimental realisation of electromagnetic metamaterials , 2010 .

[47]  L. Scharf,et al.  Statistical Signal Processing: Detection, Estimation, and Time Series Analysis , 1991 .

[48]  J. Wolfrum,et al.  An extended scheme for counting fluorescent molecules by photon-antibunching , 2010 .

[49]  Travis J Gould,et al.  Nanoscale imaging of molecular positions and anisotropies , 2008, Nature Methods.

[50]  B. Frieden,et al.  Physics from Fisher Information by B. Roy Frieden , 1998 .

[51]  S. Ram,et al.  Beyond Rayleigh's criterion: a resolution measure with application to single-molecule microscopy. , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[52]  Stefan W. Hell,et al.  Depolarization by high-aperture focusing , 2002, SPIE BiOS.

[53]  J. Fourkas,et al.  Rapid determination of the three-dimensional orientation of single molecules. , 2001, Optics letters.

[54]  M. Hartmann,et al.  Light scattering by small particles. Von H. C. VANDE HULST. New York: Dover Publications, Inc. 1981. Paperback, 470 S., 103 Abb. und 46 Tab., US $ 7.50 , 1984 .

[55]  Peter Török,et al.  Photon statistics in single molecule orientational imaging. , 2007, Optics express.