Simultaneous, accurate measurement of the 3D position and orientation of single molecules

Abstract

Recently, single molecule-based superresolution fluorescence microscopy has surpassed the diffraction limit to improve resolution to the order of 20 nm or better. These methods typically use image fitting that assumes an isotropic emission pattern from the single emitters as well as control of the emitter concentration. However, anisotropic single-molecule emission patterns arise from the transition dipole when it is rotationally immobile, depending highly on the molecule's 3D orientation and z position. Failure to account for this fact can lead to significant lateral (x, y) mislocalizations (up to ∼50-200 nm). This systematic error can cause distortions in the reconstructed images, which can translate into degraded resolution. Using parameters uniquely inherent in the double-lobed nature of the Double-Helix Point Spread Function, we account for such mislocalizations and simultaneously measure 3D molecular orientation and 3D position. Mislocalizations during an axial scan of a single molecule manifest themselves as an apparent lateral shift in its position, which causes the standard deviation (SD) of its lateral position to appear larger than the SD expected from photon shot noise. By correcting each localization based on an estimated orientation, we are able to improve SDs in lateral localization from ∼2× worse than photon-limited precision (48 vs. 25 nm) to within 5 nm of photon-limited precision. Furthermore, by averaging many estimations of orientation over different depths, we are able to improve from a lateral SD of 116 (∼4× worse than the photonlimited precision; 28 nm) to 34 nm (within 6 nm of the photon limit).

Ultrafast, accurate, and robust localization of anisotropic dipoles

“…The same argument exists for biplane fi tting algorithms where the increase of fi tting parameters and fi tting with more complicated 3D PSFs exacerbate the problem of slowness and convergence. Other than developing more accurate algorithms, one can also extract the orientation information by clever hardware engineering, i.e., excitation and/or emission with multiple polarizations (Ha et al, 1999), or doublehelix PSF (DH-PSF) microscopy (Backlund et al, 2012). The hardware solutions require sophisticated hardware confi gurations and are usually more time-consuming, limiting their wide application.…”

Determining the Rotational Mobility of a Single Molecule from a Single Image: A Numerical Study

“…Reliance on LD data alone may obscure relevant physical phenomena or, as we will demonstrate in a numerical experiment, may cause an experimenter to form patently incorrect conclusions about a specimen under observation. In order to avoid many of the ambiguities inherent in LD measurements, many researchers have turned to widefield image-based analysis in order to determine the orientation of single molecules [14][15][16][17][18][19][20][21][22]. The combination of image-based analysis with polarized detection configurations has been considered in [23].…”

Fluorescence nanoscopy. Methods and applications

“…It is worth noting that all localisation algorithms have been developed under the assumption of freely rotating dipole emitters imaged through unaberrating optics or with symmetric aberrations, such as defocus or spherical aberration. Under these conditions, the PSF is isotropic and resembles a Gaussian model, but accuracy drops significantly for emitters which are not allowed to rotate (on the order of 50 to 100 nm) [75], in particular in 3D PALM imaging [76,77]. Recent works are considering the effect of the orientation of molecules on localisation [72,77,78].…”

“…Under these conditions, the PSF is isotropic and resembles a Gaussian model, but accuracy drops significantly for emitters which are not allowed to rotate (on the order of 50 to 100 nm) [75], in particular in 3D PALM imaging [76,77]. Recent works are considering the effect of the orientation of molecules on localisation [72,77,78]. It is worth noting that STED is also affected by molecular orientation, but being a scanning technique, the read-out position is predefined by the zero of the depletion distribution and therefore the effect of molecular orientation is smaller.…”