Localizing and Tracking Single Nanoscale Emitters in Three Dimensions with High Spatiotemporal Resolution Using a Double-Helix Point Spread Function

Abstract

Three-dimensional nanoscale localization and tracking of dim single emitters can be obtained with a widefield fluorescence microscope exhibiting a double-helix point spread function (DH-PSF). We describe in detail how the localization precision quantitatively depends upon the number of photons detected and the z position of the nanoscale emitter, thereby showing a ~10 nm localization capability along x, y, and z in the limit of weak emitters. Experimental measurements are compared to Fisher information calculations of the ultimate localization precision inherent in the DH-PSF. The DH-PSF, for the first time, is used to track single quantum dots in aqueous solution and a quantum dot-labeled structure inside a living cell in three dimensions.A critical problem in nanoscale science is the need to noninvasively and from a distance determine the location of a nanoscale object in three dimensions. Even though the diffraction limit of visible light is on the order of 200 nm, the two-dimensional (2D) image of a single molecule can be fit to find the x-y position of the molecule with nanometer precision1 , 2. The localization precision scales roughly as σ/(N) 1/2 where σ is the diffraction-limited standard deviation of the microscope point spread function (PSF) and N is the number of photons detected from a point-like emitter. This "super-localization" property, well-known in many areas of science 3 , was used to great effect by many groups to track isolated point-like singlemolecule emitters in a variety of contexts 4 , 5. However, imaging a continuous structure requires a high density of fluorescent labels, and the nanoscale detail is lost because the PSFs overlap. By using photoswitchable or photoactivatable fluorophores to keep the concentration of active emitters low at any one time, super-resolution images can be extracted by successive single-molecule localizations 6 -8 . These methods were, until recently, mostly limited to 2D imaging. Unfortunately, three-dimensional (3D) position information is difficult to obtain using a diffraction-limited conventional fluorescence microscope for two reasons: (1) the PSF is symmetric about the focal plane meaning that a molecule × nm above the focal plane cannot be distinguished from a molecule × nm below the focal plane, and (2) the PSF contains little information about the axial position of the emitter for a few hundred nanometers about the focal plane 9, 10, meaning that it is quite difficult to super-localize molecules that are in the focal plane of the microscope. Recently, several solutions to these problems have been described including using astigmatism 11 -13, imaging in two different focal planes 14,10,15,16 and interferometry 17, 18 . Fast 3D fluorescent particle tracking has also been performed using confocal imaging [19][20][21] and by using two rotating laser beams to track single quantum dots 21 . We recently demonstrated that a Double-Helix Point Spread Function (DH-PSF) can be used to super-localize single molecules in three dimensions 22 . Combining...

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

“…Individual correction reduced this number by more than a factor of two (55 nm), whereas the average correction brought σ a to within 6 nm of the precision (34 nm) along that direction. This channel is still relatively diffuse along the x direction on correction, however, because of limited photon detection (the DH-PSF in general gives unequal σ x and σ y , because it is not circularly symmetric) (27). In the green channel of molecule 2, σ a (48 nm) was nearly two times as large as the precision (25 nm).…”

“…1A), the DH-PSF response is generated by convolution with the standard SM image using an appropriate phase mask at the Fourier plane of a 4f imaging system built directly after the intermediate image plane of a standard microscope. Typically, the phase mask is loaded onto a phase-only reflective liquid crystal spatial light modulator (SLM) (27)(28)(29). This type of SLM can only modulate vertically polarized light, and therefore, the emission must be polarized before being detected.…”

Three-dimensional superresolution colocalization of intracellular protein superstructures and the cell surface in live Caulobacter crescentus

“…1A) (20,31,32). The DH-PSF converts the normal fluorescence spot of a single molecule into two spots by processing the image with a specially designed phase mask on a spatial light modulator.…”

“…Three-dimensional localizations are possible with SMACM techniques by breaking the axial symmetry of the standard point spread function (PSF) (14)(15)(16), imaging in multiple focal planes simultaneously (17), or projecting the axial dimension onto a lateral dimension (18). These methods can achieve precisions below 100 nm in 3D over a 2-μm range (14,19,20). In addition, sub-10-nm precision can be obtained via interferometry (21); however, these methods severely restrict the sample geometry, have a shallower operational depth of field (∼650 nm) (22), and are not yet conducive to live-cell imaging.…”

“…Moreover, the use of wide field imaging techniques instead of spatial patterning of the excitation beam allows a large field of view to be imaged in 3D simultaneously. Combining this technique with the 3D imaging capabilities of the double-helix PSF (DH-PSF) (15,20), we show remarkable 3D superresolution images of Crescentin-eYFP (CreS-eYFP), a cytoskeletal protein fusion, colocalized with the cell surface of live C. crescentus. The blinking behavior and localization characteristics of CreS-eYFP are also characterized.…”