Fast and Precise 3D Fluorophore Localization based on Gradient Fitting

Abstract

Astigmatism imaging approach has been widely used to encode the fluorophore's 3D position in single-particle tracking and super-resolution localization microscopy. Here, we present a new high-speed localization algorithm based on gradient fitting to precisely decode the 3D subpixel position of the fluorophore. This algebraic algorithm determines the center of the fluorescent emitter by finding the position with the best-fit gradient direction distribution to the measured point spread function (PSF), and can retrieve the 3D subpixel position of the fluorophore in a single iteration. Through numerical simulation and experiments with mammalian cells, we demonstrate that our algorithm yields comparable localization precision to the traditional iterative Gaussian function fitting (GF) based method, while exhibits over two orders-of-magnitude faster execution speed. Our algorithm is a promising high-speed analyzing method for 3D particle tracking and super-resolution localization microscopy.

Figure 1. The principle of the gradient fitting based algorithm.

(a) The image of a single fluorescent emitter, where the red dot indicates the exact x–y position of the molecule, the red and blue arrows show the exact gradient directions and the calculated gradient directions of that position, respectively; the green dashed lines indicate the corresponding exact gradient lines, and the magenta dashed ellipse indicates the shape of the PSF. (b) The z–e (ellipticity) calibration curve used to look up the axial position according to the calculated ellipticity. Three representative patterns of a single emitter are shown to indicate the PSFs at the corresponding axial positions. Note that a 4th-order polynomial function is used to fit the z–e calibration curve.

Figure 2. Comparison of localization precision using simulation.

Localization precision in x dimension (a), y dimension (b), and z dimension (c) at different imaging depths. Note that the localization precision is quantified as the standard deviation of the estimated positions. Given the known position of the simulated image, we also compared the localization accuracy, or the root mean square error between the actual position and the estimated position using these five methods, which is shown in Supplementary Figure S1.

Figure 3. Localization performance of our gradient fitting based algorithm, QuickPALM, MLE-WA, NLLS-WA and NLLS-WD for experiments with fluorescent nanospheres.

Localization precision is compared in X, Y and Z dimensions at the depth of 160 nm (a), 0 nm (b) and −160 nm (c). The localization precision of different algorithms is presented in the figure legend.

Figure 4. Localization performance in single-particle tracking experiments.

The tracking trajectory of (a) a single fluorescent nanosphere and (c) a single telomere tracked by our gradient fitting based algorithm. Comparison of mean square distance (MSD) of (b) the nanosphere and (d) telomere movement for different localization algorithms.

Figure 5. 3D STORM imaging of microtubules in MEF cells.

(a) The 3D STORM image reconstructed by our gradient fitting based algorithm. (b,c) The higher zoom of (b) the conventional wide-field image and (c) the lateral plane projection of STORM image for the area shown in the green box of (a). Localization performance of different algorithms are compared in lateral dimension (d) and axial dimension (e). Scale bar: 500 nm.