Localization Precision for Asymmetric Single-Molecule Images in Superresolution Localization Microscopy

Abstract

We present theoretical localization precision formulae for asymmetric single-molecule images in superresolution localization microscopy. Superresolution localization microscopy, such as photoactivated localization microscopy (PALM) and stochastic optical reconstruction microscopy (STORM), have demonstrated superior performances in cell imaging and enable the investigation of cellular processes at close to the molecular scale. All these techniques rely on the precise localization measurements of single-molecules at the nanoscale by using statistical estimators to fit diffraction-limited single-molecule images with the theoretical point spread function (PSF) of the imaging system, which is commonly approximated as a two-dimensional Gaussian. However, to our best knowledge, all previous theories [e.g., R. E. Thompson et al, Biophys. J. 82, 2775 (2002) and R. J. Ober et al, Biophys. J. 86, 1185 (2004)] on theoretical localization precision are developed for circularly symmetric single-molecule images. In contrast, many of the recent advances in the developments of localization microscopy have demonstrated that astigmatism can occur and result in asymmetric PSFs as a result of optical aberrations in the imaging system [S. Quirin et al. Proc. Natl. Acad. Sci. USA 109, 675 (2012)] and asymmetric molecular emission [K. I. Mortensen et al., Nat Meth 7, 377 (2010)]. Asymmetric PSF has also been implemented in localization microscopy to achieve astigmatic imaging for three-dimensional single-molecule localization techniques [B. Huang et al., Science 319, 810 (2008)]. Therefore, our new theory for asymmetric single-molecule images can be particularly useful where asymmetric PSFs have been used or observed in localization microscopy.