Robust and bias-free localization of individual fixed dipole emitters achieving the Cramér Rao bound for applications in cryo-single molecule localization microscopy

Single molecule localization microscopy (SMLM) has the potential to resolve structural details of biological samples at the nanometer length scale. Compared to room temperature experiments, SMLM performed under cryogenic temperature achieves higher photon yields and, hence, higher localization precision. However, to fully exploit the resolution it is crucial to account for the anisotropic emission characteristics of fluorescence dipole emitters with fixed orientation. In case of slight residual defocus, localization estimates may well be biased by tens of nanometers. We show here that astigmatic imaging in combination with information about the dipole orientation allows to extract the position of the dipole emitters without localization bias and down to a precision of 1 nm, thereby reaching the corresponding Cramér Rao bound. The approach is showcased with simulated data for various dipole orientations, and parameter settings realistic for real life experiments.


Reviewer 1
Overall the paper is well written and the figures are well designed. It is a purely computational work, but with several interesting aspects. The manuscript deserves publication in PlosOne, but I ask the authors to address the following points: Question: As the approach of the work treats a particular problem of SMLM experiments at cryogenic temperatures, this should be mentioned in the abstract, probably also in the title.
Answer: We thank the reviewer for this suggestion. We amended the title and abstract accordingly. Question: Can the authors please justify why they have chosen half a million photons per emission, e.g. by referring to experimental evidence.
Answer: Indeed, values above 10 6 for the number of obtained photons per fluorophore were reported previously for experiments performed under cryogenic conditions, due to decelerated photophysics. We included a short statement in lines 204-206 of the manuscript and added two references (Li, 2015 andWeisenburger, 2013).
Question: How realistic is the chosen background noise (b = 300 photons standard deviation)?
Answer: For data recorded at the cryo-setup in our own laboratory, we typically observe a background with a standard deviation of 10-12 photons per image. In practice, however, researchers may combine images until photobleaching of the fluorophore. In this case, background noise would increase with the square root of the added images. For example, to obtain a noise level of b = 300 one would need to add 900 frames; hence, the choice of b = 300 represents a rather high estimate for the noise in the data. We included a short statement in lines 206-209 of the manuscript.
Question: Please also simulate photon numbers <10,000 photons, which would be realistic in classical SMLM experiments at RT. Figure S4 could be extended by one or two further panels.
Answer: We included an additional panel row in Figure S4, including four new panels for the different dipole orientations simulated with N = 5000 photons. We refer to the new panel in line 252 of the manuscript.
Question: Based on the proposed method, could any other 3D approaches be advantageously exploited, such as multiplane/biplane imaging?
Answer: We thank the reviewer for this question. Indeed, also other 3D approaches will be helpful for determining the amount of defocus and, hence, also the correct lateral position of the fluorophores. We included a corresponding statement in lines 315-321 of the manuscript and added references (Deschout 2014, Backlund 2012, Hulleman 2021.
Question: Although dipole moments of fluorophores employed in aqueous solution are considered to be freely rotating, are there any situations in which the suggested approach could be of use?
Answer: Primarily, our approach is intended for applications in cryo-SMLM, where the mobility of molecules is prohibited and, hence, the orientation of fluorophore dipoles is fixed. At room temperature, fluorophore dipoles are typically freely rotating. However, for fluorophores with two attachment sites the mobility could be restricted. Of note, our approach only yields optimal results if the orientation of the fluorophore is fixed and does not allow for wobbling of the dipole orientation. We included a paragraph on the rotation of fluorophores in the Discussion Section in lines 332-337 of the manuscript.