Computational Techniques Toward 1 nm Super-resolution Microscopy

This thesis explores advanced computational techniques in super-resolution microscopy (SRM), with the primary goal of pushing the limits of achievable resolution towards the 1 nm scale. It includes developments in particle fusion algorithms, data analysis of complex biological structures, and exploration of the impact of molecular dipole orientation on MINFLUX localization accuracy and precision.

In the first part, we present a novel fast particle fusion method tailored to single molecule localization microscopy (SMLM). This method first registers particles based on Joint Registration of Multiple Point Clouds (JRMPC) and then classifies and reconnects misaligned locally optimally clustered sets of particles. This approach significantly reduces computational cost compared to earlier template free methods in particular for a large number of particles.. This advancement enables more detailed and accurate reconstructions of super-particles, enhancing the capabilities of SMLM.

The second part of the dissertation deals with a data analysis of nuclear pore complexes (NPCs) reconstructed by the earlier developed particle fusion technique. By fusing thousands of NPCs labeled at nucleoporin Nup96 and analyzing the high-resolution reconstructions, we reveal intricate details of the NPC structure, in particular the unit structure of Nup96. This analysis showcases the potential of SRM in combination with advanced data analysis to contribute to structural biology on the length scale below 10 nm.

The third part focuses on the influence of the dipole orientation on the localization accuracy and precision of MINFLUX. We simulate the imaging process with a physically realistic vector diffraction Point Spread Function (PSF) model and then localize the emitters based on the simplified Gaussian doughnut PSF model used in MINFLUX so far. Our study, including dipoles with free and fixed orientations and key simulation parameters, reveals the need for more refined modeling to overcome the bias, especially for fixed dipole orientations and background fluorescence. This investigation helps to understand the limitations of MINFLUX in its current form and paves the way for future improvements of the technique.

Finally, we discuss potential future directions for improving SRM techniques. These include refining the fast particle fusion method by incorporating localization uncertainties and prior knowledge, optimizing experimental parameters in MINFLUX, and developing advanced localization strategies to improve accuracy and efficiency. By addressing these future challenges, SRM technologies can move closer to the goal of 1 nm resolution in super-resolution imaging.