The low degree of labeling and limited photon count of fluorescent emitters in single molecule localization microscopy results in poor quality images of macro-molecular complexes. Particle fusion provides a single reconstruction with high signal-to-noise ratio by combining many single molecule localization microscopy images of the same structure. The underlying assumption of homogeneity is not always valid, heterogeneity can arise due to geometrical shape variations or distinct conformational states. We introduce a Point Cloud Variational Auto-Encoder that works directly on 2D and 3D localization data, to detect multiple modes of variation in such datasets. The computing time is on the order of a few minutes, enabled by the linear scaling with dataset size, and fast network training in just four epochs. The use of lists of localization data instead of pixelated images leads to just minor differences in computational burden between 2D and 3D cases. With the proposed method, we detected radius variation in 2D Nuclear Pore Complex data, height variations in 3D DNA origami tetrahedron data, and both radius and height variations in 3D Nuclear Pore Complex data. In all cases, the detected variations were on the few nanometer scale.

High-resolution microscopy techniques, such as Single-Molecule Localization Microscopy (SMLM) and Cryogenic Electron Microscopy (Cryo-EM), can utilize particle fusion or averaging to reconstruct a macromolecular structure of increased signal-to-noise ratio and of potentially higher resolution. This process assumes that all fused particles are structurally equal. Structural heterogeneity, however, is often present due to biological variations and should not be ignored. In particularly continuous and subtle conformational changes present in the data lead to undesired blurring of the reconstruction. This thesis develops methods to detect continuous structural heterogeneity and to exploit it for more faithful reconstructions, enabling more accurate interpretations and insights into molecular structures.

In Chapter 2, we propose a method to detect continuous structural heterogeneity in SMLM datasets based on an all-to-all pairwise comparison of the found structures. The method is applied to both experimental and simulated data, where continuous variations such as the height of 3D DNA origami tetrahedrons and the radius of 2D Nuclear Pore Complexes (NPCs) are detected. The chapter highlights how accounting for these structural variations leads to more reliable particle fusion and reconstruction.

In Chapter 3, we propose a Point Cloud Variational Auto-Encoder (PCVAE) that operates directly on 2D and 3D localization data to detect structural heterogeneity. Unlike common neural networks that rely on pixelated images, our method utilizes raw localization coordinates. This not only reduces the required memory but also has low computational complexity and thus allows scalability to many structures. In contrast to multi-dimensional scaling approaches, where the computational complexity scales quadratically, here it remains linear with the number of particles. Our method is capable of identifying multiple modes of variation and reveals nanometer-scale changes such as radius and height variations in both simulated and experimental datasets.

In Chapter 4, we propose a method to detect continuous structural heterogeneity in Cryo-EM datasets. Recent approaches rely on machine learning models that often require large training datasets and careful tuning of hyperparameters.
%These machine learning methods are often hindered by a lack of interpretability and consistency due to the non-linear mapping onto a low-dimensional latent space.
In contrast, our method detects underlying continuous variations in 2D projections by pairwise comparison of images within orientation classes. The approach reconstructs intermediate conformational states representing the continuous structural heterogeneity in synthetic SARS-CoV-2 spike protein data, simulated under ideal conditions. More realistic simulations, incorporating varying defocus per particle and radiation damage, do not lead to the same favourable results, still posing a challenge for future research.

Fusion of multiple chemically identical complexes, so-called particles, in localization microscopy, can improve the signal-to-noise ratio and overcome under-labeling. To this end, structural homogeneity of the data must be assumed. Biological heterogeneity, however, could be present in the data originating from distinct conformational variations or (continuous) variations in particle shapes. We present a prior-knowledge-free method for detecting continuous structural variations with localization microscopy. Detecting this heterogeneity leads to more faithful fusions and reconstructions of the localization microscopy data as their heterogeneity is taken into account. In experimental datasets, we show the continuous variation of the height of DNA origami tetrahedrons imaged with 3D PAINT and of the radius of Nuclear Pore Complexes imaged in 2D with STORM. In simulation, we study the impact on the heterogeneity detection pipeline of Degree Of Labeling and of structural variations in the form of two independent modes.