Statistical methods for reference-free single-molecule localisation microscopy
MINFLUX (Minimal Photon Flux) is a single-molecule imaging technique capable of resolving fluorophores at a precision of <5 nm. Interpretation of the point patterns generated by this technique presents challenges due to variable emitter density, incomplete bio-labelling of target molecules and their detection, error prone measurement processes, and the presence of spurious (non-structure associated) fluorescent detections. Together, these challenges ensure structural inferences from single-molecule imaging datasets are non-trivial in the absence of strong a priori information, for all but the smallest of point patterns. In addition, current methods often require subjective parameter tuning and presuppose known structural templates, limiting reference-free discovery. We present a statistically grounded, end-to-end analysis framework. Focusing on MINFLUX derived datasets and leveraging Bayesian and spatial statistical methods, a pipeline is presented that demonstrates 1) uncertainty aware clustering of measurements into emitter groups that performs better than current gold standards, 2) rapid identification of molecular structure supergroups, and 3) reconstruction of repeating structures within the dataset without substantial prior knowledge. This pipeline is demonstrated using simulated and real MINFLUX datasets, where emitter clustering and centre detection maintain high performance (emitter subset assignment accuracy > 0.75) across all conditions evaluated, while structural inference achieves reliable discrimination (F1 approx. 0.9) at high labelling efficiency. Template-free reconstruction of Nup96 and DNA-Origami 3x3 grids are achieved.