MINFLUX - A microscopic spatial statistics problem

MINFLUX (Minimal Photon Fluxes) is a cutting-edge super-resolution fluorescence microscopy technique that achieves <5nm precision in molecular localisation. By utilising a donut-shaped excitation beam and iteratively refining molecular position estimates, MINFLUX surpasses the resolution of conventional fluorescence microscopy techniques such as STORM and PALM, that typically reach 10-20nm precision. This approach enables the visualisation of biological structures and dynamic processes with unprecedented detail, offering new insights into molecular organisation and interactions. Identifying such structures allows researchers to correlate molecular positions with functional states of the subject of the image. However, analysing MINFLUX data presents challenges due to the complexity of signal processing and the need for robust spatial statistical modelling.

Current analysis techniques utilise template matching. Current implementations involve aligning detected localisations with known molecular templates, using metric-based evaluations such as cross-correlation and root-mean-square deviation to assess fit quality. These methods have been applied to detect cytoskeletal filaments, nuclear pores, and synaptic protein arrangements, and to refine localisation accuracy. However, the approach is highly sensitive to noise, sparse biolabelling, and depends on the availability of accurate models with which to compare. Additionally, the subjective selection of localisations may lead to an incomplete analysis of the image, and therefore biased interpretations of the present molecular structures. This approach of fitting a pre-defined model to the data can even result in the fabrication of positive results, that are in reality entirely observed from noise.

This work presents a Python-based simulator for MINFLUX data, aimed at improving the spatial statistical analysis of fluorescence microscopy images by considering the data as a point pattern. The simulator generates MINFLUX-type images through stochastic processes; Poisson distributed centroids surrounded by unseen, repeating structures that form the parent locations for the Gaussian distributed measurements, or localisations, that MINFLUX detects. This provides a flexible tool for evaluating clustering and structural identification methods; one that may be applied to other super resolution techniques, such as STORM. The ultimate objective is to develop a global spatial statistical model capable of identifying molecular clusters and structures.

The data created from this simulator is analysed via the currently accepted techniques. Following this, results are compared with other methods of analysis currently under investigation. The efficacy of the applied methods are discussed, alongside the utility of such a simulator.