BPS2026 – The cliques of Monte Carlo: Spatial point-processes and reversible-jump MCMC in super-resolution clique-based analysis

Recent advances in super-resolution fluorescence microscopy, such as MINFLUX, enable the localization of single molecules with nanometer precision. These developments offer new opportunities to investigate molecular organization at an unprecedented spatial scale, offering insights into emitter tracking in live cells and stationary biomolecule-associated fluorescent emitter position estimation in fixed samples. However, the increasing resolution of microscopy data introduces new analytical challenges—particularly in detecting and characterizing repeating structure of these molecules within noisy, sparse, and complex data sets. Current approaches for the analysis of such data include template matching that require strong a priori information yielding subjective results, or Bayesian approaches that are typically intractable for data sets containing more than a few hundred measurements. To overcome these limitations, we present novel measurement clustering and clique sampling algorithms that are scalable to data sets containing millions of measurements and can provide robust structural insight without strong a priori information. By considering super-resolution data as a spatial point pattern and applying statistical concepts grounded in both point-process theory and reversible-jump Markov Chain Monte Carlo (RJMCMC), the existence and shape of any repeating structures found in the data can be demonstrated. Using a Python-based simulator and real MINFLUX data sets, we validate the efficacy of the intertwined point-process and RJMCMC technique formulated here; the results of which are compared against the current standard of analysis.