Stochastic approach to the molecular counting problem in superresolution microscopy

Significance Large and complex macromolecular assemblies—like RNA and DNA polymerases, the kinetochore, the ribosome, ATP synthase, and many others—are critical components of the cell. To fully characterize these molecular machines, it is not sufficient to rely solely on traditional structural methods, like cryo-EM and X-ray crystallography that provide great structural detail in vitro; we need experimental and theoretical tools that can describe the organization of these machines in their native cellular environment so as to better understand their function. Here we provide a strategy for extracting precisely this information directly from superresolution imaging data, a state-of-the-art technique for probing biological structures in living cells below the diffraction limit. Superresolution imaging methods—now widely used to characterize biological structures below the diffraction limit—are poised to reveal in quantitative detail the stoichiometry of protein complexes in living cells. In practice, the photophysical properties of the fluorophores used as tags in superresolution methods have posed a severe theoretical challenge toward achieving this goal. Here we develop a stochastic approach to enumerate fluorophores in a diffraction-limited area measured by superresolution microscopy. The method is a generalization of aggregated Markov methods developed in the ion channel literature for studying gating dynamics. We show that the method accurately and precisely enumerates fluorophores in simulated data while simultaneously determining the kinetic rates that govern the stochastic photophysics of the fluorophores to improve the prediction’s accuracy. This stochastic method overcomes several critical limitations of temporal thresholding methods.