Superresolution Microscopy as a Percolation Problem: Maximum Achievable Imaging Density and Resolution Cost

Abstract

Superresolution microscopy experiments can be accelerated by utilizing software and algorithms that estimate multiple fluorophore positions from overlapping images. While these approaches enable faster imaging via simultaneous activation of more fluorophores, there is a cost in computational complexity and resolution, as estimates become less precise. We have estimated the maximum achievable density of activated fluorophores by applying percolation theory, and we find that each fluorophore should have (on average) no more than 4 activated fluorophores overlapping it. When more fluorophores are activated, there is a network of overlapping images that span the computational window, leading to significant edge effects and ill-posed computational problems. For typical imaging conditions, this corresponds to approximately 8 activated fluorophores per square micron, a common experimental condition. When we perform Cramer-Rao Lower Bound calculations for localization precision when a fluorophore has 4 activated neighbors we get a predicted localization precision that agrees well with Monte Carlo simulations performed by other investigators. We conclude that a percolation model can provide useful insight into localization problems in microscopy, correctly predicting maximum achievable experimental speed and resolution, while also enabling generalization to some 3D imaging conditions (e.g. elliptical point spread functions).