Bayesian counting of photobleaching steps with physical priors

Counting fluorescence photobleaching steps is commonly used to infer the number n₀ of monomeric units of individual oligomeric protein complexes or misfolded protein aggregates. We present a principled Bayesian approach for counting that incorporates the statistics of photobleaching. Our physics-based prior leads to a simple and efficient numerical scheme for maximum a posteriori probability (MAP) estimates of the initial fluorophore number n^₀. Our focus here is on using a calibration to precisely estimate n^₀, though our approach can also be used to calibrate the photophysics. Imaging noise increases with n^₀, while bias is often introduced by temporal averaging. We examine the effects of fluorophore number n^₀ of the oligomer or aggregate, lifetime photon yield μ_eff of an individual fluorophore, and exposure time Δt of each image frame in a time-lapse experiment. We find that, in comparison with standard ratiometric approaches or with a "change-point" step-counting algorithm, our MAP approach is both more precise and less biased.