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 . Our focus here is on using a calibration to precisely estimate , though our approach can also be used to calibrate the photophysics. Imaging noise increases with , while bias is often introduced by temporal averaging. We examine the effects of fluorophore number of the oligomer or aggregate, lifetime photon yield μeff 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.
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In this paper, we ignore the individual photon arrival times and consider only a timeseries of photon counts for each macromolecule that is uniformly binned in time, as characterized by α.
We do require that enough photons are delivered per Δt to satisfy our Gaussian approximation of the Poisson photon statistics, i.e. αμeff ≫ 1.
