Open Access
September 2019 A hidden Markov model approach to characterizing the photo-switching behavior of fluorophores
Lekha Patel, Nils Gustafsson, Yu Lin, Raimund Ober, Ricardo Henriques, Edward Cohen
Ann. Appl. Stat. 13(3): 1397-1429 (September 2019). DOI: 10.1214/19-AOAS1240


Fluorescing molecules (fluorophores) that stochastically switch between photon-emitting and dark states underpin some of the most celebrated advancements in super-resolution microscopy. While this stochastic behavior has been heavily exploited, full characterization of the underlying models can potentially drive forward further imaging methodologies. Under the assumption that fluorophores move between fluorescing and dark states as continuous time Markov processes, the goal is to use a sequence of images to select a model and estimate the transition rates. We use a hidden Markov model to relate the observed discrete time signal to the hidden continuous time process. With imaging involving several repeat exposures of the fluorophore, we show the observed signal depends on both the current and past states of the hidden process, producing emission probabilities that depend on the transition rate parameters to be estimated. To tackle this unusual coupling of the transition and emission probabilities, we conceive transmission (transition-emission) matrices that capture all dependencies of the model. We provide a scheme of computing these matrices and adapt the forward-backward algorithm to compute a likelihood which is readily optimized to provide rate estimates. When confronted with several model proposals, combining this procedure with the Bayesian Information Criterion provides accurate model selection.


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Lekha Patel. Nils Gustafsson. Yu Lin. Raimund Ober. Ricardo Henriques. Edward Cohen. "A hidden Markov model approach to characterizing the photo-switching behavior of fluorophores." Ann. Appl. Stat. 13 (3) 1397 - 1429, September 2019.


Received: 1 January 2018; Revised: 1 September 2018; Published: September 2019
First available in Project Euclid: 17 October 2019

zbMATH: 07145962
MathSciNet: MR4019144
Digital Object Identifier: 10.1214/19-AOAS1240

Keywords: forward-backward algorithm , Hidden Markov models , Markov processes , rate estimation , super-resolution microscopy

Rights: Copyright © 2019 Institute of Mathematical Statistics

Vol.13 • No. 3 • September 2019
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