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A hidden Markov model approach to characterizing the photo-switching behaviour of fluorophores

A hidden Markov model approach to characterizing the photo-switching behaviour of fluorophores
A hidden Markov model approach to characterizing the photo-switching behaviour of fluorophores
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.
1932-6157
1397-1429
Patel, Lekha
94149796-9453-4ce7-9bce-233cd4e591be
Gustafsson, Nils
37367c7e-9bc2-4bd9-a386-aa185d6b04e2
Lin, Yu
9d6cf03d-f6a6-4f1a-b613-3a6615a5358c
Ober, R.J.
31f4d47f-fb49-44f5-8ff6-87fc4aff3d36
Henriques, Ricardo
9c90d984-ef5b-4ecf-9c48-3958185c91f4
Cohen, Edward
df5112ce-f48a-4e1f-b7de-4e7d6fbc7cf8
Patel, Lekha
94149796-9453-4ce7-9bce-233cd4e591be
Gustafsson, Nils
37367c7e-9bc2-4bd9-a386-aa185d6b04e2
Lin, Yu
9d6cf03d-f6a6-4f1a-b613-3a6615a5358c
Ober, R.J.
31f4d47f-fb49-44f5-8ff6-87fc4aff3d36
Henriques, Ricardo
9c90d984-ef5b-4ecf-9c48-3958185c91f4
Cohen, Edward
df5112ce-f48a-4e1f-b7de-4e7d6fbc7cf8

Patel, Lekha, Gustafsson, Nils, Lin, Yu, Ober, R.J., Henriques, Ricardo and Cohen, Edward (2019) A hidden Markov model approach to characterizing the photo-switching behaviour of fluorophores. The Annals of Applied Statistics, 13 (3), 1397-1429. (doi:10.1101/223875).

Record type: Article

Abstract

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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Accepted/In Press date: 18 January 2019
e-pub ahead of print date: 17 October 2019
Published date: 2019

Identifiers

Local EPrints ID: 430271
URI: http://eprints.soton.ac.uk/id/eprint/430271
ISSN: 1932-6157
PURE UUID: 9874a4de-9471-4fb8-8bb1-5e7417c027d6
ORCID for R.J. Ober: ORCID iD orcid.org/0000-0002-1290-7430

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Date deposited: 23 Apr 2019 16:30
Last modified: 16 Mar 2024 04:37

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Contributors

Author: Lekha Patel
Author: Nils Gustafsson
Author: Yu Lin
Author: R.J. Ober ORCID iD
Author: Ricardo Henriques
Author: Edward Cohen

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