Modelling and inference of spatio-temporal processes in Single Molecule Localisation Microscopy
File(s)
Author(s)
Patel, Lekha
Type
Thesis
Abstract
Recent advancements in super-resolution microscopy have enabled cellular structures to be imaged beyond sub-diffraction limits. In order to do so, a widely used class of super resolution methods called single molecule localisation microscopy (SMLM) exploit the stochastic nature of fluorescent probes, or fluorophores, that move between bright and dark states until they permanently cease to transition. When observing a large number of fluorophores, this behaviour enables only a sparse subset of them to be detected at any one time, resulting in the ability to accurately record and accumulate their spatial measurements to produce a super-resolved image. While this stochastic behaviour has been heavily exploited, it induces multiple localisations per molecule which gives rise to misleading representations of the true structures of interest. Accurate quantification of the underlying photo-kinetic behaviour is therefore required before any spatial analysis can be conducted.
In this thesis, we model the photo-kinetic behaviour of a molecule as a continuous time Markov process that can transition between a photo-emitting On state, several (unknown) non-photon emitting dark states and an permanently dark state. From this, we develop the Photo-Switching Hidden Markov Model (PSHMM) which relates this underlying behaviour to an observed signal indicating whether or not a molecule is detected in a given frame. Under this model, we derive a maximum likelihood estimator which is used to estimate the unknown transition rates and photo-kinetic model. Under different experimental conditions, the statistical properties of this estimator are also investigated. When an unknown number of fluorescing molecules is filmed, the PSHMM set-up subsequently allows us to derive the distribution of the total number of observed localisations in an experiment, from which an accurate molecular counting tool can be constructed. Finally, we formulate true molecular positions as a spatio-temporal hidden point process and describe the observation process it generates at each time step. The full Bayes filter is then derived, from which the point process and static parameters of the model can be inferred using Markov Chain Monte Carlo (MCMC).
In this thesis, we model the photo-kinetic behaviour of a molecule as a continuous time Markov process that can transition between a photo-emitting On state, several (unknown) non-photon emitting dark states and an permanently dark state. From this, we develop the Photo-Switching Hidden Markov Model (PSHMM) which relates this underlying behaviour to an observed signal indicating whether or not a molecule is detected in a given frame. Under this model, we derive a maximum likelihood estimator which is used to estimate the unknown transition rates and photo-kinetic model. Under different experimental conditions, the statistical properties of this estimator are also investigated. When an unknown number of fluorescing molecules is filmed, the PSHMM set-up subsequently allows us to derive the distribution of the total number of observed localisations in an experiment, from which an accurate molecular counting tool can be constructed. Finally, we formulate true molecular positions as a spatio-temporal hidden point process and describe the observation process it generates at each time step. The full Bayes filter is then derived, from which the point process and static parameters of the model can be inferred using Markov Chain Monte Carlo (MCMC).
Version
Open Access
Date Issued
2019-11
Date Awarded
2020-02
Copyright Statement
Creative Commons Attribution Non-Commercial No Derivatives Licence
Advisor
Cohen, Edward Aidan Kingsley
Publisher Department
Mathematics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)