Modelling and inference of spatio-temporal processes in Single Molecule Localisation Microscopy

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).Open Acces

A mutation in the endonuclease domain of mouse MLH3 reveals novel roles for MutLγ during crossover formation in meiotic prophase I

During meiotic prophase I, double-strand breaks (DSBs) initiate homologous recombination leading to non-crossovers (NCOs) and crossovers (COs). In mouse, 10% of DSBs are designated to become COs, primarily through a pathway dependent on the MLH1-MLH3 heterodimer (MutLγ). Mlh3 contains an endonuclease domain that is critical for resolving COs in yeast. We generated a mouse (Mlh3DN/DN) harboring a mutation within this conserved domain that is predicted to generate a protein that is catalytically inert. Mlh3DN/DN males, like fully null Mlh3-/- males, have no spermatozoa and are infertile, yet spermatocytes have grossly normal DSBs and synapsis events in early prophase I. Unlike Mlh3-/- males, mutation of the endonuclease domain within MLH3 permits normal loading and frequency of MutLγ in pachynema. However, key DSB repair factors (RAD51) and mediators of CO pathway choice (BLM helicase) persist into pachynema in Mlh3DN/DN males, indicating a temporal delay in repair events and revealing a mechanism by which alternative DSB repair pathways may be selected. While Mlh3DN/DN spermatocytes retain only 22% of wildtype chiasmata counts, this frequency is greater than observed in Mlh3-/- males (10%), suggesting that the allele may permit partial endonuclease activity, or that other pathways can generate COs from these MutLγ-defined repair intermediates in Mlh3DN/DN males. Double mutant mice homozygous for the Mlh3DN/DN and Mus81-/- mutations show losses in chiasmata close to those observed in Mlh3-/- males, indicating that the MUS81-EME1-regulated crossover pathway can only partially account for the increased residual chiasmata in Mlh3DN/DN spermatocytes. Our data demonstrate that mouse spermatocytes bearing the MLH1-MLH3DN/DN complex display the proper loading of factors essential for CO resolution (MutSγ, CDK2, HEI10, MutLγ). Despite these functions, mice bearing the Mlh3DN/DN allele show defects in the repair of meiotic recombination intermediates and a loss of most chiasmata

Deep Learning Aerosol-Cloud Interactions from Satellite Imagery

Satellite imagery can detect a wealth of ship tracks, temporary cloud trails created via cloud seeding by the emitted aerosols of large ships, a phenomenon that cannot be directly reproduced by global climate models. Ship tracks are satellite-observable examples of aerosol-cloud interactions, processes that constitute the largest uncertainty in climate forcing predictions, and when observed are also examples of Marine Cloud Brightening (MCB), a potential climate intervention strategy. Leveraging the large amount of observed ship track data to enhance understanding of aerosol-cloud interactions and the potentials of MCB is hindered by the computational infeasiblity of characterization from expensive physical models. In this paper, we focus on utilizing a cheaper physics-informed advection-diffusion surrogate to accurately emulate ship track behavior. As an indication of aerosol-cloud interaction behavior, we focus on learning the spreading behavior of ship tracks, neatly encoded in the emulator's spatio-temporal diffusion field. We train a convolutional LSTM to accurately learn the spreading behavior of simulated and satellite-masked ship tracks and discuss its potential in larger scale studies

Classification of Photovoltaic Failures with Hidden Markov Modeling, an Unsupervised Statistical Approach

Failure detection methods are of significant interest for photovoltaic (PV) site operators to help reduce gaps between expected and observed energy generation. Current approaches for field-based fault detection, however, rely on multiple data inputs and can suffer from interpretability issues. In contrast, this work offers an unsupervised statistical approach that leverages hidden Markov models (HMM) to identify failures occurring at PV sites. Using performance index data from 104 sites across the United States, individual PV-HMM models are trained and evaluated for failure detection and transition probabilities. This analysis indicates that the trained PV-HMM models have the highest probability of remaining in their current state (87.1% to 93.5%), whereas the transition probability from normal to failure (6.5%) is lower than the transition from failure to normal (12.9%) states. A comparison of these patterns using both threshold levels and operations and maintenance (O&M) tickets indicate high precision rates of PV-HMMs (median = 82.4%) across all of the sites. Although additional work is needed to assess sensitivities, the PV-HMM methodology demonstrates significant potential for real-time failure detection as well as extensions into predictive maintenance capabilities for PV

Classification of Photovoltaic Failures with Hidden Markov Modeling, an Unsupervised Statistical Approach

Failure detection methods are of significant interest for photovoltaic (PV) site operators to help reduce gaps between expected and observed energy generation. Current approaches for field-based fault detection, however, rely on multiple data inputs and can suffer from interpretability issues. In contrast, this work offers an unsupervised statistical approach that leverages hidden Markov models (HMM) to identify failures occurring at PV sites. Using performance index data from 104 sites across the United States, individual PV-HMM models are trained and evaluated for failure detection and transition probabilities. This analysis indicates that the trained PV-HMM models have the highest probability of remaining in their current state (87.1% to 93.5%), whereas the transition probability from normal to failure (6.5%) is lower than the transition from failure to normal (12.9%) states. A comparison of these patterns using both threshold levels and operations and maintenance (O&M) tickets indicate high precision rates of PV-HMMs (median = 82.4%) across all of the sites. Although additional work is needed to assess sensitivities, the PV-HMM methodology demonstrates significant potential for real-time failure detection as well as extensions into predictive maintenance capabilities for PV

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