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Cardim Falcāo, Rebeca

University of British Columbia

The single-particle tracking technique, where individual molecules are fluorescently labelled and recorded over time, is an important tool that allows us to study the spatiotemporal dynamics of subcellular biological systems at very fine temporal and spatial resolution. Mathematical models of particle motion are typically based on Brownian diffusion, reflecting the noisy environment that biomolecules inhabit. To detect changes in particle mobility within a trajectory, hidden Markov models (HMMs) featuring multiple diffusive states are commonly used. In this thesis, we start by modifying a two-state hidden Markov model to take into account experimental errors and further improve the estimation of diffusion coefficients. In addition, we present a constrained hidden Markov model to analyze a specific set of experiments, where two fluorescence colours microscopy data is provided: molecules labelled at low density in one colour, and the second colour is molecules labelled at high density. Hidden Markov models are typically specified with an \textit{a priori} defined number of particle states, and it has not been clear how such assumptions have affected their outcomes. Here, we propose a method for simultaneously inferring the number of diffusive states alongside the dynamic parameters governing particle motion. We use the general framework of Bayesian nonparametric models and use an infinite HMM (iHMM) to fit the data. These concepts were previously applied in molecular biophysics. We directly extended iHMM models to the SPT framework and tested an additional constraint to accelerate convergence and reduce computational time. We tested our infinite hidden Markov model using simulated data and applied it to a previously analyzed large SPT dataset for B cell receptor motion on the plasma membrane of B cells of the immune system. We also incorporated experimental errors into this model, developing an algorithm that further improves the accuracy of parameter estimation, which we demonstrated using simulated data.

Text

2021-12-21

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/80488

Mathematics

University of British Columbia

UBCV

http://creativecommons.org/licenses/by-nc-nd/4.0/