Daniel Coombs

With the large global burden of virus-associated diseases, research on viral transmission and pathogenesis is essential. HIV-1, Epstein-Barr virus (EBV), cytomegalovirus (CMV), and SARS-CoV-2 are some of the most ubiquitous infections among global populations, each associated with an enormous disease burden. Using combinations of cohort data, mouse models, and mathematical modelling, we addressed specific questions related to each of these infections. EBV-HIV-1 coinfections correlate with high risks of cancerous malignancies and elevated EBV viral loads in saliva. To discern how HIV-1 exacerbates EBV infection, we analyzed cohort data and developed a mathematical model of the EBV infection dynamics within the tonsils. Our results suggest that coinfected individuals have a weaker EBV-specific immune response and higher rates of B cell reactivation than individuals with only EBV infection, which together explain their higher EBV loads and more frequent shedding in the saliva. CMV is the number one cause of congenital infection. However, no approved vaccine is available in part due to a lack of knowledge on how primary infection becomes established and the determinants of reinfection. Using mathematical and mouse infection models, we examined the dynamics of primary infection and reinfection, determined the drivers of CMV transmission, and tested vaccination strategies. Our results bring insight into the immune correlates of protection and the importance of strain differences in determining the efficiency and severity of reinfection. Further, we show that even modestly-protective vaccines administered to children are likely sufficient for decreasing infection in the population and the burden of congenital CMV. The high transmissibility of SARS-CoV-2 has caused the historic COVID-19 pandemic. Mathematical models have proven essential to predict the spread and impacts of COVID-19. We created a mathematical model of SARS-CoV-2 transmission, focusing on within-household transmission to discern its contribution to the pandemic. We showed that these interactions are essential for determining SARS-CoV-2 spread during times of social distancing and determined what testing strategies can help reveal the true amount of transmission occurring within homes. Together, this work reveals novel insights into the determinants of viral transmission and the within-host dynamics that can help inform future prevention and treatment strategies.

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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.

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Detecting clusters of data points in physical or high-dimensional (HD) space is a common task in biology and biomedicine. Single-molecule localization microscopy (SMLM), a category of super-resolution microscopy, is often used to analyze spatial distributions of proteins on the surface membranes of, or inside, biological cells. Proteins sometimes need to form clusters to surpass a critical signalling threshold for functional activity. Therefore, investigating protein clustering can yield important insights about protein and cell functions in health and disease. Mass cytometry, also called CyTOF, is a high-throughput technique for investigating the abundance of multiple proteins simultaneously in single cells, resulting in HD data in which cells cluster into different phenotypes. Cluster analysis of CyTOF data is important for understanding heterogeneity in biological cell populations, which has clinical implications in cancer biology.This dissertation first describes a new method, called StormGraph, to detect clusters in diverse SMLM data. StormGraph converts 2D or 3D SMLM data to a weighted graph, applies a community detection algorithm to assign localizations to clusters at multiple scales, and includes a new algorithm to generate a single-level clustering from a multi-level cluster hierarchy. Unlike most other clustering algorithms, StormGraph utilizes uncertainties associated with point positions. Results of using SMLM and StormGraph to analyze clustering of B-cell antigen receptors on the membranes of normal and malignant B cells are presented. Next, this dissertation describes a new measure of similarity between clusters in HD data. Computed by a method called ASTRICS, it is based on local dimensionality reduction and triangulation of alpha shapes. A strategy for clustering and visualizing HD data, with ASTRICS used to construct a graph from an initial set of fine-grained clusters, is presented and demonstrated on three very different HD datasets, including public CyTOF data. Finally, new CyTOF experiments were designed and performed to analyze heterogeneity among diffuse large B-cell lymphoma (DLBCL) cell lines. Results of the analysis, including clustering and visualization using the strategy based on ASTRICS, are presented. Most interesting were revelations about signalling dynamics linked to the cell cycle, which differed between DLBCL subtypes.

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Fluorescence microscopy has provided cellular biologists with quantifiable data, that can be paired with mathematical models to discover the mechanics of the imaged processes. We developed mathematical models to analyze data from two fluorescence techniques: direct Stochastic Optical Reconstruction Microscopy (dSTORM) and fluorescence recovery after photobleaching (FRAP). dSTORM is a super-resolution technique that uses photo-switchable fluorophores to achieve nanometer resolution images, allowing us to visualize the organization of proteins at nano-scales. However, dSTORM images can suffer from recording a single photo-switchable fluorophore multiple times, possibly creating artificial features. This is specially relevant in the analysis of membrane B-cell receptors clustering, where spatial clustering might relate to immune activation. I developed a protocol to estimate the number of unique fluorophores present in the experiment by coupling their temporal (with a Markov-chain model) and spatial (with a Gaussian mixture model) dynamics within a maximum likelihood framework. Previous studies have used the temporal information, but they have not coupled it with the spatial information (both localization and localization estimation error). I tested my protocol on simulated data, well-characterized DNA origami data and B-cell receptor data with positive results. My model is general enough to apply to other biological systems besides B-cell data and will enhance a microscopy technique that is widely used in biological applications.FRAP can be used to quantify the mobility of membrane proteins. We used it on live Drosophila organisms to study the outside-in pathway in cell adhesion to the extracellular matrix (ECM). We developed an ODE model to describe the recycling of the membrane protein, integrin, in charge of the adhesions. We found that both integrin and ECM ligands stabilize outside-in signalling and that relevant chemical treatments do not balance mutant integrin activation but stabilize the adhesions in control organisms. We also analyzed inside-out activation with a similar ODE model and by labeling the cytosolic protein talin. We found that talin is sensitive to increases and decreases in applied force. Disruptions of the intracellular force negatively affected adhesion stability. Increasing the force resulted in a faster assembly of new adhesions, whereas decreased forces increased the talin turnover.

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We develop and apply mathematical models to obtain insights into the dynamics of HIV and malaria infection. We consider three case studies.1. The duration of the time between exposure and detectability of HIV infection is difficult to estimate because precise dates of exposure are rarely known. Therefore, the reliability of clinical HIV testing during the first few weeks of infections is unknown, creating anxiety among HIV-exposed individuals and their physicians. We address this knowledge gap by fitting stochastic models of early HIV infection to detailed viral load time-courses, taken shortly after exposure, from 78 plasma donors. Since every plasma donor in our data eventually becomes infected, we condition our model to reflect this bias before fitting to the data. Our model prediction for the mean eclipse period is 8-10 days. We further quantify the reliability of a negative test t days after potential exposure to inform physicians about the value of initial and follow-up testing.2. The recently launched Get Checked Online (GCO) program aims at increasing the HIV testing rate in the Vancouver men who have sex with men population by facilitating test taking and result delivery. We develop mathematical models and extract parameter values from surveys and interviews to quantify GCO's population-level impact. Our models predict that the epidemic is growing overall, that its severeness is increased by the presence of a high-risk group and that, even at modest effectiveness, GCO might avert 34-66 new infections in the next five years.3. Metarhizium anisopliae is a naturally occurring fungal pathogen of mosquitoes that has been engineered to act against malaria by effectively blocking onward transmission from the mosquito vector. We develop and analyse two mathematical models to examine the efficacy of this fungal pathogen. We find that, in many plausible scenarios, the best effects are achieved with a reduced or minimal pathogen virulence, even if the likelihood of resistance to the fungus is negligible. The results depend on the interplay between two main effects: the ability of the fungus to reduce the mosquito population, and the ability of fungus-infected mosquitoes to compete for resources with non-fungus-infected mosquitoes.

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A critical step in mounting an immune response is antigen recognition by T cells. This step proceeds by productive interactions between T cell receptors (TCR) on the surface of T cells and foreign antigen, in the form of peptide-major-histocompatibility-complexes (pMHC), on the surface of antigen-presenting-cells (APC). Antigen recognition is exceedingly difficult to understand because the vast majority of pMHC on APCs are derived from self-proteins. Nevertheless, T cells have been shown to be exquisitely sensitive, responding to as few as 10 antigenic pMHC in an ocean of tens of thousands of self pMHC. In addition, T cells are extremely specific and respond only to a small subset of pMHC by virtue of their specific TCR.To explain the sensitivity of T cells to pMHC it has been proposed that a single pMHC may serially bind multiple TCRs. Integrating present knowledge on the spatial-temporal dynamics of TCR/pMHC in the T cell-APC contact interface, we have constructed mathematical models to investigate the degree of TCR serial engagements by pMHC. In addition to reactions within clusters, the models capture the formation and mobility of TCR clusters. We find that a single pMHC serially binds a substantial number of TCRs in a TCR cluster only if the TCR/pMHC bond is stabilized by coreceptors and/or pMHC dimerization. In a separate study we propose that serial engagements can explain T cell specificity. Using Monte Carlo simulations, we show that the stochastic nature of TCR/pMHC interactions means that multiple binding events are needed for accurate detection of foreign pMHC.Critical to our studies are estimates of TCR/pMHC reaction rates and mobilities. In the second half of the thesis, we show that Fluorescence Recovery After Photobleaching (FRAP) experiments can reveal effective diffusion coefficients. We then show, using asymptotic analysis and model fitting, that FRAP experiments can be used to estimate reaction rates between cell surface proteins, like TCR/pMHC. Lastly, we use FRAP experiments to investigate how the actin cytoskeleton modulates TCR mobility and report effective reaction rates between TCR and the cytoskeleton.

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