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Dissertations completed in 2010 or later are listed below. Please note that there is a 6-12 month delay to add the latest dissertations.
Host-virus interactions and the determinants of infection dynamics (2022)
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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Multi-states inference for analysing noisy single-particle trajectories (2022)
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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New methods for cluster analysis and their applications to the biology of B cells and diffuse large B-cell lymphoma (2021)
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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Interpretation of fluorescence microscopy experiments on cell surface receptor dynamics with stochastic and deterministic mathematical models (2020)
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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On the Dynamics of HIV and Malaria Infection - Insights from Mathematical Models (2015)
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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Mathematical modeling in cellular immunology: T cell activation and parameter estimation (2009)
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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Master's Student Supervision
Theses completed in 2010 or later are listed below. Please note that there is a 6-12 month delay to add the latest theses.
Modeling maternal and neonatal pertussis immunization (2023)
I used mechanistic ordinary differential equations (ODEs) to model the maternal and neonatal immune responses to pertussis (Tdap) immunization. I recapitulated the dynamics of IgG, long and short-lived plasma cells (PCs), memory B cells, and immune complexes and used their results as a metric of short and long-term protection against pertussis. I developed a metric of the risk of severe infection in neonates that incorporated the protection of maternal origin IgG and used it to optimize the timing of the maternal vaccination as well as the first and second shots of the neonatal vaccination series. I found that vaccinating in the 32nd week of pregnancy (?ᵥₘ = −76 ????) resulted in the lowest short-term risk posed to neonates in the first year of life. I found that vaccinating neonates as late as possible (10 months) and with a significant gap in between immunizations had a potential benefit to short-term immunity. When using this thesis’ metric of risk I found that neonates from unvaccinated mothers benefit from an initial vaccination date of 109 days after birth (compared to 120 in North America). I modeled the significant effect that maternal antibody interference has on neonatal immune dynamics and contrasted its hindering effect with its short-term protection of neonates. The model suggests a clear increase in the overall risk of a severe pertussis infection in the first year of life in a neonate born to an unvaccinated mother compared to that of a vaccinated mother. I found that despite a lack of quantifiable calculation of necessary parameters in the model, one can still recapitulate the dynamics of pertussis to a relative degree of accuracy and give effective insights into the optimization of the pertussis vaccination strategy. Future clinical work into the estimation of the rates of IgG production by plasma cells, the composition of the B cell population, and the clearance of immune cells and complexes would have a significant impact on increasing the accuracy of the model and of similar equations representing complex immune processes.
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Epidemic modeling of a simple respiratory pathogen (2022)
Since the emergence of COVID-19, several vaccines have been rolled out at a rapidrate, but the uptake of vaccines is not high enough to eradicate the virus globally.Although most of the population has gotten their vaccines, there is a smallnumber of people who are resistant to receiving vaccine and will never get vaccinated.This is one of the greatest threats to global public health as it could lead tothe reemergence of previously eliminated diseases. We proposed a new modifiedSIR-vaccination model to study the transmission dynamics of COVID-19. We includedthe impact of individuals who choose to be vaccinated and individuals whochoose not to be vaccinated on the final size of the epidemic, in homogeneouslyand heterogeneously mixed populations. In the homogeneous mixing model, wefurther analyze two cases: first, where the vaccination campaign has already happenedand the second, where the vaccination campaign is happening dynamicallyduring the epidemic. It is shown that both homogeneous and heterogeneous mixingmodels have a conditionally stable disease-free equilibrium. The reproductionnumber is derived analytically using the next generation matrix. Using numericalsimulations, we investigated the effect of different mixing scenarios between vaccinatedand unvaccinated individuals on the final epidemic size and the maximumnumber of infected people during the epidemic. It is found that as the numberof people choosing to never be vaccinated increases, the final epidemic size andthe maximum number infected at any time during the epidemic increase as well.We provide interpretation of the results in the context of practical epidemiology,especially vaccination during the epidemic.
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Extending Susceptible-Infected-Recovered modeling to COVID-19 (2022)
The onset of the novel coronavirus, SARS-CoV-2, has been trying for both modellers and public health officials as predictions and policies are made amidst the ongoing pandemic. The emergence of new strains, many vaccine-resistant, continue to present modellers with further challenges in predicting the complex infectious disease dynamics. Susceptible-Infected-Recovered (SIR) models are one of the most common models for studying infectious disease. When reinfection is possible, SIRS models are typically used, and have been seen frequently throughout the COVID-19 pandemic. We propose a series of SIRS adaptations to examine waning immunity and reinfection with the evolution of new strains.First, we develop a two-cycle SIRS model with vaccination and varying transmission in which individuals are either immunologically naive and experiencing exposure for the first time, or have some history of exposure, whether through vaccination, infection, or both. The long-run model results are similar to those of the classic SIRS model, predicting an endemic state in which infection exists and all individuals are in the second SIRS cycle.However, implementing two cycles allows for a more detailed transition from pandemic to endemic state.Next, we develop a multi-strain SIRS model, in which new strains are introduced into the population at various time points. Memory exists for the most recent strain exposure, however individuals are susceptible to reinfection for any other strain. We implement a classic SIRS model with varying waning immunity at various time points to represent susceptibility to new strains, and compare this model to our multi-strain model. We find that both models approach the same long-term equilibrium; however, our multi-strain model captures more total infections.Finally, we use a two-strain model to examine the most likely time for a new strain to emerge. Using our two-strain SIRS model, we predict the window of opportunity within which a new strain can be successful with varying transmissibilities, and using an early time stochastic model we investigate the timing of new strain mutation.
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Mathematical Modelling of Partially Absorbing Boundaries in Biological Systems (2016)
This project presents a mathematical framework for identifying partially permeable biological boundaries, and estimating the rate of absorption of diffusing objects at such a boundary based on limited experimental data. We used partial differential equations (PDEs) to derive probability distribution functions for finding a particle performing Brownian motion in a region. These distribution functions can be fit to data to infer the existence of a boundary. We also used the probability distribution functions together with maximum likelihood estimation to estimate the rate of absorption of objects at the boundaries, based on simulated data. Furthermore, we consider a switching boundary and provide a technique for approximating the boundary with a partially permeable boundary.
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Spatial Stochastic Models of HSV-2 Lesion Dynamics and Their Link with HIV-1 Acquisition (2016)
Patients with Herpes Simplex Virus-2 (HSV-2) infection face a significantly higher risk of contracting HIV-1. This marked increase is thought to be due not only to herpetic lesions serving as an entry point for the HIV-1 virus, but also to the increase in CD4+ T cells in the human genital mucosa during HSV-2 lesional events. By creating a stochastic, spatial, mathematical model describing the behaviour of the HSV-2 infection and immune response in the genital mucosa, I first capture the dynamics that occur during the development of an HSV-2 lesion. I then use this model to quantify the risk of acquiring HIV-1 in HSV-2 positive patients upon sexual exposure, and determine whether antivirals meant to control HSV-2 can decrease HIV-1 infectivity. While theory predicts that HSV-2 treatment should lower HIV-1 infection probability, my results show that this may not be the case unless a critical dosage of HSV-2 treatment is given to the patient. These results help to explain the conflicting data on HIV-1 infection probability in HSV-2 patients and allow for further insight into the type of treatment HSV-2 positive patients should receive to prevent HIV-1 infection.
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Mathematical Models for Immunodeficiency Virus, Post-Treatment and Memory Activation (2012)
Nowdays, HIV infection can be controlled by anti-retroviral drug therapy (ART). However, a persistent viral reservoir in treated patients prevents the eradication of HIV infection. H-iART is an innovator treatment that consists of regular ART and the drugs Maraviroc and Darunavir, and H-iART was enforced with Auranofin. The drug Maraviroc (MRV) was proved to be a good CCR5 inhibitor, which is a HIV correceptor. The drug Auranofin has been shown to accelerate the activation rate of latent cells and also alters the kinetics of viral rebound when drug treatment is interrupted. Recent studies on monkeys infected with SIV have shown a complete suppression of the viral load during H-iART with Auranofin treatment and a persistent suppression of it in the absence of ART. Motivated by the results of the experiments I present deterministic and stochastic models of HIV after treatment interruption. For H-iART treatment, the ODE models were used as a start point to create three different continuous time multi-type branching process. From equations for the probability generating function we use analytic solutions, numerical approximations, or numerical simulations to extract the probability of observable viral blips. We compare our results with the data of two rhesus macaques. We find that more than one latent cell needs to activate in order to observe the data blips, and that the net reproductive number of virus must be very close to one. Since this is unlikely, these results suggest that the viral dynamics must be more complex than our model allows for. For the ART+Auranofin treatment, I will present an ODE model of HIV population dynamics including drug treatment and the immune response to model the viral rebound at treatment interruption.
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Two Mathematical Approaches to a Study of T Cell Motion and Activation in the Lymph Node (2012)
T cells are part of the immune system and as such play a very important role in keeping us healthy. One crucial step in the complex process which is the immune response to pathogens is T cell activation. The general goal of my thesis is to mathematically describe the migration patterns followed by T cells while waiting to be activated in the lymph node. Insight into these migration patterns could lead to better knowledge of the strategies T cells take to make activation such an efficient process.In order to fulfill my goal I have used two different approaches: one mainly computational and the other mainly theoretical.On the computational side, I analyzed three-dimensional microscopic movies of mice lymph nodes inside of which labelled T cells are moving. From the movies I extracted the trajectories of the cells. I studied movies from two experimental frameworks, exogenous and endogenous. On the former, more frequent type of experiment, T cells are labelled outside the mouse and then transferred in. The endogenous experiments, on the contrary, involve genetically modified mice whose T cells are born labelled. I concluded that there is a significant difference in labelled T cell motion between the two experimental frameworks. This suggests that previous results from exogenous experiments should be treated with caution due topossible errors introduced by the methods specific to that type of experiment.On the theoretical side I studied the time it takes for a model T cell to be activated under different scenarios regarding the characteristics of the lymph node as well as of the other cells in it. Since T cells become activated after establishing contact with a specific cell among many similar ones which also move within the lymph node, what I effectively computed was the mean first passage time for a model T cell to reach a defined target within the model lymph node.
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Deciphering multi-state mobility within single particle trajectories of proteins on the plasma membrane (2010)
Single particle tracking is a powerful technique often used in the study of dynamic mechanisms on the cell surface such as binding, confinement and trafficking. Experimental trajectories can be used to detect changes in the lateral mobility of individual molecules over time and space. Therefore, a potential problem in the analysis of single particle trajectories is to account for transitions between modes of mobility. Here we present two coupled statistical methods which characterize particle mobility that is temporally and spatially heterogeneous. The first method detects periods of drift diffusion or reduced mobility within single trajectories due to transient associations with other biomolecules. The second locates spatial domains which have higher or lower concentrations of these associating molecules. The trajectory is modeled as the outcome of a two-state Hidden Markov model parameterized by the diffusion coefficients and drift velocities of each state and the rates of transitions between them (which may change in space). Transitions between states arise from association and disassociation with a binding partner, either membrane-associated or cytosolic. These associations lead to either reduced Brownian diffusion or drift diffusion. An adapted Markov chain Monte Carlo algorithm was used to optimize parameters and simultaneously select the most favorable model of lateral mobility (transient reduced mobility or transient drift diffusion) and to locate spatial domains. Analysis of simulated particle tracks with a wide range of parameters successfully distinguished between the two models, gave accurate estimates for parameters and accurately located spatial domains.
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