Daniel Coombs

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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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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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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