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Mathematical Modeling of Neural Stem Cell Dynamics in the Adult Hippocampus

Ziebell, Frederik

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The mammalian hippocampus is a brain region in which neural stem cells (NSCs) continuously generate new neurons and astrocytes during adulthood. The production of the former cell type is known as adult neurogenesis. This new progeny, neurons and also astrocytes, is crucial for cognitive tasks such as learning and memory. Understanding the mechanisms that allow for adult neuron generation forms the basis of new clinical applications. Due to the complexity of adult neurogenesis, mathematical modeling is needed in order to identify its dynamics and to evaluate experimental data.

In this thesis, we model the dynamics of neural stem cells and downstream cell compartments using systems of ordinary differential equations (ODEs). To study the role of sudden changes in neural stem cell dynamics, we develop a method to compute the sign of the derivative of the ODE solution with respect to model parameters. Moreover, we compare different hypotheses about NSC dynamics by analyzing the quasi steady-state to which the respective system converges and propose a compromise model. The quasi steady state approach is also used to reveal age-related changes of neural stem cell dynamics. In the case of evaluating single-cell level data, we additionally employ stochastic simulations utilizing the Gillespie algorithm.

Finally, to achieve the original aim of this modeling project, we apply our developed model to evaluate the knockout experiment of the Dkk1 gene, a study published by the group of our collaborator Prof.\ Martin-Villalba (DKFZ). We demonstrate that our model is a suitable description of adult hippocampal neurogenesis and give a data-driven identification of the parameters most probably changing to explain the observed effects upon Dkk1 deletion.

Item Type: Dissertation
Supervisor: Marciniak-Czochra, Prof. Dr. Anna
Date of thesis defense: 23 September 2015
Date Deposited: 15 Oct 2015 08:04
Date: 2015
Faculties / Institutes: The Faculty of Mathematics and Computer Science > Department of Applied Mathematics
Subjects: 510 Mathematics
570 Life sciences
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