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Mathematical modelling of the kinetic parameters of haematopoietic stem cells and their progeny

Barile, Melania

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Abstract

Haematopoiesis, the process by which blood cells are formed, is extensively studied because of its relevance for animal life. Uncovering the mechanisms of blood formation and its regulation is fundamental to cope with anomalies or illnesses such as anaemia and leukaemia, or massive blood loss. Haematopoiesis is driven by the haematopoietic stem cells, HSCs. HSCs are able to reconstitute, upon transplantation, all blood lineages of an animal deprived of its haematopoietic cells (multipotency), and to generate one or two HSCs upon division (self-renewal). However, it is unclear how often they self-renew or differentiate into more mature compartments, according to which differentiation pathways, and how physiological and stressed conditions differ. Similarly, the kinetic properties of the progenies of the stem cells are mostly unknown. Here we present an approach to quantify the kinetics of the haematopoietic system via a deterministic mathematical model. The model is driven by two different sets of in vivo measurements: fate mapping of HSCs and BrdU accumulation data. In the first experiment we consider, an inducible, inheritable label is switched on in the stem cells without altering the physiological conditions. The fraction of labelled cells in the stem and in the downstream populations is measured over time. We build a model of population dynamics, which describes the time course increase of the labelled cells fraction in the progenies. The model has only one parameter, the time a cell resides in a population. Fitting reveals that the immediate progenies of stem cells have a long residence time, which suggest a small role of stem cells in normal haematopoiesis, sustained rather by early progenitors. We then infer the differentiation rate of a cell into its progeny by incorporating in the model the ratio of population sizes, and again confirm an infrequent contribution of stem cells. In the second experiment we consider, the thymidine analogue BrdU is fed to mice over time. BrdU labels the cells that undergo DNA replication. The fraction of labelled cells in the stem cells and in the downstream populations is measured over time. We adapt the population dynamics model of the previous part, incorporating the simplified assumption that cells are BrdU positive if and only if they have divided at least once. We fit the adapted model to BrdU and fate mapping data simultaneously and infer the rate at which cells divide, as well as the frequency at which division of different types (symmetric or asymmetric) happen. This analysis reveals infrequent and mainly symmetric divisions of the stem cells. Moreover, we investigate whether a subdivision of the stem cells and their immediate progeny into several heterogeneous sub-populations is compatible with the parameters inferred as described above. We adapt the model to again fit data that consider this subdivision. We find coherent estimates for quantities that are model-invariant, which supports the robustness of our approach. Finally, we adapt our model to describe fate mapping and cell-cycle-related data in non-stationary conditions, namely after irradiation. Contrary to normal conditions, stem cell proliferation and differentiation are significantly activated, demonstrating their importance in reconstituting a severely compromised system. In conclusion, we suggest via data-driven deterministic modelling that HSCs fuel but do not majorly sustain normal haematopoiesis, role played by their immediate progenies. On the contrary, they are very responsive in stressed conditions, rapidly replenishing the depleted cells via enhanced proliferation and differentiation.

Item Type: Dissertation
Supervisor: Höfer, Prof. Dr. Thomas
Place of Publication: Heidelberg, Germany
Date of thesis defense: 18 December 2018
Date Deposited: 01 Feb 2019 08:26
Date: 2019
Faculties / Institutes: The Faculty of Bio Sciences > Dean's Office of the Faculty of Bio Sciences
Subjects: 500 Natural sciences and mathematics
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