Modelling the impact of cyclic hypoxia on cell-cycle regulation in cancer cells

Thesis

In vivo observations show that oxygen levels in tumours can fluctuate on fast timescales. As a result, cancer cells can be periodically exposed to pathologically low oxygen levels; a phenomenon known as cyclic hypoxia. Even though in vitro models of cyclic hypoxia exist, they fail to capture the complex and heterogeneous oxygenation dynamics of real tumours. Mathematical models can help to overcome current experimental limitations and, by doing so, offer new insights into the biology of cyclic hypoxia by predicting cell responses to a wide range of cyclic dynamics. Recent experimental evidence suggests that cyclic hypoxia alters the progression of cancer cells along the cell-cycle. In this thesis, we use a range of mathematical approaches to study cell-cycle dysregulation in cyclic hypoxia and its impact on the growth and survival of cell cultures.

Accordingly, we develop and analyse a series of mathematical models that can be used, alongside in vitro experiments, to increase understanding of cell responses to cyclic hypoxia. First, we present a deterministic cell-cycle model to describe the dynamics of a population of cells growing in different oxygen environments, in the absence of competition for space. Our model comprises a system of 6 linear differential equations with two time delays and describes the evolution of the number of cells in different cell-cycle states. The impact of hypoxia on cell-cycle progression is captured by introducing arrest (or checkpoint compartments) and allowing the rates at which cells transition between different cell-cycle states to depend on the oxygen environment they experience. We then develop a corresponding individual-based model to study the impact of cyclic hypoxia on cell survival in the presence and absence of treatment.

We apply the models we develop in two different ways. On the one hand, we use a combination of analytical and numerical approaches to identify cell-cycle control strategies that favour proliferation and/or cell survival in different oxygen environments. Specifically, we identify environmental regimes in which cells may, or may not, benefit from having defective cell-cycle checkpoints. Furthermore, we illustrate how our models can be used as a tool to complement and design in vitro experiment to uncover the biological mechanisms that drive cell responses to constant and cyclic hypoxia.

Authors: Celora, G

• DOI: 10.5287/ora-mzkqj96k0
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: cancer; delay-differential equations; structured population models; cyclic hypoxia
• Subjects: Lungs--Cancer--Epidemiology--Mathematical models; Population biology--Mathematical models