Understanding the implications of fluctuating environments on cell progress through the cell cycle

Most current models of the cell cycle are based on the cell experiencing a normal level of oxygen in a constant way. However, experimental evidence suggests that cells do not move constantly through the stages of the cycle, and that the rate of progression through a stage is affected by exposure to fluctuating oxygen environments.

Checkpoints at different phases of the cycle are more or less active in response to the environment, allowing oxygen levels to affect the rate of cell progression. This is particularly important when considering cancerous cells, as tumour cells have different sensitivities to treatment at different points along the cell cycle. Hence investigating the points of the cell cycle at which different cells with different mutations do best under hypoxia (low oxygen) and normoxia (normal oxygen) can suggest how far cells should progress through the cycle before response to treatment is maximised.

For example, radiotherapy resistance can develop when cells become arrested, which occurs at certain checkpoints and is affected by the cell's oxygen environment. This has therapeutic implications, as understanding the points at which cells are most and least responsive to treatment, as well as the type of oxygen environment required to force them into that point may allow for the administering of more effective therapies.

The aim of this project is to understand how cancer cells progress when exposed to a fluctuating environment, and to consider the implications for growth of tumours and the subsequent response to treatment.

To do this, the project will aim to build mathematical models of the cell cycle. Initially a continuum approach will be used, with a nonlinear coupled system of stage-structured partial differential equations. Delay differential equations will be used to account for the effect that the oxygen level experienced by the cell in the recent past has on the cell's progression through the cycle.

Current progress with this work does not include spatial effects in the model, and so this project will aim to consider such effects. The method of characteristics may be used to analyse the system, along with numerical simulation. Data fitting methods will be used in order to fit models to current data and to analyse the accuracy of the models, and model selection will be considered using Bayesian methods.

In order to compare the models with the data it will be necessary to account for small cell numbers, and so a continuum approach would no longer be appropriate. Hence stochastic effects and agent-based models will be included. In order to access experimental data to use in the project's models, the project will run closely with the Hammond laboratory at the Department of Oncology, University of Oxford. This project falls within the EPSRC "Mathematical Biology" research area.