Abstract
In experimental studies, it has been found that certain cell lines are more sensitive to low-dose radiation than would be expected from the classical Linear–Quadratic model (LQ model). In fact, it is frequently observed that cells incur more damage at low dose (say 0.3 Gy) than at higher dose (say 1 Gy). This effect has been termed hyper-radiosensitivity (HRS). The effect depends on the type of cells and on their phase in the cell cycle when radiation is applied. Experiments have shown that the G2-checkpoint plays an important role in the HRS effects. Here we design and analyze a differential equation model for the cell cycle that includes G2-checkpoint dynamics and radiation treatment. We fit the model to surviving fraction data for different cell lines including glioma cells, prostate cancer cells, as well as to cell populations that are enriched in certain phases of the cell cycle. The HRS effect is measured in the literature through \(\frac{\alpha _s}{\alpha }\), the ratio of slope \(-\,\alpha _s\) of the surviving fraction curve at zero dose to slope \(-\,\alpha \) of the corresponding LQ model. We derive an explicit formula for this ratio and we show that it corresponds very closely to experimental observations. Finally, we identify the dependence of this ratio on the surviving fraction at 2 Gy. It was speculated in the literature that such dependence exists. Our theoretical analysis will help to more systematically identify the HRS in cell lines, and opens doors to analyze its use in cancer treatment.
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Acknowledgements
The authors are grateful for the feedback from the Journal Club of the Collaborative Mathematical Biology Group at the University of Alberta. OO is supported by the University of Alberta President’s International Doctoral Award and Queen Elizabeth II Graduate Scholarship - Doctoral level, GdeV and TH are supported by the Natural Sciences and Engineering Research Council of Canada (NSERC).
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Dedicated to the memory of Professor Karl-Peter Hadeler.
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Olobatuyi, O., de Vries, G. & Hillen, T. Effects of G2-checkpoint dynamics on low-dose hyper-radiosensitivity. J. Math. Biol. 77, 1969–1997 (2018). https://doi.org/10.1007/s00285-018-1236-8
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DOI: https://doi.org/10.1007/s00285-018-1236-8
Keywords
- Linear–Quadratic model
- Induced Repair model
- Early G2 checkpoint
- Increased radioresistance
- Hyper-radiosensitivity
- Cell cycle
- Cell cycle arrest
- Mitotic catastrophe