Mathematical Modelling of the Cell Cycle: Implications for Cancer Treatment with Cell-Cycle-Dependent Chemotherapy Drugs

Kirsty E. Gordon, M.A.J. Chaplain, R.C. Jackson

Abstract:
The cell cycle is a sequence of events through which a cell grows by duplication of its contents and then divides into two daughter cells. The cell cycle can be split into four phases: G1, S, G2 and M. DNA is duplicated in S-phase and the cell divides in M-phase. G1 and G2 are gap phases which allow extra time for cell preparation, growth and to check if conditions are optimal. Eukaryotic cells have a distinct control system of biochemical switches which regulate progression through the cell cycle, and respond to internal and external signals. A damaged cell can be halted by this regulation mechanism, and allowed time to repair itself. In cancer, control of the cell cycle is lost and cells can proliferate even with damaged DNA. Mutations in the cell accumulate leading to a more aggressive state. To optimise chemotherapy it is important to determine whether certain cell-cycle-specific-drug combinations or the order of delivery will produce antagonistic, additive or synergistic affects due to pharmacodynamic or pharmacokinetic interactions. Modelling cell-cycle-specific drug delivery has implications in developing new drug therapies and optimising new drug development for cancer treatment. The mathematical model we present distinguishes between different cell-cycle phases and looks at the effect of cell-cycle-specific drugs such as seliciclib, docetaxel and cisplatin, alone and in combination on tumour regression. The model focuses on the spatial aspect of this problem, using and comparing a variety of mathematical techniques, ranging from a partial differential equation model and an age-structured model, to a cellular automaton model. Results from computational simulations demonstrate cell-cycle-specific anti-cancer drug treatment and possible underlying mechanisms for tumour recurrence. The long term research aim is to provide information for optimal drug delivery to improve patient treatment.

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