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

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

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 cancer chemotherapy it is important to determine whether certain cell-cycle-specific-drug combinations or the order of drug 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 the treatment of cancer. The mathematical model we will present in this talk distinguishes between different cell-cycle phases and will look at the effect of cell-cycle-specific drugs such as seliciclib, docetaxel and cisplatin, alone and in combination on tumour regression. The model will also focus 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. The long term aim of the research is to provide insight for development of cell-cycle-specific anti-cancer drugs and information on drug scheduling, dosage and interval time to determine an optimal drug delivery strategy to improve patient treatment.