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

The cell cycle is a sequence of events through which a cell grows by duplication of its contents and then divides into two genetically identical daughter cells. Eukaryotic cells have a distinct control system of biochemical switches which regulate progression through the cell cycle, and respond to internal and external signals. 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. Major events in the cell cycle are triggered when a group of enzymes called cyclin dependent kinases (CDKs) are activated by association with cyclin. CDK-cyclin complexes are regulated primarily by phosphorylation by CDK-activating kinase (CAK), inhibition by CKI binding, gene transcription, proteolysis and location in the cell of the cell cycle regulatory components. Modelling the cell cycle and checkpoint mechanisms has implications in developing new drug therapies and optimising new drug development for the treatment of cancer cells with cell cycle dependent drugs. The vast number of proteins and interactions involved make the cell cycle an extremely complex system and to understand the underlying mechanisms completely we must use mathematical modelling. Mutations of restriction point regulators are extremely common in human cancer. The regulator p21(WAF1) binds to the Proliferating Cell Nuclear Antigen (PCNA) and inhibits DNA replication, a fact that some biopharmaceutical companies are using as a starting point for rational drug design. Therefore, in this presentation we focus on modelling G1/S phase, specifically focusing on pathways involving p21, p53 and CDK2/cyclinE. We begin using a system of coupled, nonlinear ordinary differential equations describing key intracellular signalling pathways governing the cell cycle, and analyse them using bifurcation theory and numerical analysis. The long term aim is to develop drugs which target specific points of the cell cycle, are cancer specific and are beneficial to patient treatment.

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