Digital Object Identifier (DOI): 10.1007/s00285-003-0203-0 J. Math. Biol. 47, 295–312 (2003) Mathematical Biology Britta Basse · Bruce C. Baguley · Elaine S. Marshall · Wayne R. Joseph Bruce van Brunt · Graeme Wake · David J. N. Wall A mathematical model for analysis of the cell cycle in cell lines derived from human tumors Received: 25 August 2002 / Revised version: 21 January 2003 / Published online: 15 May 2003 – c  Springer-Verlag 2003 Abstract. The growth of human cancers is characterised by long and variable cell cycle times that are controlled by stochastic events prior to DNA replication and cell division. Treatment with radiotherapy or chemotherapy induces a complex chain of events involving reversible cell cycle arrest and cell death. In this paper we have developed a mathematical model that has the potential to describe the growth of human tumour cells and their responses to therapy. We have used the model to predict the response of cells to mitotic arrest, and have compared the results to experimental data using a human melanoma cell line exposed to the anticancer drug paclitaxel. Cells were analysed for DNA content at multiple time points by flow cytometry. An excellent correspondence was obtained between predicted and experimental data. We discuss possible extensions to the model to describe the behaviour of cell populations in vivo. 1. Introduction The mammalian cell division cycle forms one of the cornerstones of our current understanding of tumour growth in humans and is dominated by four phases, G 1 - phase, S -phase, G 2 -phase and M-phase, with DNA replication occurring in S -phase and mitosis and cell division occurring in M-phase. The transitions from G 1 -phase to S -phase, and from G 2 -phase to M-phase, are controlled by all-or-nothing tran- sitions involving a positive feedback system of cyclin-dependent kinases, cyclins and phosphatases ([16]). These transitions are the likely cause of the highly variable length of the cell cycle, most of which is accounted for by variability in G 1 -phase duration ([22]). Early studies on cell cycle dynamics in cultured cells suggested the existence of a ‘transition probability’ regulating the commitment of G 1 -phase cells to S -phase in order to account for this variability ([28]). In human cancers, the B.C. Baguley, E.S. Marshall, W.R. Joseph: Auckland Cancer Society Research Centre, Faculty of Medical and Health Sciences, University of Auckland, Private Bag 92019, Auckland, New Zealand B. Basse, G.Wake, D.J.N.Wall: Biomathematics Research Centre, University of Canterbury, Private Bag 4800, Christchurch, New Zealand. e-mail: britta.basse@canterbury.ac.nz B. van Brunt: Institute of Fundamental Sciences, Massey University, Private Bag 11 222, Palmerston North, New Zealand. Key words or phrases: Human tumour cells – Flow cytometry – Cell division cycle – Steady state – Exponential growth – Paclitaxel