# A mathematical model for the in vitro kinetics of the anti-cancer agent topotecan

#### Model Status

This is the original unchecked version of the model imported from the previous CellML model repository, 24-Jan-2006.

#### Model Structure

The compartmental approach to modelling the kinetics of a drug can be used to provide a mathematical description of the characteristcis of that drug and how it is delivered to a particular target. With this aim in mind, Evans *et al.* propose a compartmental model for the anti-cancer agent topotecan (TPT). The mathematical equations used to describe the physiological processes are based on biological assumptions, and the model parameters are estimated using high performance liquid chromatograpy data.

TPT is a water soluble anti-cancer drug which has been approved for use against ovarian and small cell lung carcinomas. The drug's molecular target is DNA topoismerase I, an enzyme which resolves topological distortions in DAN by cleavage and re-ligation of one strand of the double stranded helix. TPT administration traps topoismerase I in a covalently bound intermediate complex with DNA. When the DNA replication machinary collides with this complex, the double stranded DNA breaks apart.

The activity of TPT is pH dependent. AT physiological pH the active form of the agent is not stable, and it undergoes reversible hydrolisis to form the more stable, inactive form. The reversible hydrolisis of TPT is first modelled by a linear, two compartment model. This simple model then forms the basis of a cell based model for drug activity in live cell experiments (see the figure below).

The cell based model has been described here in CellML (the raw CellML description of the Evans *et al.* 2004 model can be downloaded in various formats as described in ).

The complete original paper reference is cited below:

A mathematical model for the in vitro kinetics of the anti-cancer agent topotecan, Neil D. Evans, Rachel J. Errington, Micchael Shelley, Graham P. Feeney, Michael J. Chapman, Keith R. Godfrey, Paul J. Smith, Michael J. Chappell, 2004,
*Mathematical Biosciences*
, 189, 185-217. (Full text (HTML) and PDF versions of the article are available to subscribers on the *Mathematical Biosciences* website.) PubMed ID: 15094319

Schematic diagram of the mathematical model used to investigate the effect of injecting the anticancer drug TPT into a culture of human lymphoma cells. |