Exploration of the intercellular heterogeneity of topotecan uptake into human breast cancer cells through compartmental modelling

A mathematical multi-cell model for the in vitro kinetics of the anti-cancer agent topotecan (TPT) following administration into a culture medium containing a population of human breast cancer cells (MCF-7 cell line) is described. This non-linear compartmental model is an extension of an earlier single-cell type model and has been validated using experimental data obtained using two-photon laser scanning microscopy (TPLSM). A structural identifiability analysis is performed prior to parameter estimation to test whether the unknown parameters within the model are uniquely determined by the model outputs. The full model has 43 compartments, with 107 unknown parameters, and it was found that the structural identifiability result could not be established even when using the latest version of the symbolic computation software Mathematica. However, by assuming that a priori knowledge is available for certain parameters, it was possible to reduce the number of parameters to 81, and it was found that this (Stage Two) model was globally (uniquely) structurally identifiable. The identifiability analysis demonstrated how valuable symbolic computation is in this context, as the analysis is far too lengthy and difficult to be performed by hand.