Paclitaxel is a major chemotherapeutic drug used to treat a variety of tumour types. Through targeting microtubules, paclitaxel induces abnormal or arrested cell mitosis, leading to tumour shrinkage. The cytotoxicity of paclitaxel limits its clinical use, it is effective only at treating certain tumour types and it is not possible to predict which patients will respond well to treatment. The newer anti-mitotic drugs that have been developed to overcome some of these problems have thus far been less effective than paclitaxel in the clinic. One property of paclitaxel that distinguishes it from many other anti-mitotic drugs is its ability to attain relatively high intracellular concentrations. In this paper we combine experiments and mathematical modelling in order to understand the dynamics of paclitaxel uptake in cell monolayer cultures. We perform a series of experiments on HeLa cell monolayers in which intracellular paclitaxel concentrations are measured under different treatment protocols. We then derive a spatially homogeneous model of paclitaxel dynamics and use Bayesian inference to identify model parameters. When a prediction from the model is found to be inconsistent with a further set of experimental results, we consider a generalisation of the model that accounts for spatio-temporal dynamics and resolve the disparity between theory and experiment. The subsequent inclusion of the spatio-temporal dynamics provides a theoretical frame-work that can be extended to explore drug retention within multilayered, three-dimensional tissues.

A spatio-temporal mathematical model for the dynamics of paclitaxel in cell monolayers