Mathematical models of the transitions between endocrine therapy responsive and resistant states in breast cancer.

Endocrine therapy, targeting the oestrogen receptor pathway, is the most common treatment for oestrogen receptor-positive breast cancers. Unfortunately, these tumours frequently develop resistance to endocrine therapies. Among the strategies to treat resistant tumours are sequential treatment (in which second-line drugs are used to gain additional responses) and intermittent treatment (in which a 'drug holiday' is imposed between treatments). To gain a more rigorous understanding of the mechanisms underlying these strategies, we present a mathematical model that captures the transitions among three different, experimentally observed, oestrogen-sensitivity phenotypes in breast cancer (sensitive, hypersensitive and independent). To provide a global view of the transitions between these phenotypes, we compute the potential landscape associated with the model. We show how this oestrogen response landscape can be reshaped by population selection, which is a crucial force in promoting acquired resistance. Techniques from statistical physics are used to create a population-level state-transition model from the cellular-level model. We then illustrate how this population-level model can be used to analyse and optimize sequential and intermittent oestrogen-deprivation protocols for breast cancer. The approach used in this study is general and can also be applied to investigate treatment strategies for other types of cancer.