Oscillations and bistability in the dynamics of cytotoxic reactions mediated by the response of immune cells to solid tumours

In this paper, we study the competition between tumour progression due to cancer cell replication and tumour regression due to immune cell cytotoxicity. We show that the increase of specificity alone during the development of the immune response is not sufficient in general to reject the tumour. Moreover, we describe three distinct and independent mechanisms that can, in the absence of external treatment, produce regular temporally alternating phases of progression and regression: (i) a deviation from homeostasis where the population of cytotoxic cells varies; (ii) a competition for space between replicating and dead cancer cells; (iii) a formation of multi-conjugate cellular complexes where one cytotoxic cell may bind and kill several cancer cells. In the latter case, the coexistence of a low cancer cell population (interpreted as tumour dormancy) and a high population state is observed.