Stochastic fluctuations in apoptotic threshold of tumour cells can enhance apoptosis and combat fractional killing

Fractional killing, which is a significant impediment to successful chemotherapy, is observed even in a population of genetically identical cancer cells exposed to apoptosis-inducing agents. This phenomenon arises not from genetic mutation but from cell-to-cell variation in the activation timing and level of the proteins that regulates apoptosis. To understand the mechanism behind the phenomenon, we formulate complex fractional killing processes as a first-passage time (FPT) problem with a stochastically fluctuating boundary. Analytical calculations are performed for the FPT distribution in a toy model of stochastic p53 gene expression, where the cancer cell is killed only when the p53 expression level crosses an active apoptotic threshold. Counterintuitively, we find that threshold fluctuations can effectively enhance cellular killing by significantly decreasing the mean time that the p53 protein reaches the threshold level for the first time. Moreover, faster fluctuations lead to the killing of more cells. These qualitative results imply that fluctuations in threshold are a non-negligible stochastic source, and can be taken as a strategy for combating fractional killing of cancer cells.