Bifurcations and critical transitions in cell population dynamics: Why it is so hard to control cancer?*

It is increasingly recognized that development of drug resistance and recurrence in cancer is to some extent driven by treatment-induced cell state transitions, namely from a drug-sensitive to a resilient, stem-cell-like state, instead of solely a selection of mutant cells that ``happen'' to be drug resistant. We have previously postulated non-genetic, non-Darwinian (quasi-Lamarckian) evolution of drug resistance and now provide experimental support for our model for acquisition of resistance: In general, state transition of a cell from one stable phenotype --represented by a high-dimensional attractor state in gene expression space-- to another one requires the destabilization of the original attractor such that cells can, without overcoming an ``energy barrier'', enter the new attractor state (``alternative regime'') that encodes the gene expression profile conferring the resistant, stem-like phenotype. In response to cytotoxic treatment cells undergo such a transition which represents a bifurcation event --and is thus observable as a critical transition. Single-cell resolution gene expression profiles of entire cell populations undergoing such cell state transitions were consistent with two major predictions from the theory: appearance of the equivalent of ``Early Warning Signals'' and emergence of ``rebellious cells''. The latter have undergone a state change in the ``opposite direction''. Indeed, cancer therapy seeks a state transition of tumor cells to the apoptotic state but as predicted by theory, also generates stem-cell like cells, which are the source of recurrence. But experiments now expose a complication due to cell-cell interactions, giving rise to non-linear tumor behaviors which have serious implications for treatment of cancer. Theoretical and practical consequences of this cell-population level resilience will be discussed, including alternatives to cell-killing therapies and possible theoretical limits of ``curability'' of cancer.