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Issue 184: The Galton board of phenotypic plasticity and resistance to therapy. An untreated tumour falls through a Galton board organized by treatment sensitivity, where the left most trajectories represent treatment resistance (purple cells) and the rightmost trajectories represent regrowth of a sensitive (orange cells) tumour. Transitions between drug sensitive and tolerant states is random and illustrated as a tumour bouncing in either direction-- towards drug resistance or sensitivity. Applying treatment closes the gates and biases the tumour’s trajectory towards resistance or regrowth. The tumour’s path is determined by both its current state; its history, as an explicit representation of stochastic phenotypic inheritance; and when treatment is applied, with the aim of selectively closing gates to direct the tumour towards extinction. In our recent work, we developed a simple mathematical model of this non-genetic phenotypic memory and fit the model to ex vivo NSCLC data. Using a combination of classical techniques from population dynamics, we derived simple thresholds that determine which gates to close to direct the tumours evolution away from resistance and towards extinction.