Effect of aspirin on tumor cell colony formation and evolution

To describe the stochastic dynamics of cellular growth, and in particular, to calculate the chances of generating mutants, we formulate a fully stochastic model of cellular expansion, see also [1]. We consider a stochastic continuous time birth-death process, which represents the growth of a colony of tumor cells. The following parameters are used to describe the kinetics of wild-type cells: Rw stands for the division rate, and Dw for the death rate, with Dw < Rw. Wild type cells can mutate with probability u per cell division. Mutant cells are characterized by the division rate, Rm and the death rate, Dm. We assume that initial, there are N0 wild-type cells and 0 mutant cells in the colony. The size of the colony at the time when the number of mutants is assessed is denoted by N . Please note that in the main text, we referred to the wild type division and death rates as R and D respectively, such that R ≡ Rw, D ≡ Dw. In the supplement, since equations contain more types, the notation Rw and Dw is used for the wild type cells. To describe the birth-death process with mutations, we can use the standard method of probability generating function, see e.g. [1]. Denoting by φiw,im(t) the probability to have iw wild type cells and im mutant cells at time t, the Kolmogorov forward equation for this quantity can be written as: