Figure 1. Mathematical model of BRCA-associated cancer progression (A) until diagnosis and (B) during treatment.

(A) We consider an exponentially growing population of cancer cells starting from a single cell that has potential mutation targets within two genomic regions. There are two types of mutations: one facilitates (epi)genetic mutations at rate u ₁ and the other accelerates tumor growth at rates u ₂ and u ₃. Cancer cells with functional BRCA and an intact mutation target site for accelerated growth rates are called type-0. Cells with dysfunctional BRCA and an intact mutation target site for accelerated growth rates are called type-1. Cells carrying a mutation that accelerates uncontrollable tumor growth are called type-2 cells. Type-1 and -2 cells emerge from type-0 cells at mutation rates u ₁ and u ₂, respectively. Cells harboring both types of mutations are called type-3 cells. Type-3 cells emerge from either type-1 or -2 cells at mutation rates u ₃ and u ₁, respectively. The growth and death rates of type-0 and -1 cells are r and d, and those of type-2 and -3 cells are a and b, respectively. Once the total cell number reaches a certain size, M, the cancer is diagnosed. (B) To consider the situation during treatment, two populations (type-4 and -5 cells) are added to the model. Type-4 and -5 cells newly arise from type-1 and -3 cells, respectively, at rate u ₄ and are resistant to platinum drugs and PARPis after treatment. The growth and death rates of type-4 cells are r and d, and those of type-5 cells are a and b, respectively. The initial numbers within each type of population at diagnosis are calculated by the analytical equations derived in Eq. (S12), Eq. (S13), and Eq. (S22). We assume that neither type-4 nor -5 cells exist at the time of initial treatment. The reduced growth rates of drug-sensitive and -resistant cells caused by drug treatments are given by γ and η, respectively. Once the total cell number reaches a certain size (1.1 M), the cancer is considered to have relapsed.