Model descriptions. (A). A simplified model of selenium metabolism and the effects of its metabolites on DNA damage. The level of selenium affects the flux through reactions 1, 2, and 3, and can lead to low amounts of damaged DNA (dmDNA) when peroxide reduction (reaction 2) dominates or higher amounts when direct selenide damage to DNA (reaction 1) or peroxide-induced damage (reaction 3) dominates. A full list of reactions and model parameters is shown on the right. (B). A multistage model represents cancer initiation as the progressive accumulation of mutations. Cells can divide symmetrically at rate β, divide with mutation at rate μ, or die at rate δ. A population of cells Xk(t) with k mutations propagates through the division, death, and mutation of individual cells. When a cell mutates, it leaves the k-mutant population and enters the (k + 1)-mutant population. The initial population of healthy cells X0 produces mutated cells at a fixed rate ν and a cell is considered the first tumor cell when it progresses to a set number of mutations, often set at four, but can also be fit.