Figure 1. Schematic illustration of the model in which inactivation of MSGs is required for the acquisition of metastatic ability.

Cancer-initiating cells that have not yet evolved the ability to metastasize are termed type-0 cells. Type-0 cells give rise to type-1 cells through an alteration in one allele of an MSG with probability u₁ per cell division. Type-1 cells give rise to type-2 cells through another alteration in the other allele of the MSG with probability u₂ per type-1 cell division. Type-2 cells have metastatic ability due to loss of function of an MSG. Once a type-2 cell has been produced, it has a certain probability of emigrating to distant organs, which is denoted by q. The metastasized cells at distant sites are referred to as type-3 cells. The total number of tumor cells upon diagnosis is denoted by M. Cancer cells divide at rate r, a₁, a₂, and a₃ and die at rate d, and b₁, b₂, and b₃, per unit time for type-0, -1, -2, and -3 cells, respectively.