Abstract

© 2014, Society for Mathematical Biology. Genetic instability promotes cancer progression as well as hinders it. With the loss of tumor suppressor gene function known to be responsible for a high percentage of breast and colorectal cancer, it is important to understand how genetic instability can be orchestrated toward carcinogenesis. In this context, this paper gives a complete characterization of the optimal cell mutation rate for the fastest time to a target cancerous cell population through the loss of both copies of a tumor suppressor gene. Similar to the oncogene activation model previously analyzed, the optimal mutation rate of the present two-step model changes qualitatively with the convexity of the cell death rate. However, the structure of the Hamiltonian for the new model differs significantly and intrinsically from that of the one-step model, and a completely new approach is needed for the solution of the present two-step problem. Considerable insight into the biology of optimal switching is extracted from numerical results for cases with nonconvex death rates.