title: Fastest time to cancer by loss of tumor suppressor genes.
abstract: Genetic instability promotes cancer progression (by increasing the probability of cancerous mutations) as well as hinders it (by imposing a higher cell death rate for cells susceptible to cancerous mutation). With the loss of tumor suppressor gene function known to be responsible for a high percentage of breast and colorectal cancer (and a good fraction of lung cancer and other types as well), 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 (time-varying) 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 (one-step) oncogene activation model previously analyzed, the optimal mutation rate of the present two-step model changes qualitatively with the convexity of the (mutation rate-dependent) 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 (between corner controls) is extracted from numerical results for cases with nonconvex death rates.
authors.affiliation: Department of Mathematics, University of California, Irvine, Irvine, CA , 92697-3875, USA, hixacyn@gmail.com.
authors.forename: Cynthia
authors.initials: C
authors.lastname: Sanchez-Tapia
authors.forename: Frederic Y M
authors.initials: FY
authors.lastname: Wan
mesh_terms: D063646:Carcinogenesis / Q000235:genetics / Q000473:pathology; D016147:Genes, Tumor Suppressor; D042822:Genomic Instability; D006801:Humans; D055641:Mathematical Concepts; D008957:Models, Genetic; D009369:Neoplasms / Q000235:genetics* / Q000473:pathology; D013997:Time Factors