#### Tumor Suppressor Gene and Carcinogenesis

FREDERIC WAN - University of California, Irvine

The tumor suppressor gene (TSG) is known to be instrumental in maintaining homeostasis in cell proliferation. A loss of both copies of the TSG through cell mutation induces carcinogenesis. This talk analyzes the optimal (time-varying) cell mutation rate for the fastest time to a target cancerous cell population as a possible form of Darwinian microevolution. It is shown that the optimal mutation rate of the present 2-step mutation process depends on the convexity of the (mutation rate dependent) cell death rate. For death rates concave in the cell mutation rate, the optimal rate is again shown to be bang-bang and bounds are found for the optimal switch time Ts and the shortest time T to target. For strictly convex death rates, the stationary solution is shown to be well-defined and its range of admissibility is delineated for the development of an appropriate method for obtaining numerical solutions. While these results are similar to the (1-step) oncogene activation model previously analyzed, there is a qualitatively significant difference in the structure of the Hamiltonian between the two models and a completely new approach is needed for the solution of the present problem. Explanations are sought for the qualitative dependence of the optimal cell mutation rate on the convexity of the cell death rate.

**Location:**
209 Eno Hall

**Date/Time: **05/20/14
at
12:30 pm
- 05/20/14
at
1:30 pm

**Category: **Special Seminar

**Department: **EEB