Pinning Control to Regulate Cellular Response in Cancer for the p53-Mdm2 Genetic Regulatory Network.

This chapter presents the pinning control strategy applied to the p53-Mdm2 regulatory network to achieve a target cellular response in cancer cells. The network, regulated by p300 and HDAC1, is modeled by a system of 14 ordinary differential equations. Based on this model, an oncogenic condition of Mdm2 overexpression is derived and the functional suppression of p53 is simulated as one possible carcinogenic behavior. Then, control action is introduced to induce an increased expression of p53 levels and downregulation of Mdm2 and p53 activation using only three controlled states (pinned nodes) of the network for the first case and two states for the second case, respectively. The analytic results are simulated, which illustrate the feasibility of the proposed control scheme.