Modeling Defensive Response of Cells to Therapies: Equilibrium Interventions for Regulatory Networks

A major objective in genomics is to design interventions that can shift undesirable behaviors of such systems (i.e., those associated with cancers) into desirable ones. Several intervention policies have been developed in recent years, including dynamic and structural interventions. These techniques aim at making targeted changes to cell dynamics upon intervention, without considering the cell's defensive mechanisms to interventions. This simplified assumption often leads to early and short-term success of interventions, followed by partial or full recurrence of diseases. This is due to the fact that cells often have dynamic and intelligent responses to interventions through internal stimuli. This paper models gene regulatory networks (GRNs) using the Boolean network with perturbation. The dynamic and adaptive battle between intervention and the cell is modeled as a two-player zero-sum game, where intervention and the cell fight against each other with fully opposite objectives. An optimal intervention policy is obtained as a Nash equilibrium solution, through which the intervention is stochastic, ensuring the optimal solution to all potential cell responses. We analytically analyze the superiority of the proposed intervention policy against existing intervention techniques. Comprehensive numerical experiments using the p53-MDM2 negative feedback loop regulatory network and melanoma network demonstrate the high performance of the proposed method.