Dynamic Intervention in Gene Regulatory Networks: A Partially Observed Zero-Sum Markov Game

Gene Regulatory Networks (GRNs) are pivotal in governing diverse cellular processes, such as stress response, DNA repair, and mechanisms associated with complex diseases like cancer. The interventions in GRNs aim to restore the system state to its normal condition by altering gene activities over time. Unlike most intervention approaches that rely on the direct observability of the system state and assume no response of the cell against intervention, this paper models the fight between intervention and cell dynamic response using a partially observed zero-sum Markov game with binary state variables. The paper derives a stochastic intervention policy under partial state observability of genes. The optimal Nash equilibrium intervention policy is first obtained for the underlying system. To overcome the challenges of partial state observability, the paper employs the optimal minimum mean-square error (MMSE) state estimator to estimate the system state, given all available information. The proposed intervention policy utilizes the optimal Nash intervention policy associated with the optimal MMSE state estimator. The performance of the proposed method is examined using numerical experiments on the melanoma regulatory network observed through gene-expression data.