An optimal Bayesian intervention policy in response to unknown dynamic cell stimuli

Interventions in gene regulatory networks (GRNs) aim to restore normal functions of cells experiencing abnormal behavior, such as uncontrolled cell proliferation. The dynamic, uncertain, and complex nature of cellular processes poses significant challenges in determining the best interventions. Most existing intervention methods assume that cells are unresponsive to therapies, resulting in stationary and deterministic intervention solutions. However, cells in unhealthy conditions can dynamically respond to therapies through internal stimuli, leading to the recurrence of undesirable conditions. This paper proposes a Bayesian intervention policy that adaptively responds to cell dynamic responses according to the latest available information. The GRNs are modeled using a Boolean network with perturbation (BNp), and the fight between the cell and intervention is modeled as a two-player zero-sum game. Assuming an incomplete knowledge of cell stimuli, a recursive approach is developed to keep track of the posterior distribution of cell responses. The proposed Bayesian intervention policy takes action according to the posterior distribution and a set of Nash equilibrium policies associated with all possible cell responses. Analytical results demonstrate the superiority of the proposed intervention policy against several existing intervention techniques. Meanwhile, the performance of the proposed policy is investigated through comprehensive numerical experiments using the p53-MDM2 negative feedback loop regulatory network and melanoma network. The results demonstrate the empirical convergence of the proposed policy to the optimal Nash equilibrium policy.