Optimal Fault Detection in Stochastic Boolean Regulatory Networks

Boolean networks have emerged as an effective model of the dynamical behavior of regulatory circuits consisting of bi-stable components, e.g. genes that can be in an activated or suppressed transcriptional state. Such Boolean circuits are not deterministic, nor are they directly observable. We present a methodology for fault detection in stochastic Boolean dynamical systems observed though noisy continuous measurements. The methodology utilizes a single time series and does not require any prior knowledge about the fault model. It is a change detection model based on the principle of uncorrelated innovations based on the optimal state estimator, which in this case is the Boolean Kalman Filter (BKF). We carry out a numerical simulations using a Boolean model for the p53-MDM2 negative feedback loop with stuck-at faults, observed through noisy continuous measurements. The results show that the methodology is able to detect the time of the fault with close accuracy, without any prior knowledge about the fault model.