Optimal Fault Detection and Diagnosis in Transcriptional Circuits Using Next-Generation Sequencing

We propose a methodology for model-based fault detection and diagnosis for stochastic Boolean dynamical systems indirectly observed through a single time series of transcriptomic measurements using Next Generation Sequencing (NGS) data. The fault detection consists of an innovations filter followed by a fault certification step, and requires no knowledge about the possible system faults. The innovations filter uses the optimal Boolean state estimator, called the Boolean Kalman Filter (BKF). In the presence of knowledge about the possible system faults, we propose an additional step of fault diagnosis based on a multiple model adaptive estimation (MMAE) method consisting of a bank of BKFs running in parallel. Performance is assessed by means of false detection and misdiagnosis rates, as well as average times until correct detection and diagnosis. The efficacy of the proposed methodology is demonstrated via numerical experiments using a p53-MDM2 negative feedback loop Boolean network with stuck-at faults that model molecular events commonly found in cancer.