Adaptive Particle Filtering for Fault Detection in Partially-Observed Boolean Dynamical Systems

We propose a novel methodology for fault detection and diagnosis in partially-observed Boolean dynamical systems (POBDS). These are stochastic, highly nonlinear, and derivativeless systems, rendering difficult the application of classical fault detection and diagnosis methods. The methodology comprises two main approaches. The first addresses the case when the normal mode of operation is known but not the fault modes. It applies an innovations filter (IF) to detect deviations from the nominal normal mode of operation. The second approach is applicable when the set of possible fault models is finite and known, in which case we employ a multiple model adaptive estimation (MMAE) approach based on a likelihood-ratio (LR) statistic. Unknown system parameters are estimated by an adaptive expectation-maximization (EM) algorithm. Particle filtering techniques are used to reduce the computational complexity in the case of systems with large state-spaces. The efficacy of the proposed methodology is demonstrated by numerical experiments with a large gene regulatory network (GRN) with stuck-at faults observed through a single noisy time series of RNA-seq gene expression measurements.

Fault detection and therapeutic intervention in gene regulatory networks using SAT solvers

Random somatic mutations disrupt homeostasis of the cell resulting in various undesirable phenotypes including proliferation. One of the most important questions in systems medicine research is the therapeutic intervention design, which requires the knowledge of these mutations. A single or multiple mutations can occur in the diseases like cancer. These mutations have been successfully modeled as stuck-at faults in the Boolean network model of the underlying regulatory system. Identification of these fault types for multiple stuck-at faults is a non-trivial problem and requires some system theoretic introspection. This manuscript addresses the dual problem of the fault identification and the therapeutic intervention. Both the problems are mapped to the Boolean satisfiability (SAT) problem. The underlying problems are solved using a fast SAT solver. The synthetic and biological examples elucidate the effectiveness of the mapping.

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.

Statistical Detection of Intrinsically Multivariate Predictive Genes

Canalizing genes possess broad regulatory power over a wide swath of regulatory processes. On the other hand, it has been hypothesized that the phenomenon of intrinsically multivariate prediction (IMP) is associated with canalization. However, applications have relied on user-selectable thresholds on the IMP score to decide on the presence of IMP. A methodology is developed here that avoids arbitrary thresholds, by providing a statistical test for the IMP score. In addition, the proposed procedure allows the incorporation of prior knowledge if available, which can alleviate the problem of loss of power due to small sample sizes. The issue of multiplicity of tests is addressed by family-wise error rate (FWER) and false discovery rate (FDR) controlling approaches. The proposed methodology is demonstrated by experiments using synthetic and real gene-expression data from studies on melanoma and ionizing radiation (IR) responsive genes. The results with the real data identified DUSP1 and p53, two well-known canalizing genes associated with melanoma and IR response, respectively, as the genes with a clear majority of IMP predictor pairs. This validates the potential of the proposed methodology as a tool for discovery of canalizing genes from binary gene-expression data. The procedure is made available through an R package.