Gene regulatory network state estimation from arbitrary correlated measurements

Background: Advancements in gene expression technology allow acquiring cheap and abundant data for analyzing cell behavior. However, these technologies produce noisy, and often correlated, measurements on the transcriptional states of genes. The Boolean network model has been shown to be effective in capturing the complex dynamics of gene regulatory networks (GRNs). It is important in many applications, such as anomaly detection and optimal intervention, to be able to track the evolution of the Boolean states of a gene regulatory network using noisy time-series transcriptional measurements, which may be correlated in time. Results: We propose efficient estimators for the Boolean states of GRNs using correlated time-series transcriptional measurements, where the nature of the correlation and of the measurements themselves are entirely arbitrary. More specifically, we propose new algorithms based on a hypothesis tree to compute optimal minimummean square error (MMSE) filtering and smoothing state estimators for a Partially-Observed Boolean Dynamical System (POBDS) with correlated measurements. The algorithms are exact but may be computationally expensive for large state spaces or long time horizons, in which case a process for pruning the hypothesis tree is employed to obtain an approximation of the optimal MMSE estimators, while keeping computation tractable. Performance is assessed through a comprehensive set of numerical experiments based on the p53-MDM2 negative-feedback loop Boolean regulatory network, where the standard Boolean Kalman Filter (BKF) and Boolean Kalman Smoother (BKS) for uncorrelated measurements are compared to the corresponding new estimators for correlated measurements, called BKF-CORR and BKS-CORR, respectively.