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Background: Single-cell gene expression measurements offer opportunities in deriving mechanistic understanding of complex diseases, including cancer. However, due to the complex regulatory machinery of the cell, gene regulatory network (GRN) model inference based on such data still manifests significant uncertainty. Results:The goal of this paper is to develop optimal classification of single-cell trajectories accounting for potential model uncertainty. Partially-observed Boolean dynamical systems (POBDS) are used for modeling gene regulatory networks observed through noisy gene-expression data. We derive the exact optimal Bayesian classifier (OBC) for binary classification of single-cell trajectories. The application of the OBC becomes impractical for large GRNs, due to computational and memory requirements. To address this, we introduce a particle-based single-cell classification method that is highly scalable for large GRNs with much lower complexity than the optimal solution. Conclusion:The performance of the proposed particle-based method is demonstrated through numerical experiments using a POBDS model of the well-known T-cell large granular lymphocyte (T-LGL) leukemia network with noisy time-series gene-expression 

Partially-observed Boolean dynamical systems (POBDS) are large and complex dynamical systems capable of being monitored through various sensors. However, time, storage, and economical constraints may impede the use of all sensors for estimation purposes. Thus, developing a procedure for selecting a subset of sensors is essential. The optimal minimum mean-square error (MMSE) POBDS state estimator is the Boolean Kalman Filter (BKF) and Smoother (BKS). Naturally, the performance of these estimators strongly depends on the choice of sensors. Given a finite subsets of sensors, for a POBDS with a finite observation space, we introduce the optimal procedure to select the best subset which leads to the smallest expected mean-square error (MSE) of the BKF over a finite horizon. The performance of the proposed sensor selection methodology is demonstrated by numerical experiments with a p53-MDM2 negative-feedback loop gene regulatory network observed through Bernoulli noise.