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Point-Based Methodology to Monitor and Control Gene Regulatory Networks via Noisy Measurements

This paper proposes a methodology to monitor and control gene regulatory networks (GRNs) via noisy measurements in an infinite observation space. Toward this end, we employ the partially observed Boolean dynamical system (POBDS) signal model. The proposed methodology consists of offline and online steps. In the offline step, a family of point-based methods is applied to the POBDS model to gather the necessary control policy prior to the online (execution) step. This is accomplished by developing efficient backup and belief expansion processes to make the computation scale with the log of the number of states, as opposed to the complexity of existing point-based methods, which grows with the number of states. In the online step, simultaneous monitoring and control is achieved by a one-step look-ahead search procedure using the optimal state estimation algorithm for the POBDS model, known as the Boolean Kalman filter (BKF), as well as the information gathered in the offline step. The online one-step look-ahead process confers robustness to changes in system dynamics, possibility of starting the execution process before the completion of the offline step. The use of the BKF for simultaneous monitoring and control during the online stage can be key in assessing possible side effects of intervention. The performance of the proposed methodology is investigated through a comprehensive set of numerical experiments using synthetic gene expression data generated from a melanoma GRN.