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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.

Engineering systems are often composed of many subsystems that interact with each other. These subsystems, referred to as disciplines, contain many types of uncertainty and in many cases are feedback-coupled with each other. In designing these complex systems, one needs to assess the stationary behavior of these systems for the sake of stability and reliability. This requires the system level uncertainty analysis of the multidisciplinary systems, which is often computationally intractable. To overcome this issue, techniques have been developed for capturing the stationary behavior of the coupled multidisciplinary systems through available data of individual disciplines. The accuracy and convergence of the existing techniques depend on a large amount of data from all disciplines, which are not available in many practical problems. Toward this, we have developed an adaptive methodology that adds the minimum possible number of samples from individual disciplines to achieve an accurate and reliable uncertainty propagation in coupled multidisciplinary systems. The proposed method models each discipline function via Gaussian process (GP) regression to derive a closed-form policy. This policy sequentially selects a new sample point that results in the highest uncertainty reduction over the distribution of the coupling design variables. The effectiveness of the proposed method is demonstrated in the uncertainty analysis of an aerostructural system and a coupled numerical example.

Stabilization of complex cyber-physical systems is extremely important in keeping the critical infrastructure and the environment safe. This is, in particular, critical in coupled multidisciplinary systems with several subsystems interacting with each other in an uncertain environment. The design of stabilized complex systems depends on a proper set of inputs to these subsystems, in such a way that the best stationary behavior of these systems is achieved. Despite several attempts for stabilizing the coupled multidisciplinary systems, the existing techniques still have their critical limitations and issues due to the unrealistic deterministic assumption in some cases as well as inability in handling large-scale systems. In this paper, we introduce a Bayesian framework using the combination of Bayesian optimization technique and Gibbs sampling method, which enables scalable, efficient and fast learning of the best input to achieve the best design of multidisciplinary systems. The accuracy and speed of the proposed framework will be demonstrated in numerical experiments using an aerodynamics- structures system and a mathematical example.

Design has become a salient part of most of the scientific and engineering tasks, embracing a wide range of domains including real experimental settings (e.g., material discovery or drug design), simulation-based design, and hyperparameter tuning. Model-based experimental design refers to a broad class of techniques, applicable to domains that a partial knowledge about the underlying process exists. Unlike entropy- based techniques which aim to reduce the whole uncertainty in the process, the mean objective cost of uncertainty (MOCU) is a rigorous statistically-oriented experimental design framework which takes the main objective into account during the decision making. However, the lack of scalability of this framework has restricted its application to domains with very small design spaces. This paper proposes a framework using the combination of Bayesian optimization and MOCU policy, which enables experimental design to much larger design spaces and systems. The reliability, scalability and efficiency of the proposed framework are investigated through experimental design for optimal structural intervention in gene regulatory networks.

This paper proposes an approach for finite-horizon control of partially-observed Boolean dynamical systems (POBDS) with uncertain continuous control input and infinite observation space. To cope with the partial observability of states, the proposed method first maps the POBDS to an unnormalized belief space. The nonlinear dynamics in this continuous belief space are linearized over a nominal trajectory. Then, the optimal feedback controller is derived, based on the well-known linear quadratic regulator (LQR), to push the system to follow the nominal trajectory. This nominal trajectory is computed in a planning stage before starting execution, and updated efficiently during execution, whenever the system is found to deviate from the nominal trajectory. We prove that, under mild regularization conditions, the proposed controller approaches the cost of the nominal trajectory as the linearization error approaches zero. The performance of the proposed controller is demonstrated by numerical experiments with a Melanoma gene regulatory network observed through noisy gene expression measurements.

We present a framework for the simultaneous estimation of state and parameters of partially observed Boolean dynamical systems (POBDS). Simultaneous state and parameter estimation is achieved through the combined use of the Boolean Kalman filter and Boolean Kalman smoother, which provide the minimum mean-square error state estimators for the POBDS model, and maximum-likelihood (ML) parameter estimation; in the presence of continuous parameters, ML estimation is performed using the expectation–maximization algorithm. The performance of the proposed ML adaptive filter is demonstrated by numerical experiments with a POBDS model of gene regulatory networks observed through noisy next-generation sequencing (RNA-seq) time series data using the well-known p53-MDM2 negative-feedback loop gene regulatory model.

In a previous contribution, a method was proposed for on-line fault detection in Boolean gene regulatory networks based on the Boolean Kalman Filter and hypothesis testing on next-generation sequencing (NGS) data. In this paper, we present a related methodology, which differs in two main points: (1) it uses the Boolean Kalman Smoother on the entire data set stored off-line; (2) it employs a maximum-likelihood approach for simultaneous change detection and categorization. The efficacy of the proposed methodology is assessed using a p53-MDM2 negative feedback loop Boolean network with stuck-at faults that model molecular events commonly found in cancer.

Partially-observed Boolean dynamical systems (POBDS) are a general class of nonlinear state-space models that provide a rich framework for modeling many complex dynamical systems. The model consists of a hidden Boolean state process, observed through an arbitrary noisy mapping to a measurement space. The optimal minimum mean-square error (MMSE) POBDS state estimators are the Boolean Kalman Filter and Smoother. However, in many practical problems, the system parameters are not fully known and must be estimated. In this paper, for POBDS under model uncertainty, we derive an optimal Bayesian estimator for state and parameter estimation. The exact algorithms are derived for the case of discrete and finite parameter space, and for general parameter spaces, an approximate Markov-Chain Monte-Carlo (MCMC) implementation is introduced. We demonstrate the performance of the proposed methodology by means of numerical experiments with POBDS models of gene regulatory networks observed through noisy measurements.

Scientists are attempting to use models of ever-increasing complexity, especially in medicine, where gene-based diseases such as cancer require better modeling of cell regulation. Complex models suffer from uncertainty and experiments are needed to reduce this uncertainty. Because experiments can be costly and time-consuming, it is desirable to determine experiments providing the most useful information. If a sequence of experiments is to be performed, experimental design is needed to determine the order. A classical approach is to maximally reduce the overall uncertainty in the model, meaning maximal entropy reduction. A recently proposed method takes into account both model uncertainty and the translational objective, for instance, optimal structural intervention in gene regulatory networks, where the aim is to alter the regulatory logic to maximally reduce the long-run likelihood of being in a cancerous state. The mean objective cost of uncertainty (MOCU) quantifies uncertainty based on the degree to which model uncertainty affects the objective. Experimental design involves choosing the experiment that yields the greatest reduction in MOCU. This article introduces finite-horizon dynamic programming for MOCU-based sequential experimental design and compares it with the greedy approach, which selects one experiment at a time without consideration of the full horizon of experiments. A salient aspect of the article is that it demonstrates the advantage of MOCU-based design over the widely used entropy-based design for both greedy and dynamic programming strategies and investigates the effect of model conditions on the comparative performances.

Most of the existing methodologies for control of Gene Regulatory Networks (GRNs) assume that the immediate cost function at each state and time point is fully known. In this paper, we introduce an optimal control strategy for control of GRNs with unknown or partially-known immediate cost function. Toward this, we adopt a partially-observed Boolean dynamical system (POBDS) model for the GRN and propose an Inverse Reinforcement Learning (IRL) methodology for quantifying the imperfect behavior of experts, obtained via prior biological knowledge or experimental data. The constructed cost function then is used in finding the optimal infinite-horizon control strategy for the POBDS. The application of the proposed method using a single sequence of experimental data is investigated through numerical experiments using a melanoma gene regulatory network.

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 minimum mean 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.

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.

This paper is concerned with developing an adaptive controller for Partially-Observed Boolean Dynamical Systems (POBDS). Assuming that partial knowledge about the system can be modeled by a finite number of candidate models, then simultaneous identification and control of a POBDS is achieved using the combination of a state-feedback controller and a Multiple-Model Adaptive Estimation (MMAE) technique. The proposed method contains two main steps: first, in the offline step, the stationary control policy for the underlying Boolean dynamical system is computed for each candidate model. Then, in the online step, an optimal Bayesian estimator is modeled using a bank of Boolean Kalman Filters (BKFs), each tuned to a candidate model. The result of the offline step along with the estimated state by the bank of BKFs specify the control input that should be applied at each time point. The performance of the proposed adaptive controller is investigated using a Boolean network model constructed from melanoma gene expression data observed through RNA-seq measurements.

Partially-observed Boolean dynamical systems (POBDS) are a general class of nonlinear models with application in estimation and control of Boolean processes based on noisy and incomplete measurements. The optimal minimum mean square error (MMSE) algorithms for POBDS state estimation, namely, the Boolean Kalman filter (BKF) and Boolean Kalman smoother (BKS), are intractable in the case of large systems, due to computational and memory requirements. To address this, we introduce approximate MMSE filtering and smoothing algorithms based on the auxiliary particle filter (APF) method, which are called APF–BKF and APF–BKS, respectively. For joint state and parameter estimation, the APF–BKF is used jointly with maximum-likelihood (ML) methods for simultaneous state and parameter estimation in POBDS models. In the case the unknown parameters are discrete, the proposed ML adaptive filter consists of multiple APF–BKFs running in parallel, in a manner reminiscent of the Multiple Model Adaptive Estimation (MMAE) method in classical linear filtering theory. In the presence of continuous parameters, the proposed ML adaptive filter is based on an efficient particle-based expectation maximization (EM) algorithm for the POBDS model, which is based on a modified Forward Filter Backward Simulation (FFBSi) in combination with the APF–BKS. The performance of the proposed particle-based adaptive filters is assessed through numerical experiments using a POBDS model of the well-known cell cycle gene regulatory network observed through noisy RNA-Seq time series data.

This paper is concerned with the problem of stochastic control of gene regulatory networks (GRNs) observed indirectly through noisy measurements and with uncertainty in the intervention inputs. The partial observability of the gene states and uncertainty in the intervention process are accounted for by modeling GRNs using the partially observed Boolean dynamical system (POBDS) signal model with noisy gene expression measurements. Obtaining the optimal infinite-horizon control strategy for this problem is not attainable in general, and we apply reinforcement learning and Gaussian process techniques to find a near-optimal solution. The POBDS is first transformed to a directly observed Markov decision process in a continuous belief space, and the Gaussian process is used for modeling the cost function over the belief and intervention spaces. Reinforcement learning then is used to learn the cost function from the available gene expression data. In addition, we employ sparsification, which enables the control of large partially observed GRNs. The performance of the resulting algorithm is studied through a comprehensive set of numerical experiments using synthetic gene expression data generated from a melanoma gene regulatory network.

External control of a genetic regulatory network is used for the purpose of avoiding undesirable states, such as those associated with disease. This paper proposes a strategy for state-feedback infinite-horizon control of Partially-Observed Boolean Dynamical Systems (POBDS) using a single time series of Next-Generation Sequencing (NGS) RNA-seq data. A separation principle is assumed, whereby first the optimal stationary policy is obtained offline by solving Bellman's equation, and then an optimal MMSE observer, the Boolean Kalman Filter, is employed for online implementation of the policy using the RNA-seq observations of the evolving system. Performance is investigated using a Boolean network model of the mutated mammalian cell cycle and simulated RNA-seq observations.