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19
Intervention in Gene Regulatory Networks Via a Stationary Meanfirstpassagetime Control Policy
 IEEE Transactions on Biomedical Engineering
, 2008
"... Abstract—A prime objective of modeling genetic regulatory networks is the identification of potential targets for therapeutic intervention. To date, optimal stochastic intervention has been studied in the context of probabilistic Boolean networks, with the control policy based on the transition p ..."
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Abstract—A prime objective of modeling genetic regulatory networks is the identification of potential targets for therapeutic intervention. To date, optimal stochastic intervention has been studied in the context of probabilistic Boolean networks, with the control policy based on the transition probability matrix of the associated Markov chain and dynamic programming used to find optimal control policies. Dynamical programming algorithms are problematic owing to their high computational complexity. Two additional computationally burdensome issues that arise are the potential for controlling the network and identifying the best gene for intervention. This paper proposes an algorithm based on mean firstpassage time that assigns a stationary control policy for each gene candidate. It serves as an approximation to an optimal control policy and, owing to its reduced computational complexity, can be used to predict the best control gene. Once the best control gene is identified, one can derive an optimal policy or simply utilize the approximate policy for this gene when the network size precludes a direct application of dynamic programming algorithms. A salient point is that the proposed algorithm can be modelfree. It can be directly designed from timecourse data without having to infer the transition probability matrix of the network. Index Terms—Dynamic programming, genetic regulatory networks, mean firstpassage time, probabilistic Boolean networks, stochastic optimal control. I.
Validation of inference procedures for gene regulatory networks
 Curr. Genomics 2007
"... Abstract: The availability of highthroughput genomic data has motivated the development of numerous algorithms to infer gene regulatory networks. The validity of an inference procedure must be evaluated relative to its ability to infer a model network close to the groundtruth network from which th ..."
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Abstract: The availability of highthroughput genomic data has motivated the development of numerous algorithms to infer gene regulatory networks. The validity of an inference procedure must be evaluated relative to its ability to infer a model network close to the groundtruth network from which the data have been generated. The input to an inference algorithm is a sample set of data and its output is a network. Since input, output, and algorithm are mathematical structures, the validity of an inference algorithm is a mathematical issue. This paper formulates validation in terms of a semimetric distance between two networks, or the distance between two structures of the same kind deduced from the networks, such as their steadystate distributions or regulatory graphs. The paper sets up the validation framework, provides examples of distance functions, and applies them to some discrete Markov network models. It also considers approximate validation methods based on data for which the generating network is not known, the kind of situation one faces when using real data.
A tutorial on analysis and simulation of boolean gene regulatory network models
 Curr Genomics
"... Abstract: Driven by the desire to understand genomic functions through the interactions among genes and gene products, the research in gene regulatory networks has become a heated area in genomic signal processing. Among the most studied mathematical models are Boolean networks and probabilistic Boo ..."
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Abstract: Driven by the desire to understand genomic functions through the interactions among genes and gene products, the research in gene regulatory networks has become a heated area in genomic signal processing. Among the most studied mathematical models are Boolean networks and probabilistic Boolean networks, which are rulebased dynamic systems. This tutorial provides an introduction to the essential concepts of these two Boolean models, and presents the uptodate analysis and simulation methods developed for them. In the Analysis section, we will show that Boolean models are Markov chains, based on which we present a Markovian steadystate analysis on attractors, and also reveal the relationship between probabilistic Boolean networks and dynamic Bayesian networks (another popular genetic network model), again via Markov analysis; we dedicate the last subsection to structural analysis, which opens a door to other topics such as network control. The Simulation section will start from the basic tasks of creating state transition diagrams and finding attractors, proceed to the simulation of network dynamics and obtaining the steadystate distributions, and finally come to an algorithm of generating artificial Boolean networks with prescribed attractors. The contents are arranged in a roughly logical order, such that the Markov chain analysis lays the basis for the most part of Analysis section, and also prepares the readers to the topics in Simulation section.
Recent advances in intervention in markovian regulatory networks
 Curr Genomics
, 2009
"... Abstract: Markovian regulatory networks constitute a class of discrete statespace models used to study gene regulatory dynamics and discover methods that beneficially alter those dynamics. Thereby, this class of models provides a framework to discover effective drug targets and design potent therap ..."
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Abstract: Markovian regulatory networks constitute a class of discrete statespace models used to study gene regulatory dynamics and discover methods that beneficially alter those dynamics. Thereby, this class of models provides a framework to discover effective drug targets and design potent therapeutic strategies. The salient translational goal is to design therapeutic strategies that desirably modify network dynamics via external signals that vary the expressions of a control gene. The objective of an intervention strategy is to reduce the likelihood of the pathological cellular function related to a disease. The task of finding an effective intervention strategy can be formulated as a sequential decision making problem for a predefined cost of intervention and a costperstage function that discriminates the geneactivity profiles. An effective intervention strategy prescribes the actions associated with an external signal that result in the minimum expected cost. This strategy in turn can be used as a treatment that reduces the longrun likelihood of gene expressions favorable to the disease. In this tutorial, we briefly summarize the first method proposed to design such therapeutic interventions, and then move on to some of the recent refinements that have been proposed. Each of these recent intervention methods is motivated by practical or analytical considerations. The presentation of the key ideas is facilitated with the help of two case studies.
Optimal control of gene regulatory networks with effectiveness of multiple drugs: a boolean network approach,”
 BioMed Research International,
, 2013
"... Developing control theory of gene regulatory networks is one of the significant topics in the field of systems biology, and it is expected to apply the obtained results to gene therapy technologies in the future. In this paper, a control method using a Boolean network (BN) is studied. A BN is widel ..."
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Developing control theory of gene regulatory networks is one of the significant topics in the field of systems biology, and it is expected to apply the obtained results to gene therapy technologies in the future. In this paper, a control method using a Boolean network (BN) is studied. A BN is widely used as a model of gene regulatory networks, and gene expression is expressed by a binary value (0 or 1). In the control problem, we assume that the concentration level of a part of genes is arbitrarily determined as the control input. However, there are cases that no gene satisfying this assumption exists, and it is important to consider structural control via external stimuli. Furthermore, these controls are realized by multiple drugs, and it is also important to consider multiple effects such as duration of effect and side effects. In this paper, we propose a BN model with two types of the control inputs and an optimal control method with duration of drug effectiveness. First, a BN model and duration of drug effectiveness are discussed. Next, the optimal control problem is formulated and is reduced to an integer linear programming problem. Finally, numerical simulations are shown.
Optimal state estimation for boolean dynamical systems,” 2011
 Proceedings of 45th Annual Asilomar Conference on Signals, Systems, and Computers
"... Abstract—A novel statespace signal model is proposed for discretetime Boolean dynamical systems. State evolution is governed by Boolean functions plus binary noise. The current system state is observed through an arbitrary function plus observation noise. The optimal recursive MMSE estimator for ..."
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Abstract—A novel statespace signal model is proposed for discretetime Boolean dynamical systems. State evolution is governed by Boolean functions plus binary noise. The current system state is observed through an arbitrary function plus observation noise. The optimal recursive MMSE estimator for this model is called the Boolean Kalman filter (BKF), and an efficient algorithm is presented for its exact computation. The BKF is illustrated through an example of optimal context inference for
Verification and Optimal Control of ContextSensitive Probabilistic Boolean Networks Using Model Checking and Polynomial Optimization
"... One of the significant topics in systems biology is to develop control theory of gene regulatory networks (GRNs). In typical control of GRNs, expression of some genes is inhibited (activated) by manipulating external stimuli and expression of other genes. It is expected to apply control theory of G ..."
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One of the significant topics in systems biology is to develop control theory of gene regulatory networks (GRNs). In typical control of GRNs, expression of some genes is inhibited (activated) by manipulating external stimuli and expression of other genes. It is expected to apply control theory of GRNs to gene therapy technologies in the future. In this paper, a control method using a Boolean network (BN) is studied. A BN is widely used as a model of GRNs, and gene expression is expressed by a binary value (ON or OFF). In particular, a contextsensitive probabilistic Boolean network (CSPBN), which is one of the extended models of BNs, is used. For CSPBNs, the verification problem and the optimal control problem are considered. For the verification problem, a solution method using the probabilistic model checker PRISM is proposed. For the optimal control problem, a solution method using polynomial optimization is proposed. Finally, a numerical example on the WNT5A network, which is related to melanoma, is presented. The proposed methods provide us useful tools in control theory of GRNs.
Probabilistic polynomial dynamical systems for reverse engineering of gene regulatory networks
, 2011
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INTRODUCING A PROBABILISTIC STRUCTURE ON SEQUENTIAL DYNAMICAL SYSTEMS, SIMULATION AND REDUCTION OF PROBABILISTIC SEQUENTIAL NETWORKS
, 707
"... Abstract. A probabilistic structure on sequential dynamical systems is introduced here, the new model will be called Probabilistic Sequential Network, PSN. The morphisms of Probabilistic Sequential Networks are defined using two algebraic conditions. It is proved here that two homomorphic Probabilis ..."
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Abstract. A probabilistic structure on sequential dynamical systems is introduced here, the new model will be called Probabilistic Sequential Network, PSN. The morphisms of Probabilistic Sequential Networks are defined using two algebraic conditions. It is proved here that two homomorphic Probabilistic Sequential Networks have the same equilibrium or steady state probabilities if the morphism is either an epimorphism or a monomorphism. Additionally, the proof of the set of PSN with its morphisms form the category PSN, having