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Intervention in contextsensitive probabilistic Boolean networks
, 2005
"... Motivation: Intervention in a gene regulatory network is used to help it avoid undesirable states, such as those associated with a disease. Several types of intervention have been studied in the framework of a probabilistic Boolean network (PBN), which is essentially a finite collection of Boolean n ..."
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Cited by 45 (15 self)
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Motivation: Intervention in a gene regulatory network is used to help it avoid undesirable states, such as those associated with a disease. Several types of intervention have been studied in the framework of a probabilistic Boolean network (PBN), which is essentially a finite collection of Boolean networks in which at any discrete time point the gene state vector transitions according to the rules of one of the constituent networks. For an instantaneously random PBN, the governing Boolean network is randomly chosen at each time point. For a contextsensitive PBN, the governing Boolean network remains fixed for an interval of time until a binary random variable determines a switch. The theory of automatic control has been previously applied to find optimal strategies for manipulating external (control) variables that affect the transition probabilities of an instantaneously random PBN to desirably affect its dynamic evolution over a finite time horizon. This paper extends the methods of external control to contextsensitive PBNs.
Optimal infinitehorizon control for probabilistic Boolean networks
 IEEE Transactions on Signal Processing
"... Abstract—External control of a genetic regulatory network is used for the purpose of avoiding undesirable states, such as those associated with disease. Heretofore, intervention has focused on finitehorizon control, i.e., control over a small number of stages. This paper considers the design of opt ..."
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Cited by 35 (14 self)
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Abstract—External control of a genetic regulatory network is used for the purpose of avoiding undesirable states, such as those associated with disease. Heretofore, intervention has focused on finitehorizon control, i.e., control over a small number of stages. This paper considers the design of optimal infinitehorizon control for contextsensitive probabilistic Boolean networks (PBNs). It can also be applied to instantaneously random PBNs. The stationary policy obtained is independent of time and dependent on the current state. This paper concentrates on discounted problems with bounded cost per stage and on averagecostperstage problems. These formulations are used to generate stationary policies for a PBN constructed from melanoma geneexpression data. The results show that the stationary policies obtained by the two different formulations are capable of shifting the probability mass of the stationary distribution from undesirable states to desirable ones. Index Terms—Altering steady state, genetic network intervention, infinitehorizon control, optimal control of probabilistic Boolean networks. I.
Steadystate analysis of genetic regulatory networks modelled by probabilistic Boolean networks
, 2003
"... Probabilistic Boolean networks (PBNs) have recently been introduced as a promising class of models of genetic regulatory networks. The dynamic behaviour of PBNs can be analysed in the context of Markov chains. A key goal is the determination of the steadystate (longrun) behaviour of a PBN by analy ..."
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Cited by 25 (1 self)
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Probabilistic Boolean networks (PBNs) have recently been introduced as a promising class of models of genetic regulatory networks. The dynamic behaviour of PBNs can be analysed in the context of Markov chains. A key goal is the determination of the steadystate (longrun) behaviour of a PBN by analysing the corresponding Markov chain. This allows one to compute the longterm influence of a gene on another gene or determine the longterm joint probabilistic behaviour of a few selected genes. Because matrixbased methods quickly become prohibitive for large sizes of networks, we propose the use of Monte Carlo methods. However, the rate of convergence to the stationary distribution becomes a central issue. We discuss several approaches for determining the number of iterations necessary to achieve convergence of the Markov chain corresponding to a PBN. Using a recently introduced method based on the theory of twostate Markov chains, we illustrate the approach on a subnetwork designed from human glioma gene expression data and determine the joint steadystate probabilities for several groups of genes. Copyright # 2003 John Wiley & Sons, Ltd.
Mappings between Probabilistic Boolean Networks
, 2003
"... Probabilistic Boolean Networks (PBNs) comprise a graphical model based on uncertain rulebased dependencies between nodes and have been proposed as a model for genetic regulatory networks. As with any algebraic strucicf theckxxzkfjx#[xk of important mappings between PBNs isckT#G for both theory ..."
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Cited by 22 (12 self)
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Probabilistic Boolean Networks (PBNs) comprise a graphical model based on uncertain rulebased dependencies between nodes and have been proposed as a model for genetic regulatory networks. As with any algebraic strucicf theckxxzkfjx#[xk of important mappings between PBNs isckT#G for both theory andapplickfjj This paper treats the ckxjH[[kfjj of mappings to alter PBNstruc#V while at the same time maintaining cintaining with the original probability strucilit It ctkx[[jH projecHkfj onto subnetworks, adjuncwork of new nodes, resolution reducuti mappings formed by merging nodes, and morphological mappings on the graph structure of the PBN. It places PBNs in the framework of manysorted algebras and in that context defines homomorphisms between PBNs.
Inference of a Probabilistic Boolean Network from a Single Observed Temporal Sequence
, 2007
"... The inference of gene regulatory networks is a key issue for genomic signal processing. This paper addresses the inference of probabilistic Boolean networks (PBNs) from observed temporal sequences of network states. Since a PBN is composed of a finite number of Boolean networks, a basic observation ..."
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Cited by 19 (6 self)
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The inference of gene regulatory networks is a key issue for genomic signal processing. This paper addresses the inference of probabilistic Boolean networks (PBNs) from observed temporal sequences of network states. Since a PBN is composed of a finite number of Boolean networks, a basic observation is that the characteristics of a single Boolean network without perturbation may be determined by its pairwise transitions. Because the network function is fixed and there are no perturbations, a given state will always be followed by a unique state at the succeeding time point. Thus, a transition counting matrix compiled over a data sequence will be sparse and contain only one entry per line. If the network also has perturbations, with small perturbation probability, then the transition counting matrix would have some insignificant nonzero entries replacing some (or all) of the zeros. If a data sequence is sufficiently long to adequately populate the matrix, then determination of the functions and inputs underlying the model is straightforward. The difficulty comes when the transition counting matrix consists of data derived from more than one Boolean network. We address the PBN inference procedure in several steps: (1) separate the data sequence into “pure ” subsequences corresponding to constituent Boolean networks; (2) given a subsequence, infer a Boolean network; and (3) infer the probabilities of perturbation, the probability of there being a switch between constituent Boolean networks, and the selection probabilities governing
Robust intervention in probabilistic Boolean networks
 IEEE Trans
, 2008
"... Abstract—Probabilistic Boolean networks (PBNs) have been recently introduced as a paradigm for modeling genetic regulatory networks. One of the objectives of PBN modeling is to use the network for the design and analysis of intervention strategies aimed at moving the network out of undesirable state ..."
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Cited by 17 (8 self)
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Abstract—Probabilistic Boolean networks (PBNs) have been recently introduced as a paradigm for modeling genetic regulatory networks. One of the objectives of PBN modeling is to use the network for the design and analysis of intervention strategies aimed at moving the network out of undesirable states, such as those associated with disease, and into desirable ones. To date, a number of intervention strategies have been proposed in the context of PBNs. However, all these techniques assume perfect knowledge of the transition probability matrix of the PBN. Such an assumption cannot be satisfied in practice since the presence of noise and the availability of limited number of samples will prevent the transition probabilities from being accurately determined. Moreover, even if the exact transition probabilities could be estimated from the data, mismatch between the PBN model and the actual genetic regulatory network will invariably be present. Thus, it is important to study the effect of modeling errors on the final outcome of an intervention strategy and one of the goals of this paper is to do precisely that when the uncertainties are in the entries of the transition probability matrix. In addition, the paper develops a robust intervention strategy that is obtained by minimizing the worstcase cost over the uncertainty set. Index Terms—Control of biological networks, estimation errors, robust dynamic programming, robust minimax control, perturbation bounds. I.
Effect of Function Perturbation on the Steadystate Distribution of Genetic regulatory Networks
 Optimal Structural Intervention’, IEEE Transactions and Signal Processing
, 2008
"... Abstract—The dynamics of a rulebased gene regulatory network are determined by the regulatory functions in conjunction with whatever probability distributions are involved in network transitions. In the case of Boolean networks (BNs) and, more generally, probabilistic Boolean networks (PBNs), the ..."
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Cited by 14 (8 self)
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Abstract—The dynamics of a rulebased gene regulatory network are determined by the regulatory functions in conjunction with whatever probability distributions are involved in network transitions. In the case of Boolean networks (BNs) and, more generally, probabilistic Boolean networks (PBNs), there has been a significant amount of investigation into the effect of perturbing gene states, in particular, the design of intervention strategies based on finite or infinitehorizon control polices. This paper considers the less investigated issue of function perturbations. A single function perturbation affects network dynamics and alters the longrun distribution, whereas any individual gene perturbation has only transient effects and does not change the longrun distribution. We derive analytic results for changes in the steadystate distributions of PBNs resulting from modifications to the underlying regulatory rules and apply the derived results to find optimal structural interventions to avoid undesirable states. The results are applied to a WNT5A network and a mammalian cell cycle related network, respectively, to achieve more favorable steadystate distributions and reduce the risk of getting into aberrant phenotypes. Index Terms—Boolean networks (BNs), genetic regulatory networks, Markov chains, metastasis, optimal structural intervention, probabilistic Boolean networks (PBNs), steadystate distribution. I.
Symbolic approaches to finding control strategies in boolean networks
 Proceedings of The Sixth AsiaPacific Bioinformatics Conference, (APBC
, 2008
"... We present an exact algorithm, based on techniques from the field of Model Checking, for finding control policies for Boolean networks (BN) with control nodes. Given a BN, a set of starting states, I, a set of goal states, F, and a target time, t, our algorithm automatically finds a sequence of cont ..."
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Cited by 13 (4 self)
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We present an exact algorithm, based on techniques from the field of Model Checking, for finding control policies for Boolean networks (BN) with control nodes. Given a BN, a set of starting states, I, a set of goal states, F, and a target time, t, our algorithm automatically finds a sequence of control signals that deterministically drives the BN from I to F at, or before time t, or else guarantees that no such policy exists. Despite recent hardnessresults for finding control policies for BNs, we show that, in practice, our algorithm runs in seconds to minutes on over 13,400 BNs of varying sizes and topologies, including a BN model of embryogenesis in D. melanogaster with 15,360 Boolean variables. We then extend our method to automatically identify a set of Boolean transfer functions that reproduce the qualitative behavior of gene regulatory networks. Specifically, we automatically (re)learn a BN model of D. melanogaster embryogenesis in 5.3 seconds, from a Computational cellular and systems modeling is playing an increasingly important role in biology, bioengineering, and medicine. The promise of computer modeling is that it becomes a conduit through which reductionist data can be translated into scientific discoveries, clinical practice, and the design of new technologies. The reality of modeling is that there are still a number of unmet
Bayesian robustness in the control of gene regulatory networks
 Signal Processing, IEEE Transactions on 2009
"... Abstract—The errors originating in the data extraction process, gene selection and network inference prevent the transition probabilities of a gene regulatory network from being accurately estimated. Thus, it is important to study the effect of modeling errors on the final outcome of an intervention ..."
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Cited by 13 (7 self)
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Abstract—The errors originating in the data extraction process, gene selection and network inference prevent the transition probabilities of a gene regulatory network from being accurately estimated. Thus, it is important to study the effect of modeling errors on the final outcome of an intervention strategy and to design robust intervention strategies. Two major approaches applied to the design of robust policies in general are the minimax (worst case) approach and the Bayesian approach. The minimax control approach is typically conservative because it gives too much importance to the scenarios which hardly occur in practice. Consequently, in this paper, we formulate the Bayesian approach for the control of gene regulatory networks. We characterize the errors emanating from the data extraction and inference processes and compare the performance of the minimax and Bayesian designs based on these uncertainties. Index Terms—Bayesian robustness, gene regulatory networks, intervention, parameter estimation, robust control. I.