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124
Classification of Random Boolean Networks
, 2002
"... We provide the first classification of different types of RandomBoolean Networks (RBNs). We study the differences of RBNs depending on the degree of synchronicity and determinism of their updating scheme. For doing so, we first define three new types of RBNs. We note some similarities and difference ..."
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Cited by 70 (14 self)
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We provide the first classification of different types of RandomBoolean Networks (RBNs). We study the differences of RBNs depending on the degree of synchronicity and determinism of their updating scheme. For doing so, we first define three new types of RBNs. We note some similarities and differences between different types of RBNs with the aid of a public software laboratory we developed. Particularly, we find that the point attractors are independent of the updating scheme, and that RBNs are more different depending on their determinism or nondeterminism rather than depending on their synchronicity or asynchronicity. We also show a way of mapping nonsynchronous deterministic RBNs into synchronous RBNs. Our results are important for justifying the use of specific types of RBNs for modelling natural phenomena.
Graphic Requirements for Multistability and Attractive Cycles in a Boolean Dynamical Framework
, 2008
"... ..."
Abstract machines of systems biology
 Transactions on Computational Systems Biology
, 2005
"... Abstract. Living cells are extremely wellorganized autonomous systems, consisting of discrete interacting components. Key to understanding and modeling their behavior is modeling their system organization. Four distinct chemical toolkits (classes of macromolecules) have been characterized, each com ..."
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Cited by 47 (2 self)
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Abstract. Living cells are extremely wellorganized autonomous systems, consisting of discrete interacting components. Key to understanding and modeling their behavior is modeling their system organization. Four distinct chemical toolkits (classes of macromolecules) have been characterized, each combinatorial in nature. Each toolkit consists of a small number of simple components that are assembled (polymerized) into complex structures that interact in rich ways. Each toolkit abstracts away from chemistry; it embodies an abstract machine with its own instruction set and its own peculiar interaction model. These interaction models are highly effective, but are not ones commonly used in computing: proteins stick together, genes have fixed output, membranes carry activity on their surfaces. Biologists have invented a number of notations attempting to describe these abstract machines and the processes they implement. Moving up from molecular biology, systems biology aims to understand how these interaction models work, separately and together. 1
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.
A Bayesian connectivitybased approach to constructing probabilistic gene regulatory networks
, 2004
"... Motivation: We have hypothesized that the construction of transcriptional regulatory networks using a method that optimizes connectivity would lead to regulation consistent with biological expectations. A key expectation is that the hypothetical networks should produce a few, very strong attractors, ..."
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Cited by 29 (14 self)
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Motivation: We have hypothesized that the construction of transcriptional regulatory networks using a method that optimizes connectivity would lead to regulation consistent with biological expectations. A key expectation is that the hypothetical networks should produce a few, very strong attractors, highly similar to the original observations, mimicking biological state stability and determinism. Another central expectation is that, since it is expected that the biological control is distributed and mutually reinforcing, interpretation of the observations should lead to a very small number of connection schemes.
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.
Epistemology of computational biology: mathematical models and experimental prediction as the basis of their validity
 Biological Systems
, 2006
"... tant for computational biology because these roles determine to a great extent how research in this field should be pursued and how it should relate to biology in general. The present paper examines the epistemology of computational biology from the perspective of modern science, the underlying pri ..."
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Cited by 23 (19 self)
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tant for computational biology because these roles determine to a great extent how research in this field should be pursued and how it should relate to biology in general. The present paper examines the epistemology of computational biology from the perspective of modern science, the underlying principle of which is that a scientific theory must have two parts: (1) a structural model, which is a mathematical construct that aims to represent a selected portion of physical reality and (2) a welldefined procedure for relating consequences of the model to quantifiable observations. We also explore the contingency and creative nature of a scientific theory. Among the questions considered are: Can computational biology form the theoretical core of biology? What is the basis, if any, for choosing one particular model over another? And what is the role of computation in science, and in biology in particular? We examine how this broad epistemological framework applies to important statistical methodologies pertaining to computational biology, such as expressionbased phenotype classification, gene regulatory networks, and clustering. We consider classification in detail, as the epistemological issues raised by classification are related to all computationalbiology topics in which statistical prediction plays a key role. We pay particular attention to classifiermodel validity and its relation to estimation rules.
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.