Simplifying Boolean Networks

Richardson, Kurt A.

doi:10.1142/s0219525905000518

Cited by 23 publications

(24 citation statements)

References 19 publications

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“…These models are increasingly employed in modeling systems wherein the values of the kinetic parameters are missing. In order to overcome the complexity associated with the exponential size of the state transition graphs of these models, a number of network reduction methods have been proposed [40][41][42][43][44].…”

Section: Boolean Modelsmentioning

confidence: 99%

A comparative study of qualitative and quantitative dynamic models of biological regulatory networks

Saadatpour

Albert

2016

EPJ Nonlinear Biomed Phys

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Background: Mathematical modeling of biological regulatory networks provides valuable insights into the structural and dynamical properties of the underlying systems. While dynamic models based on differential equations provide quantitative information on the biological systems, qualitative models that rely on the logical interactions among the components provide coarse-grained descriptions useful for systems whose mechanistic underpinnings remain incompletely understood. The middle ground class of piecewise affine differential equation models was proven informative for systems with partial knowledge of kinetic parameters. Methods: In this work we provide a comparison of the dynamic characteristics of these three approaches applied on several biological regulatory network motifs. Specifically, we compare the attractors and state transitions in asynchronous Boolean, piecewise affine and Hill-type continuous models.

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Section: Boolean Modelsmentioning

confidence: 99%

A comparative study of qualitative and quantitative dynamic models of biological regulatory networks

Saadatpour

Albert

2016

EPJ Nonlinear Biomed Phys

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“…Its application to two relatively large signaling networks with more than 10 12 states in their state transition graphs demonstrated its ability to identify all attractors of the underlying systems and to make experimentally testable predictions about the long-term behaviors of the systems. Integration of our reduction method with the removal of leaf nodes (nodes with out-degree=0) as proposed in [2,11,14] can be very effective in simplifying biological regulatory networks.…”

Section: Clearly For Anymentioning

confidence: 99%

“…There have been several efforts to reduce the state space of Boolean models by simplifying the underlying networks. In [2,11,14] a network reduction method based on the removal of stable variables (i.e, variables that stabilize in an attracting state after a transient period, irrespective of updating strategy or initial conditions) and leaf nodes (i.e., nodes with out-degree = 0) was proposed. In another study, Naldi et al [12] proposed a reduction method for simplifying finite-state logical models by iteratively removing nodes without a self loop from the network.…”

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confidence: 99%

A Reduction Method for Boolean Network Models Proven to Conserve Attractors

Saadatpour¹,

Albert²,

Reluga³

2013

SIAM J. Appl. Dyn. Syst.

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Abstract. Boolean models, wherein each component is characterized with a binary (ON or OFF) variable, have been widely employed for dynamic modeling of biological regulatory networks. However, the exponential dependencse of the size of the state space of these models on the number of nodes in the network can be a daunting prospect for attractor analysis of large-scale systems. We have previously proposed a network reduction technique for Boolean models and demonstrated its applicability on two biological systems, namely, the abscisic acid signal transduction network as well as the T-LGL leukemia survival signaling network. In this paper, we provide a rigorous mathematical proof that this method not only conserves the fixed points of a Boolean network, but also conserves the complex attractors of general asynchronous Boolean models wherein at each time step a randomly selected node is updated. This method thus allows one to infer the long-term dynamic properties of a large-scale system from those of the corresponding reduced model. Key words. Boolean models, Network reduction, Asynchronous methods, Attractors, Biological regulatory networks AMS subject classifications. 92C42, 37G351. Introduction. The ever-accelerating pace of experimental data generation has laid the foundation for developing network models of biological systems wherein the components of a system are represented by nodes and the interactions among them by edges. Analyzing these network models and studying their dynamics can unravel unknown facets of the underlying biological systems. Among different dynamic modeling approaches, discrete models, in which each component is assumed to have a finite number of qualitative states, have been increasingly employed in modeling biological regulatory networks [10,18,19,20,23]. The simplest discrete dynamic models are the so-called Boolean models that assume only two states (ON or OFF) for each component [8,21].Since Boolean models are parameter free, they serve as a suitable starting point for modeling biological systems for which a detailed kinetic characterization of the interactions is not available. In particular, attractor analysis of these models is of immense biological importance as it can provide valuable insights into the long-term behaviors, i.e. observed phenotypes, of these systems in response to environmental stimuli and internal perturbations [1,5,6,9,15,16]. For example, it allows one to predict the long-term activity levels of components or to determine key components influencing different cellular traits. However, the exponential dependence of the size of the state space of Boolean models on the number of nodes in the network makes the identification of all attractors of even relatively small systems computationally intractable. In particular, it has been proven that determination of the existence of fixed points in Boolean networks is a strong NPcomplete problem [24]. There have been several efforts to reduce the state space of Boolean models by simplifying the underlying networks. In [2...

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“…The process employed to identify and remove the nonconserving loops is detailed in [8]. As network size…”

Section: The Emergence Of a Dynamic Corementioning

confidence: 99%

“…10 6 random Boolean networks with N 5 15 and k 5 2 (with random connections and random transition functions, excluding the two constant functions) were constructed. For each network its dynamic core was determined using the method detailed in [8]. The average dynamical robustness was calculated for both the (unreduced) networks and their associated dynamic cores.…”

Section: Dynamic Robustness Of Complex Networkmentioning

confidence: 99%

Robustness in complex information systems: The role of information “barriers” in Boolean networks

Richardson¹

2009

Complexity

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In this supposed ''information age,'' a high premium is put on the widespread availability of information. Access to as much information as possible is often cited as key to the making of effective decisions. While it would be foolish to deny the central role that information and its flow has in effective decision-making processes, this chapter explores the equally important role of ''barriers'' to information flows in the robustness of complex systems. The analysis demonstrates that (for simple Boolean networks at least) a complex system's ability to filter out, i.e., block, certain information flows is essential if it is not to be beholden to every external signal. The reduction of information is as important as the availability of information.2009 Wiley Periodicals, Inc. Complexity 15: [26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42] 2010

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Simplifying Boolean Networks

Cited by 23 publications

References 19 publications

A comparative study of qualitative and quantitative dynamic models of biological regulatory networks

A comparative study of qualitative and quantitative dynamic models of biological regulatory networks

A Reduction Method for Boolean Network Models Proven to Conserve Attractors

Robustness in complex information systems: The role of information “barriers” in Boolean networks

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