Mean-field Boolean network model of a signal transduction network

Kochi, Naomi; Matache, Mihaela Teodora

doi:10.1016/j.biosystems.2011.12.001

Cited by 12 publications

(11 citation statements)

References 12 publications

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“…However, we are also adding one of the outlier networks, namely the signal transduction in fibroblast cells network with 130 nodes. The Fibroblast Signaling network has been investigated before in various publications (Kochi and Matache, 2012 ; Kochi et al, 2014 ; Matache and Matache, 2016 ; Puniya et al, 2016 ).…”

Section: Numerical Results and Analysismentioning

confidence: 99%

Identification of Biologically Essential Nodes via Determinative Power in Logical Models of Cellular Processes

et al. 2018

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A variety of biological networks can be modeled as logical or Boolean networks. However, a simplification of the reality to binary states of the nodes does not ease the difficulty of analyzing the dynamics of large, complex networks, such as signal transduction networks, due to the exponential dependence of the state space on the number of nodes. This paper considers a recently introduced method for finding a fairly small subnetwork, representing a collection of nodes that determine the states of most other nodes with a reasonable level of entropy. The subnetwork contains the most determinative nodes that yield the highest information gain. One of the goals of this paper is to propose an algorithm for finding a suitable subnetwork size. The information gain is quantified by the so-called determinative power of the nodes, which is obtained via the mutual information, a concept originating in information theory. We find the most determinative nodes for 36 network models available in the online database Cell Collective (http://cellcollective.org). We provide statistical information that indicates a weak correlation between the subnetwork size and other variables, such as network size, or maximum and average determinative power of nodes. We observe that the proportion represented by the subnetwork in comparison to the whole network shows a weak tendency to decrease for larger networks. The determinative power of nodes is weakly correlated to the number of outputs of a node, and it appears to be independent of other topological measures such as closeness or betweenness centrality. Once the subnetwork of the most determinative nodes is identified, we generate a biological function analysis of its nodes for some of the 36 networks. The analysis shows that a large fraction of the most determinative nodes are essential and involved in crucial biological functions. The biological pathway analysis of the most determinative nodes shows that they are involved in important disease pathways.

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Section: Numerical Results and Analysismentioning

confidence: 99%

Identification of Biologically Essential Nodes via Determinative Power in Logical Models of Cellular Processes

et al. 2018

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“…A Boolean representation of this network has been provided in Helikar et al. (2008), and has been studied further in Kochi and Matache (2012) and Kochi et al. (2014).…”

Section: Determinative Power and Strengthmentioning

confidence: 99%

Logical Reduction of Biological Networks to Their Most Determinative Components

Matache

2016

Bull Math Biol

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Boolean networks have been widely used as models for gene regulatory networks, signal transduction networks, or neural networks, among many others. One of the main difficulties in analyzing the dynamics of a Boolean network and its sensitivity to perturbations or mutations is the fact that it grows exponentially with the number of nodes. Therefore, various approaches for simplifying the computations and reducing the network to a subset of relevant nodes have been proposed in the past few years. We consider a recently introduced method for reducing a Boolean network to its most determinative nodes that yield the highest information gain. The determinative power of a node is obtained by a summation of all mutual information quantities over all nodes having the chosen node as a common input, thus representing a measure of information gain obtained by the knowledge of the node under consideration. The determinative power of nodes has been considered in the literature under the assumption that the inputs are independent in which case one can use the Bahadur orthonormal basis. In this article, we relax that assumption and use a standard orthonormal basis instead. We use techniques of Hilbert space operators and harmonic analysis to generate formulas for the sensitivity to perturbations of nodes, quantified by the notions of influence, average sensitivity, and strength. Since we work on finite-dimensional spaces, our formulas and estimates can be and are formulated in plain matrix algebra terminology. We analyze the determinative power of nodes for a Boolean model of a signal transduction network of a generic fibroblast cell. We also show the similarities and differences induced by the alternative complete orthonormal basis used. Among the similarities, we mention the fact that the knowledge of the states of the most determinative nodes reduces the entropy or uncertainty of the overall network significantly. In a special case, we obtain a stronger result than in previous works, showing that a large information gain from a set of input nodes generates increased sensitivity to perturbations of those inputs.

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“…Canalizing functions may induce stability in certain genetic networks [ 24 ]. The nodes of the fibroblast network model [ 7 ] obey various Boolean rules including canalizing functions with one or more canalizing inputs, or nested/partially nested canalizing functions [ 32 ].…”

Section: Methodsmentioning

confidence: 99%

“…Furthermore, we also consider 100 different initial states of the network for each of the mutations above. In our previous analysis of a Boolean network model for the fibroblast network considered in this work [ 32 ], we noticed that the different types of Boolean rules governing the node dynamics lead to similar equilibria when modifying some of the parameters. These rules include various canalizing functions, threshold functions, and bias functions.…”

Section: Methodsmentioning

confidence: 99%

“…The signal transduction network of a generic fibroblast cell considered in this paper consists of several main signaling pathways, including the receptor tyrosine kinase, the G-protein coupled receptor, and the integrin signaling pathway. A Boolean representation of this network has been provided in [ 7 ], and has been studied further in [ 32 ]. Furthermore, the fully annotated signal transduction model is freely available for simulations and/or download via the Cell Collective software from www.thecellcollective.org [ 33 ],[ 34 ].…”

Section: Network Node Attributes and Target Measurementioning

confidence: 99%

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Sensitivity analysis of biological Boolean networks using information fusion based on nonadditive set functions

et al. 2014

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BackgroundAn algebraic method for information fusion based on nonadditive set functions is used to assess the joint contribution of Boolean network attributes to the sensitivity of the network to individual node mutations. The node attributes or characteristics under consideration are: in-degree, out-degree, minimum and average path lengths, bias, average sensitivity of Boolean functions, and canalizing degrees. The impact of node mutations is assessed using as target measure the average Hamming distance between a non-mutated/wild-type network and a mutated network.ResultsWe find that for a biochemical signal transduction network consisting of several main signaling pathways whose nodes represent signaling molecules (mainly proteins), the algebraic method provides a robust classification of attribute contributions. This method indicates that for the biochemical network, the most significant impact is generated mainly by the combined effects of two attributes: out-degree, and average sensitivity of nodes.ConclusionsThe results support the idea that both topological and dynamical properties of the nodes need to be under consideration. The algebraic method is robust against the choice of initial conditions and partition of data sets in training and testing sets for estimation of the nonadditive set functions of the information fusion procedure.

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Mean-field Boolean network model of a signal transduction network

Cited by 12 publications

References 12 publications

Identification of Biologically Essential Nodes via Determinative Power in Logical Models of Cellular Processes

Identification of Biologically Essential Nodes via Determinative Power in Logical Models of Cellular Processes

Logical Reduction of Biological Networks to Their Most Determinative Components

Sensitivity analysis of biological Boolean networks using information fusion based on nonadditive set functions

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