Mechanisms of Gene Regulation: Boolean Network Models of the Lactose Operon in Escherichia coli

Robeva, Raina; Kirkwood, Bessie H.; Davies, Robin

doi:10.1016/b978-0-12-415780-4.00001-6

Cited by 5 publications

(6 citation statements)

References 17 publications

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“…Note that Equations (14)- (16) show the example of S with several terms but in our example we have established S with only one term (Equation 13);…”

Section: The Couple Of the Example Has A Conflict Because The Pathwaymentioning

confidence: 76%

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Modelling Biological Systems: A New Algorithm for the Inference of Boolean Networks

et al. 2021

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Biological systems are commonly constituted by a high number of interacting agents. This great dimensionality hinders biological modelling due to the high computational cost. Therefore, new modelling methods are needed to reduce computation time while preserving the properties of the depicted systems. At this point, Boolean Networks have been revealed as a modelling tool with high expressiveness and reduced computing times. The aim of this work has been to introduce an automatic and coherent procedure to model systems through Boolean Networks. A synergy that harnesses the strengths of both approaches is obtained by combining an existing approach to managing information from biological pathways with the so-called Nested Canalising Boolean Functions (NCBF). In order to show the power of the developed method, two examples of an application with systems studied in the bibliography are provided: The epithelial-mesenchymal transition and the lac operon. Due to the fact that this method relies on directed graphs as a primary representation of the systems, its applications exceed life sciences into areas such as traffic management or machine learning, in which these graphs are the main expression of the systems handled.

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“…Note that Equations (14)- (16) show the example of S with several terms but in our example we have established S with only one term (Equation 13);…”

Section: The Couple Of the Example Has A Conflict Because The Pathwaymentioning

confidence: 76%

“…Canalisation enables species to preserve and develop sophisticated structures, e.g., eyes, throughout evolution. Since NCBF represent this phenomenon, they have been proven effective to model biological systems [12,14,16].…”

Section: Introductionmentioning

confidence: 99%

Modelling Biological Systems: A New Algorithm for the Inference of Boolean Networks

et al. 2021

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“…Gene Regulatory Networks (GRNs) form a flexible modeling scheme for synthesizing and analyzing the interactions of clusters of up to thousands of factors such as functional genes, enzymes, and other proteins in a cell (all loosely called genes) that affect one another's function in a particular biological process, such as the successfully deciphered lac operon in Escherichia coli [18][19][20]. A GRN consists of a wiring diagram, which is a labeled digraph on n vertices (genes), where a directed edge indicates an influence of the gene at the initial vertex on the one at the terminal vertex.…”

Section: Structure and Examples Of Grnsmentioning

confidence: 99%

Spectral Functional-Digraph Theory, Stability, and Entropy for Gene Regulatory Networks

Akman

2018

Front. Appl. Math. Stat.

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Spectral graph theory is an indispensable tool in the rich interdisciplinary field of network science, which includes as objects ordinary abstract graphs as well as directed graphs such as the Internet, semantic networks, electrical circuits, and gene regulatory networks (GRN). However, its contributions sometimes get lost in the code, and network theory occasionally becomes overwhelmed with problems specific to undirected graphs. In this paper, we will study functional digraphs, calculate the eigenvalues and eigenvectors of their adjacency matrices, describe how to compute their automorphism groups, and define a notion of entropy in terms of their symmetries. We will then introduce gene regulatory networks (GRNs) from scratch, and consider their phase spaces, which are functional digraphs describing the deterministic progression of the overall state of a GRN. Finally, we will redefine the stability of a GRN and assert that it is closely related to the entropy of its phase space.

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“…In this paper we study the simplified mesendoderm gene regulatory network (mGRN) for two species, Xenopus laevis and Ambystoma mexicanum using Boolean net-works [8,9,12,10,11]. Both Xenopus (the frog) and Ambystoma mexicanum (the axolotl) are amphibians, but from different orders, and these differences extend to the topology of the mGRN for both species [1].…”

Section: Introductionmentioning

confidence: 99%

“…It has been shown that these discrete models can capture key dynamic features of biological networks and can be used for hypothesis generation ( [9], [11]). Finally, these models tend to be more intuitive and easility accessible to life scientists, aiding in their increasing popularity in systems biology [8].…”

Section: Introductionmentioning

confidence: 99%

Modeling and Analysis of Germ Layer Formations Using Finite Dynamical Systems

Garza¹,

Eberle²,

Eager³

2016

SPORA

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The development of an embryo from a fertilised egg to a multicellular organism proceeds through numerous steps, with the formation of the three germ layers (endoderm, mesoderm, ectoderm) being one of the first. In this paper we study the mesendoderm (the tissue that collectively gives rise to both mesoderm and endoderm) gene regulatory network for two species, Xenopus laevis and the axolotl (Ambystoma mexicanum) using Boolean networks. We find that previously-established bistability found in these networks can be reproduced using this Boolean framework, provided that some assumptions used in previously-published differential equations models are relaxed. We conclude by discussing our findings in relation to previous work modeling gene regulatory networks with Boolean network models.

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Mechanisms of Gene Regulation: Boolean Network Models of the Lactose Operon in Escherichia coli

Cited by 5 publications

References 17 publications

Modelling Biological Systems: A New Algorithm for the Inference of Boolean Networks

Modelling Biological Systems: A New Algorithm for the Inference of Boolean Networks

Spectral Functional-Digraph Theory, Stability, and Entropy for Gene Regulatory Networks

Modeling and Analysis of Germ Layer Formations Using Finite Dynamical Systems

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