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Boolean Modeling of Biological Networks

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Encyclopedia of Complexity and Systems Science

Definition of the Subject

Boolean Networks (BN) are a class of discrete dynamical systems that can be characterized by the interaction of a set of Booleanvariables. Random Boolean Networks (RBN), which are ensembles of random network structures, were first introduced by Stuart Kauffman in 1969 asa simple model class for studying dynamical properties of gene regulatory networks [1,2]. Since then, Boolean Networks have been used as generic models fordynamics of complex systems of interacting entities, such as social and economic networks, neural networks, as well as gene and protein interactionnetworks. Despite their conceptual simplicity, Boolean Networks exhibit complex nonlinear behaviors that are, to this day, a challenging object ofinvestigation for theoretical physicists and mathematicians. Further, a discretization of gene expression is often regarded as an experimentallyjustifiable simplification [3,4], making Booleannetwork models attractive tools for the application oriented...

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Abbreviations

Connectivity matrix:

In a Boolean network model, the information about who is interacting with whom is stored in the connectivity matrix. This static wiring diagram can be described by parameters from graph theory, such as the degree distributions of its elements or nodes.

Activity, sensitivity :

Boolean functions define how elements of a network interact. Activity and sensitivity are parameters describing the dynamic properties of single network elements or nodes. The activity of a node measures its influence on another node and conversely, the sensitivity of a node measures how sensitive it is to random changes in one of its inputs.

Phase transition and criticality:

Regarding the propagation of perturbations, one can distinguish between an ordered phase, where perturbations will not influence the network dynamics and an chaotic phase, where small perturbations will increase over time. Networks that operate at the transition of these two phases, such that perturbations are neither attenuated nor amplified on average, are called critical.

Attractors:

In Boolean networks, dynamically stable patterns are called attractors. In their biological context, attractors may be interpreted as different cell types in models of cell differentiation or as cell states in models of cell signaling. Analyzing the influence of perturbations on attractor dynamics is thus of pivotal biological interest.

Relevant and irrelevant nodes :

Only the perturbation of certain elements will move the system from one attractor to another. These dynamically relevant nodes are potential lever points for system intervention.

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Author information

Authors and Affiliations

  1. Fakultät für Physik, Ludwig Maximilians Universität, München, Germany

    Peter Krawitz

  2. Institute for Systems Biology, Department of Bioengineering University ofWashington, Seattle, USA

    Ilya Shmulevich

Authors
  1. Peter Krawitz
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  2. Ilya Shmulevich
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Editor information

Editors and Affiliations

  1. RAMTECH LIMITED, 122 Escalle Lane, Larkspur, CA, 94939, USA

    Robert A. Meyers Ph. D. (Editor-in-Chief) (Editor-in-Chief)

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© 2009 Springer-Verlag

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Krawitz, P., Shmulevich, I. (2009). Boolean Modeling of Biological Networks. In: Meyers, R. (eds) Encyclopedia of Complexity and Systems Science. Springer, New York, NY. https://doi.org/10.1007/978-0-387-30440-3_40

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