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Detection of attractors of large Boolean networks via exhaustive enumeration of appropriate subspaces of the state space

Nikolaos Berntenis* and Martin Ebeling

Author Affiliations

Non-Clinical-Safety, F. Hoffmann – La Roche AG, Grenzacherstrasse 124, 4070, Basel, Switzerland

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BMC Bioinformatics 2013, 14:361  doi:10.1186/1471-2105-14-361

Published: 13 December 2013



Boolean models are increasingly used to study biological signaling networks. In a Boolean network, nodes represent biological entities such as genes, proteins or protein complexes, and edges indicate activating or inhibiting influences of one node towards another. Depending on the input of activators or inhibitors, Boolean networks categorize nodes as either active or inactive. The formalism is appealing because for many biological relationships, we lack quantitative information about binding constants or kinetic parameters and can only rely on a qualitative description of the type “A activates (or inhibits) B”. A central aim of Boolean network analysis is the determination of attractors (steady states and/or cycles). This problem is known to be computationally complex, its most important parameter being the number of network nodes. Various algorithms tackle it with considerable success. In this paper we present an algorithm, which extends the size of analyzable networks thanks to simple and intuitive arguments.


We present lnet, a software package which, in fully asynchronous updating mode and without any network reduction, detects the fixed states of Boolean networks with up to 150 nodes and a good part of any present cycles for networks with up to half the above number of nodes. The algorithm goes through a complete enumeration of the states of appropriately selected subspaces of the entire network state space. The size of these relevant subspaces is small compared to the full network state space, allowing the analysis of large networks. The subspaces scanned for the analyses of cycles are larger, reducing the size of accessible networks. Importantly, inherent in cycle detection is a classification scheme based on the number of non-frozen nodes of the cycle member states, with cycles characterized by fewer non-frozen nodes being easier to detect. It is further argued that these detectable cycles are also the biologically more important ones. Furthermore, lnet also provides standard Boolean analysis features such as node loop detection.


lnet is a software package that facilitates the analysis of large Boolean networks. Its intuitive approach helps to better understand the network in question.

Boolean network; Attractor; Fixed state; Cycle; Regulatory network; State space