Scalar Equations for Synchronous Boolean Networks With Biological Applications

Abstract

One way of coping with the complexity of biological systems is to use the simplest possible models which are able to reproduce at least some nontrivial features of reality. Although two value Boolean models have a long history in technology, it is perhaps a little bit surprising that they can also represent important features of living organizms. In this paper, the scalar equation approach to Boolean network models is further developed and then applied to two interesting biological models. In particular, a linear reduced scalar equation is derived from a more rudimentary nonlinear scalar equation. This simpler, but higher order, two term equation gives immediate information about both cycle and transient structure of the network.

An efficient algorithm for computing fixed length attractors based on bounded model checking in synchronous Boolean networks with biochemical applications

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“…For the same GRNs, different modeling methods can be used, such as synchronous (Farrow et al, 2004;Fauré et al, 2006;Remy et al, 2006), asynchronous (Fauré et al, 2006;Garg et al, 2008) and semi-asynchronous (Fauré et al, 2006) models. Dubrova et al (2005) presented a basic algorithm known as BooleNet to identify attractors in synchronous Boolean networks.…”

An efficient algorithm for finding attractors in synchronous Boolean networks with biochemical applications

“…An SBN is a set of n nodes (node 1 , node 2 , node 3 ,..., node n ) which interact with each other in a synchronous manner (Farrow et al, 2004). At each given time t ∈ N each node has only one of two different values: 1 (ON) or 0 (OFF).…”

“…Recently, Heidel (Heidel et al, 2003) and Farrow (Farrow et al, 2004) found the SCAs in synchronous Boolean networks. Zhao (Zhao, 2005) also proved the computing SCAs' methods in synchronous Boolean networks to be a nondeterministic polynomial time (NP) complete problem.…”

Realization of Boolean Control Networks

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