Abstract
Boolean networks are important models of biochemical systems, located at the high end of the abstraction spectrum. A number of Boolean gene networks have been inferred following essentially the same method. Such a method first considers experimental data for a typically underdetermined “regulation” graph. Next, Boolean networks are inferred by using biological constraints to narrow the search space, such as a desired set of (fixed-point or cyclic) attractors. We describe Griffin, a computer tool enhancing this method. Griffin incorporates a number of well-established algorithms, such as Dubrova and Teslenko's algorithm for finding attractors in synchronous Boolean networks. In addition, a formal definition of regulation allows Griffin to employ “symbolic” techniques, able to represent both large sets of network states and Boolean constraints. We observe that when the set of attractors is required to be an exact set, prohibiting additional attractors, a naive Boolean coding of this constraint may be unfeasible. Such cases may be intractable even with symbolic methods, as the number of Boolean constraints may be astronomically large. To overcome this problem, we employ an Artificial Intelligence technique known as “clause learning” considerably increasing Griffin's scalability. Without clause learning only toy examples prohibiting additional attractors are solvable: only one out of seven queries reported here is answered. With clause learning, by contrast, all seven queries are answered. We illustrate Griffin with three case studies drawn from the Arabidopsis thaliana literature. Griffin is available at: http://turing.iimas.unam.mx/griffin.
Highlights
Synchronous Boolean networks (Kauffman, 1969), as simple as they are, can encode meaningful biological information (Huang, 1999; Bornholdt, 2001, 2005, 2008; Fisher and Henzinger, 2007)
Our objective is to present and illustrate the practical use of Griffin, a computer tool for the inference of synchronous Boolean networks
The original prototype of Griffin appeared in Rosenblueth et al (2014), where the authors presented a formal framework for the inference of Boolean networks from a standard regulation graph by direct application of a SAT solver to Boolean formulas codifying regulations, fixed-point attractors, and single-point mutations
Summary
Synchronous Boolean networks (Kauffman, 1969), as simple as they are, can encode meaningful biological information (Huang, 1999; Bornholdt, 2001, 2005, 2008; Fisher and Henzinger, 2007) Such models have emerged as valuable candidates for representing dynamics of molecular networks. The inference of network dynamics from experimental data (sometimes called the “inverse problem”) has become increasingly relevant with the advent of high-throughput technologies. Because of their simplicity, synchronous Boolean networks could become excellent. The Supplementary Material includes all query files for the case studies, and a detailed explanation of the syntax used to formulate partially defined fixed-point constraints
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