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Front. Genet. | doi: 10.3389/fgene.2018.00039

Griffin: a tool for symbolic inference of synchronous Boolean molecular networks

  • 1Instituto de Investigaciones en Matematicas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, Mexico
  • 2Facultad de Ingeniería, Universidad Nacional Autónoma de México, Mexico
  • 3Maestría en Ciencias de la Complejidad, Universidad Autónoma de la Ciudad de México, Mexico
  • 4project-team Virtual Plants, Institut national de recherche en informatique et en automatique (INRIA), France
  • 5Centro de Ciencias de la Complejidad, Universidad Nacional Autonoma de Mexico, Mexico

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:

Keywords: Molecular networks, Boolean networks, Model inference, Boolean satisfiability problem, Clause learning, Biological constraints, attractors

Received: 20 Oct 2017; Accepted: 29 Jan 2018.

Edited by:

Marco Pellegrini, Consiglio Nazionale Delle Ricerche (CNR), Italy

Reviewed by:

Xiaodan Fan, The Chinese University of Hong Kong, Hong Kong
David Murrugarra, University of Kentucky, United States  

Copyright: © 2018 Muñoz, Carrillo, Azpeitia and Rosenblueth. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

* Correspondence: Dr. David A. Rosenblueth, Universidad Nacional Autónoma de México, Instituto de Investigaciones en Matematicas Aplicadas y en Sistemas, Apdo 20-126, Ciudad de Mexico, 01000, D.F., Mexico,