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"Antelope": a hybrid-logic model checker for branching-time Boolean GRN analysis

Gustavo Arellano5, Julián Argil5, Eugenio Azpeitia12, Mariana Benítez134, Miguel Carrillo5, Pedro Góngora5, David A Rosenblueth15* and Elena R Alvarez-Buylla12

Author Affiliations

1 Centro de Ciencias de la Complejidad, piso 6, ala norte, Torre de Ingeniería, Universidad Nacional Autónoma de México, Coyoacán, 04510 México D.F., México

2 Laboratorio de Genética Molecular, Desarrollo y Evolución de Plantas, Instituto de Ecología, Universidad Nacional Autónoma de México, 3er Circuito Universitario Exterior, Junto al Jardín Botánico, Coyoacán, 04510 México D.F., México

3 Department of Functional Genomics and Proteomics, Masaryk University, Kotlářská 2, CZ-61137 Brno, Czech Republic

4 CEITEC-Central European Institute of Technology, Masaryk University, Žerotínovo nám. 9, CZ-60177 Brno, Czech Republic

5 Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, Apdo. Postal 20-726, 01000 México D.F., México

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BMC Bioinformatics 2011, 12:490  doi:10.1186/1471-2105-12-490

Published: 22 December 2011



In Thomas' formalism for modeling gene regulatory networks (GRNs), branching time, where a state can have more than one possible future, plays a prominent role. By representing a certain degree of unpredictability, branching time can model several important phenomena, such as (a) asynchrony, (b) incompletely specified behavior, and (c) interaction with the environment. Introducing more than one possible future for a state, however, creates a difficulty for ordinary simulators, because infinitely many paths may appear, limiting ordinary simulators to statistical conclusions. Model checkers for branching time, by contrast, are able to prove properties in the presence of infinitely many paths.


We have developed Antelope ("Analysis of Networks through TEmporal-LOgic sPEcifications", webcite), a model checker for analyzing and constructing Boolean GRNs. Currently, software systems for Boolean GRNs use branching time almost exclusively for asynchrony. Antelope, by contrast, also uses branching time for incompletely specified behavior and environment interaction. We show the usefulness of modeling these two phenomena in the development of a Boolean GRN of the Arabidopsis thaliana root stem cell niche.

There are two obstacles to a direct approach when applying model checking to Boolean GRN analysis. First, ordinary model checkers normally only verify whether or not a given set of model states has a given property. In comparison, a model checker for Boolean GRNs is preferable if it reports the set of states having a desired property. Second, for efficiency, the expressiveness of many model checkers is limited, resulting in the inability to express some interesting properties of Boolean GRNs.

Antelope tries to overcome these two drawbacks: Apart from reporting the set of all states having a given property, our model checker can express, at the expense of efficiency, some properties that ordinary model checkers (e.g., NuSMV) cannot. This additional expressiveness is achieved by employing a logic extending the standard Computation-Tree Logic (CTL) with hybrid-logic operators.


We illustrate the advantages of Antelope when (a) modeling incomplete networks and environment interaction, (b) exhibiting the set of all states having a given property, and (c) representing Boolean GRN properties with hybrid CTL.