title: The combination of the functionalities of feedback circuits is determinant for the attractors' number and size in pathway-like Boolean networks.
abstract: Molecular regulation was initially assumed to follow both a unidirectional and a hierarchical organization forming pathways. Regulatory processes, however, form highly interlinked networks with non-hierarchical and non-unidirectional structures that contain statistically overrepresented circuits or motifs. Here, we analyze the behavior of pathways containing non-unidirectional (i.e. bidirectional) and non-hierarchical interactions that create motifs. In comparison with unidirectional and hierarchical pathways, our pathways have a high diversity of behaviors, characterized by the size and number of attractors. Motifs have been studied individually showing that feedback circuit motifs regulate the number and size of attractors. It is less clear what happens in molecular networks that usually contain multiple feedbacks. Here, we find that the way feedback circuits couple to each other (i.e., the combination of the functionalities of feedback circuits) regulate both the number and size of the attractors. We show that the different expected results of epistasis analysis (a method to infer regulatory interactions) are produced by many non-hierarchical and non-unidirectional structures. Thus, these structures cannot be correctly inferred by epistasis analysis. Finally, we show that the combinations of functionalities, combined with other network properties, allow for a better characterization of regulatory structures.
authors.affiliation: INRIA project-team Virtual Plants, joint with CIRAD and INRA, Montpellier Cedex 5, France.
authors.forename: Eugenio
authors.initials: E
authors.lastname: Azpeitia
authors.affiliation: Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, Apdo. 20-126, 01000 México, D.F., México.
authors.forename: Stalin
authors.initials: S
authors.lastname: Muñoz
authors.affiliation: CONACYT, Instituto de Ecología, A. C., Antiguo camino a Coatepec 351, El Haya, 91070 Xalapa, Veracruz, México.
authors.forename: Daniel
authors.initials: D
authors.lastname: González-Tokman
authors.affiliation: Programa de Doctorado en Ciencias Biomédicas, Universidad Nacional Autónoma de México, México.|Instituto de Ecología, Universidad Nacional Autónoma de México, México.
authors.forename: Mariana Esther
authors.initials: ME
authors.lastname: Martínez-Sánchez
authors.affiliation: ABACUS: Laboratorio de Matemáticas Aplicadas y Cómputo de Alto Rendimiento del Departamento de Matemáticas, Centro de Investigación y de Estudios Avanzados CINVESTAV-IPN, Carretera México-Toluca Km 38.5, La Marquesa, Ocoyoacac, Estado de México, 52740 México.
authors.forename: Nathan
authors.initials: N
authors.lastname: Weinstein
authors.affiliation: DIMNP UMR CNRS 5235, Université de Montpellier, France.
authors.forename: Aurélien
authors.initials: A
authors.lastname: Naldi
authors.affiliation: Instituto de Ecología, Universidad Nacional Autónoma de México, México.|Centro de Ciencias de la Complejidad, Universidad Nacional Autónoma de México, México.
authors.forename: Elena R
authors.initials: ER
authors.lastname: Álvarez-Buylla
authors.affiliation: Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, Apdo. 20-126, 01000 México, D.F., México.
authors.forename: David A
authors.initials: DA
authors.lastname: Rosenblueth
authors.affiliation: Instituto de Investigaciones Biomédicas, Universidad Nacional Autónoma de México, México.
authors.forename: Luis
authors.initials: L
authors.lastname: Mendoza