Eur. Phys. J. E (2012) 35: 107
https://doi.org/10.1140/epje/i2012-12107-9

Regular Article

Boolean versus continuous dynamics in modules with two feedback loops

Institut für Festkörperphysik, TU Darmstadt, Hochschulstraße 6, 64289, Darmstadt, Germany

^* e-mail: evachr@fkp.tu-darmstadt.de

Received: 5 June 2012
Revised: 20 September 2012
Accepted: 26 September 2012
Published online: 26 October 2012

Abstract

We investigate the dynamical behavior of simple networks, namely loops with an additional internal regulating connection. Continuous dynamics for mRNA and protein concentrations is compared to a Boolean model for gene activity. Using a generalized method and within a single framework, we study different continuous models and different types of regulatory functions, and establish conditions under which the system can display stable oscillations or stable fixed points. These conditions depend only on general features such as the degree of cooperativity of the regulating interactions and the logical structure of the interactions. There are no simple rules for deciding when Boolean and continuous dynamics agree with each other, but we identify several relevant criteria.