title: Preservation of dynamic properties in qualitative modeling frameworks for gene regulatory networks.
abstract: Mathematical modeling often helps to provide a systems perspective on gene regulatory networks. In particular, qualitative approaches are useful when detailed kinetic information is lacking. Multiple methods have been developed that implement qualitative information in different ways, e.g., in purely discrete or hybrid discrete/continuous models. In this paper, we compare the discrete asynchronous logical modeling formalism for gene regulatory networks due to R. Thomas with piecewise affine differential equation models. We provide a local characterization of the qualitative dynamics of a piecewise affine differential equation model using the discrete dynamics of a corresponding Thomas model. Based on this result, we investigate the consistency of higher-level dynamical properties such as attractor characteristics and reachability. We show that although the two approaches are based on equivalent information, the resulting qualitative dynamics are different. In particular, the dynamics of the piecewise affine differential equation model is not a simple refinement of the dynamics of the Thomas model.
authors.affiliation: Freie Universität Berlin, DFG Research Center Matheon, Arnimallee 6, D-14195 Berlin, Germany. jamshidi@zedat.fu-berlin.de
authors.forename: Shahrad
authors.initials: S
authors.lastname: Jamshidi
authors.forename: Heike
authors.initials: H
authors.lastname: Siebert
authors.forename: Alexander
authors.initials: A
authors.lastname: Bockmayr
mesh_terms: D000465:Algorithms; D019295:Computational Biology / Q000379:methods; D003198:Computer Simulation; D053263:Gene Regulatory Networks / Q000235:genetics*; D007700:Kinetics; D008957:Models, Genetic; D015203:Reproducibility of Results