Analysis of gene regulatory network models with graded and binary transcriptional responses.

The steep sigmoid framework developed by Plahte and Kjøglum [Plahte, E., Kjøglum, S., 2005. Analysis and generic properties of gene regulatory networks with graded response functions. Phys. D 201, 150-176, doi:10.1016/j.physd.2004.11.014] provides a uniform description of gene regulatory networks in which there may be both graded and binary transcriptional responses, as well as a method for analysing the models developed. Here we extend this framework. We show that there is a relation between the location of steady states and the feedback structure of a system, thus generalising existing results for Boolean type models. In addition, we justify underlying assumptions and generic features of the modelling framework in terms of biology and generalise the overall approach to take into account that each transcription factor only regulates one gene at a given threshold. By this assumption, the analysis of the models are greatly simplified.