Stability and Flexibility from a System Analysis of Gene RegulatoryNetworks Based on Ordinary Differential Equations

The inference of large-scale gene regulatory networks from high-throughput data sets has revealed a diverse picture of only partially overlapping descriptions. Nevertheless, several properties in the organization of these networks are recurrent, such as hubs, a modular structure and certain motifs. Several authors have recently claimed cell systems to be stable against perturbations and random errors, but still able to rapidly switch between different states from specific stimuli. Since inferred mathematical models of large-scale systems need to be extremely simple to avoid overfitting, these two features are hard to attain simultaneously for a model. Here we review and discuss possible measures of how system stability and flexibility may be manifested and measured for linearized models based on systems of ordinary differential equations. Furthermore, we review how the network properties mentioned above together with the nature of the interactions contribute to these systems level properties. It turns out that the presence of repressed hubs, together with other phenomena of topological nature such as motifs and modules, contribute to the overall stability and/or flexibility of the model