Analysis of dynamics and stability of hybrid system models of gene regulatory networks

I will present several gene regulatory models that our group has recently developed for phage viruses (lambda phage, HK022 and Mu phage) and also for mammalian circadian cycle 'core oscillator', and results that have been obtained about possible dynamic behaviour of these models – i.e. stability regions in model state spaces, switching conditions and constraints on state transition trajectories.
The models are described in hybrid system based HSM framework, in which GRNs are regarded to be fully defined by some underlying hybrid system, but, at the same, it is assumed that the knowledge about the underlying model is limited with information on comparative values of its parameters. The main objective of model analysis is to derive qualitative constraints on model parameters that significantly impacts/changes behavioural dynamics that is possible according to that particular model.