Hybrid Gene Regulation Models of Mammalian Circadian Cycles

We present hybrid system based gene regulation models of mammalian circadian cycle and the results of model behaviour analysis. The models cover genes of two recently proposed biological models with 5 and 3 gene 'core oscillators'. The advantage of the used HSM framework is limited model dependence on parameter values, which are described only at qualitative level at the extent they affect models' observable behaviour. The models represent gene regulatory networks in terms of genes, proteins, binding sites, regulatory functions, and constraints on growth rates and binding affinities. Although such models do provide limited accuracy, they are less dependent from parameter fitting and can provide predictions on some biological aspects of gene regulation that are not dependent form the choice of particular parameter values. The models can provide biologically feasible predictions about synchronised oscillation of the involved genes and functions that regulate gene activity on basis of regulatory network topology alone. The work also includes developments of new analysis methods, in particular, for analysis of available trajectories in HSM state spaces and derivation of constraints that are needed for state transition trajectories to satisfy the required specific properties.