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Identification of stochastic hybrid models of genetic networks


E. Cinquemani

IfA Internal Seminar Series

Biochemical network modelling has been mostly developed in terms of either purely continuous or purely discrete dynamics. However, it appears that certain processes are more naturally described by models that feature both continuous evolution and discrete events. In addition, it is being recognized that many biological processes are intrinsically uncertain. For instance, stochastic phenomena appear to be instrumental for certain biochemical processes to induce variability or even to improve robustness. In this talk I will discuss modelling and identification of genetic regulatory networks in a stochastic hybrid framework. A piecewise deterministic model is considered where the deterministic evolution of protein concentration levels is driven by the random activation and deactivation of gene expression. In turn, gene expression follows the laws of a finite Markov chain whose transition rates depend on the current protein concentrations. in our opinion, this modelling framework provides a tradeoff between accuracy and tractability which is not offered by more complex models and is well suited for genetic network analysis and model identification/validation. Based on this framework, I will discuss identification of the regulatory network. First I will review our results on the parameter etimation problem, where the interaction pattern of the network is assumed to be known. I will discuss an estimation procedure that allows for the separate identification of the dynamics of every gene from sparse and noisy measurements of the protein concentration levels. This procedure scales well with the size of the network and is therefore applicable to networks of realistic size. Next I will discuss the structure identification problem in the case where the system has reached a stationary regime. Contrary to traditional identification approaches, requiring the application of perturbations to the system, the randomness of the system is exploited as an inherent perturbation signal. Then, concepts from the linear stochastic realization (identification) theory are used to match a local stochastic model to the data. Although this method is conceived for genetic regulatory network models, it can as well be applied to any model in the family of piecewise deterministic systems with switching inputs.


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J. Lygeros

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