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Stochastic dynamics of genetic regulatory networks: Modelling and identification


E. Cinquemani

Systems Biology workshop, Padova

Genetic regulatory networks govern the synthesis of proteins in the living cell and are thus responsible for fundamental cell functions such as metabolism, development and replication. Genetic 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. 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. This modelling framework provides a convenient tradeoff between accuracy and tractability 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 consider the parameter etimation problem, where the interaction pattern of the network is assumed to be known. I will describe 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, a local stochastic model retaining information on the structure of the network is fitted to the data. Results from numerical experiments will be shown to discuss the performance of these methods.


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